From 6b1f5241d3aa0a4c666cd05160aba9deaff59331 Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Wed, 9 Aug 2023 16:37:13 -0500 Subject: [PATCH 01/25] feat: adding citeStructure elements in refsDecl --- edition.xml | 82 +++++++++++++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 79 insertions(+), 3 deletions(-) diff --git a/edition.xml b/edition.xml index 93ce595..f838fdb 100644 --- a/edition.xml +++ b/edition.xml @@ -1,6 +1,8 @@ - - - + + + @@ -107,6 +109,9 @@ padding-left:1em; margin-top:0; margin-bottom:0; padding-top:0; padding-bottom:0; + + + @@ -152,6 +157,77 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + From e5a14aa4d056678dee4d454b315e914ae355493a Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Mon, 9 Oct 2023 13:07:08 -0500 Subject: [PATCH 02/25] update: prefixDef --- edition.xml | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/edition.xml b/edition.xml index f838fdb..b129b00 100644 --- a/edition.xml +++ b/edition.xml @@ -109,9 +109,6 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> padding-left:1em; margin-top:0; margin-bottom:0; padding-top:0; padding-bottom:0; - - - @@ -157,6 +154,9 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/pdf-edition.xml b/pdf-edition.xml new file mode 100644 index 0000000..2e12889 --- /dev/null +++ b/pdf-edition.xml @@ -0,0 +1,33359 @@ + + + + + Expositio problematum Aristotelis, Particula XIX: De harmonia + Pietro d’Abano + Caleb Mutch + Medieval Academy of America + + TEI XML encoding: + Caleb Mutch + + + TEI XML encoding: + Samuel J. Huskey + + + + First Edition + + + The Digital Latin Library +
+ 650 Parrington Oval + Carnegie Building 101 + Norman + OK + 73019 + USA +
+ The University of Oklahoma + Norman, OK + 202? + + Creative + Commons Attribution-ShareAlike 4.0 International Licence (CC BY-SA 4.0) + + + + Library of Digital Latin Texts + + Edited by + Samuel J. Huskey + + ? + + + +

Born digital.

+ + + + + + Latin Letter Small B Squared; a.k.a. Flat, hard b (mi) + + + U+E9E1 + + + + Classes + combiningStaffPositions + + + + + Latin Small Letter Con + + + 9 + ꝯ + + + + +

+ + Ea, Gu, Pp, Pz, and Vz’s armoniac* emended to armonic* + Gu and Pq’s rigm* emended to rithim* + Nu's duppl* emended to dupl* + Gu’s *ypote emended to *ypate + Px, Py, and Pz's anthiphon* emended to antiphon* + Nu and Pp's mellodi* emended to melodi* + Pz's sinegengium emended to sinezengium + Gu, Py, and Vz's sesqui* emended to sexqui* + Ma, Va, and v's hi* emended to hii* + Px's "fati*" emended to faci* + Px and Py's sicud emended to sicut + Ma, Px, Py and Pz's velud emended to velut + Va's unique orthographical variants ignored + All: standardized spellings of lychanos, mese, and paramese + All: standardized spellings of dyatesseron, dyapente, and dyapason + All: lira* emended to lyra* + All: *ij and *ijs emended to *ii and *ijs + All: *cia, *cio, *cium, etc. emended to *tia, *tio, *tium, etc. + All: adinuicem emended to ad inuicem + All: probleuma* emended to problema* + All: Tironian et emended to et + All: ampersand emended to et + All: Tall s ( ſ ) emended to round s + All: contractions expanded + All: changes of hand/ink for problems' marginal numbering is ignored + +

+ + + + font-weight: bold + vertical-align:sub; font-size:50%; + display:block; font-size:100%; margin-left:3em; + padding-left:1em; margin-top:0; margin-bottom:0; padding-top:0; padding-bottom:0; + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ Preface +
+ I. Pietro d’Abano’s Expositio problematum Aristotelis +
+ 1.1 General +

The pseudo-Aristotelian Problems is an extensive + collection of questions and proposed answers concerning a wide range of subjects, + including biology, mathematics, and physics, divided topically into thirty-eight + sections. The nineteenth of these sections preserves the first substantial account of + ancient Greek music making and theorizing to have been rediscovered in the medieval + period. This material held great promise for medieval thinkers seeking to learn more + about the foreign world of ancient Greek music, whose legendary emotional power had + been lamentedly lost, and the text’s attribution to Aristotle imbued it with special + authority. Yet the Problems was also a challenging text to + decipher. Not only was the subject manner often unfamiliar, the manuscript tradition + of the Greek text is also corrupt in places. Furthermore, the first complete Latin + translation, made by Bartholomew of Messina (fl. 1258–66), observed the common + medieval practice of verbatim, indeed servilely literal, word-for-word translation. + For all these reasons, potential readers of the Problems + were in sore need of orientation and explanation.

+

Into the breach strode Pietro d’Abano (c. 1257–1316), who was a professor of + medicine with wide-ranging interests and expertise. Pietro composed his + Expositio, the first commentary on the entirety of the + Problems in the first decade of the fourteenth century, and there are + more than twenty extant manuscripts of it, as well as multiple early print editions. + His commentary also attracted the attention of his contemporaries, most notably Jean + de Jandun (c. 1285–1328), a philosopher and theologian of considerable importance + based at the University of Paris, who produced a revision of the entire + Expositio. Moreover, Pietro’s commentary on the problems of section + XIX, in particular, was the first widely circulated medieval attempt to interpret and + assimilate rediscovered knowledge about music in the ancient world, and his + explanations consequently became a touchstone for later generations of music scholars + who referred to the Problems, including Franchino Gaffurio, + Girolamo Mei, and Francisco de Salinas. Most recently, Claude Palisca has called + attention to Pietro’s anticipation of Renaissance modes of scholarship (1985), and David E. Cohen has demonstrated that Pietro’s + idiosyncratic interpretations of some of the problems concerning music played an + important role in the development of the music-theoretical concept of harmony (2012). Yet despite the inherent interest of Pietro’s + commentary as a site of cross-cultural engagement and its historical significance to + later music theorizing, his commentary on section XIX, on music, has been inaccesible + to scholars, for until recently it had not been published in any form since the + sixteenth century’s sadly unreliable print editions. Even that recent publication + (Meyer 2022), however, does not provide a proper + critical edition of the text, as it is based on a sixteenth-century print edition, + only considers half the extant manuscripts, and fails to distinguish between Pietro's + first version of his commentary and his later revision (see section 2.1). The present critical edition rectifies + that situation, establishing a base text informed by a stemmatic hypothesis of the + complete manuscript tradition. Furthermore, this edition is openly accessible, and it + presents a semantically encoded version of the text, allowing readers to select the + types of variants they wish to consider. As a result, it provides a better informed + version of Pietro's commentary and makes it more widely available than ever before. +

+
+ +
+ 1.2 Structure +

Each of the pseudo-Aristotelian problems follows a set structure. First, a + question is posed, such as at the start the first problem: Why do + those who are suffering and those who are rejoicing have pipes played for + them? (Propter quid dolentes et gaudentes + fistulantur?) Then one or more possible reasons are proposed, often + accompanied by additional explanation. For instance, the first problem continues: + Is it so that the former mourn less, but the latter rejoice + more? (Aut ut hii quidem minus tristentur, alii autem + ut magis gaudeant?) In his commentary Pietro follows a similar pattern. He + first paraphrases the opening question, and then addresses the remainder of the + problem, dividing it into between one and seven parts, depending on its length. He + signals the beginning of each successive division of the text with its first word or + two, followed by a partial or complete paraphrase. Given the unidiomatic Latin of + Bartholomew of Messina’s translation and the common occurrence of obscure vocabulary, + Pietro’s paraphrases provide an important means of ingress to the text on their own. + He often supplements these paraphrases with additional explanatory material, both his + own and by authors from antiquity. In the latter case, he often provides + cross-references to other pertinent passages within the Problems (from both section XIX and other sections), and he also inserts + abbreviated quotations, most often from the Aristotelian and medical corpora.

+
+ +
+ + +
+ II. The Textual Tradition +
+ 2.1 Introduction +

Establishing the best text of Pietro d’Abano’s commentary is no simple task, + for it survives in several different forms. By analyzing variants in the introduction + with which Pietro starts his commentary on the Problems, + Gijs Coucke has demonstrated that Pietro produced a revised version of his commentary + after the initial version was complete (2008, vol. 2, + xlii–xliv). About a quarter of the extant manuscripts derive from the initial version, + another quarter from the revision, and the remaining half of the manuscripts descend + from the revision made by Jean de Jandun (concerning which see Swaenepoel 2009). While these latter manuscripts do + not aid in the reconstruction of the text(s) Pietro himself wrote, they provide + important testimony as to the work’s reception in the Parisian university scene, and + consequently I have recorded variants from five selected manuscripts in the critical + apparatus. Coucke notes that “all manuscripts appear to have the identical explicit, + which refers to 1310 as the year in which Peter finished his Expositio” + (2008, vol. 2, xliv)—that presumably being the date + when the initial version was completed.

+

Further complicating matters, some of the manuscripts change affiliations + partway through the lengthy work. As Joan Cadden has observed, manuscript Pz + contains the first half of Pietro’s version and the second half + of Jean’s, and manuscript Ea has the converse + arrangement (2013, 228). Additionally, in his edition + of section IV of the Expositio, Coucke identifies manuscript Vb as deriving from Pietro’s revised version, whereas by + section XIX it hews more closely to the initial version. (Furthermore, manuscript Pq contains Jean’s version in sections IV and XIX, but by + section XXVII it appears to have changed to Pietro’s version [Coucke 2008, vol. 2, xxvi].) As a result, I have preserved Coucke’s + manuscript sigils, but not his labeling of families and conjectured sub-types. For + instance, Coucke labels Pietro’s first and second versions Pa and Pb, respectively whereas I call them α and κ. (This + change is made in part to avoid the confusing use of letters in Coucke’s Conspectus siglorum, where the manuscripts elsewhere labeled + as Pb are listed under + heading A, and those as Pa under heading B.)

+

In classifying the manuscripts I used Coucke’s findings on section IV as a + point of departure. I collated all the manuscripts’ versions of section XIX’s tenth + problem to test the validity of Coucke’s findings to section XIX. Then I collated all + the manuscripts representing solely either Pietro’s first or his second version (with + the exception of Mb, to be discussed below), along with + manuscripts Ea and Pz (since + their classification differs between sections IV and XIX), and four representative + manuscripts from the Jean de Jandun redaction.

+
+ +
+ 2.2 List of Sources +
+ Manuscripts + + Pietro's first version (α) + β + Consensus of Nu and Py, where Nu is extant + + + Nu + Nuremberg, Stadtbibliothek, Cent. III.38, ff. 61v–64v + before 1389 + + + Py + Paris, Bibliothèque Nationale man. lat. 6541 (accessed + 2022-01-03), ff. 179v–91v + fourteenth century. + + + + γ + Consensus of V<hi rend="superscript">a</hi> and V<hi rend="superscript">b</hi> + + + Va + Vatican, Biblioteca Apostolica lat. 2174 (accessed 2022-01-03), + ff. 72r–77r + fourteenth century. + + + Vb + Vatican, Biblioteca Apostolica lat. 2175 (accessed 2022-01-03), + ff. 107–16r + fifteenth century. + + + + + Ea + Erfurt, Bibliothek Amploniana fol. 15, ff. 136v–47r + early fourteenth century + + + + Pietro's revised version (κ) + + Px + Paris, Bibliothèque Nationale man. lat. 6540 (accessed 2022-01-03), + ff. 154v-64v + Fourteenth century. Italy. + + + λ + Consensus of Ma, Vm, + and Vz + + + Ma + Cesena, Malatestiana D.XXIV.2 (accessed 2022-01-03), ff. 96v–104r + before 1381. + + + Vm + Venice, Biblioteca Nazionale Marciana, lat. VI. 126, ff. 95r–100r + fifteenth century + + + Vz + Venice, Biblioteca Nazionale Marciana, lat. Z. 263, ff. 48v–70r + ca. fourteenth century, or after 1451 on the basis of watermark. + On paper, in one column + + + Mb + Cesena, Malatestiana S.VI.2/3 (accessed 2022-01-03), S.VI.3, ff. 38v–56r + 1381. A copy of Ma + + + + + + Jean de Jandun's redaction + + π + Collated manuscripts + + + Gu + Ghent, Bibliothéek van de Rijksuniversiteit, ms. 72 (accessed + 2022-01-03), ff. 234r–49v + fourteenth century. + + + Pp + Paris, Bibliothèque Nationale man. lat. 6542 (accessed + 2022-01-03), ff. 183v–94v + 1385. + + + Pu + Paris, Bibliothèque de l'Université 122, 114v–23r + fifteenth century + + + Pz + Paris, Bibliothèque Nationale man. lat. 6541A (accessed + 2022-01-03), ff. 179r-92r + fourteenth century. + + Pz + + + + + Pz2 is + responsible for the header, and writes in an ink that has faded + significantly. It may be the same scribe who wrote the large initials + which begin each problem. + + + + + + Vo + Vatican, Biblioteca Apostolica Ottobon. lat. 1764, ff. 147r–57v + fourteenth century + + + + + Other manuscripts from the Jean de Jandun redaction + + + Ca + Cambridge, Peterhouse 79, ff. + 76r–81v + fourteenth century + + + Pa + Paris, Bibliothèque Arsenal, 723, ff. 183v–97r + fourteenth century + + + Pq + Paris, Bibliothèque Nationale man. lat. 15454, ff. 127r–36r + fifteenth century + + + Sc + Seville, Biblioteca Colombina, 7.7.9, ff. 121r + ff. + fourteenth to fifteenth century + + + Vc + Vatican, Biblioteca Apostolica lat. 2176 (accessed 2022-01-03), + ff. 62r–65r + fourteenth century. + + + + +
+
+ Editions: Witnesses + + + m + + Illarius, Stephanus. Expositio succinta + problematum Aristotelis quam Petrus edidit Paduanus (accessed + 2022-01-03). Mantua: Paulus de + Butzbach, 1475. + + + + v + + Anonymous. Expositio preclarissimi atque + eximii artium ac medicine doctoris Petri de Ebano Patauini in librorum + problematum Aristotelis (accessed 2022-01-03). + [Venice]: Johannes Herbort, + 1482. + + + +
+
+
+ 2.3 Pietro d’Abano’s First Version +

The first version of Pietro’s commentary on section XIX of the Problems, which I label α, is found in five manuscripts: Nu, Py, Va, Vb, and Ea. + Manuscripts Nu and Py usually + carry the best version of this text. Unfortunately, Nu’s + codex has lost a number of pages, resulting in total loss of the text from a point + partway into problem 9 through problem 15, and again from the end of problem 38 + through the end of the section.

+

Manuscripts Va and Vb + are associated by shared error. The most salient of these occurs in problem 20, where + they repeatedly mistake discussion of the Greek language (oratio greca) for “grammatical speech” (oratio + gramatica). The scribe of manuscript Va + evidently prioritized speed over neatness of script and also had very idiosyncratic + orthography, regularly doubling single consonants or omitting one where they are + normally doubled. Given the ubiquity of these variants, I have omitted them from the + critical apparatus unless they are shared by other manuscripts. In his edition of + section IV, Coucke finds that Vb contains the second + version of Pietro’s commentary, but by section XIX there is little evidence of Vb sharing readings characteristic of that second version. In + addition, the sub-family represented by Va and Vb is particularly important for the commentary’s reception + history since the incunable editions of the text align most closely with them.

+

The situation is more complicated with manuscript Ea. Coucke assigns manuscript Ea to the Jean de + Jandun redaction, and in section XIX the manuscript adopts many (though not all) of + the omissions that characterize that redaction, and it sometimes shares readings with + Pz. Nonetheless, in non-omitted passages Ea’s text more closely resembles the manuscripts transmitting + Pietro’s first version. As a result, I primarily affiliate it with that family of + texts, with the proviso that the scribe of Ea evidently + consulted a Pz-related manuscript from the Jandun + redaction as well.

+
+
+ 2.4 Pietro d’Abano’s Second Version +

The second version of Pietro’s commentary, which I label κ, is also found in + five manuscripts: Px, Vm, Vz, Ma, and Mb. With respect to the fourth section, Coucke hypothesized + that manuscripts Px and Vb + (which in section IV transmits Pietro’s second version) most closely follow the + original form of the second version, that a further revised form of the second version + was the model for manuscripts Ma, Mb, and Pz, and that manuscript Vm shares common error with these latter three (Coucke 2008, vol. 2, xxxix). Only some of Coucke’s + observations hold true in section XIX, however. I agree that a revised version, which + I call λ, was the model for many of these manuscripts. As mentioned above, however, + manuscript Vb has switched its affiliation and now follows + Pietro’s first version, and Pz likewise has shifted to + Jean of Jandun’s redaction. Additionally, Coucke does not consider Vz, since it does not contain section IV.

+

The resulting picture is that Px follows the + original form of the second version, and that Ma, Mb, Vm, and Vz derive from λ, a revised version thereof. Coucke’s + hypothesis of a further revised source for Ma, Mb, and Pz (but not Vm) is not supported in section XIX, since there is good + reason to believe that Mb is copied either directly from + Ma or from another copy of Ma. For instance, in problem 2 the scribe of Ma + erroneously wrote unaa instead of una, and Mb’s scribe wrote unaa before deleting the superfluous a. Still stronger evidence of copying + is found in problem 3’s table of Greek note names, where Mb’s scribe was consulting a manuscript that breaks the word prollabamenos (recte: + proslambanomenos) into prolla and bamenos, as Ma does. We can tell + this because Mb’s scribe evidently thought the line break + divided two distinct words: in Mb, following prolla the rest of the line (about six characters’ worth) is + left blank, before the table of note names begins at the top of the next column with + bamenos. Furthermore, in problem 6 Mb’s scribe follows the word magnatis with the superfluous phrase uel huius est + inequale non eundem seruans tenorem ahead of where it should occur in the + text, and then repeats it in the correct place, following excellentis. In this case of homeoteleuton the -tis endings of magnatis and excellentis are nearly aligned in two successive lines of + Ma (f. 97v), so it is very likely that Mb’s scribe’s eyes skipped from the end of magnatis down a line to excellentis, and then erroneously copied the words that followed. In sum, + because my collation of Mb across the first ten problems + revealed no meaningful discrepancies with Ma, but rather + signs of direct copying, I conclude that it is not useful for establishing the best + text of Pietro’s second version.

+

Of the remaining manuscripts in sub-family λ, Vm + often preserves better readings than Ma and Vz. Zanetti dates Vz to about the + fourteenth century (1741, 121), but it may have + been copied later, as it is written on paper and is the only extant manuscript to be + copied in a single column. I have examined its watermark, which is a bellflower with + a five-petalled bell, two leaves that curl up, and a stem that curves sharply; it + closely resembles watermark DE4620-PO-127158, + which has been dated to 1447, in Rome, though its bell is straighter. Nonetheless, + the manuscript's unique readings are not obviously inferior to those of + Ma, so I have included its variants in the critical + apparatus throughout.

+
+
+ 2.5 Jean de Jandun’s Redaction +

The redaction undertaken by Jean de Jandun necessarily cannot help reconstruct + the best text of Pietro’s commentary, but it is still of some interest. This is in + part because Jandun is one of the most important thinkers in the + Latin Averroist tradition (South 2002, 372), + and consequently his understanding of the Problems and + Pietro’s commentary merits attention. Furthermore, due to the significant circulation + of Jean’s redaction in the environs of the University of Paris it is valuable for + understanding the Problems’ reception. As a result, I have + included readings from selected manuscripts of Jean’s redaction in my critical + edition, but have also tagged them so that readers may filter out readings only found + in that redaction.

+

Three broad feature of Jean’s redaction identified by Coucke in section IV also + occur in section XIX. First, the redaction is most saliently characterized by + omissions that either cover well defined text-units (paragraphs, + or entire (subordinate) clauses), or entail the removal of repetitive or superfluous + speech (2008, vol. 2: xxvii). Second, as a + whole the manuscripts of Jean’s redaction largely agree with those of Pietro’s first + version, but on occasion they follow his second version instead, as Coucke found + (xxx–xxxi). Third, as in section IV manuscript Vo appears to be most valuable for + establishing the text of the redaction (xxxiii). It has almost no unique errors of any + importance, but a brief passage in problem 9 (utrobique + existente. Et hoc quia in cantu), which it alone omits, indicates that it + cannot be the direct (or at least the sole) model for the rest of the redaction’s + manuscripts.

+

Beyond these broad characteristics, however, further clarity is elusive. + Whereas Coucke found that manuscripts Pp and Vc are “contaminated,” since in section IV they complete the + omissions which are otherwise characteristic of Jean’s redaction (xxxi–xxxii), in + section XIX Pp never does so and Vc only sometimes does. Coucke then goes on to note of section IV (and he + observes that Delaurenti’s [then]-in-progress edition of section VII confirms the + same), that: The other representatives of + J [Jean’s redaction], however, are hardly differentiated, and among them the + relations are volatile and changing. Yet, the samples allow for a division of the + manuscripts along two main branches: (1) one of them is built around Vo, Ca and Ea; (2) another unites the distinct pair Pq Pu (xxxii). Broad + outlines of these relations among manuscripts are still present in section XIX: in the + first branch, Ca and Vo are + still closely related, but Ea now aligns better with + Pietro’s first version. In the second branch, moreover, frequent agreements of Pq with Gu and Pu with Pp also emerge. The + remaining manuscripts, Vc, Pa, + and Sc, do not clearly align with either branch.

+

Given that Jean’s redaction cannot help to establish Pietro’s text, I have not + included all its manuscripts in the apparatus. I follow Coucke (xxxiv) in selecting + manuscripts Vo, due to its paucity of errors, and Gu, because of its careful preparation and occasional unique + variants. I also selected manuscript Pz, on account of its + interest as it switches from Pietro’s second version to Jean’s redaction. Because + Coucke identified manuscripts Pu and Pq as constituting a differentiated branch in section IV, I + selected manuscript Pu, since by section XIX Pq closely matches Gu. And + finally I included manuscript Pp to help establish the + second branch’s readings. (Other manuscripts from Jean’s redaction are also + occasionally cited when they support variants that would otherwise appear unique.)

+
+
+ 2.6 Stemmatic Hypothesis +

+ +

+
+
+
+ III. Pietro d’Abano’s Practices of Quotation +

In section XIX of his commentary Pietro employs quotations in the same two ways + observed by Coucke in section IV: more literal quotations, which come immediately after + the source’s reference (usually cited by the work’s author, title, and book number, when + applicable), and loose paraphrases, which precede the reference (2008 vol. 2, lxi). To this general pattern we may add a more + specific observation: in section XIX Pietro’s more literal quotations draw exclusively + on Boethius and Isidore, and he uses them to lay out background information about the + discipline of music’s terminology and its received history. He does this most + prominently in problem 1, but also later, too, for example in problems 3, 7, and 16. + Pietro uses paraphrases, by contrast, largely to support or exemplify his interpretive + claims, and they come from a significantly wider range of sources, as will now be + addressed.

+

The sources with which Pietro engages in section XIX fall into three main + categories: the Aristotelian corpus, medical texts, and late-Antique writings on music. + Pietro cites sources from the first category most frequently. Cross-references abound to + passages within the Problems, from both section XIX and other + sections, and Pietro also cites other Aristotelian works that were well known in his + day, especially book VIII of the Politics. (Other + Aristotelian works with which Pietro engages in medical-focused sections of the Problems, such as the De generatio animalium and + De historia animalium [Coucke 2008, vol. + 2, lxii], make no appearance here.)

+

Given section XIX’s dedication to the subject of music, the extent to which + Pietro incorporates medical sources, the second category, undoubtedly speaks to his + training as a physician. Three of these treatises are by Galen, whom Claude Palisca + misidentified as an otherwise unknown author Balienus in a + chapter on Pietro (1985, 55). The other medical sources + range from the better known, such Avicenna’s Canon medicinae, + to the obscure, for instance the Aphorismi of + Yuḥannā ibn Māsawaiyh, which Pietro attributes to John of Damascus.

+

The number of texts in the third category, writings on music, is very small. + While Pietro makes reference to Macrobius and Ptolemy, he demonstrates first-hand + knowledge of only Boethius’s De institutione harmonica and + the section (III.15–23) of Isidore’s Etymologies which + concerns music. He also has at least passing familiarity with some aspects of medieval + music theory, as he makes reference to the Guidonian + tradition (traditio Guidonis) in problem 1 + and on occasion employs solmization syllables, but he displays no further awareness of + music-theoretical writing from after late Antiquity. (He is, however, certainly aware of + his day’s musical culture, as he discusses antiphonal singing and medieval instruments, + which are unmentioned in Boethius or Isidore.)

+
+
+ IV. Principles of Edition +
+ 4.1 Latin Translation by Bartholomew of Messina +

The textual tradition of Bartholomew of Messina’s Latin translation of the + pseudo-Aristotelian text is largely independent of Pietro’s commentary, as only six of + the twenty extant medieval manuscripts of Pietro’s commentary include the entirety of + Bartholomew’s translation. Furthermore, sixty manuscripts contain part or the entirety + of Bartholomew’s text, compared to only around thirty for the commentary (Coucke 2008 vol. 1, xxxvi; vol. 2, xxiii). As a result, a + critically established text of the Latin translation of section XIX is beyond the + scope of this edition. For readers’ convenience, though, I have included as a variant + a reconstruction of the version of Bartholomew’s translation which Pietro likely + consulted. This reconstruction is based on a critical edition of that text, which I am + preparing for publication, along with alterations to the base text reflecting readings + found in Pietro's commentary.

+
+
+ 4.2 The Expositio problematum by Pietro d’Abano +

To constitute the text and the critical apparatus I have accounted for all the + manuscripts containing Pietro’s first and second versions of the commentary (except + for manuscript Mb, since it is a copy of Ma). I have also included a selection of manuscripts from + Jean of Jandun’s recension: Vo, Gu, Pp, and Pz. + Furthermore, readings from the two incunable editions are mentioned when they agree on + a unique reading or with variants found in other manuscripts.

+

In the edition’s text I aim to reconstruct Pietro’s second version of the + commentary, and consequently readings shared by manuscript Px and family λ are preferred. Where their readings diverge, if either Px or λ agree with multiple manuscripts from Pietro’s first + version, I prefer that shared text. Where the surviving manuscripts of Pietro’s second + version are corrupt, manuscript Py (and Nu, when not lacunate) is generally preferred.

+

With respect to orthography, I have largely preserved medieval spellings, + rather than changing them to classical Latin standards. (The most prominent exceptions + are that words ending with -cio, -cia, and the like have been changed to –tia, etc., + and the –ij and –ijs endings to –ii and –iis.) Because the digital critical edition + allows readers to choose whether to view orthographical variants, I have recorded most + spelling variances in the apparatus. Certain commonly occurring differences have been + silently normalized, however: + Ea, Gu, Pp, Pz, and Vz’s armoniac* emended to armonic* + Nu's duppl* emended to dupl* + Pp and Nu's mellodi* + emended to melodi* + Pz's sinegengium emended to sinezengium + Gu, Py, nd Vz's sesqui* emended to sexqui* + Ma and Va's hi* + emended to hii* + Px's fati* emended to faci* + Px and Py's sicud + emended to sicut + Pz, Px and Py's velud emended to velut + Va's ubiquitous unique orthographical variants + ignored + All: adinuicem emended to ad inuicem + All: probleuma* emended to problema* + All: lira* emended to lyra* + All: standardized spellings of rithim*, chor*, and antiphon* + All: standardized spellings of dyatesseron, dyapente, and dyapason + All: standardized spellings of lychanos, mese, and paramese + Gu’s *ypote emended to *ypate + All contractions have been silently expanded, including the ampersand and + Tironian et, and tall s ( ſ ) has been changed to + round s. I have ignored all changes of hand and/or ink for the marginal numbering of + the problems.

+

Punctuation varies widely among the manuscripts. I initially adopted manuscript + Px’s punctuation, which is relatively sparse. Thereafter + I added further punctuation in keeping with modern practice, especially where it was + lacking at points of significant syntactic divisions. I followed a similar practice + with paragraph divisions, basing them on those found in Px, and adding others at moments clearly signaled by the text (such as new + thoughts introduced by nosce quod, notandum, and the + like).

+

Relatedly, it should be noted that in section XIX manuscript Va and the incunable editions mark the beginnings of new + paragraphs with deinde. In section IV, however, + Coucke shows while that the manuscripts of Pietro’s second version (excepting Vb, which Coucke assigns to the second version) use deinde in that way, the remaining manuscripts do not. The + change of practice in Va is easily explained: a new + copyist takes over at f. 47r, at which point that use of deinde to mark new paragraphs begins. In the manuscripts from Pietro’s + second version, by contrast, that use of deinde + gradually fades away, and seems largely to disappear after problem 15 of section + 11.

+
+
+
+ V. Bibliography + + + Cadden 2013Cadden, Joan. Nothing Natural is Shameful: Sodomy and Science in Late Medieval Europe. + Philadelphia: University of Pennsylvania + Press, 2013. + + Cohen 2012Cohen, David E.. Harmonic Mediation and the Triad: Gaffurio, Zarlino, Lippius and Pietro + d’Abano’s Commentary on the Pseudo-Aristotelian <title>Problems. + Paper presented at the annual conference of the Music Theory Society of New + York State. New York, N.Y., March + 31, 2012. + + Coucke 2008Coucke, Gijs. Philosophy between Text and Tradition The Reception of Aristotle's + <title>Problemata in the Middle Ages: Peter of Abano's Expositio + Problematum. Leuven: Ph.D. + dissertation, Katholieke Universiteit Leuven, 2008. + + Coucke 2009Coucke, Gijs. Needle in the Haystack: In Search of the Model of Peter of Abano's <title>Expositio + Problematum. Revue d'histoire des textes + 4 (2009): 179–213 + + + Klek 1922Klek, Joseph, + Knoellinger, Hermann, Ruelle, Charles Emanuel, + Pseudo-Aristotle. Aristotelis quae feruntur + problemata physica + Leipzig: Teubner, 1922. + + Kuksewicz 1985Kuksewicz, Zdzislaw. Les <title>Problemata de Pietro d'Abano et leur 'Rédaction' par + Jean de Jandun. Medioevo 11 (1985): 113–37 + + + Leemans and Coucke 2011Leemans, Pieter De, and + Coucke, Gijs. <foreign xml:lang="la">Sicut vidi et + tetigi</foreign>...: Ego-statements and Experience in Pietro d'Abano's + <title>Expositio Problematum Aristotelis. In + <foreign xml:lang="la">Expertus sum</foreign>: l'éxperience par les + sens dans la philosophie naturelle médiévale, ed. + + Thomas + Bénatouïl + + and + + Isabelle + Draelants + + , 405–26. + Florence, SISMEL, Edizioni del + Galluzzo, 2011. + + + Meyer 1922Meyer, Christian, + d'Abano, Pietro. Expositio problematum (XIX): Édition, + introduction et notes critiques et explicatives + Leuven: Leuven University Press, 2022. + + Palisca 1985Palisca, Claude. The Earliest Musical Humanists: Pietro d’Abano. Chap. 3 in + Humanism in Italian Renaissance Musical Thought. + New Haven, Yale University Press, + 1985. + + + Siraisi 1970Siraisi, Nancy. The <title>Expositio Problematum Aristotelis of Peter of + Abano. Isis 61, no. 2 (1970): 321–39 + + + South 2002South, James B. John of Jandun. In + A Companion to Philosophy in the Middle Ages, ed. + + Jorge + Gracia + + and + + Timothy + Noone + + , 372–76. + Malden, Mass., Blackwell, 2002. + + + Swaenepoel 2009Swaenepoel, Tine. Les deux versions des «<title ref="#ArPr">Problemata» de Pierre + d'Abano. Filologia mediolatina 16 (2009): 215–45 + + + Zanetti 1741[Zanetti, Anton Maria]. + Latina et italica D. Marci Bibliotheca codicum manu scriptorum per titulos + digesta. [Venice]: Apud Simonem Occhi + Bibliopolam, 1741. + +
+
+ + + +
+ Expositio problematum Aristotelis, Particula XIX: De harmonia +
+ + + + + + + + + + + + + + + + + + + Incipit + Incipit decimanona particula. + Incipit decimanona particula etcetera + De problematibus Aristotelis que sunt + circa Musicam l'armoniam particula .19a. + xix + Sequitur xviiii. + 20a + 20a particula + Incipit particula 20a de armonia continens problemata 47 + Aristotelis + problemata de hiis que sunt circa armoniam + particula 20m. + Capitulum primum + de problematibusarestotelis que sunt circa armoniam + uel musicam particula 19a. + + +
+ + + + Primum problema + + .1. + problema primum + +

+ PROPTER QUID DOLENTES + PROPTER QUID DOLENTES ET GAUDENTES + PROPTER QUID DOLENTES FISTULANTUR + + PROPTER QUID DOLENTES ET DELECTANTES FISTULANTUR?AUT UT HII QUIDEM MINUS TRISTENTUR? ALII AUTEM MAGIS + GAUDEANT + . + + Propter quid dolentes etcetera. + Propter quid dolentes et gaudentes fistulantur + etcetera + Determinatis problematibus circa + mathematicam + mathematica + methaphysica + methaca a.c. + + mathaca p.c. + + methaphysicam + methacam + + et orationes, determinat + nunc + + problemata circa + armonicam + armoniam + uel + musicam + musica + , eo quod in + ipsa + ipso + est + quidam + + amor sermonis, ut + in + + + + priori + posteriori + particula. Et primitus ad + huius + huiusmodi + + + maiorem + amorem + + expositionem + premittantur + premittuntur + quedam + communia + coloris + , + sicut + scilicet + + + quid + quidem + est musica et que + ipsius + sint ipsius species + prius + ? + Que + + secundum + + boecium + musice + 5° + boeciummusice + 4° + boeciummusicce + boecium raritate 4° + boecium + inprimomusice + + Boethius + De inst. mus. + V.2 (ed. Friedlein p. 352, ll. 4–5) + + est armonica + armonica est + est armonice + Armonia est + facultas + differentias + differens + + + acutorum et grauium sonorum + sensu + sensum + + + et + ac + ratione + acutorum sonorum et grauium sonorum ratione + perpendens. + Secundum + uero + + + + ysidorum + + in + ut + + + + ethymologiis + + + + ethicis + + Isidore of Seville, Etym. + III.15.1 + est peritia modulationis, + sono + sonorum + + cantuque consistens. +

+

Dicitur etiam quod + sit scientia numeri ad sonos + proportionati + proportionatos + proportionatisrelati + . + Arist. + An. post. + 90a, 14–23 + + Que secundum + + ysidorum + + yrodorum + + dicitur + a muso + autem misso + + + quasi a querendo + + quasi acquirendo + que acquerendo + id est acquirendo + , quia + per eam uis + per eam ius + per ea uix + per ius + paruis + + + carminum + corninum + + + querebatur + queratur + acquiritur + . Unde a poetis iouis et + memorie + + + uenem + + + filias + philos + + + mutas + musas + unitas + + + esse + + confictum + est + esse + + , nam + memoria soni + soni memoria + si memoria soni + non + teneantur, pereunt + teneatur, pereunt + teneatur, perit + , cum non + possint + + possunt + possit + scribi. + Isidore of Seville, Etym., + III.15.1–2 + + + A nonnullis + Amat nonnullis + nullus + Aut + + + uero dicitur + dicitur uero + dicitur + + + a moys + + amois + + + quod + que + est aqua, + + quia + + + + olim primitus + primitus olim + olim amicus + olim tali primitus + + + inuenta fuit + fuit inuenta + + + in illa + et illa + in aqua + , et + in + + + + ydriis + + + + + + siue + instrumentis + in instrumentis + aquaticis + similiter + simpliciter + + + exercita + + ex certa + . + + Refert autem + + Refertur + + + moyses + hanc + + hanc moyses + inuenisse + + tubal + + + + + aabal + tubal fratrem + cayn + + de + stirpe + + + + cayn + + + + + + + ante diluuium + + + + + . + Isidore of Seville, Etym. + III.16.1 + + + + Sed + greci + gressi + , + ut apparet per macrobium et + boecium + + bonum + , + dicunt eam + inuenisse + + + + + + + pytagori samium + + + pictagorius + samium + pitagoram + samium + pictagoram + samium + pictagoram + pythagorici samium + pitagorici + sonitu + malleorum + + , + cum + cum pro + casu in + publicum + + + + exiret + iret + + + ad + cum + fabros, et cordarum + demum impulsione + + deinde impulsione + deinde pulsione + . + Boethius, De inst. mus. + I.10 (Friedlein p. 196–7); + Macrobius, Comm. in somn. + Scip. + II.1 (Eyssenhardt p. 572–575) +

+

+ Diuiditur + Dicitur + autem musica + iuxta + secundum + + + eosdem + easdem + eo sedem + in + mundanam + + , + humanam + habentiuam + , + et + + organicam + uel + seu + + instrumentalem. + Mundana + + + mundanam + + + uero + quidem + non + + + attenditur + + + intenditur + + in sono armonico, + quem + que + quam + causant orbes celestes, secundum + pictagoram + + + pithagoricos + pictagoricos + pitagoricos + cum aliis musicis, + differenter + + + + differuntur + drntur + + + + commotos + commoti + . + + Sonum + + + + enim + + + + armonicum + organicum + + + causant + causatur + , + sed + per + + + eum + eius + eum sed eum + non + percipimus + percipimus ut + , dicunt, + propter quod + propter hoc quod + propter ea quod + preterea + + + in auribus nostris a principio + in auribus et nostris a principio + a principio nobis in auribus nostris + + + natiuitatis + natum + notum + + + est + est et + + + complantatus + complantatur + , + ut + + + + in eris apparet + apparet in eris + in eis apparet + + + malleatoribus + + malleationibus + strepitum + suum + + + + vix + vis + percipientibus + consuetudine + + et ex consuetudine + + + quos + quod + quo + quorum + + + aristotelem impugnat + celi et mundi + + + et + + 2°. + aristotelem impugnat + 2° + celi et mundi. + aristotelem + in 2° + celi et mundi inpungnat. + + Arist. + De caelo, II.9, 290b, l. 25 +

+

Musica uero + humana + mundana + + + dicitur + + + + que + que est + circa + concordantiam elementorum + concordantia elementorum + elementa + + + diuersorum + diuersi + ad inuicem + in vno composito + non composito + + uel + compositionem + compositione + compositum + corporis + uersatur + similatur + , per + eam + ea + enim natura spiritualis coniungitur + corpori et rationalis + corpori et in rationalis + rationalis + + + + concorditer + + concordie + cum + irrationali + + irrationabili + rationali + + + coniungitur + + . + Quod + erum + + + videtur + aristotelem + + + a platonicis + apolatonicis + habitum ponentibus animam quandam + armonicam + fore consistentiam + esse consistentiam + . Vnde + + datum in afforismis + + dictum est in afforismis + damascenus in afforismis + + + colligatio + + colicgio + + + anime et corporis + corporis et anime + secundum + ordinis + cordis + naturalis consonantiam + facta + factam + + + est + + , ut + substat + subsistat + , + Yuḥannā ibn Māsawaiyh, + Aph., (Vat. Lat. 2460, f. 39v, ll.7–8) + quare + huius + huiusmodi + + + musice + musice naturali + numeratione naturali + + + videntur scientie + scientie videntur + videntur hec scientie + numeri scientie + uidentur sane + + + supponi + + .

+

Instrumentalis + uero + + dicitur que quibusdam + exercetur + exercet + armonicis instrumentis, que + predicamentis videtur + predicamentis videntur + videntur predicamentis + possunt uidetur + + + fore + esse + + + considerationis + speculationis + + contristationis + 9tātionis + + + + existens duplex + existens + dicendum + dd' + + existens dicendum + existens + + : + nam + + quedam exercetur instrumento naturali, ut + hominis + homines + + + uoce + uoces + , + cum reliquis + reliquis cum + organis + locutionis + + locutiones + locutiuis + + , + aut + an + + + artificiali + artificiale + . Et + id + illud + + + + multipliciter + multiplicatur aut artificiali et + id multipliciter + : + aut + ut + tactu + ut + + + + viellis + + + + + vincul + , + uel + aut + + pulsu + ceu + seu + sicut + + + + cimbalis + + + + ebalis + , + uel + ut + + + flatu + flatum + flacio + + + ut + sicut + in + + + tubis + tibiis + , aut quasi + omni modo + omnino + + + sicut + ut + + + fistulis + + .

+

+ Que + Qui + Dicitur + iuxta + + ysidorum + + + + + + diuiditur + diuidetur + dicitur + in + armonicam + armonicam et + metricam et + rithimicam + et rithimicam + rethoricam + . + Quarum + Quorum + + + + armonica + armonica metricam + + + graue in sonis et + acutum + acutis + + graue et acutum in sonis + graue in sonis acutum + discernit. + Metrica + etricam + Matricam + + + est + etiam + que ratione probabili + cognoscit + mensuram + + mensuras + + mensuram cognoscit + diuersorum pedum ut + heroycum + + + + + + heronicam + + + iambicum + + + in abitio + + + et + + + + heliacum + + + + + + + + + + . Rithimica + uero + uero est + est + + + que + + uerborum + incursionem + intercessionem + + + inquirit + iungit + , + ut + uerum + + + aut + autem + + aut + aū + + an + + suauiter + uel + an + aut + non suauiter sonus + cohereat + + + adhereat + . + Isidore of Seville, Etym. + III.18.1–2 + +

+

+ Que + Quasi + + + siquidem + quidem + quedam + + + tria + tripliciter + + ad genus + videntur concurrere + + concurrere uidentur + videtur concurrere + videntur currere + uidentur concinere + + + cantilene + + + canticule. + caticlʼe + + + canticule + canule + + causa mille + , armonica tamen, ut + tactum + tactu + tactum est + dictum est + , + consonantiam + consonantia + grauis et + acuti + accuta + + + attendit + + , + rithimica + rithimica uero + rithimicam ut tactum est + + + consonantiam + + consonantia + + + terminationum + durationum + , metrica + uero + vel + temporum ut apparet + in + + + + traditione + traditionem + introductione + musice + guidonis + + grauidons + gradionis + . et circa + has + + + tres partes musice, et + maxime + maxime circa + + + duas + duos + et + + + priores + + , + dubitat + dubitabit + + + aristoteles + + vtilitas + vnitas + volitas + + + uero + + musice est, + Arist. + Pol. + VIII.5, 1339a, l. + 11 + quia delectat + animos + animas + + + excitat, et + exercitas et + exercitat et + et exercitat + exitat et + et + affectus mouet, + et + + + + furiam + + furias + placat, + siluestrem + siluestres + siluestre + + + mansuescere + mansuestrem + + + facit + + , ut apparet clangore, + namque + enim + tubarum et similium fortiores + redduntur bellatores. Similiter + lassatos et exercitio + + et laxatos exercitio + lasatas et exercitio + laxatiuo et exercitio + laxatos exercitio + lassatos exercitio + + + laborioso + laborioso et + + + detentos + + detento + reddit + faciles + facille + facilius + tollerare. Unde + + <app> + <lem wit="#Ea #Ma #Nu #Pz #Va #Vo #Vz #m #v">politicorum</lem> + + </app> + 8°: + 8° + politicorum + palliticorum + duo + + musica habet delectationem naturalem propter quod omnibus + etatibus et omnibus + moribus + et moribus + horis + usus ipsius est amicus. + Arist. + Pol. + VIII, 1340a, ll. 3–5 +

+

Recitat + etiam + et + + + + boecius + boecium + + + pictagoram + + + primae pyctoragam + pythagoricos + pictagoricas + + + iuuenem + in uenere + + + furentem + + in + combustionem + combustione + domus + riualis + + + in qua + sortum + scortum + continebatur melodiis + musicis + musicum + eius animum + sedasse + + + . + Boeth. + De inst. mus. + I.1 (Friedlein p. 185, l. 3) + Cuius + vtilitatem + subtilitatem + + + tangit + agit + + + + <app> + <lem wit="#γ #κ #Ea #Nu #Vo #m #v">politicorum</lem> + + </app> + 8° + 8° + politicorum + aristotelis + 8° + politicorum + , + + ponitur + ponuntur + ponit + enim + vnum quatuor + quatuor + ibi quatuor + quatuor ibi + + + que debet + + que debent + quedam + + + adiscere + + + + puer + pueri + + : que sunt + littere + littera + lingue + + + + luctatiua + + + luctatio + luctatio + luctatio + licatio + iutatio + britatio + musica et + protractiua + + protractiua + p't'actā + + + protractura + pertractiua + porctiua + , + Arist. + Pol. + VIII, 1337b, l. 23 + + + ceu + seu + + + scribere + scriptura + et pingere.

+

Querit + igitur + ergo + + aristoteles more + consueto + solito + + + problema, dicens + + : Quare dolentes + et contristantes et + contristantes + et + contristantes + et tristantes et + et contristantes sunt + delectantes + gaudentesque + et gaudentes + gaudentes + + + fistulas + + et + vniversaliter instrumenta + vniuersaliter omnia + instrumenta + + + + delectationem et gaudium inducentia + delectationem inducentia et gaudium + delectationem inducentia + gaudium et letitiam inducentia + letitiam quod inducentia + expedit audire? Unde + + alexander + + + + + in problematibus + + + et maxime + et maxime et maxime + + + quantum + + + + ad primam + partem: + ad primam: + + Propter + quid + + + + coram + corpora + patientibus fistule + et + aut + + + tympana. + + tympane. + timpana etcetera. + + Ps.-Alex. Aph., Prob. + I.78 (Vat. reg. lat. 747, f. 75v) +

+

+ Nosce quod + + omnes passiones + licet omnes passiones + licet omnes + omnes passiones licet + omnes passiones sint + + + sint coniuncti + sint coniuncte + sint coniecti + sicut continetur + , + 1° + de anima + Arist. + De an. + I.1, 403a, l. + 25(Cf. 403a l. + 16) + ; + quedam + quedam te + + + tamen se plus tenet + tamen se tenet + tamen se plus tenent + tamen plus se tenent + tamen plus tenent + se plus tenent + ex parte + corporis, ut dolere et delectari, + alie uero ex parte + exparte uero + + + anime ut + gaudere + gaudium + et tristari; ita + ut + + per vnum expressum + aliud aristoteles + audiat + aristoteles audiat + aliud + aliud audiat aristoteles + + + recitatum + + + + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens + causam esse + ut + nisi + + + qui + quod + tristantur + ac etiam + et + + + dolent + doleant + + minus + contristentur + tristentur + + + et + ac etiam + doleant + propter + propter melodiam uel + iocunditatem inductam ex sonitu + instrumenti + instrumenta + . In + oppositis + oppositis uero + causa + extat + extet + existit + est + ut magis + gaudeant + + et + delectentur + iocundentur + , si enim + aliqui + alia + sunt iocundi + addita + a dicta + causa + iocunditatis + + , + ut + et + scilicet + fistulationis + armonice + armonia + + + amplius delectabuntur. + delectabuntur amplius. + magis iocundabuntur. +

+

Nosce quod + id + illud + potest contingere quia idem + potest esse + est + causa diuersorum aut + ratione + ratione diuersorum aut + ratione + dispositionis + susceptiui + susceptum + suscepti + susceptorum + subscopii + ; uel quia + diuersa + + dictum + dm + + diuersimode + dum + + + egeant + egeat + agat + + + eadem + eodem + eorum + + + + uel + et + + + + ratione + idem + eius + quod + + per se + aut + an + et + per accidens + extat + existat + , + ut + nauta + + per + sui + suam + + + presentiam + presentia + + + causa + causa est + est causa + salutis nauis, + eius + enim + uero + absentia + + absentiam + absentia causa + + submersionis + + 2° + <app> + <lem wit="#λ #Gu #Nu #Pu #Vb #Vo">physicorum</lem> + + </app> + physicorum + 2° + . + Arist. + Phys. + II.3, 195a, l. 13 + + + + et cetera + sequitur 2m. problema. +

+
+ +
+ + Secundum problema + 2m + Secundum + Secundum + + +

+ PROPTER QUID LONGIUS + PROPTER QUID LONGIUS AUDITUR + + PROPTER QUID LONGIUS IDEM EADEM UOCE AUDITUR CUM ALIIS CANTANS ET CLAMANS + QUAM SOLUS? + AUT QUIA COADUNATE ALIQUID FACERE, AUT REPRIMERE + AUT IMPELLERE, NON TANTA PROPE SUNT QUANTUS NUMERUS. + SED SICUT LINEA BIPEDALIS NON DUPLUM SED QUADRUPLUM + ALIQUID SCRIBIT, ITA COMPOSITA PLUS + POSSUNT, AUT SECUNDUM NUMERUM AUT QUANDO FUERINT DIUERSA. + COADUNATIS IGITUR EXISTENTIBUS UNA FIT UOCIS + FORTITUDO ET SIMUL IMPELLIT AEREM. QUARE MULTIPLICITER PREIT, + ETENIM EX OMNIBUS UOX UNIUSCUIUSQUE + MULTIPLEX + . + + Secundum problema + etcetera. + + + Quare + Querit quare + vnus et + idem + idem Secundum + numero + eadem + + + + similiter + simpliciter + uoce cantans + et + + + + uociferans + uociferaret + + + + remotius auditur + auditur remotius + quando cum aliis + vna cantat et + una uoce cantat et + una uoce cantant uel + clamat quam si solus + tantum + + cantaret + aut + an + uociferaret + + ? Non tamen + adeo + + + + distantur + distantantes + distante + distant + distanter + + , + sicut + sint + vnus post alium + ordinatus + ordinatus uero + distantia + uociferaret + uociferat + + + ut in + ut + in + et in + + + proicientibus + + lapidem + successiue + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit + dicens primo causam esse + dicens causam esse primo + primo dicens causam esse + dicens causam esse + + quia + coniunctim + + coniuncti + coniunctum + coniunctus + + + aliquid + aliquod + ad + agere, puta + est reprimere + reprimere est + reprimere + + + coangustante + coangustantem + coangustare + coangustando + angustatis + + + an + aut + + + impellere + repellere + compellere + + + contendendo + + continendo + , uel + aliquid + aliquod + adeo + + + singulariter + simile + simpliciter + tale, non + tamen + + tantum + + + + potest + + + + per se vnumquodque + vnum per se + , + + sicut quando plura + quantum quando duo + simul + + coniunguntur + numerum + vnum + + + constituentia + constituentia ut + , + dummodo + dum tamen + + + ordinentur + ordinetur + in vnum + ut + velut + uel + nauis + tractus + + ostendit.

+

+ + Deinde. + + + SED SICUT. + SED SED + SICUT. + Declarat secundo + dicens + quod + quia + + + istud + illud + + + apparet + apparens + ex tali simili quoniam sicut linea duorum pedum non + solum + solum est + + + duplum + dupliciter + , sicut est potest + figurare + significare + firmare + + + intellecta moueri, sed + intellecta mouere, sed + intellectum ymmo etiam + + quadruplum et octuplum, secundum quod diuersimode + + mensurando + infundo + commensurando + + + applicatur + applicantur + + applicatur mensurando + , + ita + + + ut + super + per + semper + + + plurem numerum habeat + plurem numeri habeat + pluralem numerum habeat + plures vnam habeant + potentiam, similiter + et + in + + + ad inuicem etiam + ad inuicem et + ad inuicem + in + quibuscunque + quibusdam + quibusdamcunque + aliis. Cum + autem + aut + plura + fuerint + fuerunt + + + numero amplius possunt + numero moueri amplius possunt + , + uel + uel quam + cum diuisa fuerint quocunque + alio + alio modo + + distinguente dummodo vnum + proportionaliter compossit + proportionaliter compos sit + proportionaliter composcit + proportionaliter possit + + + alteri + alteri coadunari + .

+

+ + Deinde. + + + COADUNATIS. + + + + Concludit tertio + 3º concludit + + + quod quando + quod + + + aliqua + antequam aliqua + plura numero + uel + aut + specie + aut + uel + qualitercunque diuisa + coniungantur + coniunguntur + ad inuicem + uirtute + virtutem + uirtute cum + uirtute quod quantum + , + utpote + ut potentia + ut puto + + + in uoce una + in uoce + voce vna + in uoce sua + ex + omnibus + hominibus + + + contingit + contingitur + contingit simul + + + uocum + uocis + + + fortitudo + fortificando + + + simul + uel + + + + impellens + + implens + + + aerem + aera + . Et ideo + ualde amplius + amplius ualde + amplius + + + potest + potest amplius + ponit + preire + et + et in + + + longinquius + + + audiri quam uox vnius quod + ostenditur. Nam ex uoce + uniuscuiusque + + uox + quedam + quidem + #Gu scribe later changes to "quedam" in the dittographic + version of this clause + una constituitur + multiplicium + multiplicem + + + habens + habet + potentiam, + ceu + seu + sicut + #Gu scribe later changes to "sceu" in the dittographic version + of this clause + + + tractus + + #Py could be totus with a misplaced a-squiggle above the o, or + tractus with an o accidentally replacing the c. + + tractum + tracti + optime + una + + + et + diuisim + diuisius + + + denotat nauis + ostendit nauis + . + Et + + hoc + quidem + quidem denotat uoce uniuscuiusque + uox quedam una constituitur multiplicium habens potentiam seu tractus potime una + et diuisim denotat nauis. Et hoc quidem + + problema + partim + partium + + + + pertinet + pertinet enim + partini enim + + + + .xie. ut uisum particule + .xie. ut visum est particule + .xie. particule, ut uisum est + particule + ut uisum est particule + .xie. ut visum est + .5e. particule, ut visum est + + Ps.-Arist. + Prob. + XI + + + partimque isti + partimque pertinet isti + . + + etcetera. + sequitur 3a. problema 19. particule. +

+
+ +
+ + Tertium problema + 3m + tertium + Tertium + + +

+ PROPTER QUID PARYPATEM + + PROPTER QUID MAGIS FRANGITUR + + PROPTER QUID PER YPATEM CANTANTES MAXIME RUMPIMUS NICHILOMINUS QUAM + NITEM ET SUPERIORA, CUM DISTANTIA PLURI? + AUT QUIA DIFFICILLIME HANC CANTANT, ET IPSA EST PRINCIPIUM? + ID AUTEM DIFFICILE PROPTER ELEUATIONEM ET + DEPRESSIONEM UOCIS. IN HIIS AUTEM LABOR, LABORANS AUTEM MAGIS + CORRUMPITUR + . + + Tertium problema + etcetera. + + + Quare + Querit quare + + + cum cantamus + cantamus + quando cantamus + causa cantamus + cum caneamus + cum teneamus + cantantes + secundum + notam + uocem + quam + illa + ista + corda representat que uocatur + ypotes + + + potissime + interrumpimus + interrumpitur + cantum, non + potentes + potens + + + ipsum continuare + continuare ipsum + ipsum continere + sicut + accepimus + accipimus + incepimus + + + pre sui + pro sui + prefui + difficultate. Et in nullo + minus + videtur + + + ymmo + + + + + + + in omnibus + in + etiam + + + + magis frangimus + frangimus magnum + + magis in omnibus frangimus + + + cantum + totis + + + propter + per + ipsam quam + per + propter + + + nitem + nucem + uitem + + + siue netem + seu netem + uel nectere + . + Et + + vniversaliter magis + frangitur + + + + cantus + + et difficilius + seruatur + seruatur quam + quando + vtitur + vtuntur + utimur + + + notis + votis + motis + per cordas + superiores + superioribus + + + denotatis + denotatur + , et precipue quando distant inter + se + maxime + + . Hoc autem + fit + fit in + fit instans + sit + instrumentis + cantando + aut + ac + per notas illas que sunt in instrumentis + + + + proportionatas. + proportionatis. + proportionate. +

+

+ Notandum + Notandum quod + Nota + + + ad + + intellectum + eius quod + + + + hic + hic dicitur + huius + et + multorum + + in hac particula + dicendorum + contentorum et dicendorum + quod antiquitus + a pictagora + inuentum fuit instrumentum dictum monocordum + + + + + inuentum fuit a pictagora instrumentum dictum menocordum + a pictagoricis inuentum fuit instrumentum dictum + monocordum + a pitagoricis instrumentum inuentum fuit dictum + monocordum + a pithagoricis inuentum fuit instrumentum + monocordum + , eo quod vnam + solam cordam + cordam solam + solam + haberet + taliter formatum + talem formatum + formatum taliter + taliter et formatum + taliter proportionatum + + + in + etiam + quo proportiones musice + .5e. cum + 53 + 59. + + + tonis + + rationes + + simplices prius cognosci + iubebat + iubeat + iubebant + uidebantur + secundum diuersitatem + loci + loci et + + + instrumenti tacti + in fritanti + + + representante. + + representantem. + representatis. + + representatis + r'pn'tat' + + representare. + + + Deinceps + Deinde + + + inuenta sunt instrumenta + instrumenta inuenta sunt + sunt instrumenta + inuenta fuerunt instrumenta + cum pluribus cordis: + ut + ut cum + et + + duabus + + ceu rubeba + + + + seu rubeba + seu reubeba + seu rubeda + sicut rubeba + sicut rubeda + sicut rubula + que similiter organum + introductum + + introductorium + introductorum + existit. + Denique + Deinde + Deindeque + Demumque + Demum quia + Deinde quia + paulatim sunt cetere + adinuente + inuente + aduenientes + . Unde + 1° + musice + + ait + + + boecius + + nichomacum + + + + nichoantum + intomarum + inchoantum + inchoatam + dicere musicam + in principio fuisse + fuisse in principio + in principio fore + + + simplicem + simpliciter + + + in + + tantum quod tota constabat + ex + in + + quatuor cordis. Quod + durauit + durabat + vsque ad + orphei + + + + + tempus + tempore + + + puta, quod + puta ex + ex + + + prima + prima quidem + et quarta corda + constitueret + constituerent + constabat + + + consonantiam duplam + consonantiam dupla + consonantiam + consonantia dupla + dyapason + dictam + dicta + . Medie + quidem + vero + + + harum ad se inuicem + harum ad inuicem + tonum constituebant, + + et + + ad + extremas + extremas partes + comparate + + + dyapente + et + id est + dyatesseron, ut apparebit .13., + ita ut in + ita in + ita ut + hiis quatuor cordis + nichil + + dissonum + existeret + existere + existerit + existiterit + ad + imitationem + + + mutationem + immutationem + + + mundane musice + + musice mundane + antedicte que ex quatuor + + constat ut tactum elementis + ut tactum constat elementis + constat elementis ut tactum est + constat ut tactum est elementis + constat ut dictum est elementis + . Quarum quatuor + + cordarum + cordarum ut + + + + dicitur mercurium + inuentorem + dicitur mercurius inuentor + fuisse. + Unde + Ut + adhuc + aliqua instrumentorum + aliquo instrumentorum + aliquod instrumentorum + alia instrumentorum + aliud instrumentorum + + + videmus + vidimus + + + tantum + + + quatuor cordas + habere + habentia + + ut + citaram + + + et + zigam + + zita + zigam uel mygam + . + quintam + quantum causa + vero cordam + chorebus + + + + + + thozebus + ciozebus + zozebeth + tozobus + + + achis filius + ac is filius + ac hiffilius + + + lidorum + + + lindorum + + + rex + regis + + + adiunxit + + , + hiagris + + + + yagris + + + + "According to Clement, Strom. 1. 76. 5, Agnis (Hyagnis) the + Phrygian—a legendary prehistoric figure—invented 'the trichord and the + diatonic scale'; but it is not entirely clear whether 'trichord' here is + adjectival, referring to a type of scale, or a noun, the instrument that bore + [the name 'trichord']" (M. L. West, Ancient Greek Music [Oxford: Clarendon + Press, 1992], 173, n. 43). + + + quidem + quidam + quid + + + phirs + + + + + furix + firix + sirix + phinix + + + sextam + 6ta + + + apposuit + apponit + a + . + Septimam + Aliam + uero + terpanterius lesbius + + + + + + + + + + + + + crepander nilesbius + epauctus lesbius + + + inuenit + inuenit inuenit + + + planetarum + ad planetarum + + + + septem + + + + similitudinem + + similitudine + . Inter quas grauissima erat, + ypate dicta + ypate dictas + ypatem dictam + + + quasi + + maior + et + + + + honorabilior + honorabilis + honor + vnde et iouem + + ypaton uocant + + + ypate uocant + ypatem vocat + + + id est + scilicet + et + autem in + + + supremum + + et + consulem + consilem + eodem + nomine nuncupantes + + nomine + propter + dignitatis + dignitatem + excellentiam. Septem uero + fuisse cordas + cordas fuisse + antiquitus + testatur + testabitur + testabatur + detestabatur + + .25. + + et 32. + et 33 + et 34° + 232 + et 25. et + 24. + 252. + 32. + + + Et + + + + attributa + + fuit + is + hiis + hec + ea + saturno propter + tarditatem + + motus et grauitatem soni. + Parypate + + Parypaten + uero + 2a + 2o + + quasi iuxta + ypatem + + + collocata. + Lychanos 3a. + + ideo quia + ideoque + quia + + + lychanos + digitus dicitur + dicitur digitus + + + quem + quod + latini indicem + uocant + notant + ; greci uero + a lingendo lychanos + + a ligendo liginos + a lingendo diginos + alligendo lychanos + a ligando lychanos + . Et + quia + + in + cantando + cantando ad + , + hanc + hac + cordam + tertiam + + ab + ypate + + ypatem + , + digitus + digiti + + + hic + + + pertingit, quare ab + ipso + illo + + lychanos appellatur. Quarta uero + dicitur mese + + + meser dicitur + + + quasi + que + + + + media quia + quia media + media + + inter primam et + septimam + aliam + + + uere + + vera + vero + + + media est quarta + quarta est + media + . + Quinta + 5a vero + 5a est + paramese + quasi + id est + iuxta mediam + collocata + collocatam + . + Septima quidem dicitur + Septima + dicitur + Septima + dicitur quidem + 6a uero dicitur + + + nete + siete + + + quasi neate id est inferior. + Inter quam et paramese + + + Inter quam parame + et parame + quasi et parame + quasi paramese + + + est sexta dicta + paranete + + quasi iuxta + netem + + + + sita + sitam + posite + + . + Paranese + + Paramese + Parapiese + autem quia + 3a + + est a nete + eodem + eadem + uocabulo + trite + + tricte + trite id est trite + + + id est + quasi + + + tertia + entia + dicitur. + Boeth. De inst. mus. + I.20 (Friedlein pp. 205–6, ll. 28–9) + + Fiat + igitur + ergo + + + talis cordarum + cordarum talis + talis + + + parygrafia + + + + + + + + secundum + thimotheum + + + + + + + + + + + precipuum + in + et + + + hac + hic + ac + + + arte + + virum: + + ut + apparet + patet + + + + 2° + in 2° + 4° + + methaphysice + Arist. + Met. + II.1, 993b, ll. 15–17 + , incipiendo a superiori cordarum uocem grauissimam + + reddenti + reddente + + + ad inferius + + descendendo + ut + usque + et + ad ultimam acutissimam + + representantem: + + Hypate + prima. + + + Parypate + secunda. + + + Lychanos + tertia. + + + Mese + quarta. + + + Paramese + quinta. + + + Paranete + sexta. + + + Nete + septima. + +

+

+ Et + Est + + + + iste + istis + + + quidem + siquidem + + + septem + + videntur + numeri + + + esse ceteris essentialiores + ceteris esse essentialiores + ceteris essentialiores esse + ceteris essentialiores + et necessariores + essentialiores et + necessariores septem videntur + esse + , ita ut aristoteles + + + supra + ergo + + + ipsas + + non + tangat + tangit + ut apparebit ullam + ipsas solas tangat non nulli tamen + , + fueruntque + fueritque + fuerunt + fuerunt quia + fuerunt qui + consequenter + 8 + .9. et .10. + .8. + .9. + .10. + octo + nouem et decem dixerunt + iuxta + illud + istud + + + + psalmiste + + psalmiste. + psale. + + psalmi + + in + psalterio + altero + + + decacordo + decacordo psallam tibi + . + Psalm + 143:9 (Psalm 144:9 in English translations) + Et + deinceps + + inde + deinde + demum + + + in tantum + iterum + + + creuit numerus + excreuit numerus + numerus excreuit + exercuit numerus + ex trite ut numerus + + ut + boecius + 18 cum + boecius cum + boecius + 7 + reiteratione + ipsarum + ipsorum + ipsas + + + enumeret + nuetur + sub + dyatonico melo + + + dyacomcouiclo + ydyacomicomelo + et + totidem + + sub + cromatico + + + + + + ac + 18 + .xxviii. + etiam + sub enarmonico + + + + cum + quasi + + + uariatione + ua uariatione + + + quadam + quedam + + + communi + + communis + + + + sine zeugnum + + + + + + + + + + et diateuzeugnum + et dyateuzegnu dyateuzeugnum + + + + + + + + + + + et dyageogimini + + . Non enim + plura tribus sunt + plura sunt tribus + sunt plura tribus + genera + melorum + + + quibus + omnis + omnes + omnibus + + + + contexitur + + + + cantilena. + + + + Cuius hec est descriptio + Cuius est huius descriptio + Quibus hec est + descriptio + Cuiusmodi est huiusmodi descriptio + + + + + dyatonici + + dyacommunia + + + proslabanomenos + + + + + + + ypate ypaton + + + + + + parypate ypaton + + parypatem ypaton + + + + lychanos ypato dyatonici + + + + ypate meson + + meson + + + parypate meson + + + + + lychanos meson dyatonici + diacenos meson diatonici + + + mese + me――――sem + + + trite sinezeugnum dyatonici + + + trite sinezeugium + trite sinezeugmen + trite sinegeumen + trite sinezeuium paramese trite diazeuium + paramete + + + paranete sinezeugium + + paranete sinezeumen diatonici + permete sinegeumen dyatonici + paranete sinezeugnum dyatonici + paranete sine ceugnum dyatonici + paramete inmeazegium dyatonici + + + + nete sunezeugium + + + + + + + + + + paramese + + + + + trite diezeugium + + + + + + trite diazeuium paramete + Ededie zeugium + + + + paranete dyezeugium dyatonici + + + + + + + + + + + nete dyezeugnum + + + + + + + + + + trite yperboleon dyatonici + + + trite ypereboleon + + trite yperboleon + + + paranete yperboleon dyatonici + + + + + nete yperboleon. + + "Of the 'moveable' notes whose positions varied in different + genera, Lychanos was treated as especially diagnostic of genus, and as a note-name + it is sometimes augmented or replaced by enharmonios, chrōmatikē, or diatonos, + depending on its actual station. The same happens more rarely with Paranētē" (M. + L. West, Ancient Greek Music [Oxford: Clarendon Press, 1992], 222). + Similis autem per omnia + figuratio extat + extat figuratio + est figuratio + figuratio + in + cromatico + + orematico + + + melo ac consimilis + melon ac consimilis + melo et consimilis + melcoris similis + melo et cuius similis + melo ac minus similis + in + enarmonico + armonico + , excepto + quod ut + quod + in + prima + primam + + + subscribitur + describitur + scribitur + + + dyatonici + + + dyatonicum + dyatonicis + dyaconitus + + + ita + ita ut + + in secunda + + cromaticon + + + + tromaticus + cromatico + cormanticon + cormanticum + et in tertia + + enarmonicum + ermonicum + , ita ut omnes coniuncte + liiii. + quinque + + + sunt + sint + corde. Moderni autem in aliquibus ultra lxiiii. + + apposuere + apponunt + apposuerunt + ut medius + canon + canono + canon dictus + ostendit. + + dyatonici + proslabanomenos + ypate ypaton + parypate ypaton + lychanos ypato dyatonici + ypate meson + lychanos meson + Mese + Trite sinezengium + Paranete sinezengium dyatonici + Nete sinezengium + Paramese + Trite dyazengium + paranete dyezengium dyatonici + zeze dyezengium + trite yperboleon + dyatonici + Nete yperboleon + + + + + Deinde. +

+

+ AUT. + AUT QUIA. + Soluit + dicens + + dicit + causam esse quia + cum + + difficultate + ampliori + amplior + + cantus + fit + sit + secundum + ypatem + + ypate + . Ipsa + enim est + est enim + est + enim + principium + + incipiendo + + incipiendo a + superius, ut + prescriptum + prescriptum est + descriptum est + ad quam. Si + perueniri debet + debet perueniri + perueneriet debet + + uocem + oportet + + eleuare et + ab + ad + + + ipsa + ipsam + uersus + netem + + noctem + + + deuenire + peruenire + uenire + , cum cantus perficiatur + sonorus + sonorum + ex contrariis eleuando et + deprimendo + descendendo + uocibus.

+

+ + Deinde. + + ID AUTEM. + + Contingit + Concludit + Dicitur + propter hoc + quod + quia + contraria + sunt subitam + subitam sunt + sunt subiecta + sunt subicita + sunt subtila + + + inducentia + inducentiam + alterationem. In hoc + uero + + + + intercidit + interdicit + labor et difficultas, + ubi autem huius + ubi huius + ubi autem hoc + ubi autem huiusmodi + magis accidit corrumpi sicut etiam + in + + aliis apparet potentiis. Et + ideo + + + + agonizantes + + + cantant leges et non + choros + choros ut + + 15°. Per alias + + uero + + cordas et proprie + medias + motas + per oppositum + cum + + difficultate cantatur + minime. + +

+

+ Circa predicta dubitatur + Dubitatur circa dicta + Dubitatur + quoniam videmus + plura + plurima + instrumenta habentia multo plures cordas + quam + que + + + pretacte + pretacte sunt + . + Rota + + Corda + enim habet xliiii. + + ut + + + .22.as + + in vno + + latere et in + reliquo + aliquo + + + totidem + + + + medius + melius + + uero + canon. + canorum + + lxiiii. et de + aliis + reliquis + + + similiter + + . Dicendum quod + ille + illi + plures reducuntur + ad + quid + minores + prius + prius ut + + + institutas + institutos + . + Quatuor + + 4 enim + Qua eticorum + superadditarum + sumuntur + + sumentur + pro vna + priorum + + priorum et + , ita ut + xxviii. + 24 + + + cadant + + in .vii. notiores, + et + + + + .xliiii. + 24. + 28. + .10. et .44. + + + redeant + + redeunt + in + .xi. + 12 + et + .lxiiii. + 68. + in + .xvi. + .18. + Et similiter + + de + in + aliis taliter + uariatis + uariatus + . Sicut + + + + namque + enim + + + + + quatuor positi + sunt gradus + positi sunt quatuor gradus + 4or. sunt positi gradus + sunt positi quatuor gradus + positi sunt gradus + sunt gradus + + + medicinarum + mediarum + + + prius in tegni, + + prius integri, + + Avic. + Can. med. + I, fen 2, 2.15 + + + deinde quoque + deindeque + deinde + + + quinto + simplicium vnusquisque + 4or simplicium vnusquisque + 5° + simplicium + + + diuisus est + est diuisus + diuisus est quilibet + + + in + + + tres mansiones, ut + agnoscatur + agnoscantur + cognoscatur + quantum + possibile + possibile est + + + particularius + particularis + per particularius + + + complexio + + coniunctio + conno + + + + medicine + meclicine + medie + . + Ita + Ita ut + + + posteriores + posterioris + + + musici + minus + non solum cordis + fuere + fuerunt + + + contenti + contempti + quibus essentialiores et + integraliores + irregulariores + + + denotarentur + denotaretur + + proportiones. Verum ut + sonum + solum + amplius + melodiosum + + + + construerent + constituerent + + + inter + in + + + priores + + principaliores alias + adiunxere + adiuxerunt + , ne inter eas + magna + + + + permanerent + permanerem + permaneret + + + interstitia + tristitia + in tristitia + . + + etcetera + sequitur 4m + problema. +

+
+ +
+ + Quartum problema + 4m + Quartum problema + Quartum + + +

+ PROPTER QUID SECUNDUM HANC + PROPTER QUID SECUNDUM PARYPATEN + + PROPTER QUID SECUNDUM HANC DIFFICULTER YPATEN, FACILE ETIAM DIUISIO + ALTERIUS? + AUT QUIA CUM REMISSIONE YPATE ET SIMUL POST + DIUISIONEM LEUE SURSUM PROICERE? + PROPTER HOC AUTEM UIDETUR ET QUE DICUNTUR AD VNAM + AD HANC QUAM CIRCA NITEM. + OPORTET ENIM CUM DIMISSIONE ET REMISSIONE UALDE + PROPRIA CONSUETUDINI AD + UOLUNTATEM. + HUIUS AUTEM UTIQUE CONSONANTIA QUEDAM + CAUSA + . + + Quartum problema + etcetera. + + + Quare + Querit quare + secundum + istam + illam + hanc + primam + cordam puta + ypatem + + + + difficulter + + + + cantatur + cantetur + ? Et ideo + dictum est + dictum + + + antea + ante + anima + + + secundum + secundum eam + interruptionem cantus + peruenire + peruenirem + prouenire + et licet cum difficultate + + cantetur + canta + . Tamen diuisio siue distinctio + istius + ipsius + corde a + quacunque + + + + alia + aliam + + est facilis et manifesta et + proprie + prope + ab inferioribus, ut + nete + ratione + + + ac + et + + + ei + ea + eis + etiam + propinquis.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit + et prius + + ad + id + illud + quod + subdictum + subdictum est + subditum est + subditum + subductum + + + secundo + + + + dicens + dicit + + + illud + id + ideo + + + esse + + quia faciendo remissionem et quasi quandam + interpollationem + + cum cantus fiat cum + ypate + ypatem + + + simulque + simul que + + + fere + ferre + statim post durationem + uel + et + + + diuisionem + dimissionem + + + intonationis + intonantis + grauem, + leue + leuem + + + fit + sit + + + uocem + uoce + sursum emittere, cum iam + aliqualiter cantans + cantans aliqualiter + + aliter cantans + cum nam aliqualiter cantus + + + quieuerit + quieuit + conuenerit + emittendo spiritum et + attrahendo + + mittendo + emittendo + sufficienter in uocis + organa + organe + . + Et ideo + Et ideo non + Et ideo in + Ideo + percipi videtur + discretio + distinctio + in cantu + facto + facta + per + ypatem + + + cum alia sibi opposita.

+

+ + Deinde. + + + PROPTER HOC. + PROPTER. + + + Assignat + + causam + prioris + priores + + + premissi + dicti + dicens + id + illud + + + fore + esse + quia melodie + que + + + + referuntur + feruntur + ad unam cordam, puta ad illam que est circa + netem + uenem + uene + + + ut + aut + + + paranetem + paranete + + + ac etiam paramese + aut etiam paranete + + + + facilime + + faciliter + + + cantantur + cantatur + , eo quod non interuenit multa diuersitas + uocum + uocis + secundum + acutum + auctum + et + grauem + + graue + , + sed tamen + sed cum + et inde + + + licet + sit est cum + + + per ypatem + + parypatem + cantetur + difficulter + + propter + grandem + gradem + magnam + grauem + notarum + distantiam + differentiam + . + Cum + + + + tamen + causa + + + + fit + sit + ut + tactum est + tactum + quadam + dimissione + diuisione + et + remissione + reuersione + + + quasi pausando + pausando quasi + ita + ea reddatur + ea redditur + propria + ualde + uelut + consuetudini + per uoluntatem + acquisite + + aquisittam + + + , + + quis enim + sic + sint + eligit, + tunc utique + nunc atque + consuetudine + per uoluntatem acquisite. Quis enim sic eligit tunc utique + consuetudine + inducta in cantando per + ypatem + + . + Secundum + Per + talem + dimissionem et remissionem + remissionem et demissionem + remissionem ad omissione + dimmisionem + dimisoonem + licet de se cantetur difficilime + illo + illa + autem + modo + + minime, + quoniam + quod + quia + quando + consuetudo difficilima + etiam alleuiat + alleuiat etiam + etiam illeuiauit + + + + cuncta + puncta + cetera + iuxta + illud + istud + + + + ypocratis + afforisticis + + + ypo. + affirmatio + yporetis amforisticis + iporcratis anpho. + ypoti. amplias + + assueti assuetos ferre labores et + reliqua + ceteram + . + Hipp. + Aph. + II.49 + + + + Dicit autem uoluntatem quia + + consuetudo proprie + proprie consuetudo + in habentibus rationem + acquiritur + + aquirimus + requiritur + + + apparens + ut apparet + + + + ethycorum + secundo + + + secundo + ethicorum + . + Arist. + Eth. Nic. + II, 1103a l. 17 +

+

+ + Deinde. + + + HUIUS AUTEM. + HUIUSMODI AUTEM + HUIUS ERGO + + + Subdit + Concludit + + tertio quod + etiam + illud + consonantia est + aliqua + alia + causa + eius + huius + , + + quod + + + + per ypatem + parypatem + cantus + sepe + + non + reputatur + reputata + + + difficilius + difficilimus + difficilior + difficilis + difilis + nam consonantia + fessa + fesse + falsa + + + restaurantur + restauratur + + + ut visum et + et + ut uisum est + ut uisum est et + ut uisum eius + + + uigorantur + vigorantur det + uigoratur + + + debilitata + debilitatem + et debilitata + et debilitatur + . + + Εt + + + + ideo quesitum + ideo quiritur + queritur ideo + + + quare + coram + cum + + + infirmis + interimus + + + secundum + alexander + + + fistule ac + tympana + + + tympana etcetera + . + secundum + + Ps.-Alex. Aph. + Prob. + I.78 (Vat. reg.lat. 747, f. 75v) + + + + + + + Sic + Sicut + + + igitur + ergo + + + licet de se + de se licet de se + licet se + ita de se + + + difficulter + + difficiliter + + cantetur + ypate + parypatem + per + + accidens, + tamen non + non tamen + in tantum. Puta + uel + + ratione consuetudinis + interuenientis + interueniente + + + aut + ac + + + delectabilis + delectationis + + + ipsius + + armonie, cum + fuerit + + + + amicius + + ac amicius + animi eius + cum eius + cum eis + eius + aicius was likely mistaken for amici + eius + + + adiecta + adicta + adiuncta + + + opposita, et + quod + quia + distinctio + + maxime apparet in + eo + + + + qui + quod + secundum ipsam + cantu + cantum + cantat + causatur + . + + etcetera + sequitur 5a. problema 19e. particule. +

+
+ +
+ + Quintum problema + 5m + quintum problema. Quintum. + + +

+ PROPTER QUID DELECTABILITER + PROPTER QUID HABENTES ALIQUAM NOTITIAM + + PROPTER QUID DELECTABILITER AUDIUNT CANTANTES + QUOSCUMQUE, UTIQUE PRESCIENTES ADIPISCUNTUR CANTUS, QUAM QUOS NESCIUNT? + UTRUM QUIA MAGIS MANIFESTUS ADIPISCENS SICUT + INTENTIONEM QUANDO COGNOSCUNT QUOD CANITUR? HOC AUTEM DELECTABILE CONSIDERARE, QUIA DELECTABILE + DISCERE. HUIUS AUTEM CAUSA HOC QUIDEM ACCIPERE SCIENTIAM. HOC UERO UTI ET + RECOGNOSCERE IPSAM. + ADHUC AUTEM ET CONSUETUM DELECTABILE MAGIS + INCONSUETO + . + + Quintum problema + etcetera. + + + Quare + Querit quare + cum + delectatione + delectatio + maiori + audiunt + audiuntur + homines cantatores + ac + aut + etiam + sonatores + senatores + subatores + cantantes omnes + illos cantus + cantus illos + istos cantus + + quorum + preaudientes + audientes + plaudientes + + + habuere + habuerant + habuerunt + + + + prius + + + aliquam cognitionem? Siue + sit + sint + + secundum verba, + ut + aut + ita + + + quod + quid + + + aliquid + aliqui + de + ystoria + + + + + + gesti + gesta + iam + audiuerint + audierint + audiuerit + audierunt + , uel + demum + de modo + + + cantandi + + , + eo quod + eos quod + + + audiuerint + audiuerunt + audierit + audiuerit + alias, + illum + illud + + + et + + + + consuetudinem aliquam inde acceperunt + acceperunt consuetudinem aliquam inde + consuetudinem inde acceperunt + acceperunt aliquam consuetudinem inde + consuetudinem aliquam acceperunt + quam illos + cantus + + quorum + audientes + + nullam + habuerunt + habuerint + + + precognitionem + cognitionem + omnino.

+

+ + Deinde. + + UTRUM. Soluit + et prius + et primo + primo + + + probabilius magis + probabile magis + magis probabiliter + dicens + illud + id + hoc + ideo + esse + quoniam + quia + + quando homo aliquam prescientiam + habuerit + habuerunt + circa cantum + quem + quem quem + quam + + + audiuit + audit + , adipiscitur + et attingit ei quod est + et adtingerit ei quod est + et attingit ei quod + ei quod est + + + sibi + igitur + + + magis + magis est + + + + manifestum + uisum + . Et hoc declarat + quemadmodum + + qm + quam + + quod diu + + qdm + quodammodo + + quando aliquis habuerit intentionem gesti quod cantatur + et hystoriam + + + + eius + quodammodo + quodam + + + sciuit + sciuerit + presciuit + , tunc + hoc + huic + hunc + + + intendere est + est intendere + intende est + intendetur est + delectabile + precognoscentibus + precognoscentiam + precognitionibus + , eo quod iocundum est + discere + dicere + + + aliquid + aliquod + adhuc + cuius non + perfecte habetur + habetur perfecte + + + cognitio + precognitio + , + quod fit + ut fit + quod sit + quare sit + + + iterum + iterum Iterum + audiendo + uel + ut + + + considerare + considerando + , ut + continetur + continetur in + + .xl., ubi + id + illud + hoc + + + repetitur + repetetur + . + Que + Quod + + duo interueniunt cum quis habet cognitionem + gesti + gesta + aliquam, + nam + iam + + + ipse + ipsa + + + discit + discet + adiscit + dicit + dixit + in eo quod + accipit scientiam cantus + scientiam cantus accipit + + + illius + ipsius + , eo quod gestum + illud licet + illud hoc + illud + + + aliqualiter + aliqua + + + esset + est + erat + fuit + + + scitum + situm + scituti + ab eo. Non + tamen + + + + per modum melodie + promotionem die + toto omni die + per motionem die + utitur + autem + + et + considerat + considerant + consitus + + + in + + eo quod + audit + audiat + + gestum cuius + habuit + habet + prius habuit + cognitionem. Et ideo + videmus + + homines ut plurimum + cum + quando + uolunt + amplius + in + + + cantu + cantum + + + delectari + + + + facere + faciunt facere + + + sibi + ubi + + + ystoriam + + + gesti + enarrare + + + enarari + numerare + , tunc enim + dupliciter + dicitur + dicit dupliciter dicitur + + + delectantur + delectatur + + + + + et melodia et ystoria et siquidem + cum habuerint + . + Triplex enim + tunc + + + + dilectatio + + concurrit + + + consuetudinem + consuetudine + audiendi + predictum cantum + cantum predictum + + + aliquando + in + ita + amplius + amplius aliquando + + + delectantur + delectatur + + + triplex enim tunc delectatio + concurrit + triplex enim delectatio tunc concurit + triplex enim delectatio concurrit + , + + Deinde. + unde secundo confirmat causam + prefatam + prefactam + .

+

+ ADHUC AUTEM + AD HOC AUTEM + ADHUC + . + + Dicit + Dicens + quod amplius ad hoc facit + si quod + si quid + que si + sicut + + + auditur fuerit consuetum, + auditur fuit consuetum, + auditur fuerit + audiui + + + quia + + + consuetum magis + delectat + delectant + quam oppositum, + + cum + quam + sit + factum + facta + natura + quedam + quadam + et + nobis + a nobis + + + + conuenientia + conuenientiam + conuenientius + . Quod autem + + et + etiam + et quomodo + + + consueta + consuete + + couetia + conuenientia + quod autem et quomodo consuetta + + + delectent + delectant + delectentur + , + + ostensum est + ostensum ostensum + ostensum + ostensum est in + + + sexto + 18e. + sexto + 16e. + 3e + 18e. + sexto + sexto et + octaue + , + Ps.-Arist. + Prob. + 18.6, 917a ll. 6–17 + et per oppositum + quid agant + quod agant + agant + quod agunt + quando audiunt + opposita, + et ideo + + + + audientes + audiente + qui + vnius + videntur + vuius + + + lingue sunt + lingue + + + cantum + tantum + + + alterius + anterius + alterius auertimus + minime + nisi + + + + consueti + consuete + + + delectantur + delectentur + , cum neque + ystoriam neque + + + + + + modum cantandi precognouerint + modum cantandi precognouerit + modum cantandi precognouerunt + modum precognouerunt + modum precantandi cognouerit + modum precanendi cognouerint + cantandi modum precognouerunt + cantandi precognouerunt + cantandi precognouerint + precantandi cognouerunt + . In opposito + autem secus + autem cetus + , + ceu + seu + sicut + cum + + + mihi + + + nichil + + + contingit + contigit + conuenit + + + per omne + parisius + cum ad + gallos + + me + transtuli + + + . Ut + autem + aut + + + + id + illud + + + repetitum + repetitur + reperietur + repente + + + .xl. + 48°. + quarto + + + exponatur + exponitur + + + omne + ore + esse + , aristoteles + + talem + et aliam + addit + causam + + + + dicens + dicit + + + ideo esse + id esse + + quoniam + ille qui + illi qui + illud qui + ille + + + cantantem + cantant + cantationem + + + compatitur + audit compatitur + ipsi et ab + ipso + illo + + + afficitur + efficitur + , propter uoces quas + exprimit + exprimunt + + + que + qui + + + audienti + auditui + + + videntur + numeri + + denotare + gaudium + cantum + , et ideo + consonat sibi + sibi consonat + + + id quod + illud quod + quod + ille + cantat + cantant + qui cantant + . + Et + cum + + + quadam + quandam + + naturali inclinatione + ad delectationem + mouetur + mouentur + in + seipso ceu + se seu + ille mouetur + mouetur ad delectationem in se seu ille mouetur + in se mouetur ad delectationem + . + Quando + Quoniam + + + enim + ei + + + natura + natatur + + + + vnius + unus + minus + + + percipit + perficit + + naturam alterius + congaudere + gaudere + congaudet + cum gaudere + + + + aut + et + uel + tristari uel + se + + + + purgare + purgalis + , natura etiam + illius + ipsius illius + + + ad hoc mouetur + mouetur ad hoc + mouetur ad se hoc + agendum + + , ut + declaratum est + declaratum + + + septima + + . + Quare + Aut quare + subdit in + eius + + + + verificationem sermonis + sermonis uerificationem + verificatione sermonis + quod omnis + cantans + cantus + consonat sibi et alium reddit consonum + et + affectum + affectantem + effectum + affectione + , dummodo illum + cantum + cantu + non + exprimat + exponat + propter + necessitatem + + ueritatem + , + ut + aut + + + sperans + superans + + + ita + ita ut + inde + + + victum + uitum + lucrari + ceu + seu + ut + + + ystriones + + + aut metu + pene + pone + uel + tristitia + tristitiam + , et + huius + huiusmodi + + + propter que talia + propter que talia tam + propter talia que + propter quod talia + propter talia + + + cantantes + + + + non + nec + + + magne + magis + + + consonant + consonans + consonat + consonas + aliis + et + + maxime + extraneis + + ab illo cantu + et sibimet ipsis + + minime. + + etcetera + sequitur 6m. problema 19e. particule. +

+
+ +
+ + Sextum problema + 6m + sextum. + Sextum. + + +

+ PROPTER QUID PARYPATE + PROPTER QUID RATIONABILE EST + + PROPTER QUID PAR YPATE SECUNDUM RATIONEM IN CANTIBUS TRAGICUM. + AUT PROPTER INEQUALITATEM? PASSIUUM ENIM INEQUALE, + ET IN MAGNITUDINE FORTUNE AUT TRISTITIE. EQUALE AUTEM MINUS PLORABILE UEL + ULULABILE + . + + Sextum problema + etcetera. + + + Quare + Querit quare + rationabile + existit + est + quod + genus cantandi tragicum + genus cantandi traycum + genus tragicum + + + per ypatem + per ypate + parypatem + cantetur? + + Nosce quod + Notandum quod + Nosce + + + circa + + genus + armonicum + armoniarum uel armonicum + + + quodcumque + quod + t' + talis + + + duplicem maneriem cantandi constare, + quedam enim + quidem enim + que + + + est + + + + comedia + comedia et + altera tragedia. Est autem comedia + canticum + cantus + agreste + que + + res priuatarum + et humilium personarum + personarum et humilium + et humilium + et habilium personarum + + + comprehendit + comprehendens + , et dicitur + a cosmos + acosinos + a cosinos + a camos + quod est + villa uel laus + villa + secundum aliquos. Grece + tamen + tantum + + + mundus + + et + odi + odos + cantus + quasi + quia + + + mundanus + + + + et + uel + vulgaris + cantus + + cantatus + , + de rebus enim + enim de rebus + de rebus + vulgaribus tractat et + affinibus + affinibus et + + + + cotidiane + + + + + locutionis + + locutioni + + locutioni cotidiane + . Vel + dicitur + + + + a commessatione + + a conmiseratione + a commensuratione + a commesatione + a commensatione + a commessatione quia + accessatione + accensatione + post cibum, + enim + + + + homines solebant + solebant homines + + + ad + + + + eam audiendam + audiendam eam + + + conuenire + pervenire + . Tragedia uero + est modus carminis + est modus carminum + cantans + quo poete in + luctibus + + regum utebantur. + Dicta + Dictus + Dictum + a + tragos + + + treges + quod + est + dicitur + + + yrcus + + + et + odi + + odos + + + cantus + quod est cantus + + + quasi + in + et + inde + + + hyrcinus + + + + yranus + cantus. Et quia materia erat + tristis + tristis et + + + feda + fetida + seda + , + huiusmodi + huius + + + animal + animalis + + + ut + uel + + + yrcum + + + yrcus + hircus + hincus + + + pro munere + perminuere + provire + pro numero + + + poematis + poanatis + + + + accipiebant + accipiebantur + recipiebant + + + additur. Et + additur. Etiam + quod dicitur in + + + maneries a quibus 3° + maneries a quibusdam 3a + + + satira + + + dicta + que + in + carmine + construitur + constituitur + + + reprehensorio + reprehensoris + reprehensorior + reprehensionis + + + ceu + seu + sicut + + + modus + motus + + + oratii fuit + + fuit oratii + maxime.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens + causam esse sumptam + causam esse causam sumptam + + ab + inequalitate + equalitate + , vtrobique + enim + scilicet + uidelicet + uidet + inest quedam inequalitas, ut in cantu + tragico + + + + + et + + + + per ypatem + parypaten + facto, + propter + per + + + eius esse + esse eius + eam esse + eius at esse + + + supremum + supremam + . Nam in + vnoquoque + vtroque + istorum est quedam passio et difficultas, + quod + earum + autem + tale + tale est + , + siue + seu + ceu + Inequale seu + + + sit + fit + + in magnitudine + + fortune + fortitudine + ceu cantus magne letitie alicuius + magnatis + magnatis aut + magnatis et + magnatis uel huius est inequale non + eundem seruans tenorem + + probitatis, siue in + magnitudine + magnitudine letitie + + + tristitie, + sicut + sum + mortis alicuius excellentis + uel + + + + huiusmodi + huius + ut nuper domini ubertim dicens carraria uel hoc + , est + inequale + equale + , + non eundem seruans tenorem. Quod + autem + aut + + est + inequale + in eis uale + + + et dissonum + rationabile est + rationabile erit + rationale est + est rationale + , ut + cantu + cantum + exprimatur + huiusmodi + huius + et huius + , ut pondus + meloticum + + + meloticus + + + + configeretur + + + + cum figeretur + contingeretur + velociter configeretur + uelociter consigneretur + rei de qua + existit + extitit + . Tunc cantus consurgit + + eurithimus + onrichimius + + in rich enrichimus + enrichimus + + + + sicut de huius + sicut huius de + sicut de huiusmodi + + + pulsu scribitur + pulsi scribitur + cantu scribitur + + + de differentiis + pulsuum + 8 + differentiis pulsuum et + + + a + a a + + + galeno + + . + Gal. + De diff. puls. + I.8 (I.12 in Latin trans. by Burgundio of Pisa) Cf. Conciliator diff. + 83 + + + Ceu + Seu + in + bellis + becillis + + + tubarum + tuban + clangor bellantes concitat in furorem, in oppositis autem + ut + + in + choreis + choris + + + oppositum + compositum + + + expetitur + experitur + eproexperitur + , ac similiter + in + + mortuorum lamentatione. Et + id + illud + hoc + est + quod + quod est equale + + + subditur + subdit + a contrariis probando + pretactum + pretactam + , + inquiens + in conueniens + quod + illud + id est + + + quod + + est + equale + inequale + in cantu et vnum conseruans tenorem non + est + + + + plorabile + proportionabile + + + aut + seu + + + ululabile + + amabilabile + lamentabile + , cum + non sit quid + sit quid non + passiuum, + propter quod non est + conueniens + inconueniens + ipsum + + + + parypatem + + + per ypatem + cuius est + inequalitatem + inequalitas + tenere + sed + super + per alias + cordarum + cordas + + + mitiores + + + anteriores + exponere.

+

+ Nosce + Notandum + quod + pondus est + illud + illud quod + in + quo + quod + quid + proportiones + + secundum auicenna + + + + + cadunt musice + musice cadunt + cadunt musice et + . + Avic. + Can. med. Book I, fen 2, 3 (p. 141 of 1608 ed.) + Hoc autem pondus + rebus expedit + rebus expetit + rebus accidit + expedit conformari rebus + circa quas + extat + extant + extitat + + + configurari + + , + cum eo + quod eo + + + exprimantur + exprimatur + passiones que sunt in anima. + + + Voces + enim + autem + + + sunt + + note passionum + que sunt + + in + ea + anima + + + illeque rerum + + + primo + id est + + <app> + <lem wit="#Gu #Ma #Pp #Px #Py #Vm #Vo #Vz #m #v">peryarmenias</lem> + + + + <rdg wit="#Va" ana="#lexical">pergere</rdg> + </app>. + Arist. + Peri herm. + I.1, 16a ll. 5–6 + Unde si res + fuerit + fuit + + + alta + altera + + + in signis + insignis + + + contingit tragedia + tragedia contingit + + conuenit tragedia + conuenit tregedia + querit tragedi + + + ipsam + + + + exprimere. + exponere. + Si autem econtra + comedia + + ut modus + coaptetur + coagiretur + coitetur + + + rei + ei + + + ceu + seu + + + proprietas + proprietas approprietur + subiecto. + + et cetera + sequitur 7m. problema 19e. particule. +

+
+ +
+ + Septimum problema + 7m + Septimum. + Septimum + + +

+ PROPTER QUID ANTIQUI + PROPTER QUID ANTIQUI CONSTITUENTES + + PROPTER QUID ANTIQUI SEPTEM + CORDARUM FACIENTES ARMONIAM YPATEM, SED NON NITEM RELIQUERUNT? + UTRUM HOC MENDACIUM, UTRAMQUE ENIM RELIQUERUNT, + TERTIAM UERO ELEUAUERUNT? + AUT NON, SED QUIA GRAUIOR FORTIFICAT ACUTIORIS + SONUM, QUARE MAGIS YPATE REDDIT ANTIFONUM QUAM NITE? + QUIA ACUTUM POTENTIA MAGIS, GRAUE AUTEM FACILIUS + CANTATUR + . + + Septimum problema + etcetera. + + + Quare + Querit quare + est quod antiquitus + constituentes + constitutos + constunentes + constitutiones + armoniam musicalem ex septem cordis + diuiserunt + dimiserunt + ypatem + non + + + + auferentes + + + + ipsam + eam + ab armonia, non autem + relinquerunt + + + + nete + neten + netem + uocem + , + + uerum + uelut + + + inde abstulerunt + namque abstulerunt + inabstulerunt + ?

+

+ + Deinde. + + UTRUM. Soluit et + prius + primo + + + problema + problemas + probatur + probabiliter + dicens + id + illud + illico + + + + non esse uerum + non uerum + + esse uerum + + quod + premissum est + premissum + , quoniam non + seruauerunt solum + solum seruauerunt + seruauerunt + + + + ypatem + + , + ymmo + + + + + + utramque + utraque + + + puta + piata + ypatem + ypatem + et + netem + + + nete + . + Sed + Si + + + quam + quem + quid + abstulerunt fuit tertia, + ut + et + paramese + uel + + lychanos, + utraque + utramque + enim est tertia + + eius + huius + quod est + + septem + 7a. + + + esse + circa + + esse 7 + cordas. Unde 32° + + dicetur + unde dicetur + quod + tripandius + + + extrahens tertiam cordam a + septicordo + + cordo + + + netem + + + nutio + + + apposuit + apponit + apponunt + . Sic + ergo + igitur + + + per + per 4 + + + interemptionem + interpretationem + intentionem + soluit.

+

+ + Deinde. + + + AUT NON. + AUT. + AUT QUIA. + Soluit + + magis + + ad + orationem + oratio + rationem + + + secundo + 2a. + + + secundo magis ad + orationem + + + dicens + + dicit + + + nichil + alias + hoc + esse quod dicitur ut quod + abstulissent + abstulissetur + + + netem + + + + + et + dimisissent + + dimisissentur + ad misissent + + + stare + + + + ypatem + + . Sed hoc dictum + + fortassis + + + + ex hoc + + + + pullulauit + + + ex hoc pullulauit fortassis + , quia sonus + cordis + corde + grauis + vigorat + fortificat + figurat + fiat + sumitur + sonum acutioris. Suo enim multo tempore et duratione graue + substentat + + + + + acutum + acutam + + + ne + non + ut + cito + pereat + periat + persat + + + cum breui tempore feriat + + . Propter + quod + + + + ypate + ypatem + ypaton + + + longo + + + + tempore + + + + aere + aera + aerem + percutiente + quam + quem + quod + + + nete + + uite + + + reddat + + redeat + reddit + , + ob eius + ab eius + propter eius + + acuitatem, que + potentia + ponitur + uel fortitudine indiget in + cantando, + difficile namque + difficilime namque + difilime namque + difficile enim + + + acutum + acuta + cantare + sed graue facilius, + + + + sicut pluries dicetur. Sic + itaque + ergo + quia grauis corda sonum fortificat + acute et ad se + acute et a se + acute et acute a se + conuertit. et + quia + quia quia + + + + difficile acutum cantare + acutum cantare + difficilime acutam est cantare + difficilime est acutum cantare + difficilime acutum cantare est + + + , quis credidit ex hoc + cum + causa + + + nete + + nitem + netem + voce + intensum + sonum + non + + + + perciperet + percipet + percipiet + + + proprium + + + + quod + cum + esset + sublata + sublato + ? Et fortassis aliquis leget + illud + istud + illud ut tactum multe + + + QUIA ACUTUM. + + quod aliam solutionem + subiungat. + subiungit. + subiunget. +

+

+ Nosce + Notandum + quod + + armonia + armoniam + que + est + est in + + vna + trium + + partium ut tactum est musice + partium ut tactum musice + partium musice ut tactum est + partium + , proprie pertinet ad + comedos + + + comedias + comedras + + + et + uel + + + tragedos + + uel choros, et omnino ad eos + qui + que + precipue uoce cantant. Ex ea + namque + enim + + + causatur + causatur talis + cantatur talis + armonia que + est + + + + uocis + uocum + modulatio + + et + a + concordia plurium + sonorum + plurium sonorum + + + uel + + + + coaptatio + coadapatatio + coactio + . + Simphonia + + est + uocis + uocum + modulatio + + temperata ex graui et + acuto accordantibus + + acuto concordantibus + acuto a cordantibus + #Pp and #Pu are ambiguous, because they use the character + "a" to represent "7." + sonis, + cuius + suis + quidem + contraria + contraria est + + + + dyaphonia + + + . + Euphonia + + + est suauitas + uocis + uocum + , + hec + hoc + autem melos + a melle et + amelo et + a melos a mellis + a melle + a mellis + + + suauitate + suauitatis + dicta. + Dyastema + + + + + + Dyafema + Dyaphonia + est + uocis + uocum + + spatium ex duobus uel pluribus sonis + coaptatum + coaptant + coadaptatum + . + Dyesis + + + est + spatia + spatium + + + quedam + quoddam + + + et + + + + deducens + deductiones + + + modulandi + + et + vergendi + turgendi + + + de vno + + in alterum + sonum + solum + . + Isidore of Seville, Etym., + III.20.1–6 + + + + Boecius autem + Bouus autem + + + dyesim dicit + + + dicit Dyesim + + + vnius + fore + fore unius + minus fore + fore + + + semitonii + + semitonium + . + Boeth. De inst. mus. + II.28 (Friedlein p. 260, ll. 21–24) + + + Tonus + est + est autem + autem + + + acuta uocis + uocis acuta + uox acuta + acuta + aucta acuta + vocis + arta uocis + alta uocis + acuta arta uocis + + + enunciatio + + . + Αrsis + + + Resis + quidem uocis eleuatio, + tesis + + + + enthesis + + + depressio + + . + Isidore of Seville, Etym., + III.20.7, 9 + Sic + igitur + ergo + ex + symphonia + + potest + haberi + habere + quod + antiphonum + + + antiphonori + + + + uel + + + + antiphona + + anthima + sit quedam modulatio + uel + et + intonatio + contra + circa + que + quam + + + simphoniam + + , ut + sonus + sanus + qui + post + potest + prius + eam refrangitur auditum + demultiens + + denuntians + de multotiens + . + + etcetera + sequitur 8m. problema 19e. particule. +

+
+ +
+ + Octauum problema + 8m + octauum problema. + Octauum. + + +

+ PROPTER QUID GRAUIS + PROPTER QUID SONUS GRAUIS CORDE + + PROPTER QUID GRAUIS ACUTE FORTIFICAT SONUM? + AUT QUIA MAIUS HOC GRAUE? OBTUSO ENIM ASSIMULATUR, + HOC UERO ACUTO ANGULO + . + + Octauum problema + etcetera. + + + Quia + Quare + + + dixerat + dixatur + distrahit + + grauem cordam + sonum fortificare + fortificare sonum + acute, + + causam siquidem querit huius + causa siquidem querit huius + querit causam huius + dicens + quare + quia + grauis + corde + corda + cordas + + + sonus + + + + uigorat + + uigilat + eum + qui + quia + acute?

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit + dicens causam esse + causam esse dicens + + + quoniam + quia + + illud quod est + graue + + + + maius + magis + + + est + + et fortius. Quod ostenditur quoniam + angulo + angulatio + + + simulatur + + multiplicatur + si multiplicatio + si multiplicatur + + + obtuso + acuto + trianguli, + qui + quod + quidem maior + est et + est est et + fortior + etiam + + + + uigore + minore + acuto + acuto ut res + ostendunt + ostenduntur + ostendit + nature et artis, acutum uero + angulo + anguli + triangulo + + proportionatur acuto + + , + + ceu + seu + minori et debiliori. Quod autem + maius + magis + minus + maius est + + + et + est + fortius uigorat + quod + quam + quia + minus et debilius, + + huius + huiusmodi + quidem graue + acuti respectu + respectu acuti + , quare ipsum uigorat, + ut .xii. etiam apparebit + ut 12. + apparebit + ut xii. at etiam + apparebit + ut 13º etiam + apparebit + + . + + etcetera + sequitur 9m. problema 19e. particule. +

+
+ +
+ + Nonum problema + 9m + nonum problema.Nonum. + + +

+ PROPTER QUID DELECTABILITER + PROPTER QUID DELECTABILIUS AUDIMUS + + PROPTER QUID DELECTABILITER UNITATEM CANTUS AUDIMUS SI QUIS AD FISTULAM + AUT LYRAM CANTAT ET AD CORDAS, ET + EUNDEM CANTUM CANTANT UTROBIQUE? + SI ENIM ADHUC MAGIS IDEM, POTIUS OPORTEBAT AD + MULTOS FISTULATORES ET ADHUC + DELECTABILITER ESSE. + AUT QUIA ADIPISCENS MANIFESTUS INTENTIONEM MAGIS + QUANDO AD FISTULAM AUT LYRAM? QUOD UERO AD MULTOS FISTULATORES AUT LYRAS MULTAS NON EST DELECTABILE + PROPTER ID QUOD DESTRUIT MELODIAM + . + + Nonum problema + etcetera. + + + Quare + Querit quare + + + cum delectatione + delectabiliter + audimus + cantum vnitum + unitum + tantum munentum + seu + in + + vnum + coniectum + coniunctum + , + ut + in + si quis + cantat + cantet + in fistula + uel + et + uel in + lyra et vniuersaliter in cordis + ceu + seu + + + in psalterio canone + in pulsatio canone + in psaltero causam + psalterio canone + et + huius + huiusmodi + instrumentis + ex cordis multis + sex multis + cordis + compositis, dummodo utrobique + cantet + causet + esset + eundem + cantum + cantet + ? Quoniam si vnus cantus + seu + ceu + + + dantia + + concordantia + + + fieret in + fieret + fieret in vno + in + + + instrumento + instrumentum + et + alius + alius in + uoce + cantantis + causantis + canentes + canentis + , + in + etiam + in etiam + + + illo + illum + non + consurgeret + consurget + + + propter dissonantiam delectatio + delectation propter dissonantia + .

+

+ + Deinde. + + + SI ADHUC. + SI ENIM ADHUC. + + + Quasi + quare + arguit in + contrarium + contraria + dicens quod + si unius + si huius + si huiusmodi + si talis + lilicius + + + delectatio + + + + contingat + contingit + propter + vnitatem + raritates id est unitatem + cantus et + ydemptitatem + + + , tunc + oportebit + + magis delectari cum quis cantabit + cum multis + + + + fistulantibus uel lyrantibus + lyrantibus uel fistulantibus + fistulantibus et lyrantibus + fistulationibus uel lyris + , cum magis + videantur + uideatur + super vnum + opus + corpus + + + unitari + imitari + mutari + mundari + , + ut + sicut + vel + plures trahentes + nauem + nauim + + + imitantur + + mutantur + vnitantur + , ut melius + trahant. + trahatur. +

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit dicens + Dicit + causam esse + quia + quoniam + + cum + aliquis cantat + aliquis cantet + aliquis cante + + + singulariter + signanter + singulariter cantat + intentionem et maneriem cantus magis + vnitatur + vnitur + innitatur uel vnitatur + vnitatem + + + uox + + + + cum sono + + + + instrumenti + instrumentis + + + quam + quod + + + quando + cum + + cantaret in diuersis instrumentis, + etiam + et + eodem cantu + utrobique existente. + Et hoc + Et hoc et hoc + Et + quia in cantu + + + + quedam + + quidem + quid + qui + reseruantur proportiones ut dicetur + commensurate + + commemeratione + . Quibus + obseruatis + conseruatis + + + iocunda + + + + consurgit + consistit + existit + + + armonia + euphonia et armonia + , que + quidem + proui + + + corrumpitur + corrumpuntur + + + et + + + + indelectabilis + indelectationes + redditur cum + cantans + cantares + cantatis + ad multa + cantauerit + cantauit + instrumenta.

+

Quod autem + inductum + inductum est + aductum est + + + in + ad + contrarium prius non valet quia licet + multi possint + possint multi + + + idem + id + ratione + cantare, non tamen eodem modo. + Non solum enim requiritur + Solum enim requiritur + Non enim solum requiritur + Non solum requiritur + Et non requitur solum + + + ydemptitas + + + + + + ex parte + + illius quod cantatur et cuiuslibet cantantis + ad + ad id + se ipsum + ymo + + + + + + uniuscuiusque + uniuscuiusque et + ad + alium + aliud + + + et + + + + ad + + omnes, + ita quod + itaque + ex omnibus + resultent + resultant + proportiones debite in cantu. Quod autem + subditur + subdit + subiecit + subicitur + subiecti + subieci + obicitur + de + nauis tractu + + tractu nauis + tractu nauis uel ligni + + + non huic + huic non + non habet huic + non hoc + + + similatur + + simulari + assimilatur + dicto, quoniam + plurimi + plurium + + + possunt simul idem + possunt idem simul + possint idem simul + + + ut + et + nauem eodem modo et + tempore + + + trahere ut audientes + uocem + vocem vocem + + + rectoris + retoris + nauis. + Non + Ut + autem talis + unitas + ueritas + potest in cantu plurium + obseruari + reseruari + + + armonico + armonica + armonia + , cum + eum + enim + quo + + + + ex + + pluribus + + et + + contrariis + oporteat + + oportet + + + constituere + + ⳋstuere + construere + + construere + in + unum + unam + unum tonum alias + unitatem + . + Tandem + + + + redditur + reditur + reductis + redditis + + quod + fit + sit + impossibile pluribus + + + + entibus + existentibus + + + uocibus et + uocibus in + uocibus + instrumentis. + + etcetera + sequitur 10m. problema 19e. particule. +

+
+ +
+ + Decimum problema + 10m + decimum problema. + Decimum. + + +

+ PROPTER QUID NON DELECTABILIS + PROPTER QUID DELECTABILIUS SIT + + PROPTER QUID SI DELECTABILIS HOMINIS UOX QUE SINE + SERMONE CANTANTIS NON DELECTABILE EST UT UERNANTIUM, SED FISTULA AUT LYRA? + AUT NON ILLIC, SI NON IMMUTATUR, SIMILITER + DELECTABILE? + AT UERO SED PROPTER OPUS IPSUM. UOX ENIM + DELECTABILIS QUE EST HOMINIS, PERCUSSIUA AUTEM MAGIS INSTRUMENTA ORIS. PROPTER + QUOD DELECTABILIUS AUDIRE QUAM UERNARE + . + PROPTER QUID SONANS ACUTIOR QUIA MINUS IMBECILLIOR EST + FACTA. + + + Decimum problema + etcetera. + + + Quare + Querit quare + + + si + sit + uox + humana + humani + + + est + + delectabilis + auditu + auditui + , unde + + museus + muscis + musicus + dicitur + + + <app> + <lem wit="#Ma #Vb #Vz #m #v">politicorum</lem> + + </app> + 8° + .8uo. + politicorum + policitorum + scilicet + politicorum + + + delectabilissimum + delectabili fine + quod delectabilissimum + est hominibus cantare, + Arist. + Pol. + VIII, 1339b, l. 22 + + cum + quis + qui + aliquis + cantat + etiam + et + + + + non proferendo sermonem + sermonem non proferendo + + + omnino + + aut + insignificatium + insignium + insignita + insignibus + , + cur non est delectabilis + cur non delectabilis est + non delectabilis est + cur enim est delectabilis + + + uox alicuius uernantium + + uox uernantium + Videtur tamen + , + cum sit + cum non sit + crescit + + + hominis uox + uox hominis + , + et + eti + etiam + + lyre + et + etiam + fistule sonus est delectabilis? + Qui + Que + minorem + communicationem + communitatem + + + uidetur cum homine + cum homine videtur + habere quam + uox ipsa + ipsa uox + humana. In hiis + itaque + + uerbis + aristoteles + eadem + + + + succincte tetigit + + + tetigit succincte + succincte tangit + + + motiuum + + + quesiti et confirmationem + eius + quesiti + + .

+

+ Notandum + Nota + quod uernare + uocis + uocum + uocem + est expressionem facere in qua + non + + + + manifestatur + manifestetur + aliqua + sensibilis + + subtilitas + diuersitas + extensione + + expressione + et + depressione vocis + diuersione + , ita quod eius + remaneat + remanet + maneat + equalitas, + + ad modum + aut modo + quo + uer + ut + + + + equale ponitur a medicis + + ponitur equale a medicis + ponitur a medicis equale + . Est enim quasi + illud quod dicitur + illud + + + + bordonizare + + + + bordonizare et + + + quod + + per se + minime uidetur + minime + minimam + delectationem inducere.

+

+ + Deinde. + + + AUT. + AUT QUIA. + AUT HEC. + + + Soluit + 8o + et + prius + primo + respondet ad confirmationem, dicens quod illic + scilicet in + fistula et lyra + + fistulis et lyra + + non est + delectari + delectatia + , + quoniam similiter + similiter + + + in eis ita se habet ut + in eis ita se habet sicut + in eis similiter se habet ut + in eis se habet ut + in eis se habet + se habet ut + etiam se habet eis ut + + + in + + + + uernante + uernanti + vernantem + vernantis + + terminate + tiate + + , + quia + quoniam + si non + fiat + fiet + fieret + + + immutatio + mutatio + soni secundum + ascensionem + + assentionem + immutationem + + et + depressionem + descensionem + , + ut + et + + + inde + inde de + unde + + mundum + mdʼ + + + + consurgant + surgant + desurgant + desurgat + debite proportiones armonice, non + contingit + + conuenit + delectari ex + huius + huiusmodi + instrumenti sono. + Sic + Sicut + + + igitur + ergo + uernare non est + delectabile + + delectatio + , eo quod + proportiones + + non proportiones + + + non cadunt in ipso melite + non cadunt mellite + in ipso mellite + in ipso melite + non cadunt in ipso melodice + in ipso non sunt mellite + non cadunt multipliciter + + + auditum + audientum auditum + + + demulcentes + + demulceantes + .

+

+ + Deinde. + + + AUT UERO + AT UERO + AUT QUIA + . + Respondet + motiuo + + motoris + motois + + + motiuo + mto + + + motiuo + moto + + in + + + ipsius + ipsi + + + + causam dando + dando causam + dando causi + + dicendo + di.do + + quare uox + humana + humani + cantantis sit delectabilis. Hoc enim est propter + operationem ex qua consequitur. + In + + ipsa namque + magis + + percutiuntur instrumenta + oris + + ordinata ad + formationem + formationes + + + cantus + + + + delectabilis + debilis + + + quam + quod + + + in + ex + + uernare. Ex + huius + huiusmodi + + + namque + nam + enim + autem + + + maiori percussione + + percussione maiori + maiore percussione + instrumentorum + oris que + + horisque + fit in cantu, nunc in + uocem + uoce + + + extollendo + excellendo + + + nunc + tunc + in deprimendo, modo uero medie conseruando + resultat + resultet + + + cantus + modus + armonicus suauis ualde. Et ideo + inquit + dicit + in quid + + delectabilius + fore + esse + uocem + + hominis cantantis + cantantis hominis + etiam hominis cantantis + audire, cum + hic huiusmodi + hic huius + + hic huius + hc hui9 + + hoc huius + + + contingat + contingit + quam vocem + + + + vernantis + mutatis + , + ubi + + + + minime + maxime minime + . Vox etiam + hominis delectabilis + delectabilis hominis + delectabilis + quia consueta et + quoniam + quia + + + potest + possunt + + + mutari + imitari + immitari + + + componi et contraponi + et contraponi + et componi + et potest contraponi + + + facillime + + + . + + etcetera + sequitur 11. + problema 19. particule. +

+
+ +
+ + Undecimum problema + 11m + Undecimum. + Undecimum + problema + + +

+ PROPTER QUID SONANS + + + PROPTER QUID SONANS ACUTIOR? + AUT QUIA MINUS IMBECILLIOR FACTA EST + . + + Undecimum + problema etcetera. + Propter quid sonans etcetera + + + Quare + Querit quare + aliquis sonans + sonitu + sonitum + uel uoce acutior redditur et per consequens + alius + alii + autem + grauior?

+

+ + Deinde. + + + AUT. + AUT QUIA. + QUIA. + Soluit dicens causam esse quia + hic + sicut + + sonans est + minus + unius + sonans + quam + + illud + quod + quid + grauiter sonat. Quod autem + sit + fit + minus ostenditur + quia + quod + + + fit + sit + + + a virtute + acute + + + que + quia + facta est + imbecillior + + . Grauiter autem sonans a virtute + causatur fortiori + fortiori causatur + , propter + quod + quid + + + dictum + dictum est + + + + .xia. + + + quod + pueri femine + femine pueri + + + eunuchi + et eunuchi + eunuci et + + + infirmi + + habent uoces acutas, + Ps.Arist. + Prob. + XI.16, 900b, ll. + 15–17 + oppositi + autem + vero + graues + propter + per + oppositum. + + etcetera + etcetera etcetera + sequitur 12m. + problema 19e. particule. +

+
+ +
+ + Duodecimum + problema + 12m + duodecimum problemaDuodecimum. + + +

+ PROPTER QUID CORDARUM + + PROPTER QUID CORDARUM GRAUIOR SEMPER SONUM ACCIPIT? SI ENIM OPORTET DIMITTERE + QUE EST CIRCA MEDIAM PARAMESEM CUM ALIA MEDIA, FIT MEDIUM NIHILOMINUS. SI + AUTEM MEDIA, UTRAQUE ALTA NON FUERIT. + AUT QUIA GRAUE MAGNUM EST, QUARE FORTE? ET INEST + IN MAGNO PARUUM, ET ASSUMPTIONE DUE NITE + IN YPATE FIUNT + . + + Duodecimum + problema. + + + Quare + Querit quare + que + de cordis + illa + + que grauioris + extat + est + + + toni + soni + semper accipit + sonum + tonum + et representat + pre aliis ipsum + ipsum pre aliis + ut + subiectum + sonum + + solum + som + + + + proprietatem + proprietate + , + dum + cum + tamen equaliter fiat percussio + et + + + + ad hoc + adhuc + , si oportet propter aliquam causam + ut + aut + + + + defectum ipsius + ipsius defectum + + + aut aliter + aliter + aut alteri + aliquando + + + dimittere paramese que est + iuxta mediam, scilicet + iuxta + iusta + mese + siue mediam uere + siue mediam ipso + siue mediam ipse + siue mediam ipsa + hec + hec + . + Namque + Namque linea + + + septem + id est + + cordarum + ut visum est media + ut visum media est + media ut uisum est + ut visum est + + + + + cum + + + + alia + alio + aliqua + septima + quodammodo + media existente + existente media + existente + + quodammodo cum aliquo existente + ut lychanos, ita quod ea + sonum + sonus + + + non + nisi + + + constituatur in + constituat in + armonia. + Nihilominus ex + Nihilominus in + Nicomos ex + Nichilominus + Lichanos ex + extremis + puta + + + + ypate nete parypate + + + ypate parypate nete + ypatem nete parypatem + ypanete parypate + ypate + + + etiam et + et etiam + et + etiam + + + paranete + + , + + sicut + sic + ex + illis + hiis + + tribus + mediis + medicis + + + resultat quoddam medium + constitutiuum + constitiuus + armonie, in quo grauior cordarum sonum + preaccipit + accipit pro + + + aliis + + + + acutis + totis. Deinde + . + Communis + Cum minimis + + + quidem + quidam + que + + + littera + habetur + circa + mediam partem + mediam partem habet + mediam + + + hoc tamen + habet causam + tamen + + licet possit + tollerari series + series tollerari + tamen iam exposita continens paramese + + planior et sauior + + sauior et planior + planior suauior + planior et senior + planior et sanior + planior est et uerior + . + + + + + Sed si + Sed + Et si + + + utraque media + utreque medie + utraque medio + + + coniungantur + coniungatur + ad inuicem + utpote + utputa + dicatur + intermediarum + intermediorum + , + sicut + ut + + + sunt + est + + lychanos mese paramese + + siue + trite + recte + , non + constituitur + constituit + + sonus + eleuatus + + , ita ut inde resultet grauis, + + tanquam + + + + corde + + cordis + corda + grauioris + reddentis + reddente + sonum grauiorem, + cum + ut + sonus + harum + earum + + + existat + existet + extat + + + in medio + intermedius + inter + graue + grauem + et + acutum + acutam + . Sic + itaque + igitur + + + videtur duo + duo uidetur + querere + puta + scilicet + + + quia + quare + grauior cordarum sonum + preaccipiat et + cur ex + cum cur ex + cum ex + cum + + + extremis + exterius + + + concursus + concursis + cum cursus + fiat in medium reddens grauem sonum + non autem + aut + ex mediis.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse + quia + quod + quoniam + + + id + illud + + + quod + quod est + + graue magnum et forte + diuque + diu + + + perdurans + permanens seu perdurans + preaccipit vigorem sui oppositi, talis siquidem est grauior + cordarum + cordam + ad alias, + etiam + et + in magno + continetur et + continetur + continuo et + continuo + + + occultatur + + + + parvuum, sicut in + superiori + siteriorum + siteriori + , taliter quod sonus duarum + + nitarum + + neten + notarum + ninctarum + assumptus est in sono vno + parypatem + + parametem + + + causato + + + . Ex quo habetur quod grauior cordarum + sonum preaccipit + preaccipit sonum + , + et quod + et + + + ex ultimis extremis + ex extremis ultimis + exultans extremis + + + medium potest + potest medium + + + resultare + resultari + representare + , sicut apparebit + .23° + 22° + 12º + xxiii° doooo + + The added characters in Py seem to be space fillers, but + there's also a blank space of approximately 5 characters' width to their right, + before the start of "tertiumdecimum." Also, the blank space appears to be an + erasure, but the microfilm doesn't make reading the erased characters + possible. + in 12° + . + + etcetera + sequitur 13m. + problema 19e. particule. +

+
+ +
+ + Tertiumdecimum + problema + + + 13m + Tredecimum. + Tredecimum + problema + + +

+ PROPTER QUID IN DYAPASON + + PROPTER QUID IN DYAPASON ACUTI QUIDEM ANTIFONUM FIT GRAUE, HUIUS AUTEM ACUTUM + NON? + AUT QUIA MAXIME QUIDEM IN AMBOBUS EST AMBORUM + MELODIA? SI AUTEM NON, NON GRAUE, MAIUS ENIM EST + . + + Decimumtertium + problema etcetera. + + + Quare + Querit quare + in proportione + illa + ista + + + que + quo + dicitur dyapason uel proportio + dupla uel + totius, illud + tonus, illud + quod + habet + hec + rationem + acuti + acute + + + plerumque + plerumique + plurium + + + pertransit + + transit + in + grauem + graue + , + quod autem + quod autem hec + illud autem quod + + habet rationem + grauis non permutatur in acutum + grauis non permutatur in acutum grauis non + permutatur in acutum + ?

+

+ Uidendum + Videndum est + nunc + gratia eius + eius gratia + gratia huius + quod + dicitur + dicit + dyapason + quot + quod + et que + sunt + sint + + + proportiones + proportionales + + + musicales + musicale + musicales et + mussice + mutabiles + numeri + + + quomodo + penes quid + + + + sumantur + + , + et + + + + quia originantur + quia organantur + dico quod originantur + ex proportionibus + arismetricis + + + + + intuendum + intuendum est + prius illas. + + + + + + Sunt autem secundum boecium in + primis + principiis + + arismetrice + + et musice + numeri + + quinque + + sumpte + sumptis + penes numerum inequalem. + Quarum + Quarum est + + tres sunt + simplices + simplices uel simpliciores + + + puta + + + + multiplex et submultiplex + multiplex submultiplex et + multiplex submultiplex + multiplex + , superparticularis + et + + + + subsuperparticularis + + + , + superpartiens et + subsuperpartiens + + . Due autem composite quarum prima componitur + ex + est + multiplici + et + + + + superparticulari + + superari + subsuperparticulari + + + + et ex + et + + + multiplici + supermultiplici + submultiplici + + + et subsuperparticulari + sup + et superparticulari + + + , + secunda ex + multiplici superparticulari + multiplici et superparticulari + multiplici superpartiente + multiplici similiter particulari + multiplicitati + et + submultiplici + submultiplici et + subsupermultipici et + + + subsuperparticulari + subsuperpartienti + subsuperpartiente + superparticulari + + + . + Boeth. + De inst. mus. + I.4 (Friedlein p. 191, ll. 6–10); + Boeth. + De inst. arith. + I.22 (Friedlein p. 46, ll. 6–17) +

+

Multiplex autem + est + est quando + + numerus maior minorem in se + continet + continens + pluries, ut + bis uel + bis + + ter + aut + uel + + + quater + quater ter + quater uel multociens + + + et sic + aut + deinceps, ut + nichil + uel + desit + nichilque + + + + exsuperet + + . + Huius + Hec + Huiusmodi + autem species sunt duplex + triplex + + quadruplex + + et sic in infinitum. Duplex + + quidem + + + + cum vnus numerus alium + ut vnus numerus alium + cum vnum numerum + bis continet que dicitur proportio dupla ut + quatuor ad duo. + Triplex + triplex + numerus + + + cum + tamen + vnus numerus continet + alium totum tribus + alium numerum tribus + alium tribus + alium numerum tribus totum + + + uicibus + modis + sicut + trinarius se + habet ad vnitatem + se habet trinarius ad vnitatem + trinarius ad vnitatem se habet + .

+

Proportio autem + secunda + + value="2/1">dupla secundum + dupla + iuxta + aliam + alia + alium + inequalitatem, ut superparticularis cum + eius + + + + opposita + oppositus + opponitur + opposatur + oporteat + , est cum maior + numerus + + continet in se totum + semel + solis + + + et + et adhuc + in + + + vnam + unam in + eius + insuper + + partem, + ut aut + ut autem + vltra ut aut + + + dimidia + dimidiam + + + + uel + aut + + + + tertia + tertiam et + + + ita + sic + deinceps. + Cuius + Huius + + + quidem + autem + + proportionis modi sunt + sexquialtera + + , + + sexquitertia + sequitertia + sexquiquinta + sexquiquinta + uel epitrita + sexquiquinta uel + epitria + sexquinta uel epitrica + sexquiinta uel epitrita + sexquiinta uel epuctria + sexquitertia + , + sexquiquarta + sexque quanta + et + huius + huiusmodi + . Sexquialtera + + seu emiola + + seu emialmlem + + seu enumerale + seu enucha + + + + est + + cum + quis + aliquis + numerus alium semel continet et + insuper + super + + + eius mediam partem + partem eius mediam + huius mediam partem + eius partem + , + ut + + ternarius + + se habet ad + binarium + binare + + ternarius ad + binarium + se habet + tria se habent ad duo + . + Sexquitertia + + + + cum + est qui + + semel et eius + tertiam partem + partem tertiam + + + , ut + + quaternarius + quaternarium + quaternarius + adet + ternarius + ad ternarium + quatuor ad tria + sexquiquater + numerus ad quaternarium + 4 se habent + ad 3 + quaternarius + ad quaternarium + .

+

+ Superpartiens + + Superparticularis + + + est + + + + quando + quoniam + quare + maior numerus continet minorem et + insuper + maxime + + + eius aliquas partes + aliquas eius partes + , ut + duas + 3as + 3es + + + tres etcetera. Cuius + species sunt + + species + + + superbipartiens + + ter bipartiens + superbipartiens et + subyparicus + subbipartiens et + + + supertripartiens + + triparties + + + + etcetera + et sic + + . + Superbipartiens + + + subipartiens + est cum + numerus + minor numerus + + continet numerum + semel + + simul + sil + + et + eius + etiam + + + duas + due + + + partes + partes vltra + , ut + quinarius ad ternarium se habet + quinare ad + ternare se habet + quinque ad + tria se habet + 5 ad 3 se habent + numerus + quinarius ad ternarium se habet + . + Supertripartiens + + Supertripartiens est + Superquiertiens + Superpartiens + Tripartiens + quando + semel continet + unus continet numerum semel + semel + + + totum + + + + et + + + + eius + + + + tres partes + tertiam + partem + , ut septem + + se habet ad + ad + + quatuor. + Superquadripartiens + Supertripartiens + + + etcetera, ut + etiam, sicut + + + .ix. + .ix. cum + + + se habet ad .5 + + ad 5 se + habet + ad .5 + .

+

+ Compositarum + Compositorum + uero + multiplex + simplex + superparticularis est + cum + + numerus + continet maior + maior continet + + + minorem + numerum minorem + minorem numerum + totum multotiens et insuper + aliquam + aliam + partem + eius + + , ut medietatem uel tertiam + + et + y.t. + + + huius + huiusmodi + . + Huius + Huiusmodi + autem + species sunt + sunt species + sunt + + + duplex + sexquialtera + + + + + duplex sexquin alta duplex sexquialtera + duplex sexquialtera + + sexquialtera + , + + duplex + sexquitertia + duplex + sexquitertia et + duplex + sexquialtera + , duplex sexquiquarta, etcetera, + + + + et + id ratione + id rationem + ideo ratione + rationem ratione + + + duplicitatis; + duplicis + ex + parte + + + + uero + uero uel + + + triplicitatis + triplicis + + + + + + triplex sexquialtera, + + + + triplex sexquitertia + triplex + sexquitertia + duplex sexquitertia + triplex quitertia + + , + etcetera + triplex etcetera + triplex sexquiquarta + + + . + Est + + + duplex sexquialtera + + quando + est quando + maior + numerus + numerus bis + + + continet minorem totum + minorem totum continet + minorem totum + minorem + minorem se totum + et insuper + eius partem mediam + partem eius mediam + eius medium + , ut + + .5. + quinarius + quinare + quinarium + + + se habet + se habent + + ad + .2 + binarium + binare + 3 + + 10 ad 4 + . + Duplex + sexquitertia + + Duplex + sexquialtera + 3a. + + + quando + est quando + quando ipsum + + continet totum et + ipsius + eius + + + tertiam + partem + partem 3am + , ut + septem se + habet + septem + ad + .3 + .3. + iii + . + Duplex sexquiquarta + etcetera + + Duplex + sexquiquarta + , + ut .ix. + + se habet ad + habet se ad + ad + quatuor. + Triplex + sexquialtera + Triplex + sexquitertia + + + + + est + + quando + alter + alterum continet totum + alteram continet totam + + alter continet alterum totum ter + + + et + ut + + + adhuc + ad hoc + ad + + + eius tertiam + tertiam eius + partem, + ut + decem + + quatuor + ad tria. + Triplex + sexquialtera + Triplex + sexquitertia + Quadruplex + sexquialtera + Triplex sexquiquarta + + + quando + est quando + + + + + quartam partem + continet + partem 4am. + continet + partem continet + continet + continet minorem numerum ter et 4am. partem + ultra + totum + + , ut .13. ad quatuor.

+

Multiplex + superpartiens + est superpartiens + superparticularis + + + est cum + est quando + cum + maior numerus continet + minorem + minorem numerum + maiorem + plus quam semel uel multotiens + et + ut + + + + pluries + plures + , cum + hoc + hic + + + ipsius + eius + + + partem + partes + + plures partes cum hoc ipsius + cum hoc plures eius partes + . + Cuius + Et + etiam + infinite sunt + sunt infinite + + species, ut + duplex superbipartiens, duplex supertripartiens, etcetera + duplex superpartiens, duplex supertripartiens, etcetera + duplex superpartiens, et desupertripartiens, + etcetera + duplex superpartiens, triplex + superpartiens, etcetera + duplex superpartiens etcetera, duplex + supertripartiens etcetera + duplex superpartiens, etcetera + duplex superparticularis + et + id + illud + + + ratione + ratio + + duplicitatis; ex parte + quidem + quidam + quid + uero + + triplicitatis erunt + + triplex + superbipartiens + triplex superpartiens + triplex subpartiens + triplex sibi partiens + , + triplex + supertripartiens + triplex superpartiens + + triplex superbipartiens triplex superbipartiens + , + etcetera + + . + Duplex + superbipartiens + + Duplex superpartiens + Duplex supertiens + est quando numerus maior + continet + continet bis + minorem et insuper + duas + + eius partes, ut octo + + se habet + habet se + se habent + + ad + triam + tria + tres + .3. uel .2 + . + Duplex + supertripartiens + + est quando + est + etcetera + , + ut xi. + + se habet + se habent + + ad + .3 + quatuor + . + Quadruplex + superbipartiens + + + Triplex + superbipartiens + Triplex + supertripartiens + + + est quando + quando + + + + etcetera, ut .15. + triplex + + + se habet + se habent + + ad quatuor. + Hee + + Hec + + + quidem + quidam + qua + sunt numerorum + inequalitates + inequales + ex quibus + quinque + + resultant proportiones + arismetrice + arismetricas + cum + suis oppositis + optis + antedictis.

+

Restat + quidem breuiter uidere secundo + breuiter quidem uidere secundo + quidem breuiter uidetur secundo + breuiter 2° + uidere + : + quot et que + que et quot + que et quot sunt + quod et que + + + ex hiis sint + sint ex hiis + ex hiis sunt + ex istis sint + ex hiis + + + consonantie siue simphonie + + consonantie + consonauere + musicales, + et + + a + quibus + quibus proportionibus + + + sumantur + + summatur + sumuntur + + + arismetricis + arismetricum + . Secundum + quidem + quod + quid + + + macrobium et boecium ex + omni + numerorum + modorum + uarietate pauci + numeri + + + + reperiuntur + + qui + conueniant sibi + conueniunt sibi + 9 aut 8 + ad + consonantiam + confouentiam + musicalem + constituendam + considerandam + custodiendam + . Sunt + autem + + + + hii + + hiis + + sex + + omnes + omnis + iuxta + quos + quas + quot + + + quinque + consonantie + consonantie quinque + constituuntur, + et + ut + + + tonus + totus + totius + + + ex quo + equo + + + constituunt + constituuntur + constituitur + + + dyatonum + + , scilicet + epitricus + + , + emiolus, duplaris, triplaris + + emi solus duplarum + triplarum + , + quadruplarus + + + quadruplum + quadruplaris quadriplum + , + epodous + + + epogdoii + epogdonium + .

+

+ Epitricus + + + + + + + uel + seu + et + + + sexquitertius + + + + sex quinitus + est + ut aliqualiter iam + unde iam aliqualiter + uel aliqualiter iam + + + patuit + paruit + cum maior numerus continet minorem totum et eius tertiam + partem, ut quatuor + + se habet ad + se ad + ad + + tria. Ex quo + nascitur + + + + + simphonia + + uel consonantia + consonantia seu symphonia + simphonia consonantia + + + dyatesseron dicta id est + dicta dyatesseron id est + dyatesseron dicta + + + per quatuor + per quatuor et + per 3am. + , que in + sexquitertia + proportione consistit + sexquitertia consistit proportione + sexquitertiam proportionem consistit + , ut + cum + + una uox in grauitate + uel + seu + acuitate + + se habuerit ad aliam sicut + se habet ad aliam sicut + se habuerit ad ad aliam + sicut + ad aliam se habuerit scilicet + + quatuor ad + tria + tres + + se + se hii· + sed hii + .

+

+ Iuxta uero + emiolam + + uel + sexquialteram + + ut cum maior numerus + + + + minorem continet + continet minorem + minorem minorem continet + totum et + medietatem ipsius + ipsius medietatem + medietatem ipsi + medietatem + , + ceu se habet + ceu se habent + ceu + ceu se habet + ut + seu + + tria ad + duo + 3 + . Oritur consonantia dicta dyapente + uel + per + + + + quinque + + quandoque + quecunque + communionem + + + in quinto enim loco + terminatur + teminatur + + in 5° + loco terminatur + in + monocordo + + + , + sicut + sic + dyatesseron in + quatuor + quarta + quarto + 8o + + + ceu + + seu + + + cum + ut + + una + vox + + + + se habuerit + + ad aliam + in + + + + grauitate et leuitate + leuitatem et grauitatem + + + etcetera + + .

+

Secundum + siquidem + quidem + 44. quidem + + duplarem numerum + uel + secundum + proportionem, ut quatuor + + se habet + se habent + + ad duo sumitur proportio dyapason siue + per + + totum, terminat + enim et + et + enim uel + continet + totum + + + + monacordum + + + et maxime primum cadit + enim + cum + super + octo + scilicet + 4 + incipiens + a gama greco + + a gama grece + in gama greco + agamo greco + agamatrico + .

+

+ Scilicet + .g. + + iuxta + uero triplarem + triplarem + vero + numerum + seu + siue + proportionem, ut cum numerus + se habet + se habeat + habeat se + + ad numerum + ceu + seu + sicut + ut + + tria + ad vnum, + componitur enim ex multiplici + et superparticulari + sicut se habet tria + ad vnum + sicut habet se tria ad unum + + , nascitur + simphonia + + + + + composita + et componitur + + + ut + ex + + + dyapente dyapason + dyapente et dyapason + ut quando + vna + vnam + + uox excedit + alteram + aliam + etcetera. Iuxta uero numerum quadruplum, + cum + vt cum + est + vnus alium + quater + quadruplum + quadrupliciter + continet, ut quatuor + + se habet + se habent + + ad vnum oritur + bis + hiis + diapason.

+

+ Epogdous + + + + + + + Epogodus + est + numerus + unus + qui + inter + intra + se minorem + concludit + conclaudit + claudit + continet + et insuper + octauam eius + partem + eius octauam + partem + + 8 eius partem + octauam + scilicet eius partem + , + ceu + seu + se + sicut + + nouem + + se habet + se habent + + ad octo. + Ex + Et + + + hoc + quo + quidem + numero + numerus + + + + sonus + + + + consurgit + contingit uel consurgit + + + quem + quam + quomodo + musici + tonum uocant + uocant tonum + tonum uocarunt + tonum uocauerunt + tonum uocarent + tonum + , + + qui + quod + + + autem + + + + tono minus + + tono unus minus + + + + semitonum + + + + + + dicitur + + + + , quod + non + non est + + + extimandum + existimandum + ex utis + tonum + uere fore + fere fore + fore fere + sicut + neque + + semiuocalem in + litteris + + . + Non enim + Nam + tonus + naturaliter + universaliter + in duo + + equalia + + + potest diuidi, + cum + et + + + constet + constat + constans + stet + ex + numero + numero cum + + + nouenario + + + nouenarum + nouem + , + quod + + qui + + + in duo + sono + + + diuidi minime potest equaliter + diuidi minime potest + diuidi minime equaliter potest + equalia diuidi minime potest + . + Unde et + Unde + Et + Et ideo + Ut + + + semitonium uocarunt + + uocauerunt semitonum + + sonum + tono + + tonum + minorem. Est autem + semitonum + + duplex + maius scilicet + scilicet maius + maius + et minus. + Maius + uidem + qui + dicitur + apothomi + + + + + Minus quidem dicitur apothemi + amplius quidem dicitur + apothemi + Maius quidem dicitur + + apud + uero + nomen + + + boecium + + + + decisio + + , + minus + nimis + + + autem + aut + + + dyesis + + + uel + limes + + + + lineis + , + quod + quid + qui + tam + paruo + paruum + distare a + tono + + toto + + + deprehensum + depressum + est quantum + hii + + + duo + + numeri + numerus + distant: + ut + + + + .243. + 242 + 283 + .343. + 2. + 43. + 12. 143. + + + et 256 + 256. + 2256 + . + Quorum + Quando + quidem + vnusquisque + + quisque + + + constat + constant + constituit + + ex + duabus + 29. + + + uocibus + uicibus + + + puta + + prout + + + ut + ut et + mi, + est et + est etiam + + + ditonus + + + + + + , + + qui + qui est + + + ex duobus consurgit perfectis tonis + ex duo consurgit perfectus tonus + consurgens ex duobus tonis perfectis + ex duobus perfectis consurgit sonis + , + et + ut + + + semidytonus + + semiditonis + semitonus + qui ex duobus non + integris + integer + + + . Ut + id autem + id + id aut + autem hec + per amplius + appareat + appareant + apparent + + + parigraphia + + + + + + + conscribatur + scribatur + + + ista + ista videlicet + ista in ista tolitua + talis + . + + + Γ. + 1296. + ut. + + + + + + + + + + a. + 1152. + re. + + + + b. + 1034. + mi. + dytonus. + + + c. + 972. + faut. + dyatesseron. + + + + d. + 864. + solre. + dyapente. + + + + e. + 768. + lami. + + + + f. + 739. + faut. + + + + + g. + 648. + solreut. + dyapason. + + + a. + 576. + lamire. + + + + + b. + 554. + mi. + + + + b. + 512. + fa. + + + + + c. + 486. + solfaut. + dyatesseron + dyapason. + + + d. + 432. + lasolre. + dyapente dyapason. + + + + e. + 384. + lami. + + + + f. + 366. + faut. + + + + g. + 324. + solreut. + bis dyapason. + + + + a. + 288. + lamire. + + + + b. + 277. + mi. + + + + b. + 256. + fa. + + + + c. + 243. + solfa. + + + + d. + 216. + lasol. + + + + + + + + +
+ + Pz's scribe writes two tables: one with columns one + and two (note letters and string lengths), and then a second with column three + (note names). Column four (interval sizes) is omitted. Pu's scribe writes the + interval names orthogonal to the rest of the table and does not indicate the notes + to which they apply. I have therefore omitted the names. (Vc does the + same.) + +

+ +

Sunt itaque consonantie + quinque + + + + scilicet + + : dyatesseron, dyapente, dyapason, + dyapente dyapason, et + dyapente dyapason + dyatesseron et + et + + + + bis dyapason + bisserer + . + Que quidem + Qui quidem + Siquidem + + + hiis + hii + + tonis + et + + + + semitonis + + + + + constituuntur + constituitur + , + dyatesseron + diatonici + dyatri + enim constat ex + + duobus + duabus + + + tonis + + + + et + cum + + + semitono + + + + + + + + non + + integro, dyapente + tribus + 39 + tonis et minore + semitono + + + + , + dyapason + + dyapason ex + + quinque + + tonis + + et + semitonis duobus + minoribus + + duobus + semitonis minoribus + semitoniis duobus + , + neque + nullaque + + + peruenit + per peruenit + prouenit + prout + ad + .vi. + quinque + + + tonos + + perfecte. Ex quibus apparet quod dyatesseron et + dyapente + diapentesseron + diapentesseran + + + consurgunt + consurgit + in + dyapason + diapasseron + + . + Dyapente dyapason + Dyapente dyapason que + Et in pentadyasson + ex .ix. + + tonis + + + + et ex + ex + et + + + semitono + + semitonis + minori constat, + bis uero dyapason + + sed ipsa bis dyapason + ex .12. + + perficitur + perfectis + tonis. + Et hec + Et huiusmodi + + + + + quidem + + + amplius sunt in + amplius sunt exposita in + + + + <app> + <lem wit="#Py #Vb #m #v">conciliatoris mei</lem> + + <rdg wit="#λ" ana="#lexical">conciliatoris nostri</rdg> + <rdg wit="#Ea" ana="#lexical">conciliatoris unde</rdg> + <rdg wit="#Px" ana="#subtractive">mei</rdg> + <rdg wit="#π" ana="#subtractive #J">conciliatoris</rdg> + </app> + + differentia .83a. + differentiis 93. + differentia sed + If the scribe of #Px uses tall s to mean 8 (as other places + suggest), then it is 83, not sed. + + + exposita. + + + Pietro d'Abano + Concil. diff. 83 +

+

+ Nosce + Notandum + + + quoque + + + + + ex musice + quinto + ex quinto + musice + + quod + ptholomeus + + + + thonus + + + sextam hiis + addit + sextam hiis addidit + sexta + hiis addidit + addidit + sextam + consonantiam + compositam + compositam et + ex + dyatesseron et dyapason + dyatesseron dyapason + dyatesseron + , que constat ex + multiplici + multiplici et + + + superpartiente + superpartienti + superparticulare + superparticulari + superpartem + + + qua proportione + quam proportionem + secundum quam proportionem + in qua proportione + de qua proportione + + + se habet + se habent + habet se + habet + + octo ad .3.. Continet enim + octo + + bis tria, + propter + per + + multiplicem proportionem ex qua + visum + visum est + consurgere dyapason, et duas + + eius partes + partes eius + eius partes eius + quod est + tertia + 3. + scilicet + duo + secundo + 32. + propter + superpartientem + partientem + + + a + ex + qua nascitur dyatesseron. + Boeth. + De inst. mus. + V.8–9 + + + Communiter + + + + tamen + + + + pictagorici + + + + musice + + + + institutores + + instructores + inpositores + + + posuerunt + proposuerunt + omnes + proportiones + consonantias + musicales consurgere ex multiplici et + superparticulari + supermusicales consurgere ex + multiplici et superparticulari + , + nullamque + nullam vero + ex + superpartiente + superpartienti + superparticulari + , + quod + et + videtur aristoteles sentire + xli + xiº + 4° + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit + dicens + dicentes + causam esse + quoniam in + quia in + + + ambobus scilicet + in + + graui et acuto + scilicet graui et acuto ambobus + + + est + cum + melodia + utrorumque + utrorum + , vnum enim + alteri + altero + alter + alterius + + + coniunctum + + constitum + consitum + + + melodiam + melodiam uel consonanciam + + + reddit, quia graue et acutum sunt + dissimilia + difficilima + + fieri ex dissimilibus + . + + + Et + + + + + thimoteus + + + + ethymous + thymolis + entimomus + recte: timaeus, methinks + + + quidem + qui + + + + extimauit + existimauit + musice primo melodiam uel consonantiam + fieri ex dissimilibus, non autem ex + similibus + consimilibus + + + . Si autem + proueniat + + utrorunque in utrisque + concordia + concordiam + + non fit melodia, + cum + si + autem + sic fuerit + fuerit sic + + + quod + quod quod + quia + graue + maius sit + sit maius + maius fuerit + maius fit + acuto et fortius, tunc quod est acutum + + assumit + + rationem grauis, ita quod acutum sentitur + sumit + + + graue + + , + ut + nisi + enim + + cum + due + + + + + nite + + + + concurrunt + concordant + in + ypatem + + + . Dicitur autem melodia + a melle + a melos + , + quoniam + + quantum + ȹ~tum + + est consonantia + delectabilissima + + ualde ex acuto + et graui + grauique + et graui est + + + debite + indebite + composita. + + etcetera. + sequitur 14m. + problema 19e. particule. + + + + + + G + 1296 + ut + + + + + + + + + a. + 1152. + re. + Dyatonus + + + b. + 1034. + mi. + + + + c. + 972. + fa ut. + Dyatesseron. + + + d. + 864. + solre. + + + + e. + 786. + la mi. + + + + f. + 739. + fa ut. + + + + g. + 646. + solreut. + dyapason. + + + a. + 576. + lamire. + + + + b. + 554. + mi + + + + b. + 512. + fa. + + + + c. + 486 + solfaut. + dyatesseron dyapason. + + + d. + 432. + lasolre + dyapente dyapason. + + + e. + 384. + la mi. + + + + f. + 349. + faut. + + + + g. + 324. + solreut. + bis dyapason. + + + a. + + lamire + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+

+
+ +
+ + Quartumdecimum + problema + + 13m. + problema. + 14m + QuartumdecimumQuartumdecimum. + + +

+ PROPTER QUID LATET DYAPASON + PROPTER QUID DYAPASON + + PROPTER QUID LATET DYAPASON ET UIDETUR UNIUS SONI ESSE, UT IN FINIKIO ET + IN HOMINE? QUE ENIM IN ACUTIS EXISTUNT NON UNIUS SONI, SED PROPORTIONALITER AD + INUICEM DYAPASON. + AUT QUIA SICUT IPSE ESSE UIDETUR SONUS PROPTER + ANALOGUM, EQUALITAS IN SONIS, EQUALE AUTEM UNIUS? HOC AUTEM IDEM IN FISTULIS + DECIPIUNTUR + . + + Decimum quartum + problema etcetera. + + + Quare + Querit quare + dyapason cum + sit + + proportio satis distans + quoniam dupla + quoniam duplo + quamdaperla + latet + in tantum + iterum + + + quod + quare + videtur sonus ex ipsa + resultatus + resultatis + resultans + esse vnus et + quasi + quare + vnum tonum simpliciter habere? Et + hoc + hec + declarat sicut apparet + etcetera + eidem + + . Communiter + quidem + quid + + + + inuenitur littera + + littera inuenitur + inuenitur + + + in finitis + infinitatis + in infinitis + , + alia infantis + aliam infantis + alias infantis + alia infinitis + et alia infantis + + + + aliter finikio + aliter finibrio + alia finikio + + , sed + forte + + debet + dicere in fidibus + dici in fidibus + habere in fidibus + esse in fidibus + infidibus + seu cordis. Et in homine similiter + + declarat + declaratur + ita + quod + ut + + + per hoc + hoc + + + + tangat + tangit + duplicem melodiam + tactu + tacta + tactam + uel pulsu factam et + uoce + note + . Soni + siquidem + quidem + + + existentes + existentis + + + acuti + + quia non concurrunt adeo in vnum, non sunt + unius + vinus + minus + soni ut graues aut + sic + sunt + + compositi ex grauibus + sed + ut + + + in dyapason. Hoc accidit + dyapason + quoniam toni se habent proportionaliter ad inuicem ex graui + et + ex + acuto, + + est + enim + autem + optima consonantiarum + + .35 + .xxv° + tria + quinto + + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens + causam + causa + esse + quare + quia + quoniam + sonus apparet + vnicus + mutus + esse propter + anologiam + + et proportionem sonorum ad inuicem + in + ut + dyapason, ex qua resultat equalitas + grandis in sonis. Quod autem + equalitatem habet + habet equalitatem + + + vnius + unus + + + soni existit + existit soni + , et non solum + hoc accidit + accidit hoc + accidit + in + sono voce facto + voce facto + sono uel voce + + + aut + + pulsu, sed + etiam + + + + in sono + + + + flatu + filata + facto, + uel + ut + + in + fistulis + + . In + illis + hiis + enim + decipiuntur + recipiuntur + etiam + ut in + + + + uocis sono + + uoce sono + sonis + , propter + debitam enim tonorum + debitam enim sonorum + enim debitam tonorum + + + consonantiam + dissonantiam + accidit plures tonos non + discerni + diuisi + sed vnum apparere + cum + et + + + diuersitates + diuisi + + + illic non extent + + illic non extant + illic quod extent + illic non existant + + + sensibiles + consimiles + + , + ceu + seu + videmus + ex + in + saporibus + composita ex + compositis ex + composita + conposita + diuersis + in + ex + quibus + vnus + vnius + consurgit + delectabilis + + et nullius excessus, + ut + ut qui + ut quod + + + conficitur + conficitur ex + + + decoctione + de remotione + + + ex + + + + cucurbitis + + + + + cucurbite + , + cepis + sepis + , uel + alleis + + aliis + , + cum + cum autem + + + tamen + tantum + vnum + sit + fit + saporis insipidi et + alterum + alter + + + acuti + + . + + etcetera + sequitur 15m. + probleme 19e. particule. +

+
+ +
+ + Quintumdecimum + problema + + 15m + Quintumdecimum. + Quintumdecimum + 14m. + problema: + + +

+ PROPTER QUID LEGES + + PROPTER QUID LEGES QUIDEM NON IN CONUERSIONIBUS FACIEBANT, ALII UERO + CANTUS CHORICI? + AUT QUIA LEGES QUIDEM AGONIZANTIUM FUERUNT? QUIBUS + UTIQUE MUTARI POTENTIBUS ET DISTENDI, CANTUS FIEBAT LONGUS ET MULTIFORMIS. + QUEMADMODUM IGITUR ET UERBA, ET CANTUS MUTATIONEM SEQUEBANTUR, SEMPER ALTERA + FACTA. + MAGIS ENIM CANTU NECESSE IMITARI QUAM UERBIS. + PROPTER QUOD ET DITIRAMBI, QUONIAM AUTEM IMITATIUI, FIEBANT. NON ADHUC HABENT + CONUERSIUOS, PRIUS AUTEM HABEBANT. CAUSA AUTEM QUONIAM ANTIQUITUS LIBERI + ROTABANT IPSI, MULTOS IGITUR AGONISTICE CANTARE DIFFICILE ERAT, QUARE IN + ARMONIA CANTUM DELECTABILITER. MUTARE ENIM MULTIS MUTATIONIBUS UNO FACILE QUAM + MULTIS ET AGONISTE ID EST CONSUETUDINEM SERUANT. PROPTER QUOD SIMPLICIORES + FACIEBANT SIBI MELODIAS. CONUERSIUUS AUTEM SIMPLEX, NUMERUS ENIM EST ET UNO + MENSURATUR. + EADEM AUTEM EST CAUSA ET PROPTER QUOD QUE QUIDEM A + SCENA NON CONUERSIUA, CHORI ENIM CONUERSIUA. QUI ENIM CANTAT IN SCENA AGONISTA ET MUTATOR, CHORUS + AUTEM MINUS MUTATUR + . + + Decimum quintum + problema etcetera. + + + Quare + Querit quare + + antiquitus + cantatores + + + + constituerunt + constituerint + + + quosdam + quorundam quosdam + cantus dictos leges non habentes + conuersiones + conuersionem + , sed alii cantus + + chorici + choris + conci corici + + + et conuersiui + conuersiui et + + + fuere + fuerunt + finem + fide + + fuere chorici et conuersiui + ? Nosce quod + per + + leges non in conuersionibus factas + audio + aut dyo + cantus + simplices + + + + expansos + + expansus + in quibus + potius fit + fit potius + fit + + + commutatio + comitatio + connumeratio + uerborum quam cantus, ita quod in eis non + constituantur + constituuntur + + + circuli + circula + + + conuersiui + conuersuum + , + sicut + finis + est cantus + alicuius + + insignis + gesti + egesti + testi + . + + Choricos + Per choricos + autem cantus + intelligo + ego intelligo + + + conuersiuos + conuersiuos cantus + uersiuos + primis + utcunque + utrisque + + + oppositos + oppositis + , ut apparebit in + causa + tria + . + Est autem chorus + Est autem + + + curator + curatio + inoperabilis, + beniuolentia + beniuolentiam + enim + solum prebet + prebet solum + solus prebet + quibus + adest + adest ut + + + .xlviii + 4. + scilicet + . + + This is a typical Jandun omission which #Vc also + omits. +

+

+ + Deinde. + + + AUT. + AUT QUIA. + CHORICOS. + Soluit + et primo + primo et + assignat causam quesiti. Secundo + + ex hac + + infert + causam + causam etiam + + + cuiusdam + + + + alterius + altius alterius + alterius perfectis + + + cantus + secunda EADEM + AUTEM + ibi secunda EADEM AUTEM + secunda in EADEM AUTEM + secunda eadem + EADEM + . + Etiam + Et + + primo respondet ad + primam partem + partem prima + dicens + + + + causam esse quoniam leges fuerunt + + cantus constituti ab agonizantibus et + bellatoribus + bellatorum + , + ceu + seu + sicut + sunt cantus + gestorum + + + + insignium + insignum + . Quas + quidem + quam + leges ut possent consequi recitando + quod + quid + in eis continebatur + distendebant + diffe distendebant + descendebant + discebant + cantando, + nunquam + + inde quam + + + faciendo + patiendo + conuersionem uel circulationem ad + id + idem + + + unde + unum + + + inceperant + inceperunt + ceperant + + + reddeuntes + redeuntes + . Propter quod + eorum + + cantus + fiebat + fiebant + longus et multarum manerierum, + secundum uerborum + prelatorum + prolatorum + prolapsorum + + + diuersitatem + + . Nam secundum quod uerba gestorum + fiebant continue + + + altera + alta + alto + uel melius + + altera et diuersa mutatione + similiter + simili + . + Et + + in + cantu + cantum + similem obseruabant mutationem, + ut + ut ad + et + + + commutationem + commutationi + uerborum + cantus + + + + comitaretur + + + cum comitaretur + comodaceretur + commutaretur + + + mutatio + imitatio + commutatio + , + ad uerba enim + enim ad verba + amplius quam ad cantum attendebant. Propter quod + dicte sunt + dicta sunt + leges + cantus huius + cantus huiusmodi + cantus + + + a + + ad + legendo, + uelut + ut + ultra + illud + visum + uideret + in lectionibus et + proprie + precipue + + + diuinis + in diuinis + , ut apparebit + .xlviii. + .44. + .42. + , + vna + ubi vna + + + dictio + dicto + post aliam profertur non + multum + multam + uocem + diuersificando + + diuersimode + .

+

+ + Deinde. + + + MAGIS + ENIM + EST + + . + + Tangit + + Tangit enim + Tanquam + causam + alterius + plures alterius + plus alterius + + + partis + partium + , dicens quod in cantu + armonico + armonizato + + + sufficienter + sufficientis + non + debet + debent + + + per oppositum accidere + per appositum accidere + per oppositum + hoc accidere per oppositum + , nam + in eo + + quod + dictum + + + + est + + , + in legibus + legibus + in lectionibus + amplius + oportet + + + + + imitari + + immutari + + + cantum + auiter + reddendo ipsum + melodiosum + melodicum + quam uerba, cum cantus + sit magis + magis sit + fit magis + finis + musici + amici + actus uerbis, ampliorem + inducens + iudices + delectationem, propter quod + dictum + dictum est + + 10°. quod uox delectabilis + est cantantis + cantantis est + est cantus + sine + sermone + sermonem + prouisione + + + etiam. Et + etcetera. Et + etiam. Et etiam + + + + + + ideo + + quidam modi + cantandi dicti + ditirambi + + + + + + dicti dichitambi cantando + cantandi dictirambi + dicti Tytira ubi + + + + + fiunt + fuerunt + , cum quis + magis cantum imitatur + cantum ymitatur magis + magis imitatur cantu + cantum magis imitatur + magis cantus ymitantur + magis cantum immutatur + magis cantum mutatur + uerbis. Est autem + ditirambus + + + + + + + + dichitambis + ditrambis + dytiranbum + cantus qui + concidit + accidit + in + frigistum + + fixgistum + , + unde + + + + + + 8° + politicorum + + scilicet politicum + + polliticorum + .8. + + + filoxenus + + + philoseus + filoserius + phylosherius + phiis + conatus in + dorista + corista + corialtera + facere + ditirambum + + + + + + + + + + dichitambis + distanbu + + + fabulas + fabulans + non fuit + potens + + , sed ab + ipsa + ipso + illa + + + natura + + decidit in + frigistum. + + + + Arist. + Pol. + VIII, + 1342b, + l. 9 + Hec autem + .xlviii. + 28 + + + erunt + fiunt + + manifesta adhuc. Siquidem + rediens + + rediens ad + leges + inquit + in quid + + quia + cantus huius dicti + cantus huiusmodi dicti + + + + leges fiebant ut dictum continue + ut dictum est leges fiebant continue + leges fiebant ut dictum est continue + faciendo + per mutationem + mutationem + . Secundum uerba ideo non + sunt + + amplius conuersiui, sed + tamen + cum + antiquitus + fuerunt + finitur + . + Cuius quidem + Huius + + + causa + causa est + quoniam ab antiquo + ipsimet + corpore + liberi + nobilesque + + nobiles qui + nobiles + ignobilesque + faciebant + cantus + + + + rotationes + rotatos + rotatiuos + recitatiuos + uel + conuersiuos + conuersiones + + + quoniam + quantum + quam + plures + erant + + , et ideo difficile fiebat + eis + + eos + cantare agonistice uel + leges + legem + legere + facere. + + Choros + + Coram + autem faciebant siue cantus + conuersiuos + conuersionis + qui fiunt in choris, + ubi + nisi + sufficientes + et quieti + etiam qui + amplius + imitari conantur + + + + uolunt imitari + melodiam quam + uerba + uerbo + . Propter + quod + + delectabile + cantare secundum armoniam + est cantare secundum armoniam + est secundum armoniam cantare + illam + commutatam + commutatiuam + commutationem + continentem + commitationem + connitatiuam + ubi pauci conueniebant. Nam + hii de facili + de facili hii + hii qui de facili + possunt mutare cantum + pluribus + multis + + + mutationibus + mutatoribus + , + et id est quod dicitur: quod vni mutare cantum pluribus + mutationibus + + + + facilius + + est quam + multis + multus + paucis + , quare + agoniste + agonistice + cantantes uel leges consuetudinem + huius + huiusmodi + ut tactum + est + + + + obseruant + obseruabant + . + + Qui + Quod + Que + Sed + + + mutatione + mutationem + imitatione + + uerborum + mutantur + imitantur + immutantur + , et + ideo + non + melodias ualde simplices faciebant et + incompositas + compositas + , quoniam + conuersiuus + conuersus + cantus quo utebantur est numerus + quidem + quidam + + simplex, qui + vnitate + vnitatem + in unitate + musice + + tantum + mensurabatur + mensurabitur + mensurabilis est + mensurabis + + + , ita quod conuersio si + aliqua + alia + + erat + ibi + ubi + potius + in + + simplicem + quam + in + + + + compositum + compositam + compotum + , + referebatur + + , ut in numeris + dicimus + dicto + diuinis + illum numerum simplicem + + qui + continue + + + + crescit + + mensuratus + per vnitatem + permutatione + . Similiter et cantus potest + simplex dici + dici simplex + simpliciter dici + duplex dici + + + qui + que + + + contineatur + continetur + continuatur + + + per additionem solam + solum per additionem + per additionem soli + uerbi ad + ista + istam + verba + .

+

+ + Deinde. + + + EADEM. + EANDEM. + + + Applicat + aplicat aplicat + + + istam + illam + causam + ad quesitum adhuc + ad quesitum ad hoc + ad quesitum aliud huic + , + simile + similem + dicens quod + ista + illa + ita + eadem + causa est + est causa + causa + , + quia + quare + + + illi + ille + isti + iste + + + cantus + cantus scilicet + qui + a scena + scena + ascene + dicuntur non sunt conuersiui, chori + autem + aut + + + conuertuntur + + , + quoniam + quia + + + ille + illi + qui + cantat + cantant + a scena est + sicut + sicut qui + + + agonistice + agonista + agoniste + + + cantans + cantat + + + aut + que + + + leges + legens + , + + cantat + cantus + enim + agonizantium + + + + + + gesta + + + + commutans + + + + cantum + + secundum uerba + ut + aut + + + agoniste + agonistice + agonistici + + + ceu + + + + + visum est + visum + + , una enim + dictio + + indiget + aspiratione + inspiratione + expiratione + apparatione + , + alia uero + altera uero + alia + lenitate et + huius + huiusmodi + + + consimili + consimiliter + alteratione.

+

Sed + choricus + + cantus + minus + vnus + + + commutatur + + commutatus + alteratur commutatur + commitatur + , amplius + enim + eius + vnum tenorem et circulum retinet + conseruatum + reseruatum + . + Notandum + Nota + quod + a scena + scena + multas habet significationes, aliquando + namque + enim + + + idem est + idem + eadem est + ratione est + quod + umbra + nichilominus + inquimus + uel locus umbratus + et + uel + + + coopertus + + in + teatro + + intratio + + + dicitur + diuiditur + , + interdum + etiam interdum + in circulum + + + totum + + + + teatrum + + tractum + , et + quandoque + quando + quoniam + recitatio operationis. + Vnde olim + poete + pote de + libros + suos + + deferebant a scene ut + appropriarentur + approbarentur + apropinquiuarentur + + + . Dicitur + etiam + et + enim + tabernaculum + mercenariorum + + mercendariorum + + + coopertum + + + + asseribus + aceribus + . Hic autem + per + pro + + + ascena + + ascene + potest intelligi: locus + ubi colliguntur + in quo congregantur + homines ut gesta + librorum + liberorum + + + cantare audiant et + insignium + + + + et insignium cantare audiant + cantare audiatur et insignium + cantare audiante insignum + . + Et + id + ratione + etiam + .xxix. + 30º + + + et .xlviii. + et 38º + 28 + + + apparebit + patet + + + #Vc's scribe includes this representative Jandun + omission. + . + + etcetera + sequitur 16. + problema 19e. particule. +

+
+ +
+ + Sextumdecimum + problema + + 16m + xvim.Sextumdecimum. + 15tum + problema. + + +

+ PROPTER QUID DELECTABILIUS + + PROPTER QUID DELECTABILIUS ANTIFONUM CONSONO? + AUT QUIA MAGIS MANIFESTUM FIT CONSONARE? + AUT QUANDO AD CONSONANTIAM CANTANT, NECESSE ENIM + ALTERAM CONSONARE? QUARE DUE AD UNAM + UOCEM FACTE DESTRUUNT ALTERAM + . + + Decimum sextum + problema. + + + Quare + Querit quare + cantus antiphonus in quo + + quedam extat + extat quedam + resonantia + quedam restat consonantia + + uel + contra + circa + etiam + + + consonantiam + sonantia + consonantia uel etiam consonantia + + + tonorum + tenorum + super + tonos + tonis + chanos + cantus + est + delectabilior + delectabilis magis + + + auditu + auditui + quam sonus + qui est consonus + qui est sonus + + et vniformis in quo non sentitur + contra + circa + aliqua + + + resonantia + resonantiam + sonantia + . + + Apparentur + Apparent + Apparatur + + + + uerbi gratia + + ut gratia + + + sicut + si + + + duo + + succinant + + + subcinat + equaliter et tertius + + precinat + subcinant + + + hic + hoc + + + precinens + tertius + + + contrasonat + consonat + et + antiphonizat + + + + + super illos + si super illos + super istos + gratia istos + contra illos + + + duos + duos + etcetera + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit + + + + + assignans + assignando + et assignat + + + duplicem causam + duas + causas + , dicens + id + illud + ideo + esse quoniam sonus + antiphonus + + + + redditur + redditur et + manifestior et sensibilior + sono + sonis + consonante et vniformi. + + Quod + Qui + autem + sensibilius est sufficienter + scensibilius suficienter est + est sensibilius sufficienter + magis + delectat + + , + eo quod non + + est tale sicut apparet in + tactu + cantu + relatione + aliorum + + sensuum.

+

+ + Deinde. + + + AUT QUANDO. + AUT QUESITI. + AUT QUIA. + AUT. + Assignat aliam causam, dicens quod + quando + + + + aliqui cantant + cantantur aliqua + + + consonantiam + consonantia + facientes in + qua + quo + + + acutum + acentum + non + excedat + excedit + graue + aut + uel + econuerso, + necesse + tunc necesse + necessarium + est quod uox + vnius + unius uox + huius + + + consonet + consonat + omnino uoci + alterius + alteri + , + + sed debet + si debet + sicut dicere + fieri consonantia. Si autem tertia + + adueniens + adueniet + non + antiphonet + antiphonat + autem antiphonet + antiphanizet + , + ymmo + + + + sermo + + + consonizare + + consonare + uelit, + oportet + debet + eam destrui, + + quoniam + quando + + due uoces + + equalis uigoris + uigoris equalis + equales uigoris + ad tertiam + + relate + relate et + + ad tertiam relate + equalis vigoris + + + destruunt + destruuntur + destruant + et + occultant + + + + aliam + alteram + + penitus tertiam.

+

+ + Notandum + Notandum quod + + Nota + secundum + boecium + primo + musice + + + quod + + + + consonantia + consonantiam + est acuti soni + grauisque + grauis quia + + + mixtura + + mixtatio + suauiter + vniformiterque + et uniformiterque + et uniformiter quod + et vniformiter + auribus + accidens + accedens + . Sed dissonantia est duorum sonorum + sibimet + impermixtorum + + + ad + aurem + aures + + + ueniens + perueniens + aspera + atque + et + utcunque + + + iniocunda + iocunda + + + percussio + + . Nam dum + sibimet + sibi + + + misceri + miseri + permisceri + conmisceri + + + uolunt + uoluit + et quodammodo + integri + integer + integra + + + uterque nititur + utraque nititur + nititur vterque + peruenire, + cunque alter + cum alter + equaliter + alteri + officit + + efficit + ad sensum insuauiter, + uterque + utrisque + + + transmittitur + + transmicteri + . + Boeth. + De inst. mus. + I.8 (Freidlein 195, ll. 6–13) + Videtur siquidem quantum facit ad sermonem + + aristoteles + + quod antiphonus sit delectabilior ex contrariis ualde distantibus consurgens ut ex + ypate + ypatem + et + nete + + nete uel nite + , + consonans + consonant + consonatus + + + autem + aut + + + quando + quoniam + + + + ex non adeo + non ex adeo + non ex ita + non adeo + + + differentibus + distantibus siue differentibus + , sicut ex cordis + mediis + melodiis + , ut apparebit consequenter. + + etcetera. + sequitur 17; + problema 19e. particule. +

+
+ +
+ + Decimumseptimum + problema + 17m + decimum septimumDecimumseptimum. + 16tum. + Problema. + + +

+ PROPTER QUID QUINQUE + PROPTER QUID QUANDOQUE + + PROPTER QUID QUINQUE NON CANTANT ANTIFONAM? + AUT QUIA NON EADEM CONSONA CONSONANTIE, + QUEMADMODUM IN DYAPASON? ILLA ENIM IN GRAUI PROPORTIONALE, SICUT ACUTA + IN ACUTO, QUEMADMODUM IGITUR + EADEM EST SIMUL ET ALIA. QUE AUTEM IN DYAPENTE ET DYATESSERON NON HABENT, ITA + QUARE NON APPARET QUANDO ANTIFONE SONUS, NON ENIM EST IDEM + . + + Decimum septimum + problema. + + + Quare + Querit quare + + quinque cantantes, uel + etiam + et + + + quatuor, + vnam non + vna non + non unam + cantant + antiphonam + antiphona + anphpuam + , + tres + + autem uel + aut + + sex possunt cantare?

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse quoniam + ipsa + ista + proportio + que + quam + + + habet + habent + + quinque ad inuicem non + est + est debita + + + proportio + concordia + debita que + consonet + consonat + conicet + et + correspondeat + + tali consonantie in qua + sit + + + + antiphonizare, + quemadmodum + + + + + + antiphonizare contingit + + contingit + + + in + et + dyapason, ubi + est + + + + proportio + proportio et + + dupla. Ipsa enim + habet proportionem + proportionem habet + habet proportiones + + + in graui + magnam + , graue enim proportionatum est graui + in ipsa + + , + sicut + enim + acutum acuto + et graue cum acuto + et + + + + etiam + + . Hoc autem non est + in + + aliis. + Ymmo + + + + + + sicut + in sicut + sicut in + ipsa est eadem inter se et + proportionalis + + proportionaliter + vno + modo + + ita, secundum alium modum + habet + + + + quandam alietatem et + + alietatem et + + diuersitatem inter se, eo quod in ipsa est excessus + manifestus + + , + etsi + et + sit ad + equalitatem + inequalitatem + reductus. Sed + consonantie + consonauere + uel proportiones que sunt circa dyatesseron uel dyapente non sic + se habent + habent + se habet + . + neque + + + + enim + + + + in hiis + hiis + in eis + + + tantus + cantus + + + est + + excessus, + neque + + ad equalitatem + sit + sic + reductus. Et + ideo + non + sonus licet fiat antiphonus, secundum + istas + illas + + + duas + + proportiones non redditur manifestus. Non + enim + + + + est in ipso + in ipso est + + + idemptitas + + + + cum quodam excessu sicut + dictum est + dicunt + in dyapason euenire. Id + autem + + + potest + declarari + delectari + + + ex + in + naturis, quia + si + sicut + debet cantari + antiphona + + , oportet debitam proportionem + interuenire + ante venire + + + + superantium + superantium et + ad superatos + sirantium ad frantos + et econtra + secundum + sed + + + graue et acutum + acutum et graue + . + Sed + Et + id non + accidit + + in quinque uocibus, + nam + uel + universaliter + + quatuor + + antiphonizabunt uno + + antiphonizabunt + aut + tres + tribus + uel + + duobus + + , + non quidem + non quid + nunc quid + numquam + + quatuor + + contra + 4a. + + vnum, quia uox eius oppositis + obtunderetur + obtundentur + obtundetur + omnino, ita + ut + quod + + + + non + + + + possit + possint + sufficienter + percipi + + . Neque tres contra duos, + quoniam + + + + propter + + + + paruum + + + partium paruum + excessum non poterit excedentia + manifestari vnius ad alterum, quare + non contraphonizare contingit + + + + contingit non contraphonizare + non contraphonizare + non contrasonizare contingit + non antiphonizare contingit + + + + cum id + cum illud + requiratur omnifariam + + + moueri + . + Unde relinquitur + + + + quod antiphonizare, ut apparebit + ut apparebit quod antiphonizare + quod antiphonizare + ut apparebit + + + + extet + existet + secundum dyapason proprie. + + et cetera + et cetera et cetera + sequitur 18; + problema 19e. particule. +

+
+ +
+ + Decimumoctauum + problema + 18m + Decimumoctauum. + decimum + octauum. + 17m. + Problema + + +

+ PROPTER QUID DYAPASON + + PROPTER QUID DYAPASON CONSONANTIA CANTATUR SOLA? ORGANIZANT ENIM SECUNDUM HANC, ALIAM NULLAM. + AUT QUIA SOLA EX ANTIPHONIS EST CORDIS, IN + ANTIPHONIS AUTEM ET ALTERAM SI CANTAT, IDEM FACIT. UNA ENIM QUODAMMODO + UTRORUNQUE HABET CORDAS, QUARE ET UNA CANTATA IN HAC CONSONANTIA CANTATUR + SYMPHONIA ET AMBO CANTANTES. + AUT HAC QUIDEM CANTATA. HAC UERO FISTULATA, + QUEMADMODUM UNAM UTRANQUE CANTANT. PROPTER QUOD SOLA CANTATUR, QUIA UNAM + HABENT CORDE UOCEM ANTIPHONAM + . + + Decimum octauum + problema etcetera. + + + Quare + Quare cum + Querit quare + dyapason sola consonantiarum + cantatur maxime + maxime cantatur + cantanti maxime + maxime + + + consonans + sonans + consonantiarum + inter ceteras? + Quod ostenditur + + + + quia + quoniam + secundum + ipsam + ipsas + cantantes + organizant + + + + uoces + uocem + in + altum + alterum + + + leuantes + eleuantes + , + quod secundum + quia secundum + + + + nullam + nullam uero + nullum + ullam + aliarum + ita + sic + + + + manifeste + melodice + agere + contingit + + .

+

+ + Deinde. + + + AUT + AUT QUIA + . + Soluit dicens + Dicit + + + causam esse primam + primam causam esse + causam esse + causam esse primo + causam esse propriam + + quoniam ipsa + sola + + constituitur ex cordis antiphonis seu consonantibus + ut + in + + + graui + graui et + acuto + per + propter + + proportionem duplam. + In antiphonis enim cordis ita se habet + + + + quod si altera + cantetur + cantetur simul + + + + + + siue + tangatur + tangetur + tangitur + , ut + media in quam + medio in qua + ambe + declinant + declinent + determinant + extreme ut apparebit, + idem fit + idem sit + iterum ad idem + , + + + + + ac si + si + + + ambe cantarentur + cantarentur ambe + ambe cantantur + ambe cantarent + ambo cantarentur + , + eo + ita + et + quod + illa + illam + ipsa + + + vna + non + + + habet + in se aliqualiter + aliqualiter in se + in se aliquam + + + ut in virtute + ut in unitate + ut virtute + virtute + + + cordas + cordis + vtrorumque sonorum puta grauis et + acuti + acute + , quare accidit + in + et + ex + + + huius + huiusmodi + + + consonantia + + quod vna + cantata uel + cantilena + + + pulsata + pulsetur + cantetur et altera, ac si ambe + cantarentur, propter + conuenientiam + inconuenientiam + quam + habent + habet + in + medio + media + , + ceu ostendunt + ceu ostenduntur + seu ostendunt + sicut ostendunt + + + pigmenta + + + + ex diuersis + + ex diuersis ex diuersis + ex diuersis + + optime + constructa + constituta + in saporem + consurgentia + concurrentia + + + delectamentum + delectatiuum + delectantium + delectatium + .

+

+ + Deinde. + + + AUT + AUT QUIA + QUOD + . + + Assignat aliam causam dicens + assignat aliam causam dicens causam + soluit dicens causam + + + ideo esse + esse ideo + id esse + esse + + + quia + quoniam + si vna + cordarum + corda + cantetur ut ypate et altera fistuletur ut + nete + + nete tunc + vite + cantando et fistulando utrobique cantatur + vna quia media + quia media + + . + Et ideo sola + symphonia + + cantatur + + , + quoniam + et propter hoc + corde + cantate + cantante + cantato + seu + fistulate + + vnam habent uocem scilicet + antiphonam + + amptiipheniam + , de quo + planius + plenius + amplius + apparebit .19. + et + .20. + .2º. + Omnia + enim hec + hec + enim hinc + + + problemata + problema + + + + + concidunt + coincidunt + , super eodem enim + fundantur + + fundatur + medio + concidunt + . Sic + ergo + igitur + + + ille + iste + + due + + solutiones + questiones + + ⳋones + communiones + + + + magis differunt + differunt magis + ratione modi quam + rei + + subiecti + sb'i + + , cum vna sit uocalis + et + + + + altera uocalis et + alia + + instrumentalis. + + et cetera + sequitur 19; + problema 19e. particule. +

+
+ +
+ + Decimumnonum problema + 19m + decimum nonum.Decimumnonum. + 18m + problema. + + +

+ PROPTER QUID ANTIPHONIS + + PROPTER QUID ANTIPHONIS HOC SOLIS INEST? + AUT QUIA SOLE EQUALITER DISTANT MEDIO? MEDIETAS + IGITUR SIMILITUDINEM QUANDAM FACIT SONORUM. ET UIDETUR AUDITUS DICERE QUOD + IPSA ET QUOD UTREQUE ULTIME + . + + Decimum nonum + problema etcetera. + + + Consequenter + + querit + causam causae + causam + precedentis + problematis + + , dicens quare in + antiphonis + antiphonia + cordis + inest + ita est + quod vna cantata + cantetur et altera + cantatur altera + , et quod idem + consonat + consonet + sonat + esse sonat + utrobique + sicut si + ambo + anbe + + + cantarent + cantarentur + + + ?

+

+ + Deinde. + + + AUT. + AUT QUIA. + QUIA. + + Soluit dicens causam esse + quia + quoniam + sole + huius + huiusmodi + cordarum antiphone in quibus + existit + estit + consistit + dyapason equaliter + distant a + distantia + + media + corda + + , ut dicatur a mese + que + quod + est + uere + nete + media + vii. + enim + + + cordarum + corde + , ut visum + est + + . Illud + autem + aut + quod + est + vere est + medium + conficit quandam + consistit in + quadam + + + similitudinem + similem + consonantiam + et + conuenientiam + conuenientia + sonorum cum + extremis, reddit + enim + cum + + + similitudinem fere sonum + similem fere sonum + media tacta, ac si + tangerentur ambe ultime + ambe vltimis tangerentur + . Et hoc est quod + dicit + + : auditus videtur + diiudicare + + + quod + ipsa + ista + + media cordarum et + quod + + + + utreque + + utrorunque + + extreme + constituant + constituunt + + vnum + sonum + + . Et + ideo + rem + in antiphonis + solis + solum + accidit quod vna + corda + + tacta uel + cantata + canta + + + cantetur + cantentur + cantetur et + + + reliqua + relique + altera + , cum + in + + + + medium + + mediam + + + concurratur + concurrant + concurrat + , quare dyapason + tantum + Sed + + inter alias + proportiones + concordias + + + + sola + solo + ex + antiphonis est apparentius + apparentiis antiphonis est + antiphonis est apparentior + tonis. + + etcetera + sequitur 20. + problema 19e. particule. +

+
+ +
+ + Uigesimum problema + 20m + Uigesimum. problemaUigesimum. + 19mum. + problema. + + +

+ PROPTER QUID SI QUIS + PROPTER QUOD SI QUIS + NOSTRUM + + PROPTER QUID SI QUIS NOSTRUM MEDIAM MOUET, CONCORDANS ALIAS CORDAS, + UTITUR INSTRUMENTO, NON SOLUM QUANDO SECUNDUM MEDIE FIAT SONUM DEFICIT, ET + UIDETUR NON CONCORDANS, SED ET SECUNDUM ALIAM MELODIAM? SI AUTEM LICHANUM AUT + ALIQUEM ALIUM SONUM, TUNC UIDETUR DIFFERE SOLUM QUANDO ILLA QUIS UTITUR. + AUT RATIONABILITER HOC ACCIDIT, OMNES ENIM UTILES CANTUS MULTOTIENS MEDIA + UTUNTUR. + ET OMNES BONI POETE FREQUENTER AD MEDIAM OBUIANT. + QUAMUIS DISCEDANT, CITO REUERTUNTUR, AD ALIAM AUTEM ITA NEQUE UNAM. + QUEMADMODUM EX ORATIONIBUS: QUIBUSDAM ABLATIS + CONIUNCTIONIBUS, NON EST ORATIO GRECA, UT AUTEM ET UERO. ET QUIDAM AUTEM NON + DEFICIUNT, PROPTER ID QUOD HIIS QUIDEM NECESSARIUM EST ESSE UTI MULTOTIENS, SI + ERIT ORATIO, HIIS AUTEM NON. + ITA AUTEM ET SONORUM MEDIA SICUT CONIUNCTIO EST ET + MAXIME BONORUM, PROPTER ID QUOD MULTOTIENS INEST IPSIS SONIS + . + + Uigesimum + problema. + + + Quare + Querit quare + + + si aliquis + siquis + aliquis + + + nostrum + + modorum + scientium + pulsare + pulsaret + + + instrumentum + + + + tangat + tangit + + + cordam + + mediam ut mese, utitur instrumento tali + modo + + ac si omnes + alias + + cordas extremas ad inuicem + concordantia + concordantes + reduceret, quod declarat? + Non + Nam + enim quando + media corda + corda media + tangitur sonus deficit + et videtur + uidetur + ut uidetur + et videtur videtur + non fieri + concordantia + concordia + in instrumento, + sed + serui + quod plus + est + + , + apparet + videtur + quod + tactus + cantus + + + istius corde + istius + illius corde + + + resonet + restent + insonet + in + quandam melodiam + quadam melodia + . + Id + Illud + autem + non + + contingit in aliis cordis extremis, sicut + est + est in + + lychanos, que est tertia post ypatem. Si + quis + quos + enim sonum + causaret + causet + cantet + carent + per + cordam + + hanc uel per aliam ut paramese + uel + et + paranete, + tunc + etcetera + + + solum + sonum + videtur + differentia + differri + in sono et + dissimphonia + + + + + + dissymphoniam + disynphoniam + in disinphonia + + + causari + causare + + + quando + cum + quis utitur tangendo illam cordam que + non + si + + + est + + recte media. Uel aliter quod + tunc + esse + + + solum + non + + est + differentia sonorum + sonorum differentia + + + ad inuicem + ad se inuicem + + + visa, qua + qua uissa + uisa, quo + In secunda qua + + + + discernitur + discernit + quod vnus est delectabilior + altero + altera + alio + , + quando + qua + + + quis + quamuis + + + utitur tali modo + utitur modo + + destruitur tali modo + media corda + recte + recta + taliter quod in + eam + ea + + + consonent + consonant + + due ultime, quod est + difficile + difficila + + + mihi + + minis + .

+

+ Notandum + Nota + quod aristoteles + + multotiens dicit + dicit multotiens + multotiens dicere + + + videtur + + + + eo quod + quod + + + huius + huiusmodi + scientia + consistit in sensu + in sensu consistit + + + et + ut + + auditu et ratione, + ceu + seu + sicut + + + alie + alii + . + Pictagoras + + + tamen omne quod + ipsius + ipsi + + + nitebatur + utebatur + uidebatur + + + rationi + ratione + rationem + et omni + magis + inherere + inherere aristotelem + inheretur + adherere + , + aristoxenus + + + + + + + + ar + aristoteles + vero + sensui + sensum + , quos ambos + ptholomeus in eius + + + pertheus in eius + ptolomeus in sua + + + armonica + + armonico + retorica + detestatur medium + obseruans + + cum declinatione + in + tamen + rationem amplius. + Boeth. + De inst. mus. + V.3 +

+

+ + Deinde. + + AUT. Soluit per simile + in aliis repertum dicens + primo + pro + + + rationabiliter id + id rationabiliter + rationabiliter illud + illud rationabiliter + fieri quod in + quesito + quesito est + 5to est + + + proposito + propositum + propositum est + . Nam omnes cantus utiles et + laudati + laudatiui + + + attingentes + + + + finem + fine + musice cuiuscunque + multotiens + melodie + + + utuntur + utitur + corda media + + reducendo + reducenda + + + ceteras et maxime supremas + + et maxime super primas et ceteras + + + proportionaliter + proportionatas + proportionabiliter + + ad + ipsam + + .

+

+ + Deinde. + + + ET OMNES. + OMNES. + Declarat + id + illud + + secundo + + et + + + primo in metrica, que est + + musica quedam + quedam musica + ut + apparuit + apparebit + , + dicens + + quod + musica + + + omnes boni poete utentes hac parte musice metrica + dicta, + quam + qua + + + + frequenter + conuertunt se + se conuertunt + ad mediam cordam siue ad + id + illud + quod proportionatur illi, quod si + accidat + accidit + + + recedere quandoque ab ea + quandoque recedere ab ea + quandoque ab ipsa recedere + , + cito + statim + + + ad ipsam reddeunt + + redeunt ad ipsam + ad ipsam redit + + + tanquam + + ad perfectum, + sed + seu + ad nullam + aliarum + aliorum + aliam + + + ita + + reuertuntur, + cum + + non ut + + hic tactum + hic tactum est + hic cantum + + + perficiat + proficiat + + huiusmodi + .

+

Nosce quod eximii poete + tunc + cum + + + obuiant + + ad mediam cordam et ad sibi + proportionale + proportionalem + proportionabilem + , + quando + cum + + + apud + + nos + vsitate + + + + + construuntur + construunt + construant + constituunt + consciliunt + carmina in quibus sunt tempora + sillabarum + + ad inuicem + conproportionata + aproporpationata + proportionata + composita + proportionata + ex breui et + longo + longa + . + Sillaba + + + + namque + enim + breuis vnum + + habet tempus + tempus habet + + + , longa uero duo, + quale quod constructum + quale quod constructum est + + + ex + + + + dactilo + + + + + + vicissim + + inessim + incisam + et spondeo + et + + non ex + altero. Tantum + altera + + + neque in + exametro + + + + + trocheo, nisi in fine + dactilo + + , + quidem + quodam + quod + + + nunquam + + tantum + + + + neque + spondeo in quinto + pede + ex spondeo in quinto + + + aut + haud + + + iambo + + in ambo + + + ei + sibi + eius + opposito. Constat + namque + enim + + ex + prima breui + breui prima + et + ultima + altera + longa, + quo utimur + quo utuntur + continitur + licentia + quandoque + + poetica in principio + tertii pedis + .3ii. + + . Tunc + namque + enim + + + fit aliter + aliter fit + + + ut + + cum + seceditur + sedetur + seccetur + descendit + se redditur + a media corda + uel ab eo + + + + quod + quod est + sibi + consimile + simile + . + Debent + Debet + + + namque + enim + + + carmina fore + fore carmina + bene + cantatiua + cantantia + ut + que + quia + + + ouidii + + ouii + toni + enim + eum + + + non + + + + autem que sunt + autem que + aut que sunt + autem sic que + + + oracii + + et ideo + aliqui + aliquos + versus + construunt + ostendunt + + + dictos leoninos + leoninos dictos + leoninos + quasi + rithimicam + rithimos + rithimicis + rithimia + + + commiscentes + commiscente + commiscentis + consistentes + metrice.

+

+ + Deinde. + + QUEMADMODUM. Declarat secundo in + coniunctione + coniectione + iniunctione + orationis + prosaice + + + + dicens + id + quod sicut in aliquibus orationibus + in quibus + + + + videlicet + scilicet + uidet + + multa + coadunantur + + coadunata + , non + constituitur + constituuntur + + + oratio + omnino + + + greca + + gramatica + , que est + orationum + questionum + + + congruissima + cum grauissima + et perfectissima, + remotis + motis + quibusdam + coniunctionibus + coniectionibus + + + tanquam vinculis conuenientibus + + , + puta + + ut + autem + aurem + uero + quidem + quedam + quod + quid + et + huius + huiusmodi + . Unde et + quidam + + + + construere uolentes + + uolentes construere + + + orationem + orationem orationi + + + grecam + gramaticam + + + congruissimam et perfectam + perfectam et congruissimam + congruissimam et perfectissimam + congruisima et perfectam + congrauissimam et perfectam + bene sonantem, + et + + ne sequatur vocalis + ad + post + + uocalem, + quod + que + quidam + + + grecus + gramaticus + creus + + + horret + + abhoret + oret + honoret + + etiam in scriptura, + non + in + + + deficiunt + proficiunt + + + in + et + + + huius + huiusmodi + + + coniunctionalibus + coniunctionibus + partium ligaturis, cum + oporteat + + + + eis + eos + ac eis + multotiens vti si + debet + debeat + oratio + perfici + + conuenienter; in hiis autem + deficiunt + deficiunt, quandoque + + + ceu + seu + sceu + + + et + etiam + cantus, interdum + recedunt + reddunt + a media + corda + + . Quia + quandoque + quinque + non + sit + fit + necessarium + sepe uti + + uti sepe + sepe + , sicut + in + + orationibus + minus + unus + viris + + + grecis + gramaticis + + + aut + cum + alio modo, + uelut + ualde + uniuersaliter + ultra + sunt alie partes orationis preter est uerbum + substantiuum + + substantium + subactium + + expressum + aut + uel + + + intellectum + subintellectum + in + omnibus + orationibus + . Uel aliter, quia + coniunctiones + coniectiones + sunt duplices, + quedam + quia quedam + + + namque + enim sunt + + + maxime + et maxime + ualde + necessarie in + oratione + orationibus + , cum + protenditur + protendentur + protenduntur + puta + et proprie si + et si proprie + et proprie .enim. + si + + + quia + que + + + aut + autem + et + huius + huiusmodi + similia + . Alie + uero + nec + uero nec + + + quasi + que + minime, ut + quidem siquidem nempe quippe + siquidem quidem nempe quippe + quidem siquidem nempe apparet + quippe nempe siquidem + + et + huius + huiusmodi + . Modo + oratio + oro + + + perfecte + perfecta + + + greca + + gramatica + constituitur, + quando utitur + + + + hoc + hac + modo coniunctionis + duplici + 2a. + + , puta + priori + prioris + + + significatiua + significatio + + + et non significatiua + et non significatam + et non significam + + . Dico autem + perfecte + perfecta + + + greca + + + gramatica + quia + greci + gramatici + et potissime + galienus + + Gal' + Galienus + + gallici + + + + maxime + et maxime + + + + utitur + utitur ista + utuntur + + + huius + huiusmodi + + + ligamentis + ligamentalibus + ligamentationibus + + + sinchathegorematis + + + + + + + + + The word in question in συγκατηγόρημα: "a word in logick that + imports somewhat with another, as all, none, certain, etc. + which signify little of themselves, but add to the force of other words (N. + Bailey, An Universal Eytmological English Dictionary, 17th + ed. (London: T. Osborne et al., 1759)). + + + etiam + et + secundis, + ut et + et et + et + ut + + + plura + plura plura + + + quandoque adiungat + quandoque adiungantur + quando adiungat + coniungat quandoque + vna + puta + pauca + : + ac et + a. et + Et ac + ac etiam et + , + nimirum + + + in nimirum + numerum + minimum + , quidem, + demum + deinde + . + Tales + Deles + + + autem + aut + + coniunctiones + apud + + + + grecos + gramaticos + dicuntur + parapliromatice + + + + + + + + + + + + The word in question is παραπληρωματικός, i.e. expletive. Cf. + + , + id est + et + + + + completiue + complete + copulatiue + sermonis, + utpote + ut puta + ut poete + + + di. ta. ra. ni. ge. + + + + di.ru. ru. ru. ge. + di ta ra ge + di. ca. na. ge. + etcetera.

+

+ + Deinde. + + ITA AUTEM. + + Applicat + + ad propositum + tertio + 3 + + , dicens quod simili modo se habet + cordarum + corda + media uel + ei + enim + sibi + proportionale + in + et + sonis, + ceu + seu + sicut + + + coniunctio + coniectio + in orationibus + gramaticis + gramaticalibus + gramatice + gramatico + et proprie + bonis seu grecis + grecis seu bonis + seu grecis + bonis ceu grecis + bonis ceu gramaticis + . Nam + cordarum + corda + + + media + medio + melodia + est + proprie + propria + de numero bonarum + reddentium + cordarum reddentium + mellifluum + sonum + + + + et + + + + consonum + sonum + extremis. Et quia + hiis + is + hiis + id + multotiens + debet + debent + + + in esse sonis + esse in sonis + in esse sonus + inesse sonis + ideo + ut + + + + propositum est + propositum + multotiens, + cum possunt + cum post + compositum + vtuntur + corda + verba uel vera + media secundum quod + ei + ea + et + est + + + consonant + consona + extreme, et de hoc + itidem + + + + .36°. apparebit consequenter + .36. apparebit. + apparebit consequenter + .36°. + + + problemate. + p + + + + etcetera. + et cetera. sequitur 21; problema 19e. particule. +

+
+ +
+ + Uigesimumprimum + problema + 21m + uigesimum. primum.Uigesimumprimum + Uigesimum + problema. + + +

+ PROPTER QUID CANTANTIUM + + PROPTER QUID CANTANTIUM GRAUIUS CANTANTES ACUTE CANTANTIBUS, SI + DISSONANT, MAGIS MANIFESTI FIUNT? SIMILITER AUTEM + ET RITHIMO: QUI IN GRAUIORI PECCANTES MANIFESTI MAGIS. + UTRUM QUOD PLUS TEMPUS GRAUI, HIC AUTEM MAGIS + SENSIBILIS? + AUT QUIA IN PLURI TEMPORE MULTUM EXHIBET, UELOX + AUTEM ET ACUTUM LATET PROPTER UELOCITATEM + ? + + Uigesimum primum + problema. + + + Quare cantantes + Querit quare cantantes + + de numero + grauius + grauium + + + cantantium + cantantes + , si dissonent + et + + + + errent + errarent + erteant + haberent + in cantu suo + ab + ab ab + ordine debito, + magis redduntur + + + + manifesti + manifesto + manifeste + in suo errore quam illi + qui + + cantant + acutius + acutus + ? Et addit + quod + quoniam + + + non solum accidit hoc + hoc non sollum accidit + non solum hoc accidit + in musica + armonica + armonia + + , que ex + uocibus + motibus + constat, sed etiam + in + ex + + + + rithimica + mathematica + , que coherentiam et + consonantiam + + + + uerborum + vocum + + + contemplatur + contemplantur + : utrum + bene + bene bene + uel male + consonet + consonent + constent + . + Qui + Que + Quando + Quoniam + + + enim + est + + + peccant + potest causat + + + in + secundam + ipsa + secundum + + grauius + magis manifestantur + magis manifestatur + quam si + peccarent + peccaret + secundum acutius.

+

+ + Deinde. + + UTRUM. Soluit + et + et et + + + assignat + + + + duplicem causam quasi + quasi duplicem causam + + + consimilem + + , dicens causam esse quoniam graue + plus habet + habet plus + + + temporis quam acutum. + Ubi + Illi + + + autem + aut + plus est + + + + temporis + temporis et + , amplius potest peccari, + et + ut + + + peccatum + punctum + + + similiter + + + + magis percipi + percipi magis + .

+

+ + Deinde. + + AUT QUIA. + + + Assignat + + causam dicens + Soluit dicens + Dicens + Assignat aliam causam dicens + + + id + illud + hoc + ideo + esse + quia + quare + quod + + + in + et + + tempore + maiori + + + + exhibet + + + + graue + grauem + tardum et multum sonum, + quare + fit + sit + esse ipsius manifestum propter sui tarditatem. Sed uelox et acutum, quia in + minori tempore dat uelocem + sonum + suum + + + , + ideo + acutum autem + latet propter eius uelocitatem, ita quod peccatum non perpenditur + etiam + + inexistens notabiliter. + + et cetera + sequitur 22m. + problema 19e. particule. +

+
+ +
+ + Uigesimumsecundum + problema + 22m + vigesimum secundum.Uigesimum secundum. + 21mum. + problema. + + +

+ PROPTER QUID MULTI + + PROPTER QUID MULTI MAGIS CANTANTES RITHIMUM SALUANT QUAM PAUCI? + AUT QUIA MAGIS APUD UNUM ET RECTOREM INTENDUNT ET + GRAUIUS INCIPIUNT, QUARE FACILE IDEM ATTINGUNT? IN UELOCITATE ENIM PECCATUM + EST PLUS + . + + Uigesimum + secundum problema. + + + Quare + Querit quare + multi cantantes melius + conseruant + consonant + seruant + + + rithimum + rithimum conseruando + et vniuersaliter omnem + armoniam + armonicam + + + quam + que + acceperunt cantare quam pauci?

+

+ + Deinde. + + AUT. + + Soluit dicens + dicit + Dicit id + + + causam esse + esse causam + + quoniam ipsi amplius + intendunt + attendunt + et + ordinantur + ordinant + coadunantur + + + ad vnum + + , + tanquam + + ad + rectorem + Rethorem + regulam + terrorem + + + ouium + omnium + opposittum + , et grauius possunt incipere cum + fuerint + fuerunt + multi + quoniam + quantum + + + uox vnius + unus + + + fortificat + confortat + et + substentat + + uocem alterius. Propter quod de facili + possunt in vnum + in vnum possunt + + + deuenire + peruenire + + + + illudque + et illud + illesum conseruare in uelocitate. + Autem + Aut + + + + non contingit hoc + hoc non contingit + non contingit + hoc non conuenit + + + cum difficilius sit seruare acutum + quam graue + quam grauius + graue + , ut dicetur + .26°. + .36. + 36º + 26a. + , quare in uelocitate + magis contingit + contingit magis + magis conuenit + peccare, etsi + peccatum + peccant + + + plerumque sit + sit plerumque + plerumque fit + plurimumque sit + + magis latens ut + etiam + et + + + alii + alii magis + ostendunt + actus + + . Et + id + idem + ad + quidem + .45°. + 35. + + + repetitur + + reputetur + . + + et cetera + sequitur 23. + problema 19e. particule. +

+
+ +
+ + Uigesimumtertium + problema + 23m + vigesimum tertium.Vigesimum.tertium. + 22m. + problema. + + +

+ PROPTER QUID DUPLEX + PROPTER QUID DUPLEX UITE + + PROPTER QUID DUPLEX NITE YPATE? + AUT PRIMUM QUIDEM QUIA EX MEDIO CORDA CANTATA ET + TOTA CONSONANT DYAPASON? + SIMILITER AUTEM SE HABET IN FISTULIS, QUE ENIM PER + MEDIUM FORAMEN FISTULE CONSONANT PER TOTAM FISTULAM DYAPASON. ADHUC ET IN + ALIIS IN DUPLICI DISTANTIA ACCIPITUR + DYAPASON, ET ILLI QUI PERFORANT + FISTULAS ITA ACCIPIUNT. SIMILITER ET CUM DYAPENTE EMIOLIUM, QUIA QUI FISTULAS CONCORDANT IN YPATEM CERAM + PONUNT, NITEM AUTEM USQUE AD MEDIUM REPLENT. SIMILITER AUTEM ET PER DYAPENTE + EMIOLIO, ET PER QUATUOR + EPITRICA DISTANTIA ACCIPIUNT. + AMPLIUS IN TRIANGULIS PSALTERIIS EQUALI + DISTENSIONE FACTA CONSONANT DYAPASON. HEC QUIDEM DUPLEX EXISTENS, ALIA UERO MEDIA LONGITUDINE + . + + Uigesimum + tertium problema. + + + Quare + Quia + + in + 12. + 13º + 21. + 2°. + + + dixerat + dixit + + duplicem + nitem + + uicem + + + + constituere + constituit + + + ypatem + + ? Ideo causam + huius + huiusmodi + eius + querit, dicens: quare + duplex + dupliciter + + + nite + + vite + constituit + ypatem + + ?

+

+ + Deinde. + + + AUT. + AUT PRIMUM. + + + Soluit + Soluit dicens + et primo ostendit + quomodo + quod + ex duplici + nite + + nitem + vite + causetur + ypate + ypatem + + + in + + cantu, secundo + + in instrumentis + instrumentis in + + + flatu + + , tertio + + ductu + in ductu + , + 2a + 2a + ibi + ibi 2a + + SIMILITER, + 3a + 3a ibi + + AMPLIUS, + dicens + dicit + dicens primo + dicit primo + causam + esse + + + + ex hoc primitus + sumendam + + + sumendam ex hoc + , quoniam + quando + ante + media cordarum + cuiuslibet + cuilibet + + + instrumenti + + + + cantatur + incantatur + , tunc et + omnes alie + alie omnes + omnes aut + + + coordinantur + + coadunantur + ad + ipsam + illam + mediam et + consonant + consonat + + + per eam, cum ex ea + per illam, cum ex ea + cum per eam + + + constituatur + constituitur + dyapason, ut + apparuit + apparebit + + + .20 + 2° + 3° + .

+

+ + Deinde. + + SIMILITER. + + Ostendit 2° similiter fore + Ostendit 2°. fore + similiter + Ostendit 2º + similiter + Ostendit 2º + fore + + in instrumentis + et + in + + + flatis + sufflatis + fistulatis + , dicens + simili modo + similiter + se habere in fistulis, in quibus sunt + quedam + + + + foramina + formalia + habentia similitudinem cum cordis, + in eis enim + est + + + + magnum + magno + foramen, cuius sonus + grauis + + , + proportionatum + proportionatus + proportionatur + est proportionatus + + + ypate + ypati + ypatem + + + et + ut + + + secundum + secundus + + + ut + + medium, + assimilatum + assimilatur + mese et + plura + plura et + + + parua + + . + Super + Sunt + que + fistulantur + fistulentur + fistulatur + attributa + nete + + vite + , in quibus siquidem soni qui + fiunt + sunt + per medium + foramen + foramen dicit + foramen dicte + + + fistule + fistule fistule + consonant et + inducunt + ducunt + per totam fistulam secundum + aliqua eius + eius aliqua + aliqua enim + foramina omnia dyapason, + cum + + in ipsum, + ceu + + seu + sicut + + + in + + medium, + reducantur + reducuntur + reliqua. Similiter + et + + in aliis + id accidit + accidit id + illud accidit + accidit + instrumentis, in quibus predicta + potest + possunt + + + aptari + adaptari + foraminum similitudo, + nam + uero + non + in eis + etiam + in + + + + dyapason constituitur + constituitur dyapason + dyapason constituunt + + + in esse + inest + + secundum duplicem + + distantiam + substantiam + : + puta + vnius + unus + extremi ad medium vna, et alterius ad ipsum reliqua, uel quia ex numero + consurgit duplari. Quod ostenditur quia illi qui perforant fistulas + tali modo + suscipiunt + + + + distantiam + distantia + ut + inde + in + + + consurgat + consurgit + dyapason cum reliquis proportionibus. + Nam + Quam + + + + taliter + aliter + + + operantur + opponatur + : perforando et + coaptando + coadaptando + + + ut + et + secundum proportionem sexquialteram + + reddatur + addatur + + dyapente, + quod + et + declarat. Nam + qui + si qui + si + + + fistulas taliter + taliter fistulas + + + consonas + consonans + consonantes + faciunt ut consurgat dyapason apponunt + ceram + seram + uel + aliquod + aliquod huiusmodi + + + viscosum glutinosum + + + glutinosum uiscosum + viscosum siue glutinosum + + + in + ut + foramine + maiori + maiore + + + proportionato + proportionate + ypate, ut sonus eius + subgrauetur, et foramina per + nitem + + + + representata + representatam + replent + cera + + ceram + cera et + cera ut + usque ad medium + + , + + + ut + in + eis + angustatis + + coangustatis + sonus + reddatur + + acutior, + ita + + ut + possit duplex + possint duplices + + + nite + + vite + in + ypatem + ypate + + + consurgere uel crescere + + concurrere + , + cum + ut + vna + exacuatur + exacuat + et + reliqua + altera + + + subgrauetur + sibi + sibique + + + appropinquantes + + + + appropinquent + + + utcunque + ubicunque + utrunque + uterque + utrisque + eodem modo + secundum + + + + debitam distantiam foraminum + debita distantia foraminum + debitam distantia foraminum + debita foramina + + + cum + ut + + + cere + cera + uel alterius + appositione + appone + oppositione + propositione + , ita quod + etiam + in + + + lignum + ligamen + + + submittunt + submittitur + subimmictunt + subimmittunt + + + subtile + + utile + fistule + in + foramen + foramine + medium secundum sexquialteram proportionem, + seu + ceu + + emiolam faciunt dyapente. Similiter per + epitricam + + + + + + + distantiam + distantia + que est cum numerus continet + alium totum + totum alium + alterum totum + ut visum + est + + + + et eius + in eius + 7 + etiam + + tertiam partem, + ut + et + + .4. ad + .3. + 3a et + + + se + habet + habent + + + . Accipiunt per .4. + + id est + enim + dyatesseron + grece + graue + .

+

+ + Deinde. + + AMPLIUS. Declarat + 3°. in instrumento + tactibili + tertio instrumento tactibili + 3°. in instrumento + tangibili + , dicens quod + insuper etiam + etiam insuper + + simili modo in psalteriis, que habent + figuram + triam + triangularem, + et + + in canonibus + facta + factam + + proportionali + distensione + distantia + cordarum + ipsarum + ipsorum + ex acuto et graui + consonant et adducunt + + adducunt et consonant + consonant et addunt + consonat ut adducunt + dyapason. In ipsa enim duplex corda, ut + ypate + + et + nite + + vite + , + et alia + et aliam + taliter + in + quam + qua + + + concidunt + concidat + conferat + constat + cum superat + que + est + est in + + + media + mediam + + + distantia + distante + + + uere + uero + + , + ut + et + a + mese. Vel aliter duplex + nete + + concurrit in + ypate + + : et + constituitur + construitur + tunc sonus + corde medie + medie corde + cordis medie + totidem medie + secundum distantiam ut + apparebit + apparebat + apparuit + + + vigesimo + vigesimo problemate + 22° + + . + + et cetera + sequitur 24. + problema 19e. particule. +

+
+ +
+ + Uigesimumquartum + problema + 24m + vigesimum quartvm.Vigesimumquartum. + 23m. + problema. + + +

+ PROPTER QUID IN TENUIBUS + + PROPTER QUID IN TENUIBUS MENTEM APPONERE, YPATE SOLA UIDETUR + CONTRASONARE? + AUT QUIA CONNATURALIS MAXIME FIT SONO SONUS QUI + EST AB IPSA PROPTER ID QUOD CONSONANS EST? SIMUL AUGERI AUTEM SIMILI UIDETUR + SOLUS. ALII UERO PROPTER PARUITATEM INMANIFESTI + . + + Uigesimum + quartum problema. + + + Quare + Querit quare + + + cum + cum in + in + subtilibus cordis, + ut + uti + nete et + paranete + + paranetum + , + sonum + + acutum + et paruum + + + + + reddentibus + + + + quis + siquis + mentem id est rationem et sensum seu + auditum + aditum + + + apponit + apponet + apponitum + ? Hec enim scientia, ut + pretactum est + pretactum est constat est + pretactum + tactum est + , constat + in + + ratione et sensu. Tunc sola ypate + sine + fine + aliis + videtur + ut + + + antisonare + + antiphonizare + + + + sonitu reliquas + sonitu reliqua + soni cum reliquas + + + superando + superando esse + , quod + prius dictum est + prius dictum est est + dictum est prius + + + antiphonare + + inantiphonare + + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit dicens + dicit + causam esse + quia + quoniam + sonus qui ab ipsa causatur principalissime efficitur connaturalis et + proportionalis + alii + alteri + + + sono + sono alterius + corde inferiorum sub medio existentis + , propter hoc + quod cum sua + quod quando + + + consonantia + contrasonantia + + est + etiam simul + simul etiam + et simul + etiam similis + + + consonans + + contrasonans + . + Quando + Quoniam + Contra + + + enim + est + sonus + ipsius + hominis + + cum sono alterius corde + inferiori + inferioris + sub + medio + media + + + existentis + existentibus + existente + + + construitur + constituitur + constitutus + , + consonantia + consonantia + est etiam simul sonsonans quando enim sonus ipsius cum sono alterius + corde inferioris sub medio existentis constituitur consonantia + ut iam patuit dyapason. Et similiter + solus sonus huius corde + solum sonus huius corde + solus sonus huius cordis + solus sonus huiusmodi corde + sonus huius corde solus + inter alios sonos + videtur + uideretur + + + augeri + augere + et + crementum + incrementum + in tonando accipere, quia ipsa reddit sonum sola grauiorem + aliis, alie uero + acutum + acutum aliis + + + aut + et + autem + ut + minus grauem. + + + + Sonus autem + grauis + grauis sonum + + + ebetat + + + + acute + acuto + + + , + + sed + et + + + + soni + sonus + aliarum cordarum + subtilium + subtillius + , quia sunt + parui + parue + praui + graui + , non + percipiuntur + percipitur + perciuntur + manifeste, + propter + propterea + quod + non apparent + non apparet + non apparebit + apparent non + + + consonare + contrasonare + . + Stat + Et stat + + + igitur + ergo + enim + in hoc, + quia + quod + sonus + ypate + ypatem + parypate + fortis + est + et + , aliarum uero debilis. + Qui autem + Qui + Quia + + + huius + huiusmodi + + + + consonat + consonant + contrasonat + contra consonat + + + debili + debiliter + cum eo + quod + + recipit, + magnus + maior + + + enim + est + motus minorem + debilitat et obtundit + obtundit et debilitat + . + Huius + Huiusmodi + autem sonus + cordis + corde + licet + sit + + fortior + ceteris + aliis + , quia tamen grauior et + dimensionatior + indimensionatior + dimensionationem + diuisionatorem + + sonum aliorum de facili + recipit + suscipit + et exaltat, + ita + + ut dyapason + inducat + inducit + inducta + indicat + . + + etcetera + sequitur 25. + problema 19e. particule. +

+
+ +
+ + Uigesimumquintum + problema + 25m + vigesimum. quintum.Vigesimum quintum. + 24m. + problema. + + +

+ PROPTER QUID MEDIA + PROPTER QUID MEDIA VOCATUR + + PROPTER QUID MEDIA UOCATUR IN ARMONIIS, OCTO UERO NON EST MEDIUM? + AUT QUIA SEPTEM CORDARUM ERANT ARMONIE ANTIQUITUS? SEPTEM AUTEM HABENT MEDIUM + . + + Uigesimum + quintum problema. + + + Quare + Querit quare + in armoniis + quedam + quandam + cordarum ut + mese + nete + + + appellatur + + appellantur + + media + recte + ratione + + + .7. + .a. 7 + cordarum? Equaliter enim distat ab + eis + hiis + aliis + , sed octo + cordarum non est medium + + directe + recte + + + ut + + + + arismetricum + + + , + sed + + potius geometricum. Et ideo octo cordarum + non uocatur + aliqua media + aliquod medium + .

+

+ + Deinde. + + AUT. + Soluit + dicens + dicit + causam esse quoniam antiquitus, ut + visum est + visum + , non + fuerunt + fecerunt + nisi septem corde + in + + instrumentis armonicis.Septem autem + medium habet + habet medium + medium habent + + + equidistans + + + equidistant + que distans + ab extremis, + + puta + + + .4., + ut + ait + + + mese + n mese + . Id autem + factum + factum est + + + quia + + dyapason, + que + qui + est + optima + comparatio + consonantiarum, ordinatur amplius + cum + causa + + + fuerit + fuit + medium + uerum + + in cordis inuenire. Et ideo + + musice + primo + primo + musice + + cum + estiacus colophonius + + + + ostiatus colophonius + estimatus colophimus + estimatus colofonius + existimatus + colofonius + estyrginatus colophonius + stiatiis elephinus + + + decimam + quartam + 4am. + 10am. + cordam + .9. + cum + preexistentibus + addidisset + + + + , + thimoteus + + + + + + + + + + superveniens + superveniens et + + + milexius + + + + + + + + xiam. + + aliam + nullam + unam + + + adiunxit + adiunxerunt + , + Boeth. + De inst. mus. + I.20 (ed. Friedlein, pp. 208–209) + ita ut + signato + significando + + + uero + ut + sit + medio in hiis puta sexta + + consonet + consonat + dyapason.

+

+ Nosce + Notandum + , ut + indicatum + + iudicatum + dictum + + + est + + + + superius + finis + , .7. + + antiquitus fuisse cordas + fuisse cordas antiquitus + fuisse cordas + + + septem planetarum, + + secundum + + + boecium, + + imitatione + + + imitationem + immutatione + mutatione + , + ita + ea + ut + suprema + + supra + earum + ypate + ypatem + reddatur saturno propter tarditatem motus + Boeth. + De inst. mus. + I.20 (Friedlein 206, ll. 10–1, 15–6) + utrobique. Infima lune + ceu + seu + sicut + nete ob eius + uelocitatem + velocitatem motus + . Que autem + intermedio + intermedie + in medio + in intermedio + ordine planetarum + attribuantur + + atribuatur + attribuentur + attribuebantur + + + mediis + aliis mediis + medicinis + iuxta + eorum + earum + + + mediocrem + mediocrum + mediocritatem + cursum. Et id quidem .32°. + apparebit + + et magis + magis et + et maxime + + + .44° + .44° problematum + + + . + + etcetera + sequitur 26. + problema 19e. particule. +

+
+ +
+ + Uigesimumsextum + problema + 26m + Vigesimumsextum. + vigesimum + sextum. + 25m. + problema. + + +

+ PROPTER QUID IN ACUTO + + PROPTER QUID IN ACUTO DISCORDANT PLURIMI? + UTRUM QUIA FACILIUS ACUTUM DIMITTERE QUAM + GRAUE? + AUT QUIA PEIUS GRAUI? PECCATUM PEIORIS OPERATIO + . + + Uigesimum sextum + problema etcetera. + + + Quare + Querit quare + + + plurimi + plurimum + cantantes + vna discordant + amplius + + + amplius discordant una + una discordant + in acuto quam + in + + graui?

+

+ + Deinde. + + + UTRUM. + AUT. + + + Soluit + Soluit et + + + assignans + assignando + assignat + duplicem causam probabilem prius, dicens + id + illud + + ideo + esse + quoniam + quia + + + leuius est + leuius + facilius et leuius est + + + dimittere + + + + acutum + + ? Et recessus ab eo sepius + contingit + conuenit + quam a graui propter breuitatem temporis + existentie + existentis + ex natura + ipsius, propter quod + dictum est + dictum + + + 22°. + 21°. + : quod in uelocitate + peccatum + rectatum + + + plus + magis + existit. Non tamen ut + expositum adeo est + expositum adeo + expositum est adeo + + + manifestum + magnum + + + ut + + + + peccatum + pretactum + + + in + et + graui, propter quod + apparet hoc + apparet hic + hoc quod apparet + in nullo illi + aduersari + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit assignans + Soluit assignando + Assignat + aliam causam + necessariam magis + magis necessariam + , + dicens + dicit + + + id + illud + hoc + ideo + esse + quoniam + quia + + + peccatum + pretactum + predictum + quod + committitur + + + + conuertitur + in acutum + cantando + cantum cantando + + + deterius + est + + + + seu + et + + + difficilius + difficilius est + quam peccatum quod + committitur + + in + graue + grauem + grauius + cantando + + . Cum + molestius + + molestius sit + cantare acuta quam + grauia + grauia + utrum + u + + + + .37. + + . + + Peioris autem + Peioris + Autem peioris autem + + + seu + + + + difficilioris + difficiliorum + actus peccatum + maius + maius est + + . + + Et + ideo + + + + in + + ipso amplius accidit + discordari + discordare + . Quod enim + difficilius + difficilius est + agere magis + contingit + conuenit + + peccato + corrumpere + + corpore + , ut aurum arte construere. + Et id etiam .46. + + rescribetur + rescribetur capitulo + + + . + + et cetera + sequitur 27. + problema. +

+
+ +
+ + Uigesimumseptimum + problema + 27m + vigesimum septimum. + Vigesimumseptimum + 26m. + problema. + + +

+ PROPTER QUID AUDIBILE + + PROPTER QUID AUDIBILE SOLUM HABET SENSIBILIUM? ET ENIM, IN QUANTUM + ABSQUE RATIONE, CANTUS TAMEN HABET CONSUETUDINEM, SED NON COLOR, NEQUE ODOR, NEQUE HUMOR HABET. + AUT QUIA MOTUM HABET SOLUM UNIFORMEM, QUO SONUS + NOS MOUET? HUIUS ENIM ET ALIIS INEST, MOUET ENIM ET COLOR UISUM, SED + CONSEQUENTEM HUIUS SONO SENTIMUS + MOTUM. HEC ENIM HABET SIMILLIMA IN RITHIMIS ET IN SONORUM ORDINATIONE ACUTORUM + ET GRAUIUM, NON IN MIXTIONE. SED CONSONANTIA NON HABET CONSUETUDINEM, IN ALIIS + AUTEM SENSIBILIBUS HOC NON EST. + MOTUS AUTEM IPSI OPERATIUI SUNT, OPERATIONES ENIM + CONSUETUDINIS SIGNIFICATIO EST + . + + Uigesimum + septimum problema etcetera. + + + Quare + Querit quare + audibili + tantummodo de numero sensibilium hoc inest + tantummodo hoc inest + de numero sensibilium + tantummodo sensibilium hoc inest + tantum de numero seu suum hoc inest + ? + + Quia + Qui + Quod + etiam in quantum est cantus sine + + ratione + solo + solummodo + sono + , + tamen + cum + tantum + auditus + sensibili + sensu + , quia hec scientia, ut visum + est + + , + perficitur + percipitur + ratione + et + ut + sensu. Quis + eum + cum + enim + + + reddit sibi + sibi reddit + reddit + consuetum, + non + et ideo + autem + color odori aut sapori + + colori audiri aut sapori + color odori et sapori + colorem aut odorem aut saporem + coloris odoris aut saporis + id adest quod ea fiant consueta + in + + tantum ut + que + + + + audibilia + audibili + .

+

+ + Deinde. + + AUT. Soluit et + primo tangit + tangit primo + primo assignat + + partem + cause + + + + ratione + + + + audibilium + audibilis + , + .2° + secundum + ex + parte + parte et + + + eorum + eorum ex + quibus + acquiritur + adequatur + + + consuetudo + consuetudo ibi + consuetudo .2a + consuetudo .2a + ibi: + + MOTUS + AUTEM + ERGO + + . Dicit + igitur + ergo + primo + id + idem + esse quoniam audibile solum habet motum vniformem, + propter + quod + quem + + sonus habet nos + mouere + amouere + . + + + Mouet enim potentiam + Potentiam enim mouet + audiendi, cum sit + virtus + virtus motiua + passiua, et eam deducit in + actum + actu + acutum + , + + ut apparet + ut patet in + + + 2° + 3º + + de anima. + Arist. + De an. + II.12, 424a l. 19 (Cf. 416b l. 33 and 419b l. 5) + + Sed hic + modus + motus + mouendi + aliis etiam inest + aliis inest etiam + obiectis + sensuum + sensibili + , nam color mouet + sensum + visum + sensum uisus + + + et in + actum + acutum + deducit; + et + et et + similiter odor et sapor. + + Sed + Hoc + in + auditu + auditu 8 + + + ultra hoc + ultra + universaliter + existit + quod + quia + + + percipiendo + percipiendo et + sonum + sentimus etiam motum + etiam motum sentimus + percipimus etiam motum + sentimus et motum + quo mediante defertur ad aures + quod + quam + + + etiam non solum + non solum etiam + etiam non + accidit in + sono + sono in + sono uel + sompno est + + + communi + + , uerum + etiam + + + + similiter + communiter + + + se + si + habet in rithimis et in + coordinatione + + + eo ordine + seu + coniunctione + coniectione + grauium sonorum et acutorum ad inuicem + vnius + vnus + humimus + quasi iuxta alium, ut non reddatur + vna + ulla + uera + recta + + commixtio. + + Quia + Quoniam + in ea + non id accidit + id non accidit + non accidit id + , + cum sonus + consonus + adeo + vniformiter + uniforma + + + aerem et suauiter + et suauiter aerem + aera et suauiter + aerem + + + concitet + excitet + continet + + concurrit + ycurit + ut aures + universaliter + uel + nichil + percipiant + sensibile + + ex + aeris + aere + motu. Et + ideo + + videmus infirmos + huius + huiusmodi + + adeo + melodioso + + + + melodiose + + + delectari + delectari sono + , non autem + priori + + priori scilicet difficiliori + + + + eum + + cum + + + fugientes + fugiente + et maxime + galleatam + + + + galeanterra + habentes passionem seu + ouum + + animam + . + Et ideo consonantia + sic + sit + ac + armonica non recipit consuetudinem, quemadmodum + neque + + alii pretacti + sensuum + sensum + sensu + , + cum nichil + + cum nichil aliud + uel naturaliter + sensibilius preter perceptionem speciei + sonabilis + sensibilis + subtilis + percipiatur ad auditum + peruenire + perueniente + , quod + et + + in reliquis dictum est + sensibus + sensibilibus + accidere. + Sed + Seu + in aliis + sensibus + sensibus pariter + sensibilibus + + , + ut + + + + + color odor et sapor + color sapor et odor + sapor color et odor + + colore odore et sapore + colori odori et sapori + coloribus odoribus et saporibus + coloris odoris saporis + , non inest, ut + eorum sumantur + + sumantur eorum + eorum seruatur + species cum aeris + motus + motu + + perceptione.

+

+ Nota + Notandum + quod sicut duplex + est mixtio + est vni uisio + + , + ut + vna + + ad sensum + quedam + + + + et alia + alia + + ad intellectum, id est uera et non uera, ita + et duplex grauis et acuti + duplex acuti et grauis + ut duplex grauis et acuti + et duplex est grauis et acuti + + + permixtio, taliter + permixtionaliter + ut ex + vna reddatur + una reddatur vna reddatur + vna tendatur + + + uera + vna + + consonantia, ex + altera uero + alia vero + apparens magis.

+

+ + Deinde. + + + MOTUS. + MOTUS AUTEM. + Τangit causam sumptam + ex secunda parte + ex alia parte + dicens + cum + Est + + + igitur + ergo + + + visibilia + audibilia + + + ut + + ad multum + recurrant + retractant + + + ad + + organum cum + motu + motus + aeris + sensibili + sensibilis + sensibiliter + , et + + motus + motus aeris + + + sint + sicut + sic + + + operatiui + sensicun + + + . + Operationes enim fiunt per + eos + eas + omnes + + + + actiones + aptiones uel aptiones + proprie dicte, + cum + + + + + proprium actionis + proprius actionis + proprium + + + sit + sic + esse in + motu + motu ut + , + + auctor + + auctorum + + <app> + <lem wit="#γ #κ #Ea #Py #Vc #m #v"><num type="cardinal" value="6">.6.</num></lem> + <rdg wit="#Nu" ana="#subtractive"/> + </app> principiorum. + Ps.-Herm. Tris. + De sex re. princ. + II.1 + + + Et + + signum + consuetudinis + et signum consuetudinis + + + acquirende + acquirendo + uel + acquisite + + sit operatio, nam + consuetudo + est + est in + multotiens + aliquid + aliud + id + facere. + + 13° + .21a. + ut 13° + .21a. + 13 + .21a. + 13°. + 23e. + + Ps.-Arist. + Prob. + XXI.14, 928b ll. 25–26 + Consuetudo + siquidem + + + + adipiscetur magis + magis adipiscetur + in + audibilibus quam in ceteris + audibilibus quod in ceteris + audibilibus quam ceteris + ceteris audibilibus audibilibus quam in + ceteris + + + sensibilibus + sensibus + , + et id tangetur etiam 29 + et id tangetur et 29º + et id tangetur etiam 20° + + , + nosce + notandum + quod causa + fundatur aristoteles + aristoteles + fundatur + + + super + supra + hoc: + quod + + + + generatio + + genera + genero + + + soni et uocis + uocis et soni + consistit in quodam + fieri et + motu et + + transmutari. Sunt + namque + enim + de genere successiuorum entium, cum + sunt + sint + in motu, et + fiunt + fuit + + + tantum + in tantum + + + color + color vero + odor + et + + sapor de + manerie + numero + permanentium, que post factum + habent esse + esse habent + habet esse + esse remanent + et non + prius + plus + . Quod + indicat + inducat + denotat + + + aristoteles, + + + quia singulariter de + anima + 2° + quia singulariter 2° + de anima + quia 2°. + de anima + quia similiter de alia sermo + + + determinauit + determinant + de + modo generationis + generatione + + + soni et uocis + vocis et soni + et uocis + + , + Arist. + De an. + II.8, 419b l. 9 + + et + Et modo inmutandi et + non + aliorum + + , + sed inde sensu et sensato + sic de aliis + . Cum + igitur modus + modus igitur + igitur motus + ergo modo + + generationis + soni et + soni + et + + + perceptionis + preceptionis + + + ut ad + ad + + multum + conueniat + conueniant + contingit + cum operatione + siue + seu + actione, que + fit + sit + sit in + mediante motu + qua + quam + que + quia + consuetudo ut + dictum + dictum est + + + acquiritur + + adquiratur ad + adquantur + + + visibilia + visibilis + audibilia + sensibilia + + pre aliis + sensibilibus + sensibus + sensibus uel sensibilibus + + + reddentur + redduntur + reddetur + consueta, ut + ostendunt + ostendit + + + eris + + et + nauium + + manifestum + + + malleatores + + + + + non audiendo, + quod + quia + + + in + + illis + non + + non ut + + + acquiratur + acquiratur etiam + acquiratur audibilia + pre aliis sensibus redduntur consueta ut ostendunt quod in illis non + acquiritur + consuetudo + utcunque + uterque + utrumque + . + + et cetera + sequitur 28. + problema 19e. particule. +

+
+ +
+ + Uigesimumoctauum + problema + 28m + vigesimum octauum. + Vigesimum octauum. + 27m. + problema. + + +

+ PROPTER QUID LEGES + PROPTER QUID SECUNDUM LEGES + + PROPTER QUID LEGES APPELLANTUR QUAS CANTANT? + AUT QUIA PRIUSQUAM SCIANT LITTERAS, UIDERUNT LEGES + NON LATEANT, QUEMADMODUM IN AGATHUSIS AMPLIUS CONSUEUERUNT? ET POSTERIORIBUS + IGITUR CANTIBUS PRIMOS IDEM APPELLAUERUNT QUIDAM PRIMAS + . + + Uigesimum + octauum problema. + + + Quare + Querit quare + + + illi + aliqui illi + cantus quos primitus + aliqui cantant + cantant aliqui + obliqui cantant + leges + appellantur + appellant + . + + Nosce + Nota + + + quod + + + + per + + leges hic audio cantus in quibus + mox aliqui + aliqui mox + statim aliqui + + + edocentur + docentur + cum incipiunt cognitionem habere, sicut illi + qui ordinati + ordinati qui ordinati + sunt a lege ut + cantentur + cantetur + cantent + legaliter. + Tamen + Cum + , + ut visum + est + + + .15. + + , in laudem dei + + + ceu + seu + in lege nostra + + + + docentur + docent + + + pueruli + + + + salutationem + salutatio neque + virginis + uel + aut + + + huius + huiusmodi + cantare.

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit dicens + Soluit dicit + Dicit + causam esse quia cantantes leges + ceu + + seu + sicut + + + puerili + + pueri + antequam aliquid sciuissent de litteris et cantibus choricis, iam + uiderant + uiderunt + uideant + leges + seu + ceu + + + audiuerant + + + + + scientes etiam + etiam scientes + scientes + scientes et + + + ipsas + ipsos + cantare ad hoc ut + non + + lateant. + Sed + Sed ut + Seu + + + reddantur + redduntur + declaratum + manifeste + note + uoce + nete + , + uelut + ultra + illud + uel + uolox + + uolt' + uoluit + + + + principia + in + et + scientia + et + uel + + + locus + uelud + + ianue in domo + Arist. + Met. + II.1, 993b ll. 4–5 + + ut ostensum + est + + + + .18 + 18ua. + problemate 8uo + supra + + . As cited in d'Abano's commentary on Book + XVIII, Problem 8, where the paraphrased quotation begins with + "nota" + + + Nam quod primitus + discitur + dicitur + optime + imprimitur + + cum anima sit tunc + ceu + seu + sicut + tamquam + tabula rasa, et + perfecte + bene + + + retinetur + retinere + , et + huius + huiusmodi + vnius + + + quidem + quedam + consuetudo + potissime fuit + fuit potissime + fuit + apud + quosdam nominatos + nominatos quosdam + + + agathyrsos + + + + + + + + + . Quod autem + primum quis + primus quis + primum + primitus + adipiscitur prius + nomen + notum + non + + + suscipit + + suscepit + , + tanquam + + + + notum + motum + natum + cum anima nomen + imponatur + imponat + imponat ut + + + cognoscit + cognoscat + cognoscet + . Itaque cum + alii + aliis + , cantus + ut + + + + chorici + theorici + siue conuersiui et vniuersaliter + tragici + turgici + , + sint + sunt + sit + sicut + posterius cantibus legalibus + cantati + cantari + , puta cum + sciuerint + sciuerunt + litteras et + fuerint + fuerunt + fuerit + adulti leges, + primos cantus + cantus primos + seu primas melodias quod idem + est + etiam + + + appellarunt + appellauerunt + , sicut + scientie + scire + de sermone cum prius + instruantur in hiis pueri + instruantur in hiis puer + instruantur in eis pueri + dicuntur primitiue. + + etcetera. + sequitur 29. + problema 19e. particule. +

+
+ +
+ + Uigesimumnonum + problema + 29m + vigesimum nonum. + Vigesimumnonum. + 28m. + problema. + + +

+ PROPTER QUID RITHIMI + + PROPTER QUID RITHIMI ET CANTUS, UOX EXISTENS, CONSUETUDINIBUS + ASSIMILANTUR, SAPORES AUTEM NON, SED NEQUE COLORES ET ODORES? + AUT QUIA MOTUS SUNT QUEMADMODUM ET OPERATIONES? + IAM UTIQUE ACTIO QUIDEM MORALE ET FACIT CONSUETUDINEM, SAPORES AUTEM ET + COLORES NON FACIUNT SIMILITER + . + + Uigesimum nonum + problema etcetera. + + Repetit + 27m problema dicens + .27. partem + dicens + .27m. + dicens + .27m. + particulariter dicens + problema + + + quare rithimi + + , quantum ad speciem musice + rithimicam + nebincam + , et cantus et uox + pronunciatiua + + + pronunciatam + + quantum ad armonicam + similitudinem + similem + + + + acquirunt + + adquirit + + + consuetudinis + consuetudines + consuetudinem + similitudinem consuetudinis + ? Redduntur enim consueti, sed sapores + aut + uel + + + color uel odores + colores uel odores + odores vel colores + + non + proportionantur consuetudini.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse + quia + quoniam + motus + qui + quia + sunt circa sensibilia + auditus + + + + tanquam + + operationes + existunt + existant + . Quod + declarat + declaratur + quia sicut + videmus + nos videmus + in actione morali quod actus eius + inducit + inducunt + consuetudinem et + inclinationem + delectationem uel inclinationem + ad + istud + + id + illud + + illud + id + uel + ad + + + + illud + id + aliquid + agendum, ita + similiter + + est in + sensibus + sensibilibus + auditus. Ex multotiens + enim audire + audire enim + quidem audire + + + vnum + in vnum + nimium + cantum inducitur consuetudo, + qua + que + etiam + in + habituata cantus + ille + + iste + + + reputatur + redditur + delectabilis, + etiam + et + si non sit secundum ueritatem, non autem circa sensibilia aliorum sensuum, + ut declaratum, accidit + ut declaratum est, accidit + . Et hoc + est + etiam + + quod subditur + sapores + saporem + sapor + + + qui + que + sunt sensibilia; gustus et odores qui + olfatus + + olfaciunt + non id + operantur + operatur + , quod ex ipsis consuetudo + consimilibus + similiter + consimiliter + + + audibilibus + audibilis + adeoibilibus + audientibus + + + acquiratur + + . + + etcetera + sequitur 30. + problema 19e. particule. +

+
+ +
+ + Trigesimum problema + 30m + Trigesimum. + trigesimum + problema. + 29m. + problema. + + +

+ PROPTER QUID NEQUE YPODORISTIUM + PROPTER QUID NEQUE + PROPTER QUID YPODORISTIUM + + PROPTER QUID NEQUE YPODORISTIUM NEQUE YPOFRIGISTIUM NON EST IN TRAGEDIA + ROTATIUUM? + AUT NON HABET CONUERSIUUM? SED A SCENA, IMMUTATIUA + ENIM + . + + Problema .30m. + etcetera. + + + Quare + Querit quare + + + ypodoristium + + + + + et + 7. + + + ypophirgium + + + + + + cantare + non + ut + + + est + + + + rotatiuum + + + rotatum + rota tantum + et + conuersiuum + + in + tragedia + + , + ubi + nisi + + + obseruentur + obseruantur + diuersitates sonorum secundum + graue + grauem + et acutum + ascensione + + + + et + ac + descensione per circulos + casuum + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + QUANDO. + Soluit dicens causam esse + quia + quia ut + + + huius + huiusmodi + cantare non + habent + habet + , ut expositum + est + + , + conuersiuum + masiuum + conuersionum + in quo magis + attenditur + + + ad + cantus + cantum + quam ad uerba. Sed potius + huius + huiusmodi + cantus est + immutatiuus + immitatiuus + imitatiuus + imutatiuus + , + qui + quod + quam + dicitur + ascena + + contentus sub legibus et comedia, ut visum + est + est in + + + .15., in + quo + + amplius + attenditur + + + ad verba quam ad + cantum + cantus + , et + id + illud + amplius + apparebit + + + + 48° + 4º + 8º + .

+

+ Nosce + Notandum + ut apparet + + .8. + + <app> + <lem wit="#π #Ma #Nu #Px #Va #Vz">politicorum</lem> + + </app> + aristotelem + .8. + polliticorum + aristotelem + .8. + polliticorum quod + .8. + phisicorum + aristotelem + + Arist. + Pol. + VIII, 1324b ll. 12–18 + tangere tres + + cantus modos + modos cantus + cantus mentis + : precipue + phrigistium + + + + + philigistium + , + doricum + + doricum uel doristicum + choricum + , et + lidium + + . + Phrigistius + + + + Frigisticus uel phigistius + est + troianus + + , + qui + + que + est + cantus + + + + agrestis + terrestris + + + incitatiuus + et incitatiuus + imitatiuus + mutans + + + in + ad + + + iram + + et passionem, + ceu + seu + + + qui + que + + fistule + in quam + in quem + in quo + in qua + in quod + inquit + nunquam + + + + concidit + occidit + decenter + ditirantibus + + + + + + + quid dithitambis + qui dithirambus + ex tyranbus + . + Dorista + Doristas + siquidem + maluaficiacus + + + + maluafiati cuius + cantus laudabilis + + + tanquam + + tam + + + stabilis + stabilis et + + + virilis + uiribus + + , + + + Arist. + Pol. + VIII, 1324b l. 12 + + + + + unde .48. + unde .40. + unde 41. + + + magnificus + stabilis + stabilis et + stabilisimus + + + + + cytharicissimus + + + + + cithantissimus + omnium + + + Ps.-Arist. + Prob. + XIX.48, 922b l. 15 + + + et + + + + ceu + seu + omnium + superhabundantiarum + + + + + + mediis + medius + laudatus in quo + pueruli + + sunt + edocendi + + . + Arist. + Pol. + VIII, 1324b ll. 12–18 + + Lidius + + + + + + quidem dicitur + dicitur quidem + siquidem dicitur + dicitur + a + chorebo + + + + + + + + lidorum + + rege. Qui omnibus laudabilior + est + + . + + Cum + Cum enim + + + sit + sint + + + aliorum + alium + + + medius + mediis + , tria in se + continet + continens + quod medium + rationem habens + habens rationem + commune habens + uirtutis + quod + et + decens + et + et quod + + + possibile + possibile et + , + Arist. + Pol. + VIII, 1324b ll. 32–34 + + que + quod + in cantu et maxime puerorum sunt obseruanda. Unde + + boecius + musice + .4. + boecius + .4. + musice + + si quis totas constitutiones + faciat + faciet + facit + acutiores uel + graues + grauiores + totas + remittat + + remittit + dyapason consonantie species, + efficiet + efficiat + + modos septem + + ceu + + seu + sunt + ypodorius + + + + + ypofrigius + + + + + ypolidius + + + ypodolius + + + dorius + chorius + polius + + + + frigius + + + + + + lidius + + + + + mixolidius + + + + + + Boeth. + De inst. mus. + IV.15 (Friedlein p. 342, ll. 10–14) + + ypermixolidius + + + + . Duplat + igitur + ergo + enim + 7 + uel triplat + quod aristoteles + boecius + quod aristoteles et + boecius + quod aristoteles + boecius + .31 + + . + + et cetera + sequitur 3.1; + problema 19e. particule. +

+
+ +
+ + Trigesimumprimum + problema + 31m + trigesimum.primum + Trigesimum primum. + Trigesimum + problema. + + +

+ PROPTER QUID CIRCA FRINICHUM + PROPTER QUID CIRCA + + PROPTER QUID CIRCA PHRINICUM + FUERUNT MAGIS DULCE MELODIA? + AUT PROPTER ID QUOD MULTIPLICES SUNT TUNC CANTUS IN TRAGEDIIS METRORUM + ? + + Pricesimum primum problema + + + Quare + Querit quare + est quod + apud phrinicum + + + apud plinitum + apud finitum + circa frinichum + apphimitum + id est caput frontum + , + qui + quod + est modus + cantantium + cantatiuum + cantantium uel cantuum + quorundam, + melodie + melodia + + + fuerunt + fiunt + finitur + magis suaues quam + apud + + amplius + + + alios + alias + ?

+

+ + Deinde. + + + AUT. + AUT QUIA. + APUD. + + + Soluit dicens + Soluit dicit + causam esse + quoniam + quia + + cantus + apud + + + + eum + cum + enim + fuerunt + multiplices et + differenter + differentes + + + compositi + appositi + propter + quod + + + + secundum plurimum fuerunt + fuerunt secundum plurimum + + + in + tragediis + + + + metrorum + + metris + . Tales autem sunt suaues + maxime, cum eorum + sit + + sunt + principaliter + finis + + iocunditatem inducere. + + et cetera + sequitur 32. + problema 19e. particule. +

+
+ +
+ + Trigesimumsecundum + problema + 32m + Trigesimumsecundum. + trigesimum + secundum + 31m. + problema. + + +

+ PROPTER QUID DYAPASON + + PROPTER QUID DYAPASON APPELLATUR, SED NON SECUNDUM NUMERUM DYAOCTO, + QUEMADMODUM ET DYATESSERON ET DYAPENTE? + AUT QUIA SEPTEM FUERUNT CORDE ANTIQUITUS? POSTEA EXTRAHENS TERTIAM, TERPANDERUS NITEM + APPOSUIT. ET IN HOC APPELLATA EST. DYAPASON, SED NON DYAOCTO, DYASEPTEM + ENIM ERAT + . + + Problema 32m. + etcetera. + + + Quare consonantia + Querit quare consonantia + + + + dupla + + + + dyapason + + siue per totum appellatur, + et non dicitur + non dicitur + + et omnino dicitur + + + dyocto + + + + + propter numerum + octonarium + + + octogenarium + , in + quem + quam + quod + videtur + terminari + terminatur + + + in + + + + parigraphia + + + + + + + + proportionum + portionum + ? + Terminatur + + + + enim + eius + super + octo + scilicet + . Et + subdit + tangit + + + huius + huiusmodi + hic + eius + + + motiuum + + dicens + quemadmodum + quod deinde + + + dicitur + dicitur in + dyatesseron, quia + finitur + terminatur + in + 4° + 8uo + loco in predicta descriptione, aut quia + fit + finitur + in + quatuor + 8 + cordis musice. 5°. et similiter dyapente + siue per 5°. + + + + terminatur + finitur + in 5° + + loco + + + + uel in 5. + + constat + stat + + + cordis + locis + + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse + cur + cum + dyapason dicitur et non + dyaocto + + + + dyoto + + + quia + qui + corde + instrumentorum antiquitus + .7. tantum + tantum septem + fuere + antiquitus instrumentorum 7º. tantum fuere + instrumentorum antiquitus tantum .5. + .7. fuere + instrumentorum antiquitus 7 fuere + . Postmodum superuenit + tripandius + + + + , + qui + que + quia + + + tertiam + illam + subtraxit + cordam + cordas + + + ut + + paramese + cuius + eius + quidem loco + nitem + + + + + apponit + apposuit + , ita ut + non + + videatur + mutasse + immutasse + numerum, + sed + secundum + + proportionem + potius + passio + , et propter hoc appellata est dyapason, + quoniam + quia + ex tali mutatione + optima + + opposita + + + adinuenta est + est adinuenta + inuenta est + adiuncta est + consonantia. Non itaque + dicitur + dicta est + + + dyaocto + + , + cum corde + + non + sunt + sint + nisi + .7. + octo + Potius enim + dicendum esset + debent esse + deberet esse + deberet dici + dyaseptem, cum + tantum + tanto + isto + numero + modo + + + + imitando + immutando + mutando + qui + planetarum + plerum + + + numerum ut uisum est + ut uisum est numero + numerum ut uisum + numero ut uisum + + + contineantur + contineant + + contineantur imitando numerum + planetarum vt uisum est + . + Quia + Quare + + + tamen + tam + cum + + + corde prius .7. + prius corde .7. + corde .7. + prius + corde prius + + + fuerunt + fuere + + + ut + non + + + apparuit + apparebit + + , + pauciores + + paucitores + pluresque + demum + deinde + + + + adinuente + adinuenientem + adinueniendo + adueniente + , + tamquam + + + nomen stabilius, + elegerunt + + elegerant + potius dyapason + dicere + + seu per totum et perfectum quam dyaseptem, + tanquam + + nomen magis + denotatiuum + + denotatur + denominatiuum + determinatum + deuotatiuum + essentie ipsius. + + Et + Et hoc + Ut + + + tactum quidem + tactu quidem + quidem tactum est + + + .25. problema + 25° problemate + est hoc 25º problemate + est hoc prius + + + . + + et cetera + sequitur 33m. + problema 19e. particule. +

+
+ +
+ + Trigesimumtertium + problema + 33m + trigesimum tertium. + Trigesimum quartum tertium. + 32m. + problema. + + +

+ PROPTER QUID CONSONANTIUS + + PROPTER QUID CONSONANTIUS EST IN GRAUE QUAM A GRAUI IN ACUTUM? + UTRUM QUIA A PRINCIPIO FIT INCIPERE? + MEDIA ENIM ET PRINCIPALIS ACUTISSIMA PARACORDE. + HOC AUTEM NON A PRINCIPIO, SED A FINE. + AUT QUIA GRAUE AB ACUTO FORTIUS ET MAGIS UOCALE + ? + + Problema 33m. + etcetera. + + + Quare + Querit quare + in cantu + maior extat + extat maior + maior existit + + consonantia + si + sed + incipiatur ab acuto et + terminetur + terminatur + preterminetur + in + grauem + grauim + graue + , quam si a graui + preincipiens + incipiens + terminetur in acutum?

+

+ + Deinde. + + + UTRUM. + UTRUM QUIA. + Soluit + et assignat + assignando + duplicem causam dicens primo + id + illud + esse quia + contingit + + conuenit + incipere + a + in + principio rei in qualibet re, modo + ipsum acutum + acutum ipsum + + + tenet + retinet + + + locum principii + principium locum + locum principaliter + principium + in + instrumento + ipso instrumento + . Nam prime corde minores sunt ille + que + qui + qua + + + sonum reddunt + reddunt sonum + sonum reddunt sonum + reddunt + acutum, + a + in + quibus + oportet + + + incipere, ut ordo seruetur naturalis in arte.

+

+ + Deinde. + + MEDIA. + Remouet + dubitationem + dubium + , quia + crederet + diceret + aliquis + quod + + ab omni corda acuta + esset + esse + incipiendum. + Unde + + + + id + illud + + + remouens + remouet + + + dicens + dicit + quod + + + + corda media et principalis est + corda media principalis est + corda principalis et media est + corda media est principalis et + et principalis est + + acutissima + seu + sive + fortissima + peracorde + peracordis + per .7. + cordas + , id est + cordis + corde + , iuxta ipsam + existentis + existentes + existentibus + . Unde + hec + hoc + non + est + + + + tangenda in principio + in principio tangenda + , sed potius in fine, propter eius excessum, + ista + ita + ita quod + siquidem aut est media + positione + pone + recte + ceu + seu + sicut + mese, + aut + autem + virtute + puta + pauca + sicut + + + ypate + + , cum in + mediam + media + + + condescendit + + condescendat + cum + nete + + , ut + uisum est + uisum + + 20°.

+

+ + Deinde. + + + AUT. + AUT ET. + + + Assignat + Soluit assignans + + + aliam causam + causam aliam + aliam + dicens + id etiam + id + ideo + + + esse + + + quoniam graue + incipiens ab acuto + ab acuto incipiens + descendens ab acuto + + + fortius + + est. Diutius enim + permanet + + + et + magis + + uocale existit quam econuerso. Hoc autem facere + magis est + est + + + connaturale + contra naturale + contra naturalem + cum naturale + + + ac + hoc + etiam + morale + mortale + + + quam + quod + quidem + suum contrarium. + Videmus enim in operibus nature quod ipsa in principio a leuibus et + debilibus incipit, non enim tunc est, operosa sed in fine, + + ut + dictum est + dictum + dicatur + + + 10a. + 20. + + + + Ps.Arist. + Prob. + X.45, 895b l. 27 to 896a l. + Et ideo + est videre + videndum que + optimos cantatores naturam + imitantes + + + + mutantes + #Pp could be imitantes or mutantes + + + + hoc + hec + + + seruare + obseruare + + + , + quod + cum + in acuto leuiter incipientes + in + + + + grauem + graue + postea conterminant, et non econtra concordant. + + et cetera + sequitur 34. + problema 19e. particule. +

+
+ +
+ + Trigesimumquartum + problema + 34m + trigesimum quartum. + Trigesimumquartum. + 33m. + problema. + + +

+ PROPTER QUID BIS QUIDEM + PROPTER QUID BIS + + PROPTER QUID BIS QUIDEM PER ACUTOS. ET BIS DYATESSERON NON CONSONAT, BIS + DYAPASON AUTEM? + AUT QUIA BIS PER ACUTOS NEQUE BIS DYATESSERON EST, + QUOD AUTEM PER QUATUOR AUT PER QUINQUE + ? + + Problema 34m. + etcetera. + + + Quare + Querit quare + + + bis paracutos seu bis paracuta + bis paracuta seu bis paracutos + bisperacuta + bis paraclitos seu bis paracuta + id est bis dyapente + et + seu + bis dyatesseron + siue bis per quatuor + + id est + in + dyatesseron + + non + consonant + consonat + + + et + id est + + + simphoniam + + constituunt, dyapason uero concordat? Dicitur autem bis paracutos + + + dyapente + + , quia constat ex + duobus + duabus + + + acutis + + + + et + in + + + vno + vna + non + graui + seu + siue + ceu + breuibus + et + aut + + + longo + longa + , more + dactili + + + + + + + .

+

+ + Deinde. + + + + AUT. + AUT QUIA. + Soluit dicens causam esse quoniam + bis paracutos + + + + + uel bis dyapente + uel + et + + + bis dyatesseron + dyatesseron + non est dare, quod constituant + aliquam + aliqualiter + + consonantiam, + quoniam + illud + id + quod per quatuor se habet aut per + quinque licet + proportionem + proportione + + + constituant + constituat + constituant aliquam consonantiam + et per consequens consonantiam, ut per quatuor + quoniam illud quod per + 4 + ut per quatuor + dyatesseron + uel + uel per + + quinque dyapente. + + Quando enim + Quando + epsa enim + Quoniam + + + minus extremum prime, et + minus extremum prime ad + extremum prime minus + minus + + + extremum magis + extremum maius + + 2e comparantur ad + inuicem nulla consonantiarum resultat inde, ut videbitur + .41°. + .11°. + , ubi + repetitur + reperitur + + + idem + id + inde + amplioris expositionis gratia. + + et cetera + sequitur 35. + problema 19e. particule. +

+
+ +
+ + Trigesimumquintum + problema + 35m + trigesimum quintum. + Trigesimum quintum. + 34m. + problema. + + +

+ PROPTER QUID DYAPASON + + PROPTER QUID DYAPASON OPTIMA CONSONANTIA EST? + AUT QUIA IN OMNIBUS TERMINIS RATIONES SUNT, + ALIORUM AUTEM NON IN OMNIBUS? QUONIAM AUTEM DUPLEX NITE YPATES. QUOT NITE DUE YPATEM UNUM, ET QUALIS YPATE DUO NITE QUATUOR, ET + SEMPER ITA. + MEDIE AUTEM EMIOLIA. QUOD ENIM PER QUINQUE + EMIOLIUM NON IN OMNIBUS NUMERIS EST. NON + ENIM UNUM MINUS, MAIUS TANTUM AUTEM ET ADHUC MEDIUM. QUARE NON TOTA AD TOTA + COMPARANTUR, SED INSUNT PARTES. + SIMILITER ET IN EO QUOD EST PER QUATUOR SE HABET, EPITRICON ENIM EST QUANTUM INCIDERE QUOD ET ADHUC IN QUATUOR + EPITRICON EST. + AUT PERFECTISSIMA QUE EST EX UTRISQUE, ET QUIA + MENSURA MELODIE? PER TOTUM ID QUOD FERTUR QUE EST SECUNDUM MEDIUM MOTUS + FORTISSIMUS, INCIPIENTE AUTEM ET FINIENTE MOLLIOR. QUANDO AUTEM FORTISSIMUS + MOTUS, ET UOX ACUTIOR EIUS QUΟD FERTUR, PROPTER QUOD ET CORDE TENSE ACUTIUS + SONANT, UELOCIOR ENIM MOTUS FIT. + SONUS AUTEM AUT AERIS AUT ALIUS CUIUSDAM MOTUS, + CAUSA QUE EST PER MEDIUM PORUM ACUTISSIMUM OPORTET FIERI. QUARE SI HOC NON + ACCIDIT, NON ERIT MOTUS ALICUIUS + . + + Problema 35m. + etcetera. + + + Quare + Querit quare + dyapason est optima + et + + dulcissima consonantiarum?

+

+ + Deinde. + + + + AUT. + AUT QUIA. + Soluit + et assignat + + assignando + dicit et assignat + dicens + + + duplicem causam + causam esse duplicem + , + + secunda + .2a. + ibi + + AUT. + + Adhuc + Ad hoc + Item + + + primo + post + dat causam + + + + quare + quare est + optima consonantiarum + + , + dicens + dicit + + + illud + id + ideo + esse quoniam proportiones + secundum + per + quas + constituitur huius consonantia + constituitur huiusmodi consonantia + huius consonantia constituitur + + + sumuntur + + sumitur + ex omnibus terminis summis numerorum. + + Multi enim sunt + Multi sunt enim + Et multi enim sunt + modi + quibus + qui vim + + + corde + + + + ad inuicem comparate + comparate ad inuicem + + + hanc efficiunt + efficiunt hanc + hac efficiunt + + + consonantiam + + consonantia + . Quod declarat + tam ratione substantie quam + causa ratione substantie tam + + + ex parte + + + + + quantitatis et qualitatis + qualitatis et quantitatis + quantitatis qualitatis + quantitatis et qualiter + quantitatis + , dicens + primo + primo esse + sermo + quod + + + + duplex + + nite + + nitem + , cum accepta fuerit, + assumit rationem + + + rationem assumit + affruat nomen et rationem + et substantiam + ypates + + ypatos + compates + . Et + similiter + sit + dicitur + + + ratione + rationem + + + + + quantitatis + quantitatum + , ut + querenti + querente + conuenienti + + + quot + quod + + + nite + + + + constituunt + constituerunt + ypatem + vnam + unum + ueram + + + + dicendum + dicendum est + , + quoniam + quod + + due, et secundum + quale etiam + etiam quale + qualem etiam + quale scensiam + + due + + nite + + netes + uite nete + + sunt, + qualis + quales + qualis qualis + est + ypate + ypaten + + + vna + nam + , et quatuor + + nete + + eodem modo + sunt + sunt et + + + due + ypate + ypate due + due ypates + due + ipates + duo + ypate + , + et sex + tres + et 6. et 3. + 26. + 3. + 2. + 63. + . + Et + + + + ratione substantie ac + ratione substantie et + ratione substantie + ratione substantie Et ratione substantie + accidentis + considerando + consideratio + et ita + semper + et semper + + + procedendo + + protendendo + + due + + nite + + netes + + vnam constituunt ypatem.

+

+ + Deinde. + + MEDIE. Ostendit quod dyapente et + dyatesseron non est optima + consonantia + consonantiarum + , primo dicens + quod + + + proportio + medietatis + equalitatis + + + est + et + + + emiola + + ennola + . Et exponit, + dicens quod illud quod + dicens quod id quod + + dicens quod illud + + + est + et + + + per + pro + quod + + + quinque + que + est + emiolum + + + emidelium + , et tale non reperitur in omnibus numeris; + + ymmo + + + + + + in nullis ita + nullis ita + in nulla + ut + dicatur + dicitur + omnis et perfecta, + ut dyapason dicitur perfecta + + , consonantia. Non + enim + + + + perfecte totum + totum perfecte + perfecte + + + comprehendit + comprehendunt + apprehendit + numerus maior minorem; + ymmo + + + + duorum + + numerorum + minorum + vnus + est sicut quid + est sicut qui + est sicut quem + quidem est sicut + maius + et aliud + et alius + alius + et aliud sicut + minus, eo + quod + etiam + talis consonantia consistit in proportione sexquialtera, in + qua + quo + + + vnum + vnus + continet + alium totum + aliud totum + ad totum + totum aliud + + + semel + simul + + + tantum + + et eius medietatem. Propter quod in + hac + eius + consonantia non + fit + sit + + + comparatio + operatio + + + totius ad totum, + + + + + + ut + + + quod + cum + + + vnus numerus + vnius numeri + minus numerus + + + bis quod + bisque + uel quod + + + totum + totus + mensuret + alterius + + alterum + + , + + + + + sed + + fit + sit + + comparatio + + + totius ad partes, quare non + erit + est + erunt + optima consonantiarum + dyapente + + .

+

+ + + Deinde. + + SIMILITER. Ostendit + consequenter + + + quod + dyatesseron + dyapason tesseron + non est optima + consonantiarum + + + + , + dicens + dicentes + + + quod in + + quando + + + illa + nulla + + + consonantia + + consonantiarum + que est per quatuor ut dyatesseron eodem + modo se habet. Non + enim est + tamen est + enim + optima consonantiarum, cum + non fiat + non sit + enim non + + + comparatio + compositio + totius ad totum, quoniam + epitricam + + + + + + proportionem esse + proportionem + proportio esse + + + quoddam + quoddam enim + quod + est, + quantum interuenire + cantum inuenire + , ut cum maior numerus continet + minorem + maiorem + totum et amplius cum hoc + epitritio + epitricus + epitricon + est + in + enim + + quatuor, + id est + et + continet super hoc + eius tertiam + partem + tertiam partem + eius + , ex quo + consonantia + consona + resonantia + + + resultat + + + + quaterna + quaternam + . Et sic non fit comparatio totius ad totum, sed totius ad partem, ut dictum + est + est in + in + dyapente.

+

+ + Deinde. + + + AUT. + AUT QUIA. + AUTEM. + + + Assignat + Soluit et assignat + aliam causam, uel + quod + per + + + + dictum + dictam + dictum est + confirmat per amplius, dicens + primo quod + primo + prima + + consonantia ex + hiis + + utrisque composita, + puta + + ex dyatesseron et + dyapente + dyapasson + , est perfectissima. Ipsa enim ut + dictum est + dictum + + + .13. + + 14º. + ex + hiis + + + + duabus + + + + constat + consistit + proportionibus, cum dyapason + sit + fit + fere + sex + sexto + >sexta + + + tonorum + sonorum + + + simphonia + + + . + Et + ex + + + dyatesseron + + ex duobus tonis et + semitonio + + semitonis + + + constet + constat + , + ac + ad + et + dyapente ex + tribus + tribus + tonis + duobus + + + et semitonio + + + semitonis + , + que + constat que + + + coniuncta + coniecta + + .6. + + tonos + tonis + fere constituunt. Dico autem + fere + + + + eo quod + quia + + + semitonium + + + + uel limes aut + aut limes uel + uel limes ac + + + dyesis + + + + + minor est + minorem + + + tono + toto + .

+

Quod autem sit perfectissima + ostenditur + ostendit + , quoniam mensura extat et ratio + omnium melodiarum est. + + Namque + Enim + simplicissima, ut ratio mensure + perquirit + requirit + per quare + , + + + xº apparens + ut apparet in + .10. + .10e. + .4°. + apparens + 4°. + mensure perquirit .4°. apparens + + + methaphysice + mathematice + . + Arist. + Met. + X, 1052b ll. 34–37 + Unde + 2° + + musice + mathematice + musice dixit + + boecius: + + dyapason + + dyapente + est + maxima + maxime + + max + maxime + + consonantiarum + et simplicitate + simplicitate + et simplicitati + notissima. + Boeth. + De inst. mus. + II.18 (Freidlein 250, ll. 6–8) + + Quod + Quid + autem + sit + sint + mensura apparet quia motus illius consonantie + que + qui + secundum + medium + motum + + + existit + consistit + fortissimus est per totum + id per + id + per + quod + fertur + + siue sit in principio siue in + fine + fine siue + . In medio + namque + nam + enim + + + constat uirtus + consistit virtus + virtus constat + totius, dyapason enim + ex + + + + cordis + corde + + + conficitur + efficitur + perficitur + extremis et ad inuicem + confractis + constructis + et mediis, non autem + alie + ille + consonantie. Et + quamquam + + ut + dictum est + predictum est + dictum + dicunt quidem + + + predicta consonantia + consonantia predicta + + + sit + fit + perfectissima. Tamen + quando + quia + que + motus + quo causatur + cantus + + + fuerit + fiunt + + fortissimus et uelocissimus, efficietur hec + dulcior + + delectatior + consonantia + quam + quod + quando fuerit + minus + minis + fortis + et + et minus + uelox, eo quod tunc uox eius + quod + que + mouetur + erit + est + acutior + sonus, autem + sonus + et sonus autem + + + is + hiis + alius + aeris + similiter + + dulcior + obtuso + obtusus + aperenso + , propter quod corde tense uelociter + sonant + consonant + , eo quod motus + earum + aeris + est uelox cito + pertransiens + + . Cum enim corda + fuerit + fuerit quia + fiunt qua + + + tensa + tense + , + non + ut + + potest + in tantum + iterum + + + moueri et uagari + uagari et moueri + a medio + sicut + ac + si fuerit + relaxata + + laxata + .

+

+ + Deinde. + + SONUS. + + Et + + quia fecerat + mentionem + + de sono ultimo, + vnde causatur + causatur vnde causatur + ostendit, dicens sonum esse aut motum aeris + in se + + aut + causa + causam + + + cuiusdam + eiusdem + alterius quod + in aere + + mouetur. + Cuius + Cum + autem fuerit causa motus + qui + qui + + + + per + propter + medietatem + pori + ponitur + uel meatus existit tunc et + acutissimum oportet + sonum fieri + fieri sonum + in poro. + + + Sic enim aer + Aer enim sic + Sicut enim aer + constringitur + et fortissimo motu + velocissime + velocissime + uelocissimo + + et velocissimo motu fortissimo + et fortissimo motu + et fortissime + + + + cogitur moueri + moueri cogitur + moueri + , + + ut declaratum + est + + + + xia + iia + , + + + Arist. + Prob. + XI.15, 900b ll. 10–12 + et sonum tunc reddit acutum. Et ideo instrumenta perforantur, + que foramina + quod foramina + etiam + + + si + + + + claudantur + clauduntur + minime + sonant + + . Quare + contingit + + concludit + conuenit + + + quod + + quando non + est + erit + + + porus + potest + per medium, ut + dictum + dictum est + , existens, non causabitur + maneries + + + + alicuius soni + aliqua soni uel alicuius + .

+

Sciendum + + ptolomeum + + + + per tholomeum + per + thm + tholomeum + + per thimotheum + perchium + in + armonica + armonicam + armonica sua + + + taliter declarare + alter declarare + + dyapason esse optimam et perfectissimam + consonantiarum + consonantiam + , fere siquidem + vna + + existit + uocula + notula + , vnum quodammodo sonum componens, puta + ceu + seu + + + + + si denario + si denarius + denarius + aliquis numerorum + addatur + ad + addarum + + , ut duo, semper + remanet + remanebit + + + + + denarius + binarius + + + integer + integri + illesus, + Boeth. + De inst. mus. + V.10 (Freidlein 360, ll. 6–10) + Cf. Ptol. + Harm. + I.7, where the octave is a homophone, not a concord. + + + + non + nam + enim ultra ipsum + numerus + + quis + eleuatur + + , + + ut uisum est + ut uisum + ut insum + + + .15 + in 5º + . + Arist. + Prob. + XV.3, 910b ll. 23–30 + Quod + tamen non + non tamen + tamen + contingit in ceteris proportionibus, nam si tribus + duo + + coniungantur + + statim + fiunt + + + .5. et + mutatur + mutantur + mutant + species numeri. + Sed si + Sed si tu + Sed + Si + + + duo addas + + addas duo + duo + addat + duo + addis + duo addit + duo + additur + + + denario + + denar. + denarium + + denarium + + .12. + + faciens + facies + etiam faciens + , + et + + + + utrique + uterque + utrumque + + + numerus + videtur + + + integer + integri + + + conseruabitur + conseruari + , + et similiter + et similiter et similiter + + + si addas + + + + ternarium + ternarius + ternarios + denario + et ceteros eodem modo. + Similiterque + Similiter quia + Similiter quoque + Similiter + dyapason + simphonia + + symphoniam + + + + quancunque + quantumcunque + + + consonantiam + consonantia + aliam + sumat + + suma + seruant + , + seruat + conseruat + suam + consonantiam + consonantiam ut + + + neque + + + + immutat + inmutatur + imitatur + , ut ex + consona + consonantia + reddat + se + sed + dissonam, + quod + quam + in aliis non accidit + simphoniis + + + . + + etcetera. + sequitur 36. + problema. +

+
+ +
+ + Trigesimumsextum + problema + 36m + trigesimum sextum. + Trigesimumsextum. + 35m. + problema. + + +

+ PROPTER QUID SI QUIDEM + PROPTER QUID SI QUIDEM MEDIA + + PROPTER QUID SI QUIDEM MEDIA MOUEBITUR ET ALIE CORDE SONANT, SI AUTEM + ITERUM HEC QUIDEM MANET ALIARUM AUTEM QUEDAM MOUEATUR MOTA SOLA SONAT? + AUT QUIA CONCORDARE EST OMNIBUS HABERE SE AUTEM + QUODAMMODO AD MEDIAM OMNIBUS, ET ORDINATIO QUE EST UNIUSCUIUSQUE UTIQUE PER + ILLAM EST? ELEUATA IGITUR CAUSA CONCORDANDI ET CONTINENTIS, NON ADHUC + SIMILITER APPARERE EXISTERE. UNA AUTEM DISCORDANTE EXISTENTE MEDIA AUTEM + MANENTE, RATIONABILITER QUOD EST SECUNDUM IPSAM DEFICIENS, ALIIS ENIM EXISTIT + CONCORDARE + . + + Problema 36m. + etcetera. + + + Quare + Querit quare + + si media + cordarum + corda + moueatur alie corde consonant illi, sed si postea fiat quod media + immobilis permaneat + + immobilis permaneat immobilis + + + et + est + quedam + de + + numero + aliarum a media + armoniarum aliarum + aliarum + + + moueatur + moueantur + solum + illa que + itaque + + + fuerit + fuit + sint + mota sonat, + + ita quod + itaque + + + neque + + in + alia sonat + + propter motum ipsius, neque + etiam + in + + + media.

+

+ Nosce quod + huius + huiusmodi + de huiusmodi + de huius + + + problemate + problematis + + + iam + + sermo aliqualiter + precessit + processit + in + 20a. + secundo + + + problemate + capitulo + + + #Vc includes this passage. + .

+

+ + Deinde. + + AUT. Soluit dicens causam esse + quoniam media cordarum concordat et consonat cum omnibus + cordis + cordis aliis + . + Quod + Ut + ostenditur + quoniam + quia + concordare cum + omnibus + aliis + + + nichil + + + non + + + aliud + ad + + est quam se + habere aliqualiter + aliqualiter habere + + + ad mediam + ad medium + + + + omnis + omnes + , + ordinatio enim + + enim ordinatio + + + vniuscuiusque + + uniustus quia + aliarum cordarum per illam existit. Quod probatur quoniam + ipsa + ista + illa + + media remota ex + instrumento + instrumentorum + , non amplius erit sentire + cordam + + + + aliquam + ad quam + que + existat + existit + extat + ratio concordandi alias + concorditerque + concorditerque alias + retinendi. + Sed + Sed si + vna aliarum + remota + remoueatur + ita quod causa existat discordandi + dummodo + dum + media cordarum + recte maneat + remaneat + , sicut + debet + debeat + , illud quod + erat + erit + + + deficiens + indeficiens + , ut corda ablata, + suppletur + + per + mediam + medium + , ita + quod + ut + + + illa + ista + remota + adhuc + + + + aliis cordis inerit + inerit aliis cordis + cordis non erit + concordare et consonantiam reddere per virtutem + medie + medicine + . Media enim est + ut + + + + magistra + magistram + #Px and #Pp could alternately read "nigram" + + + et regula + et 2a + + + + aliarum omnium + omnium aliarum + aliorum omnium + omnium ceterarum + . + + etcetera. + sequitur 37. + problema 19e. particule. +

+
+ +
+ + Trigesimumseptimum + problema + 37m + trigesimumseptimum + Trigesimumseptimum. + 36m. + problema. + + +

+ PROPTER QUID QUOD EST IN UOCE + PROPTER QUID QUOD + + PROPTER QUID QUOD EST IN UOCE ACUTO EXISTENTE MODICUM, GRAUI AUTEM + SECUNDUM MULTUM GRAUE? QUIDEM ENIM PROPTER MULTITUDINEM GRAUE, ACUTUM AUTEM + PROPTER PAUCITATEM UELOX EST. + MOLESTUM MAGIS CANTARE ACUTA QUAM GRAUIA, ET + PAUCI ASCENDENTIA POSSUNT CANTARE, + ET LEGES DIRIGUNT, ET ACUTI DIFFICILES DIMITTERE PROPTER ID QUOD TENSI + SUNT. + MINUS OPUS MODICUM MOUERE QUAM MULTUM, + QUARE ET AEREM. + AUT IDEM ACUTE SONANS ESSE NATURA ET ACUTE CANERE, + SED NATURA QUIDEM ACUTE UOCIS OMNIA PROPTER IMBECILLITATEM PRO EO QUOD NON + POTEST MOUERE MULTUM AEREM, SED MODICUM. MODICUS AUTEM UELOCITER FERTUR. IN + CANTANDO AUTEM ACUTUM POTENTIE SIGNUM, QUOD QUIDEM ENIM UELOCITER FERTUR, + PROPTER QUOD ET ACUTUM POTENTIE SIGNUM. PROPTER QUOD ET QUI SUNT BONI HABITUS + ACUTE UOCIS, ET MOLESTUM QUE ELEUANTUR CANTARE, GRAUIA AUTEM DEORSUM + . + + Problema .37m. + etcetera. + + + Querit + Quare + Contingit + quesitum + cuius + quarum + + + terminorum primitus + + cuiustorum primitus + corpus primo + #Nu's reading results from a dittographic cⳋ being blended with what should be tⳋorum = terminorum + tangit expositionem, dicens quod cum in uoce + acutum + acuta + + + existat + extat + secundum modicum temporis, graue + autem secundum + multum + uictum multum + . + + Nam + Namque + graue + + causatur + propter + secundum + multitudinem aeris + moti + motu + qui tarde mouetur, acutum uero propter + paucitatem ipsius + tarditatem ipsius paucitatem + , ex + qua + quo + uelocitas causatur, + + sicut ex multitudine tarditas, + + ut visum est .xia + ut visum .xia + ut visum est 11a particula. + + + Ps.Arist. + Prob. + XI.16, 900b ll. 24–28 +

+

+ + Deinde. + + + MOLESTUM. + MOLESTAM. + + + Secundo + + + + format + fertur + quesitum, dicens quare magis + difficile + difficile est + cantare + illa + ea + que sunt acuta quam + ea + illa + que sunt + grauia + + . Quod ostenditur + quoniam + quia + pauci sunt + qui possunt cantus + qui possint cantus + + + + ascendentes + + + + cantare + cantare et + maxime, cum + sint + sunt + acutissimi. Et ideo + huius non + huiusmodi non + tales non + cantant, sed potius + dirigunt + digerunt + leges, legales enim cantus constituunt. Sunt enim + tanquam + + graues remissi faciles ad cantandum, vt + visum est + uisum + + + .15 + in 15 + . Et non solum difficile + est in acutum tendere + et + id est + + + seruare + seruant + reseruare + + + cantus + cantum + , sed etiam + difficile + difficile est + + + mox cessare a cantibus acutis, eo quod + tensi + remissi + sunt ualde + ceu + + seu + + + equum + + + + extensum + excessum + + et uelocissime + currentem + currente + + + molestum + mosteli + + + est + + confestim + sistere + consistere + , atque + similiter nauem uelocissime + nauem similiter uelocissime + nauem uelocissime similiter + similiter manere uelocissime + nauem uelocissime + + + inpulsam + + .

+

+ + Deinde. + + MINUS. Tertio + arguit + argummentat + in contrarium, + quasi + quare + dicat + quod + quia + + + minus + unus + + + est + sit + opus et sic + maior + maior opus + minor + virtus + requiritur + requiratur + ad mouendum illud quod est modicum + quam quod + quod quam + quam quod est + quare illud quod est + quam ad + multum, non videtur + quod acutum + + mouere + cantando + euitando + + + sit + fit + difficile, cum sit modicum, et graue facile, quia multum + ymmo + + + econuerso, quare sicut est. Universaliter in aliis ita + etiam videtur esse + videtur esse + videtur etiam + in aere + qui + que + + + est + videtur esse + subiectum sonorum, eius enim medium + proprium + proprie + propositum + est ipse in quo + causatur + cantatur + et recipitur primitus.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens + causam esse + sumendam + + + + + ex hoc + + , + quia + quod + + + idem + + videtur esse naturaliter acute sonare et + acute cantare + acuto cantare + sonare + , + et non + non + + + differt + + differunt + dicent + + nisi + secundum quod + quod + sicut + + + superius differt + differt superius + superius + ab inferiori. + + Hoc + Huius + autem + assumit + + + + + ut + et + + + declaret + declararet + + + per + quod + + + id + illud + quod + est + + in uoce + vniversaliter + similiter + videtur + + + sic esse + est + in sono. Unde + subdens + + + + ait + + autem + aut + + + + omnia + omnis + naturaliter acute + + uocis + uocem + vox + + + fieri + + propter debilitatem + suam + + , eo quod non + possunt + possint + multum aerem + mouere, qui + remouere, quod + + + grauis uocis est causa + est causa grauis uocis + grauis uocum est causa + grauis netis est causa + grauis est causa + . Sed modicum possunt, + modicus + motus + + + autem aer motus + aut aer + uelociter + fertur + + , + + ut + visum est + visum + + .xi°. + + + Ps.Arist. + Prob. + XI.13, 900a ll. 21–27; 21, 901a ll. + 31–32 + + Sepe atque + Sepe at quia + Sepe ac + Aut quia + acutum + sic uelociter mouetur + velociter mouetur sic + si quis cantauerit secundum acutum. Signum + quidem + quid + + ex hoc + suscipitur + accipitur + sumitur + concipitur + + + cuiusdam + eiusdem + vigoris + in + + eo quod mouet aliquid uelociter, quod non + fieret + fieretur + nisi vigor adesset. Et + ideo + non + ex + hoc + hac + + + confirmatione + confirmatiue + concluditur + quod + quod si + illi qui sunt bone complexionis quorum pulmones non + redundant + + redundat + exundant + + + humiditatibus + hominibus + superfluis + existere + existunt + esse + uocis acute eo quod organum est + exsiccatum + + + excitatum + + + solidum + solum + . Et quia difficile est + cantare + cantare ea + que + eleuantur + + , cum acuta + extollantur + excellenter + , ipsa + fiet + fiat + cantare difficile, nam + + eleuare + elleuare est + eleuantur + contra + naturam, + naturam est, + + + ut + visum est + visum + + particula + secunda + 11a + . + + + Ps.Arist. + Prob. + II.38, 870a l. 34 + Et quia grauia + naturaliter tendunt + tendunt naturaliter + naturaliter + deorsum, quod + nobis magis + magis nobis + + + naturale + naturale est + , + ideo facile fit + facile fit ideo + ideo facile sit + facile igitur fit + + + ipsa + ipsam + cantare. Sic + igitur + ergo + + + soluitur + soluit + + solo + solummodo + + solum + adquesitum, + neque + + + + + ambiguitas + + + + relinquitur + + relinquatur + aliqua + que + quia + + in + + + .xia. particula + particula .11a. + 5a particula + ille particula + + + intelligenti dicta, + intelligentis dicta, + intellecto dicta, + multa dicta, + + + quoniam + quando + + + in acute cantare siue sonare + in acutis cantare siue sonare + acute cantare siue sonare + in acuto cantare siue sonare + + + duo fit + duo sit + est duo + + + considerare: puta + consingulare: puta + + + modicum + + + + aerem + aerem aerem + motum et quantum ad hoc videtur quod + acutum + acute + mouere + sit + fit + facile, + Ps.Arist. + Prob. + XI.14, 900a ll. 34–36 + cum + id + illud + + debiles agant et + impotentes + + + . + Est et + Et est + Est + Est etiam + + considerare quod + illud + id + + + modicum + motum + + aeris velociter mouetur, + et + + + + quia quod + quod + quia + + + huius + huiusmodi + non + fit + sit + nisi a + constanti + constante + virtute. + Ideo + Item + Ergo + + + acutum + acute + mouere denotat + constantiam + + + + virtutis + + , et difficultatem per consequens, quare + apparuit + apparente + + + + .xiiii°. + 24º + .34°. + + + xi°. + + + + pueros + paruos + + + uoces acutiores + acutiores uoces + acutiores + habere + senioribus + senibus + , propter + consistentiam + constantiam + + + calidi + calidi eorum + + + virtuosi + unctuosi + . + Ps.Arist. + Prob. + XI.14, 900a l. 33 to 900b l. 8 + + + etcetera. + etcetera etcetera. + sequitur 38. + problema. +

+
+ +
+ + Trigesimumoctauum + problema + 38m + trigesimum octauum. + Trigesimumoctauum. + 37m. + problema. + + +

+ PROPTER QUID ET RITHIMO + PROPTER QUID IN RITHIMO + + PROPTER QUID ET RITHIMO ET CANTU ET OMNINO CONSONANTIIS GAUDENT + OMNES? + AUT QUIA MOTIBUS QUI SUNT SECUNDUM NATURAM + GAUDEMUS SECUNDUM NATURAM? + SIGNUM AUTEM PUEROS CONFESTIM NATOS GAUDERE IPSIS. + PROPTER CONSUETUDINEM AUTEM MODIS CANTUUM GAUDEMUS. + RITHIMO AUTEM GAUDEMUS PROPTER MOTUM ET ORDINATUM + NUMERUM HABERE ET MOUERE NOS ORDINATE MAGIS. MAGIS PRIUS ENIM EST ORDINATUS + MOTUS NATURA INORDINATO, QUARE ET SECUNDUM NATURAM MAGIS. + SIGNUM AUTEM LABORANTES ENIM ET BIBENTES ET + COMEDENTES ORDINATE SALUAMUS ET AUGEMUS NATURAM ET UIRTUTEM, INORDINATE AUTEM + CORRUMPIMUS ET STUPEFACIMUS IPSAM. + EGRITUDINES ENIM ORDINATIONIS CORPORIS NON SECUNDUM NATURAM MOTUS SUNT. + CONSONANTIA GAUDEMUS QUONIAM COMPLEXIO EST + CONTRARIORUM HABENTIUM PROPORTIONEM AD INUICEM. PROPORTIO AUTEM ORDINATIO, + QUOD ERAT NATURA DELECTABILE. COMPLEXIONATUM AUTEM INCOMPLEXIONATO OMNE DELECTABILIUS ALITER. + QUAMUIS SENSIBILE SIT UTRISQUE EXTREMIS EX EQUALI + POTENTIAM HABET IN CONSONANTIA PROPORTIO + . + + Problema 38m. + etcetera. + + + Quare + Querit quare + omnia, + ita + quod + ut + + etiam + bruta + bruta itaque + + + utcunque + utrunque + + + + sicut videbitur + sint videbitur + + + .vii°. + + xxixe. + 29e particule + et 9e. + , + + + Ps.Arist. + Prob. + XXVIII.7, 949b l. 37 to 950a l. 16 + + exultantur + + exultant + + + rithimo + rithimi + + + et + + cantu + ac + ac etiam + et + + + vniuersaliter + uidetur + + + consonantiarum + consonantiam + consonantia + auditu in + hiis + huius + , + siquidem + quidem + + + verbis + + + + triplex pretacta indicatur + triplex pretacta inducatur + pretacta indicatur triplex + triplex iudicatur pretacta + #Pp, #Pu, #Px, and #Vm could be either "iudicatur" + or "indicatur" + musica?

+

+ + Deinde. + + + AUT. + AUT QUIA. + QUONIAM. + Soluit + primo dans causam vniversaliter dicens + primo vniversaliter dicens + dicens primo + causam + fore + esse + communem, + quoniam + quia + quare + + + gaudemus naturaliter + + naturaliter gaudemus + gaudere naturaliter + gaudemus vniuersaliter + giludomus naturaliter + motibus + naturalibus + naturaliter + , + cum + que + + + in temperamento + temperamento + in temperato + quodam consistant. Sicut enim + excellentie sensibilium + corrumpunt + corrumpuntur + + + sensus + sensum + , + + ut apparet de + anima + 3°., + ut apparet 3º + de anima, + ut patet 3° + de anima, + + Arist. + De an. + III.13, 435b l. 15 (Cf. 426a, l. 30) + + ita et + ita etiam + ita ut + et + itaque + + + + ipsorum + ipsarum + + + conmensurationes + + + eos custodiunt, + + ut + sicut + + + etiam + et + + + + tactum est + tactum + tactus est + + in principio + huius + huiusmodi + + + particule + + . + Ps.Arist. + Prob. + XΙΧ.2, 917b ll. 22–29 +

+

+ + Deinde. + + SIGNUM. + + Declarat + Ostendit + secundo + quomodo + quo + in + vnoquoque + unaquoque + + + trium + cum + + + predictorum + predictorum sicut + motus secundum naturam + existat + existit + existant + + et per consequens gaudere + fiat + faciat + + + ex eo + + et eo + + . + Primoque + Primo quid + Primo quod + Primo + manifestans in + tactu + cantu + sensu + + + dicens + dicit + + + huius + huiusmodi + hoc + signum esse + quoniam + quia + pueri + mox cum + cum mox + fuerint nati accidit + ipsis + eis + gaudere + cantu tum + cantu cum + cantu tamen + tamen + cantatum + + + propter + per + musicam + naturaliter + universaliter + + + ipsis + sibi + + + inditam + + + indicatiua + . + Anima + Nam + enim + + maxime nostra + nostra maxime + maxime + magis uel maxime + ad similitudinem + numeri consoni + numerum consoni + numerius soni + + + constricta + constructa + constituta + + + existit + existat + est + , + + ut apparet per + ut patet per + ut + per + + + damascenus + + + damascenum + dictum + in <app> + <lem wit="#β #Ea #Vb #Vo #m #v">afforismis</lem> + + + + + + <rdg wit="#Pz" ana="#additive #J">amphorismis suis</rdg> + </app>. + Yuḥannā ibn Māsawaiyh + Aph. (See Vat. Lat. 2460, f. 39v, ll.10–11.) + + Quare + Et + + + primo + de <app> + <lem wit="#α #π #Vz">regimine sanitatis</lem> + <rdg wit="#Ma #Px #Vm #m #v" ana="#lexical"><choice> + <abbr>re. sa.</abbr> + <expan instant="false">re<ex instant="false">gimine</ex> sa<ex instant="false">nitatis</ex></expan> + </choice></rdg> + </app> + + pueri + + + + familiariter + simili aliter + dispositi sunt ad musicam. + Gal. + De san. tu. + I.7 + + Tum + Cum + Tamen + etiam propter consuetudinem quam + adipiscimur + adispiscitur + adypiscimus + adipiscuntur + deinceps + + ex + + + + maneriebus + + + + + cantuum + cantantuum + + + + gaudere accidit, quidam + enim + vero + gaudent + vno + + cantu, alii + uero + autem + + alio + secundum + si + quod consueti + fuerunt + fuerint + audire a + natiuitate + natiuitate audiant + . Quod autem infantes + huius + huiusmodi + cantibus + delectentur + + delectantur + , id sciunt nutrices industriose que modis cantuum et + motuum + motum + motibus + + + quibusdam + quidam + communium + , cum + hii + ii + + + tristentur + tristantur + et + plorant + plorent + , + ipsorum + ipsarum + animos + demulciunt + + demulcent + , quiescere facientes et gaudere, cum ostensum sit + hanc + ac + esse + potentiam + potentie + musice. Unde + + eodem + eodem modo + + primo: + nutrices + tribus + modis consolantur + consolantur tribus modis + et ad + sompnum + + ad sompnum + prouocant pueros: ut appositione + mamillarum + + + ad os, melodia uocis, et motu. + Gal. + De san. tu. + I.7 +

+

+ + Deinde. + + + RITHIMO. Secundo dat causam + RITHIMO. Dat causam + RITHIMUS. Secundo dat causam + RITHIMO. Declarat secundo + RITHIMO. Secundo declarat + causam + AC HUIC. Dat causam 2° + + + rithimo quare + quare rithimo + rithimo + + + fit + sit + + + gaudere quod + gaude quo + + secundo + + signo manifestat + manifestat + signo ibi + signo manifestat secunda ibi + signo inanimat + + + SIGNUM AUTEM + SIGNO AUTEM + DIGNUM AUTEM + + , + dicens causam esse + dicit causam esse + dicens causam dicens causam + esse + + + + quare + quia + quoniam + + + gaudemus + gaudere + rithimo. + Est + + + + propter + propter quod + + + motum suauem et numerum + numerum suauem et numerum + ordinatum + eius + 4º + et proportionatum clausularum + vnius + vniuscuiusque + + + cum + + altera concordantium + quos + quas + + + habet + habet est + hoc + . Que + autem huius + autem huiusmodi + aut huius + ab huius + nos habent mouere + amplius + + paulatiue et ordinate, + nam + non + motus + ordinatus et vniformis + paulatiuus et ordinatus + prior est + natura + nature + + + opposito + apposito + apposita + , + + ceu + seu + sicut + habitus + priuatione + priuationem + priuationis + . + Ordinatum + Ordinatus + Ordinatam + + + enim habet + rationem + + ratione + equalitatis, + inordinatum + inordinatam + id est ordinatus + uero + inequalitatis + rationem inequalitatis + + in cardinalitatis + ī cartis + + . Omne + autem + enim + + + inequale + + + + reducitur + redditur + ad equale, + ut + sicut + + + ad + + primum et perfectum, + ut + et + + + probatum est + probant + arismetrici et musici. Et ideo concluditur quod naturaliter magis + debeamus gaudere + debemus gaudere + rithimo et + iocundari + iocundiori + iocunditati + , + tanquam + + ordinato.

+

+ + Deinde. + + SIGNUM AUTEM. + Declarat + id + illud + + + + signo + 2° + 2º signo + dicens quod + huius + huiusmodi + signum + in + + + + regimine + rithimo + + + vite + + + + sumitur + + tale, quia + nos + non + + + exercitantes + + + + et + . + + + + laborantes bibentesque + laborantesque bibentes + elaborantes bibentesque + laborantes et bibentes + + + et + ac + atque + + + comedentes + + + + conmensurate + mensurate + + + et + ac + ordinate, + + + ut precipit + precipit + + regimen + + galeni + + caloris + + <app> + <lem wit="#Ma #Px #Va #Vm">sanatium</lem> + + <rdg wit="#π" ana="#lexical #J">sanitatem</rdg> + </app>, + Gal. + De san. tu. + V.2 + + saluamus et augmentamus + nostram naturam siue complexionem + naturam nostram siue complexionem + naturamque nostram siue complexionem + nostram siue coniunctionem + nostram complexionem siue naturam + , + quantum + + ad corpus magis + et virtutem + ad virtutem + + + + quo ad animam plus. Per oppositum uero + cum + causa + indebite + ac + et + inordinate vtimur + + + + regimine sanitatis + regimine + corrumpimus + ac + et + + stupefacimus + naturam nostram + nostram naturam + naturam + + + et + ac + virtutem. + Quod + Quia + + + ostenditur + ostendit + + + quia + quam + + + egritudines + egritudinales + + + sunt + serui + motus cuiusdam + ordinationis + inordinationis + et + concursus + utrisque + corporis + nostri + + non secundum naturam + uerum + sed + preter + naturam existentis + naturam existentes + naturam existentem + naturas + . + Quomodo + Quomodo autem + Quomodo autem quod + + + egritudo sit motus + + ostensum differentia 7a + ostensum est differentia 7 + ostensum differentia 7a alia + uisum est prima + + + problemate quarto. + quarto + problemate. + + Ps.Arist. + Prob. + VII.4, 886b ll. 5–6 +

+

+ + Deinde. + + + CONSONANTIA. + CONSONANTIAM. + Assignat + tertio + 3am. + causam + delectationis + de delectatione + consonantie, dicens + causam huius + huius causam + causam huiusmodi + causam + esse, + quare + quia + + + gaudeamus + gaudemus + consonantia, quia ipsa + causatur + cantatur + ex + coniunctione + coniectione + + + contrariorum + conexorum + habentium proportionem ad inuicem secundum + acuitatem et grauitatem + grauitatem et acuitatem + . + Confranguntur + Confrangantur + Confrangitur + Cum frangantur + + + enim + enim ad inuicem + oppositorum excellentie + ita + + ut ex eis resultet vnum medium + contemperatum + + contemperamentum + contemperatiuum + temperatum + + + ac + et + proportionatum extremis, + ceu + seu + seu seu + Sicut + opposita + ostendunt + ostendit + contrariorum excellentium in + copulatione + + ad inuicem + qualitatum + qualitatis + . In + huius + huiusmodi + hac + autem proportione + copulationis + complexionis + + + saluatur + + seruatur + + + ordinatio + inordinatio + , que naturaliter + + + delectabilis existit + est delectabilis + delectabilis + . + + delectabilis + + Quod autem hoc sit delectabile + + ostenditur quoniam + habens + hiis + consonantiam est + complexionatum + + + + + seu + ceu + siue + mixtum, + + + omne autem + complexionatum + complexionatum et mixtum + + + + + est + delectabilius + delectabilis + quam + incomplexionatum + in conmixtum + + + + + uel + seu + et + simplex, aliter tamen et aliter, quoniam multo magis est delectabile + cum in simplicibus + cum simplicibus + + + + ut + et + id est + + in elementis primis remaneant + excellentie + + , in + complexionatis + conmixtis + + + autem + aut + vero + + + + consurgunt + confringantur + refranguntur + et ad medium + reducte sunt + sunt reducte + deducte sunt + ducte sunt + .

+

+ + Deinde. + + QUAMUIS. Remouet + 2° + dubitationem + dubium + , quia crederet aliquis + eo quod + quod + quia + complexionatum compositum est ex + vtrisque + utique + + + + extremorum + postrimorum + + + non + + + + posse + posset + delectabile fore. + Quod + Et + remouet, dicens + + + + + quodlibet + quod + quia licet + + + sit complexionatum + si complexionatum + complexionatum + complexionatum sit compositum + ex utrisque + + #Ca and #Pq also omit this passage. + + + extremorum excellentiis + excellentiis extremorum + extremorum excellentibus + extremorum non posse delectabile + fore excellentiis + + + constitutum + constitutis + . + + Nichilominus + + tamen est + delectabile + delectabiliter + , quoniam ipsum + constituitur + constitutum + ex + contrariis et inequalibus + inequalibus et contrariis + , et non ex + omnino + non + + similibus et equalibus, + sic + sicut + enim non + posset + possunt + potest + adeo + mouere + moue + . + Et + + ideo + thimoteus + + + + + + + + + + consonantiam + ponuit consonantiam + fieri + ait ex dissimilibus + ex dissimilibus ait ayt + aut ex dissimilibus + ut ex similibus + ex dissimilibus + in vnam et + eandem + eadem + uocem + uenientibus + euenientibus + , + nam + non + in uocibus que nulla equalitate discordant + nulla + in id + + + omnino + enim + + + extat + + existit + consonantia, + cum ea + sit + + ut tactum + est + + dissimilium inter se uocum + sed dissimilitudo. neque similiter si acutum + iungatur + + + in vnum + + + + redacta + reducta + concordia. Si enim grauis graui + misceatur, nulla + fit + sit + consonantia sed dissimilitudo, + neque similiter si + + similiter nec si + si autem similiter + ne similiter si + acutum + iungatur + coniungatur + + + acuto + acuta + . Plato + + siquidem + + + + uoluit taliter consonantiam + uoluit talem consonantiam + uoluit taliter consonantia + uoluit dicere taliter consonantiam + uoluit tradere taliter consonantiam + in + aure + aere + autem + + + causari + causare + , + necesse + necessario + uocem + + + quidem + quidam + + + ait + + sonum + uelociorem + + uelocem tunc + + + esse + esse et + acutiorem, qui cum precesserit + grauem + graue + ingreditur + celeriter + + + + in aurem + aurem + maiorem + ipsius + ledens + + + extremitatem + intrinsecam + + . Et ideo + quasi + quia + pulsus + cum tanto + cum canto + a tanto + + + motu + + modi + + + retro reuertitur + reuertitur + retrouertitur + , et quia + iam + ipse + + + + pigrescit + + exire, obuiat graui + subintranti + superintranti + et sibi + commiscetur + commiscere + + + consonantiam + consonantias + consonantia + + + constituens + consti + + + musicalem + musicales + . + Id + Illud + tamen + ut + + + + visum est + uisum et + visum + dictum est + dictis non + conuenit + continet + + + thimotei + + + + + + + . + + et cetera + sequitur 39m. + problema 19e. particule. +

+
+ +
+ + Trigesimumnonum + problema + 39m + trigesimum nonum: + Trigesimumnonum. + 38m. + problema. + + +

+ PROPTER QUID DELECTABILIUS + + + PROPTER QUID DELECTABILIUS EST SECUNDUM CONSONANTIAM EO QUOD EST UNIUS + UOCIS? + AUT ET ANTIFONUM QUIDEM CONSONUM EST DYAPASON? EX + PUERIS ENIM IUUENIBUS, ET NUMERUS FIT ANTIFONUM, QUI DISTANT COMMUNIS SICUT NITE + AD YPATEM. CONSONANTIA AUTEM OMNIS + DELECTABILIUS SIMPLICI SONO, PER QUE + AUTEM DICTUM EST, ET HORUM DYAPASON DELECTABILISSIMA QUIDEM QUAM UNIUS SONI EST + SIMPLICEM HABET SONUM. ORGANIZANT AUTEM IN DYAPASON CONSONANTIA. + QUIA QUEMADMODUM IN METRIS PEDES HABENT AD SE + IPSOS RATIONEM EQUALEM AD EQUALEM, + AUT DUO AD UNUM, AUT ALIQUEM ALIUM, + ET ITA IN CONSONANTIA SONI PROPORTIONEM HABENT + MOTUS AD SE IPSOS. + ALIARUM AUTEM CONSONANTIARUM IMPERFECTE, QUE + ALTERIUS REUERSIUE SUNT IN MEDIUM FINIUNT, PROPTER QUOD POTENTIA NON EQUALES + SUNT. EXISTENTES AUTEM INEQUALES PER CORRUPTIONEM SENSUI. QUEMADMODUM IN ROTIS + IN DISSOLUENDO MAIUS SALTANS SONANTIBUS EST. + AMPLIUS YPATE ACCIDIT EUNDEM FINEM PERIODORUM, QUI + SUNT IN SONIS, HABERE; SECUNDA AUTEM NEATIS ICTUS AERIS YPATE EST. FINIENS AUTEM IN IDEM, NON IDEM FACIENTIBUS UNUM ET COMMUNE OPUS ACCIDIT + FIERI, QUEMADMODUM SONANTIBUS SUB CANTU. ETENIM HII ALIA NON PARITER + FISTULANTUR, SI IN IDEM CONUERTANT DELECTANT MAGIS FINE QUAM CONTRISTANT + DIFFERENTIIS QUE SUNT AD FINEM, IN EO QUOD FIT EX DIFFERENTIBUS COMMUNE + DELECTABILISSIMUM EX DYAPASON. ORGANIZANT AUTEM EX CONTRARIIS UOCIBUS; PROPTER + HOC IN DYAPASON ORGANIZANT + . + + Problema .39m. + etcetera. + + + Quare + Querit quare + cantus et vniuersaliter sonus, existens secundum consonantiam, que est + copulatio + + compositio + quedam + suauem + suaue + consuauem + et mixtum reddens sonum, + delectabilior + + est quam cantus et + omnino sonus qui + sonus qui omnino + vniversaliter sonus qui + non sonus qui + fuerit vnius uocis et percussionis, et uniuersaliter dyapason ad + alias + illas + consonantias?

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit et primo assignat + causam vnam + vnam causam + , secundo + alteram + aliam + uel + priorem + primam + confirmat. + secunda + ibi + ibi secunda + secunda ibi + + AMPLIUS. Adhuc + prius dat causam + primo dat causam + dat causam + prime partis, + dicens + dicens primo + primo dicens + + + id + illud + ideo + hoc + id ideo + esse quoniam + dyapason est + antiphonum + archifonum + archisonum + + + quoddam + quiddam + + + consonum + sonum + cum sonum + cum sonu + . + Secundum enim ipsam + Secundum ipsam enim + Enim secundum ipsam + + + solam + solum + + + fit + sit + + + antiphonizare + + , ut + apparuit + apparebit + , et + organizare + + organizare ut apparuit + et organizare + agonizare + cum sit ex + pluribus + + + + sonis uel uocibus consonantibus + vocibus et consonantibus sonis + sonis uel uocibus contrasonantibus + + + coaptata + adaptata + . Ipsa + enim + enim est + ut dictum + est + fuit + + + optima + optima est + consonantiarum, + ac + et + quia + suauissima ex uocibus + acutis puerorum + puerorum acutis + et grauibus iuuenum + consurgit. Fit enim + numerus + unus + + + quidam + quidem + et proportio + consonum + sonum + reddens + antiphonum + + + . + Alias + + + + Alii + Aliquando + Aliter + Uel + + + et + et cetera + etiam + + + viris fit + fit uiris + iuris fit + uiris + et + tunc + cum + iuuenibus + ueniat + ueniet + + + indeterminatio + in determinationem + + + de li + de lii + + delectabili + deli + + ly + pueris, + prior + prius prior + tamen + scriptura + scriptura tamen + melior. Qui + siquidem + sic quidem sit + + + differunt + differenter + + + ab + ad + inuicem ratione + acuitatis et grauitatis + grauitatis et acuitatis + + + uocis + uas + + + + acquisite + acquisita + + + secundum + sed + tempus, quanta est differentia + communis uel vniversalis + universalis uel communis + communis et vniversalis + et ultime + ad ypatem communem + dyapente communem + dyapente causam + + + supremam + + supremamque + extremam + . Que quidem + due + secunde + corde tacte reddunt consonantiam delectabilem, cum sonus + earum + eorum + sit compositus. Omnis autem consonantia + delectabilior + delectabilis + + + est + est magis + + quam + sonus + + + + simplex + + . Et ideo dictum + est + + prius quod dyapason de numero + sonorum + consonantiarum + est delectabilissima + per respectum + per respectu + et per respectum + in respectu + ad + sonos + + simplices + et + + ut + + + vnum + vnam + tantum. + Unde + + secundum + eam + enim + + + solum + + sonum + + + ut prescriptum est + prescriptum est + prescriptum + ut scriptum est + + + organizare + + + accidit + .xviii. + 18° + hiis + igitur + , quod + in alia + nulla + consonantiarum + non + + contingit. Dicit autem + communis + numerus + + + + quia + quod + + + ypate + ypatem + et nete + sicut + sint + + + et + est + + + + aliarum + aliorum + quedam + preponuntur + proponuntur + + et alie supponuntur, + repetuntur + repetunt + enim + cum + + determinatione + cum + + plures + septem + enim + id est + ponuntur corde ut + policorda + + + policorde + + + edocent + edocet + edocentur + + + boecii + boni + uero + .10 + + .

+

+ + Deinde. + + + QUIA QUEMADMODUM. + QUEMADMODUM. + QUARE QUODDAM. + Declarat + deinde id + id deinde + illud deinde + demum id + id demum + dictum id + deinde + , dicens hoc esse quia + sicut + sint + in carminibus pedes + obtinent + + optinet + oportunt + + + debitam + determinatam + proportionem ad inuicem, ut sit proportio aut equalis ad + equale + equalem + equalia + , ut + dicatur + dicitur + + in + dactilo + + + + + + constante ex tribus sillabis equalium + ex tribus + sillabis equalium constante + constantem ex tribus sillabis equalium + + constare ex tribus + sillabis equalium + + + + non + ut + et + + + tandem + tamen + tantumdem + temporum, + quia + qui + ex prima longa, que + est + + + duorum temporum, et + duabus + duobus + breuibus, quarum + alter uterque + alter utram + alterum utraque + altera utraque + ad alter utraque + + + vnius + minus + , + ubi + ut + et + nisi + + + + duo + due + ad + vnum + unam + + unum ad duo + duo + + + comparantur + comparatur + operantur + , + ut + ubi + + + due + duo + breues ad + vnam + vnam ut duo breues ad vaiam + + + longam + longam ad alteram breuem + , + uel + seu + econtra, + + ceu + seu + sicut + in + anapesto + + + apeston uel anapasco + huic opposito, uel secundum alium + quendam + quamdam + quidem + modum sicut + vna + nam + + + sillaba + + + duorum temporum ad aliam consimilem, + ceu + seu + + + in + + spondeo. + Aut + An + + vnam longam + ad + et + alteram breuem + uel + aut + econtra + + , + uelut + ut + uel + in + trocheo + + + + + et + uel + + + iambo + iambico + , + spondeus + spondeo + siquidem + sono proportionatur + proportionatur sono + sonus proportionatur + graui et iuuenum uoci. + Tribrachus + + + + Tribati + Tribitus + Attributus + + + uero + quidem + est + + + + constans ex tribus + breuibus + ex + tribus breuibus constans + + + acute + acutis + , sed + dactilus + + + + + + + anapestus + + + + trocheus et iambus + iambus et trocheus + + + similantur + + assimilantur + + + uterque + + utraque + vtrique + . + Similiter + Sic + + + etiam + et + igitur + + pedes quibus + vtimur + utuntur + diuersa + optinent + + + + loca + + in metro ut visum + est + + + + 20 + 24° + .

+

+ + Deinde. + + ET ITA. + + Tunc + Nunc + + applicat ad propositum, + dicens + + + + eodem modo in + consonantia + consonantiam + + + euenire soni + eueniet soni + euenit esoni + euenire + + aduenire eodem modo in consonantia + et proprie dyapason, nam motus + sonorum + + + + causatiui + causatur + cantantium + cantanti + cantantiui + cantui + canti + proportionem habent + ad + ad se + inuicem.

+

+ + Deinde. + + + ALIARUM. + ALIORUM. + Αssignat + secundo + + + + causam partis alterius + causam alterius partis + partem alterius + , + dicens quod + + , + de numero aliarum consonantiarum + ad + a + + dyapason quia sunt alterius + + proportionis ab ea, sunt + imperfecte + + , non enim sunt per + totum + tonum + ambientes + omnia + tria + signa .vii. uel .viii. + + monocordi + + monocordia + + + prima + + sicut + dyapason + + . Sed potius reuersiue facte circa + medium terminantur, + ut + in + dyatesseron + in + quarto + quarta + + medio + + + signo + signo et + dyapente in quinto, ut visum + est + + + .13°. + + et .32° + et 12º + + . Et ideo non habent virtutem equaliter + ceu + seu + sicut + dyapason, + uerum + sed + dicendum 8m. + potius + inequaliter + in equalitatem + inequalitantur + inequaliter licantur + propter ipsas, + namque + enim + sensus + horret + + + horum + haberent + + + auditus et + et auditus + corrumpitur. + Sunt + Sicut + enim + respectu + respectum + dyapason + aspere + ac + et + + + horride + + + + horride et aspere + , quod declarat, quia sicut accidit + in rotis + rotis + in dochus + cantantibus, + id est + id est in + + cantibus + rotatiuis + + + seu + conuersis + conuersiuis + conuersiuus + , + quod si aliquis + quia si + aliquis + + eleuando sonum ultra + id + illud + quod debet, + + saltem + saltare + in + maius + magis + sursum ad aliquas notas + in + ad + quas + non + nunc + debet + + peruenire, + accidit + + + + sonum + + totum dissolui, ut + apparet + patet + in organis + ita + + + + et + etiam et + + in aliis + consonantiis + consonantibus + + + + ad + a + + dyapason + contingit + + suo modo et maxime in dyatesseron, + uel + seu + + + rotis + + totis + , + id est + + + + instrumentis + in instrumentis + + + illis + + antiquioribus habentibus duas + + acies + animas acies + cordarum, + vnam + vna + + + quidem + quidam + siquidem + in vno + laterum + latere + et reliquam in altero, + que + qui + simul manibus tanguntur ambabus. + Nunc + Non + autem si + inequaliter + equaliter + + tetigerit eas, magis + pulsans + pulsans vnam quam aliam vel + cordas vnius partis quam alterius, + adulteratur + adulterantur + adultantur + + + simphonia + + symphoni et + , primum tamen + melius et uerius + melius et uniuersalius + vniuersalius et melius + . Dicit autem corruptio + sensui + sensuum + sensus + quia + dictum est + est dictum + quod musica non + solum + + + + rationi + rationem + + + innititur, ut + + innititur, + + + sensit + sensuit + sensiunt + sentit + posuit + sensui + + + pictagoras + + + pythagoricis + pictagorici + , + neque + + nunc + sed + + + tantummodo + tantum + sensui, + sicut + sic + + + aristoxenus + aristotenus + + + + + + + , sed + utrumque + vtrunque + utroque + uterque + + + contractat + connatat + .

+

+ + Deinde. + + AMPLIUS. Ponit + aliam + + solutionem uel magis + pretactam + pretactant + confirmat et declarat + dicens + dicens quod + + + rursus + + in + ypate + ypatem + accidere + quod + quod et + habeat + vnum et eundem + unum et eiusdem + et eundum + eundem + finem + omnium + omnium omnium + + + + peridorum + + + + siue + circuitionum + + circuitionem + existentium in sonis. In + ipsa + ipsam + + + enim + eius + , + tanquam + + + + in + + + + principaliorem + priorem + , + terminantur + terminatur + uel melius finem + perydorum + + + id est + resonationum + + resonationem + resonantium + post + ictum + dictum + + + remanentium + resonantium + diu in aere, quod + tinnitus + + + + rinitus + + + potest dici + dici potest + . Et ideo + vocatur + + + + magistra + + nigram + , ipsa + enim + eas + + + suscipit + + se concipit + omnes et obtundit cum eius + sit + fit + + + proprius + proprium + prius + + + antiphonizare + + antiphonaria + + + + et + atque + ac + + + organizare + + + + + . Sed secunda corda, + correspondens + + correspondet + + + ypati + ypate + per + oppositum + appositum + omnino, est + neatis siue netes uel neatis + + + + , + id est + siue + resonantie + siue tinitus + + + sumitanter + , pretacti. Dupliciter enim accipitur + neate + + neatis + + + .xlii. + 41° + + + apparens + apparens et + , + 2° + + + + cuius + enim + + + quidem + quidam + + + ictus et + + sonus + causatus + + + cantus + in aere. + In idem + Et idem + + + + finit + fuit + sunt + cum sono qui + fit + fiunt + fuit + ab ypate, ex + ambabus + ambobus + amborum + + + enim + enim sonis + + + consurgit + surgit + , ut visum + est + + + + sepius in + sepius + + + + simphonia + + dyapason. Et + merito + + , + quia + + licet non eundem sonum + reddant + reddeant + secundum se. + Ymmo + + + + vna acutum + et + + altera grauem. + Tandem + Tamen + Et idem + cum ipsarum soni + coniungantur + coniunguntur + iungantur + ad inuicem, contingit fieri vnum et + eundem sonum + omnifariam + omnifaria + , quemadmodum accidit + illis + illi + qui sonant instrumenta sub cantu cantantium. Uel quia + aliqui + aliquis + + + precinunt + precinit + ponunt et precinunt + precipiunt + + + et alii subcinunt + + et aliqui subcinunt + alii succinunt + + licet, + et + + enim videantur discordare in principio, + concidunt + excidunt + concidunt tamen + in + finem vnum + vnum finem + fine unum + . Et + illud est + id est + hoc est + idem + quod subiungitur, tales + namque + enim + + + non + + pariter et vna + fistulantur + fistulantur et cantant + , sed + secundum + + + + alia et alia + aliam et aliam + alia + . + Si tamen + Tamen et + + quamuis + sint + sunt + sicut + + + alii + alteri + + + et alteri + et aliquando + tamen + + + + concurrant + concurrunt + + + tandem + in eundem + + + + fine in vnum + in finem vnum + finem in vnum + finaliter in vnum + finem et vnum + + + quendam + quidem + aliquando + sonum, magis habent inducere delectationem quam + tristitiam + tristitia + , propter + hoc quod + quod dicere + + + differentie + dicere + + + seu + et + diuersitates que sunt in eis secundum principium reperte + sopiuntur + + seperiunt + + et concurrunt + demum + deinde + ad eundem finem + siue + seu + terminationem. In eo enim, + ut + quod + + + declaratum est + declaratum + + declaratum prius est + + + antea + + , + quod + + + + ex + et + + + differentiis + + diuersisque + extremis + ex terminis + + + efficitur + + + + vnum + vnum et + + + quoddam + quidem + + + commune + + + + + proportionatum + proportionaliter + proportionabiliter + . + Cum + Tamen + dyapason + sit + fit + sic + + + huius + huiusmodi + + + quod + quoque + + + relinquitur + + derelinquitur + + + ab ea + + + + simphonum + + + simplex hominum + delectabilissimum + extat + est + , quod + ostenditur + ostendit + quia secundum + eam organizare + + organizare eam + organizare + ex + oppositis + diuersis + uocibus + causatur + cantatur + + + et + in + sonis + tandem in unum + in vnum tandem + + in unum tamen + in unum + + + redactis + redactus + . Et quia dyapason + ex + in + + + huius + huiusmodi + + + consistit + + existit + , ut + expositum est + expositum + dictum est + , + sepius + + ideo + secundum + per + + + ipsam + huius + dictum est + solam + solum + nullamque + aliarum + aliorum + aliam + + + organizari + + organizare + , + .20. + + problemate + partes + + + .

+

+ Nosce + Notandum + + + quod + + sicut se habet uox composita ad simplicem, ita dyapason ad + reliquas + alias + consonantias. + + et cetera + + + problema 40. + + + et huius quidem expositio sufficiens iam 5to. apparebit parte repetitur uero ut memorie + amplius comendetur. +

+
+ +
+ + Quadragesimum + problema + 40m + Quadragesimum. + Quadragesimum + problema + 39m. + problema. + + +

+ PROPTER QUID DELECTABILITER + PROPTER QUID DELECTABILIUS + PROPTER QUID DELECTABILITER AUDIUNT + + PROPTER QUID DELECTABILITER AUDIUNT CANTANTES QUOSCUNQUE UTIQUE + PRESCIENTES ATTINGANT CANTUS QUAM SI NESCIUNT? + VTRUM QUIA MAGIS MANIFESTUS EST ATTINGENS + QUEMADMODUM INTENTIONEM QUANDO COGNOSCUNT QUOD CANITUR? COGNOSCENTIBUS AUTEM + DELECTABILE CONSIDERARE. + AUT COMPATIENS EST AUDITOR CANTANTI NOTUM? CONSONAT AUTEM IPSO, CANTAT + AUTEM OMNIS CONSONANS, QUI NON PROPTER ALIQUAM NECESSITATEM FACIT + HOC + . + + PROPTER QUID BIS PARACUTA AUT BIS IIII.OR NON CONCORDANT BIS DYAPASON AUTEM ITA. AUT QUIA QUOD QUIDEM + DYAPENTE EST IN EMIOLA PROPORTIONE QUID UERO + PER IIII.OR IN ENIPIRITIO EXISTENTIBUS AUT + EMIOLIBUS + TRIBUS CONSEQUENTER NUMERIS QUE EST EPITRITIO EXTREMA AD SE INUICEM NULLAM + PROPORTIONEM HABEBUNT. NEQUE ENIM PARTICULARIA ERUNT NEQUE MULTIPLICIA DYAPASON + AUT QUONIAM EST IN DUPLICI PROPORTIONE BIS. + HOC FACTO IN QUADRUPLICI PROPORTIONE SI FIUNT + EXTREMA AD INUICEM. QUARE QUONIAM CONSONANTIA RATIONABILEM HABENTIUM SONUM AD SE + INUICEM EST RATIONEM AUT QUI QUIDEM HABENT BIS DYAPASON INTER DECISIONEM AD SE + INUICEM SONI HABENT. QUI AUTEM BIS PER IIII.OR AUT PER QUINQUE NON HABENT + QUICQUID DYAPASON CONSONABUNT UTIQUE ALII UERO NON PER EA QUE DICTA SUNT. + + + + Et + + + + huius + huiusmodi + + + quidem + quidem problematis + autem + + expositio + sufficiens iam + + iam sufficiens + sufficienter iam + iam + + + quinto + + + + apparuit + apparebit + #Px shares #Ea's reading here. + + + problemate + capitulo + + . + Repetitur + Reperitur + + + uero + autem + ergo + igitur + enim + ut + memorie amplius commendetur + amplius memorie comendetur + memorie commendetur amplius + . + + et cetera + + + + Propter quid bis. Repetit 34. ut + amplius exponat. Aut quia. Soluit Et primo assignat causam prime partis Et secundo secunde ibi dyapason .3° concludit in tantum ibi quare quoniam Primo querit quare + quoniam dyapente est in sexquialtera + proportione dyatesseron in sexquitertia. hiis + itaque ita dispositis numerus ut 3us. etiam + numeris consequenter reiterati ut tria et + quatuor. ex quibus erat Epitrica ut dictum est proportio cum erant simplices in + repetiti. Tunc si extrema huiusmodi duarum + consonantiarum duplentur ad inuicem coniuncta nullam habebunt proportionem + consurgentem inde quod probatur quia talia non reddunt nec superticularia neque + multiplicia penes que ut visum est 13. + proportiones accipiuntur musice. vnde apparet quod aristotelis consentit pictagoricis has ponentibus solum Et non + concidit cum ptolomeo ponente proportionem + compositam ex dyatesseron et dyapason consurgere ex multiplici et + superparticulari. Si namque sumatur bis dyatesseron puta prima dyatesseron fit + proportio 3. ad 4. et 2a + 5. ad 4. + Et coniungantur extrema: ut .3. ad 4. Nulla consurgit proportio pretactorum + multiplicitatis aut superparticularis Similiter in dyapente si sumatur Exempli + gratia Vna dyapente cum 2 comparantur ad 3 et 2a quando .6. ad .9. ita ut duo comparentur ad .9. modo eodem nulla consurgit proportio cum omnis ut sic + constet in numero Epitrico. Emiolis + duplari: triplari Et quadruplo ut ostensum est + superius. etcetera Dyapason. Assignat causam 2e partis dicens quia dyapason se habet in dupla proportione si bis sumatur ea erit in quadruplici extremis + comparatis ad inuicem proportionum maiorum et minorum Puta sumatur bis dyapason ut + in vnaquaque comparetur vnum comparetur ad + duo Et reliqua 2 ad 4 resultabit numerus + quadruplus Iuxta quod predictum est bis + dyapason bis Quare quoniam 3° concludit intentum dicens Et ideo quia consonantia + est compositio quedam tonorum habentium et rationabilem et proportionalem + proportionem ad inuicem Et hoc habet bis dyapason Non autem bis dyatesseron aut + dyapente et reliqua Quod declaratur quia proportio quam habent soni ad inuicem Est + habere inter se decisiones et confractionem quandam ad inuicem per quam sonsultant + quidem proportionales armonici: ut bisdyapason quod non habet consonantiam per + 4or. et quinque siue dyatesseron et dyapente Cunque ut dictum est tantum soni qui + fuerunt secundum dyapason duplatum consonant + alii vero minime: sicut ostensum est per ante dictam causam. + #Pq runs problem 40 into 41 just as #Gu does. +

+
+ + +
+ + Quadragesimumprimum + problema + 41m + Quadragesimum primum. + Quadragesimumprimum. + Quadragesimumprimum problema etcetera. + + +

+ PROPTER QUID BIS PARACUTA + PROPTER QUID BIS + + PROPTER QUID BIS PARACUTA AUT BIS QUATUOR NON CONCORDANT, BIS DYAPASON AUTEM ITA? + AUT QUIA QUOD QUIDEM DYAPENTE EST IN EMIOLIA PROPORTIONE, QUOD UERO PER QUATUOR IN EPITRITO? EXISTENTIBUS AUTEM EMIOLIBUS + TRIBUS CONSEQUENTER NUMERIS, QUE EST EPITRICON, EXTREMA AD SE INUICEM NULLAM + PROPORTIONEM HABEBUNT, NEQUE ENIM PARTICULARIA NEQUE MULTIPLICIA ERUNT. + DYAPASON AUTEM, QUONIAM EST IN DUPLICI PROPORTIONE, BIS HOC FACTO, IN QUADRUPLICI PROPORTIONE SI FUERINT EXTREMA AD + INUICEM. + QUARE QUONIAM CONSONANTIA RATIONABILEM HABENTIUM + SONUM AD SE INUICEM EST, RATIONEM AUTEM QUI QUIDEM HABENT BIS DYAPASON + INTERDECISIONEM AD SE INUICEM SONI HABENT, QUI AUTEM BIS PER QUATUOR AUT BIS PER QUINQUE NON HABENT. QUI QUIDEM BIS DYAPASON CONSONABUNT, + UTIQUE ALII UERO NON PER EA QUE DICTA + SUNT + . + + Repetit trigesimumquartum ut amplius + exponat + exponatur + . +

+

+ + + Deinde. + + AUT. Soluit et primo + assignat causam prime partis, secundo secunde + secunda + secunda + ibi + ibi secunda + ibi + + DYAPASON, + 3° concludit + intentum + intentum ibi + + + + + QUARE QUONIAM + QUARE + . + + Dicens + Dicit + causam + esse + cesse + + Dicit primo causam esse + Primo querit quare + + + + quoniam + + dyapente + est + + in + sexquialtera proportione + proportione sexquialtera + , + dyatesseron in + dyatesseron + + + epitrica + + . Hiis + igitur + ergo + + + + ita + itaque + sic + + + dispositis + expositis + + + numeris + numerus + numeris consequenter + reiteratis ut tria ad 4. + , ut + duobus + tribus + + sexquialteris et tribus, + et + etiam + + + numeris + numerus + consequenter + reiteratis + reiterati + reiterari + , ut tria ad quatuor, ex quibus + erat + erant + + + epitrica + + , ut dictum + est + + proportio cum erant simplices + inrepetiti + repetiti + etiam repetiti + ut repetiti + , + tunc + termini + si extrema + huius duarum + huiusmodi duarum + harum duarum + duarum + huiusmodi + consonantiarum duplentur, ad + inuicem + coniuncta + coniunctam + coniecta + + + nullam + in illam + habebunt proportionem consurgentem. Inde quod + + probatur + prosequitur + , quia talia non + redduntur + reddunt + + + in + neque + superparticularia + neque + + multiplicia, penes + que + quem + , ut visum + est + + + + 13°. + .xix. + , + + proportiones assumuntur + + assumuntur proportiones + proportiones accipiuntur + musice. Unde apparet quod aristoteles + + consentit + pictagoricis + + + pictagoras + , has ponentibus solum, et non concidit + cum + causa + + + ptholomeo + + + + + , ponente + fore proportionem + proportionem fore + proportionem + + + compositam + compositum + expositum + ex + dyatesseron et dyapason + dyapason et dyatesseron + consurgere ex + multiplici + multiplicatione + et + superparticulari + superpartienti + superuenienti + . + Si namque + + Si enim + Si nam + + + sumatur + + bis dyatesseron + puta prima dyatesseron + + + + sit + fit + proportio + trium + tria + tripla + ad quatuor, + et + + + + + secunda + secunda uero + secunda cessat + + + sex ad + octo + sex + .8. + sex ad + 6to. + 5 ad 4 + , + et + coniungantur + coniungant + extrema, ut .3. + + comparando + operando + + ad + .8. + quatuor. + + + + + nulla + nullo + + + consurgit proportio + consurget proportio + proportio consurgit + contingit proportio + + secunda fit proportio 5a ad 4. nulla fit + proportio + + + + pretactarum + pretactorum + quantitarum + multiplicis + aut + autem + superparticularis. + Similiter + Similiter et + + + in + + dyapente, + + ut + + si + sumatur + + exempli gratia vna dyapente + + , puta cum duo + + comparantur + + ad tria, + et secunda + et 3a + et secunda et + secunda + . + quando + quandoque + + + .6. + es + cessat + + + ad + + + + .9., ita ut duo + + comparantur + comparentur + ad + + + .9.. + Modo + Non + + + eodem + eadem + nulla consurgit proportio + + + + cum omnis ut + omnis cum + sic constet + in + ex + + + numero + + + + epitrico + + + + emiola + + + + + + duplari + triplari et + quadruplo + + + , ut ostensum + est + et + + + + anterius + anterius et + in anterius + in antedictis + superius + . +

+

+ + + Deinde. + + DYAPASON. Assignat causam + 2e partis, dicens quia + dyapason se habet in + duplici + dupla + proportione, si bis + assumatur + + sumatur + ea + erit + habet se + in + quadruplici + + quatruplicibus + quatuor + + + extremis + in extremis + comparatis ad inuicem + proportionum + proportionem + proportione + proportionatum + + + minoribus et maioribus + maioribus et minoribus + minoris et + maioris + maioris et minoris + minoris et aliis + . + Puta + Puta ut + + + sumatur + + + + bis dyapason + + + + ut in vna quarum + ut in unaquaque + ut quarum + + + comparetur vnum + vnum + comparetur + comparatur vnum + ad duo + + et in + et + in + + + reliqua + reliquo + + duo ad + quatuor + .8 + , + + tunc + etiam + si extrema comparentur ad inuicem ut vnum ad quatuor + + #Gu also omits this lemma. + + + resultabit + resultat + + numerus quadruplus iuxta + quem + quam + quod + + + dictum + dictus + dignum + est + bis dyapason + dyapason bis + + + siue + siue non + fieri + sui in + + +

+

+ + + Deinde. + + QUARE QUONIAM. + + Concludit intentum 3° + 3°. + concludit intentum + , dicens + et + esse + ideo quia consonantia est + compositio + + quedam tonorum + habentium + + + + rationabilem + rationabile + rationalem + et + proportionatum + proportionalem + sonum + ad se inuicem + ad inuicem + , et hoc habet bis dyapason, non autem bis dyatesseron + aut + ut + + + dyapente + bis dyapente + et reliqua. Quod + declaratur + declarat + quoniam proportio + quam quidem + quam + quam siquidem + siquidem quam + habent soni ad inuicem + est + etiam + habere inter + se decisionem + + decisionem + se decisiones + et + confractionem + consurrectionem + + + ad inuicem + ad inuicem est habere + quandam, per quam + resultant + resultent + + + ipsi + quidam + + + proportionales + proportionabiles + armonici, ut bis dyapason, quod non habet + consonantia + consonantiam + + per quatuor + + aut + aut per + ad + + quinque siue dyatesseron + uel + siue + et + dyapente. + Sed + Cumque + ut dictum + est + + , tantum soni qui + fuerint + fuerunt + fluerunt + secundum dyapason + duplici + + + + + consonabunt + consonat + consonant + consonanter + + , alii + uero + + minime, sicut ostensum + est + + + + per + propter + antedictam causam. + + etcetera. + sequitur 42. + problema 19e. particule. + + + + propter quid bis paracuta autem bis iiii.or non concordant bis dyapason autem ita. Aut quia quod quidem + dyapente est in emiolia proportione quod uero + per iii.or in epyptrico existentibus autem + emiolibus + tribus consequenter numerus que est epitricon extrema ad se inuicem nullam + proportionem habebunt. neque enim particularia neque multiplitia erunt dyapason + quoniam est in duplici proportione bis. hoc + factum in quadruplici proportione si fuerint + extrema ad inuicem. quoniam consonantia rationabilem habentium sonum ad se inuicem + est rationem aut qui quidem habent bis dyapason interpositionem ad se inuicem soni + habent. qui autem quidem bis dyapason. et consonabunt utique alii uero non per ea + que dicta sunt. +

+
+ +
+ + Quadragesimumsecundum + problema + 42m + Quadragesimum secundum: + Quadragesimumsecundum. + Quadragesimum + primum problema. + + +

+ PROPTER QUID SI QUIS + PROPTER QUID SI QUID ALTERA + + PROPTER QUID SI QUIS ALTERA NITEM ACCIPIAT AUT YPATEM ACCIPIAT, YPATE + SOLA UIDETUR SUBSONARE? + AUT QUIA NEATE FINIENS ET DEPERDITA YPATE + FIT? + SIGNUM AUTEM POSSE AB YPATE NEATEN POSSE CANERE. + SICUT ENIM EXISTENTE IPSA CAUSAM NEATE, SIMILITUDINEM ACCIPIUNT AB IPSA. + QUONIAM AUTEM ET ECHO CANTUS QUIDAM EST, TACTUS EST UOCIS NEATIS + FINIENTIS SONUS EXISTENS IDEM SONO + YPATES MOUET CONUENIENTER, SIMILITUDINI YPATEM NITE UIDETUR MOUERE. NEATEN + ENIM SCIMUS UBI MOUETUR ASSUMPTA. YPATEN AUTEM IPSAM UIDENTES + INCOMPREHENSIBILEM EXISTENTEM ET SONUM IPSIUS AUDIENTES, HANC PUTAMUS SONARE. + QUOD IN MULTIS NOBIS ACCIDIT, IN QUIBUS NEQUE RATIONE. NEQUE SENSU POSSUMUS + CERTIFICARE CERTUM. + AMPLIUS SI PERCUSSA NEATE MAXIME TENSA + ACCIDIT IUGUM MOUERI NICHIL UTIQUE ERIT MIRABILE. MOTO AUTEM OMNES CORDAS + PARITER MOUERI ET SONUM FACERE NON IRRATIONABILE. ALIIS QUIDEM IGITUR NEATIS + SONUS ALIENUS EST ET FINIENS ET INCIPIENS, YPATE AUTEM FINIENS IDEM. NON + APPOSITO PROPRIO SUO MOTU, ILLIUS UIDEBITUR OMNIA EORUNDEM ESSE NON EST + INCONUENIENS. ERIT AUTEM MAIOR QUAM RELIQUARUM CORDARUM SONUS, QUOD HEE QUIDEM + A NEATE SICUT IMPULSE MOLLITER SONUERUNT, NEATE AUTEM, TOTA SUI IPSIUS + POTENTIA EXISTENS, IPSARUM FORTISSIMA EST. + QUARE MERITO ET SECULARIUM IPSIUS MAIUS ERIT QUAM + QUOD EST ALIARUM, QUARE BREUES MOUERI, SICUT IPSIS + . + + Problema quadragesimum + secundum etcetera. + + + Quare + Querit quare + si quis cantu + aut tactu + aut tacta + aut atactu + + + + altera + altam + + + + suscipiat + + suscipiet + + + nitem + + nitorum + uocem + + + siue + aut + + + extremam + extremam ut + , quia + multiplex + iuxta + ut + visum + rismis quidem + dictum + + + est + + , aut + pro et + per + ypatem accipiat, simul coniungens + alias + alteras + ambas + quidem + alteram + altera + altam + uocem, tunc + sola + solo + + + ypate + ypatem + sentitur ultimo subsonare, + + non + nota + quidem quod minorem sonum reddat, + sed + seu + + + + sonat + at + posterius cum sonus + eius + enim + finitur, ipsa + enim + causa + est + illa + ista + + + ex + in + qua relinquitur + sonus, ille + ille, sonus + + + faticius + + + + + + diutius + resonatio + resonantia + dicta uel neate + seu + siue + + + tinitus + + + + timitus cantus + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit primo assignans + Primo soluit assignans + Soluit et primo assignat + + + causam + causam et + , .2° confirmat et declarat + ipsam magis + magis ipsam + . + Secunda + ibi secunda + : + AMPLIUS. Primo + igitur + ergo + + + causam dat + dat causam + dat causam causam + , + dicens hoc esse + dicens ideo esse + huius esse dicens + huiusmodi dicens esse + huiusmodi dicens hoc esse + + quoniam + cum + + sonus + nites + + vites + finitur + deperditur + disperditur + de proportione + et + occultatur + + hoc vtatur + propter + resonationem + resonantiam + + + ypates + + , + ceu + seu + sicut + maior motus + depellit minorem + minorem depulit + , ea + namque + enim + + + sola videtur posterius + videtur posterius sola + videtur sola posterius + uidetur posterius + + + subsonare + resonare + .

+

+ + Deinde. + + SIGNUM. + + Declarat 2° + Secundo declarat + per signum, dicens + signum nobis ideo + signum nobis illud + signum nobis id + signum nobis hoc + signum nobis + + + demonstrans est + + demonstrans esse + demorans est + denotans est + esse designans + quoniam + neate + meatis + potest amplius + subsonare + subsentire + + + tanta + causata + + cata + causata + + causatam + ab + ypate + ypatem + diutius + remanendo + remanente + post tactum + corde + corde quam neate + alicuius alterius corde + + + quam + per quod + neate + alicuius alterius corde + aliquis alterius cordis + . Unde cum ipsa + potissime + potissima + sit causa, + ut accidat + + ut accidet + ne accidat + neate, + omnes + quiaa + #Py has the quia symbol with the squiggly-line "a" symbol above + it + relique corde + in terminatione + iteratione + in + qnacoe + quando a commune + et + + + suorum sonorum + sonorum suorum + + + suscipiunt + + similitudinem ab + ypate + + ypatem + .

+

Nosce quod + neate interdum + + interdum neate + + + sumitur + + + + pro hypate + pro nete + + . Ut visum + est + + + + + .13. + 23º. + + + et .39. + 239. + et .19º. + : + est enim quasi corda iuuenilis et inferior accipitur + etiam + enim + pro resonatione secunda que + sentitur + retinetur + diu post + percussionem + repercussionem + , + ceu + seu + sicut + + + hic + hinc + . + Ps.Arist. + Prob. + XIX.13, 918b ll. 3–6 and XIX.39, 921a ll. 7–31 + + Sicut + Sint + + + enim + est + neate corda + est + est cum + inferior, ita + resonatio etiam + etiam resonatio etiam + resonatio et + etiam resonantia + ypates est debilior sono priori, + sic ut + + sic nunc + + + concidant + concidunt + .

+

Quod + autem + aut + ita sit + ostenditur etiam + etiam ostenditur + ostenditur et + ostenditur + per + echo + + + + + de quo dictum + est + + + + + .11a. + 14 + , + Ps.Arist. + Prob. + XI.23, 901b ll. + 18–19; XI.51, 904b ll. + 29–33 + quod est quidam + cantus + tinitus + et intus + + seu sonus + + + + reflexus. Est enim + hic + huius + + + + echo + + + + + + + cantus + aut + autem + seu + sonus + + uocis + siue + seu + soni + neatis uel + + + + + + + resonationis + + + + finientis + + finis entis + existens idem cum sono + ypates + + ypate + principaliori, quando + fuit + fuerit + + + tactus eius + eius tactus + , + differens + differentiis + , + tamen + tamen a + cum + tam + + + priori et + priori + + + posteriori + + , fortiori et debiliori. Nam + cum + causam + + + aliquid mouetur + mouetur aliquid + ita ut + decenter + decenter et + + + adaptetur + + aptetur + similitudini soni + qui + que + quo + fit secundum + ypatem + + , postremo + tunc + autem + + + + apparet + + + + ac si + sicut + + + nite + + uite + + + actu + acum + tangeretur resonatio + siquidem + + + + ypates + ypate + videtur sono + principaliori netes + + adaptari. + Tam + Vum + Illius + + + enim + causa + + + + immensus est + + est immensus + immersus est + intensus est + + + ypates + + sonus quod + deficiens + + + + equiparatur + + equiparetur + sono + netes + + principaliori. Quod ostenditur + quia + quod + + + neatem + + neate + alterius + corde + corde alterius + ab ypate scire dicimur + quando + cum + tangitur + presignata + prelibata + + + corda et + corde + + + mouetur + + ab ea altera. + Sed secus accidit circa ypatem + + quoniam etiam si videmus + quod + per + ypates non + comprehendatur + comprehenditur + ita ut manifeste + tangi eam + eam tangi + + + scimus + uidemus scimus + sentimus + , sonum + tamen + tamen autem + tantum + audientes in + communi + + communim + + + extimamus + + existimamus + propter + ipsius + ipsam + eius + + + diuturnam + + + + + resonationem + resonantiam + + fore ipsius. + Quod + + declarat eo quod + id + + non solum + hic accidit + accidit hic + huius accidit + , + uerum + sed + + + et in multis + etiam in multis + multis + aliis rebus de quibus non habemus perfectam rationem + neque + + + + sensum + + + + perspicacem + perspicationem + perspicuitatem + perfectum seu perspicacem + . ex quibus + possumus certificari omnino + possumus omnino certificari + certificari omnino + non possumus omnino certificari + in talibus tunc accipimus + inde aliquam opinionem + ap rationem aliquam + + + estimatione debili + + debili estimatione + existimatione debili + ex terminatione debili + + + constrictam + constructam + coniectiua + . + Sic itaque + Siccam + ypate + resonat + sonat + pre aliis. Neate + etiam + + , + que + quam + ultimo + relinquitur + reliquam + , ipsius extat que + aliarum + aliorum + + + occultat + + occidat + et + deperdit + departem + neatem.

+

+ + Deinde. + + AMPLIUS. Secundo + confirmat + confirmat confirmat + declarat + causam predictam uel alteram subiungit, dicens quod non est mirabile + aliquod + aliquid + si + contingat + contingit + + + iugum + iustum + istam + moueri + subito + cito + + + + a + et + + + situ suo + suo situ + cum + ypate + ypatem + + + fuerit + fuerint + fuit + maxime + tensa + sensa + . Si accidat quod + premissum est + premissum + premisit + , + neque etiam + + neque + est + mirum + vicium + . Si omnes + tunc corde + corde tunc + cum corde + + + alie + + + + pariter moueantur + pariter moueatur + moueantur pariter + moueantur + + + et + in + et in + sonum + reddant + + + + cum iugum + coniugum + coniunctum + cui + innituntur + + immittuntur + + + a + et + + + sua + suo + mox + mouetur + mouentur + mouerunt + moueantur + positione, licet tamen sic accidat + sonus + + + + neates + + + + qui + quibus + fit ab aliis + cordis + + + + preterquam + + ab ypate + extraneus + extraneus etiam + extremus + + + est et + esse + + + debilis + debilis est + in principio ac etiam in fine, + cum + cum primo + cum in + + + ypates + + ypate + + + concidat + sonum + sonat + . Sed + huius + huiusmodi + + sonus incipiens et finiens idem + permanet, non enim sono + apponitur seu adiungitur + adiungitur seu apponitur + apponitur ceu adiungitur + adiungitur seu opponitur + + concidat sonum sed huius sonus + incipiens + dat sonum sed huius + sonus incipiens et finiens + sonus incipiens + et finiens idem permanet + et finiens idem + permanet non enim sono adiungitur + permanet non enim sono adiungitur seu apponitur. + aliarum, + seu + ceu + econtra, ipsa + namque + enim + + + proportio + proprio + + + concitata + + + concita + + + motu + motum + videbitur quod omnes soni + sint + sunt + + + earundem + + + + + cordarum aliarum + aliarum cordarum + + + eius, cum + ei, cum + cuius + + in eam + concidant + concidunt + non concidant + + + + occultati + + . + Quod + + + + etiam, cum + cum etiam + est, cum + + + sit + sint + fit + + + soni + soli + ceteris + fortioris + fortiores + , + id + + non + reputatur + reparatur + inconueniens, quare tunc sonus + ipsius + eius + + + est + erit + + + maior + manifestior + quam sonus aliarum cordarum. Nam + alie + ille + + + quidem + quidam + impulse mollem + reddunt + reddiderunt + sonum et paruum, ac si esset quedam neate ypates. Cuius + equidem + eadem + eidem + quidam + + + est neate + est neates + tota, cum + extet + extat + existat + fortissima + virtute + uirtutis + ceterarum cordarum. + + Quod + Quod sicut + Quod sit + Quid + principalior ostendit + eius + ipsius + sonus, per iugum + siquidem + enim quidem + audio scabellum super quod + substentantur + + corde aut + illud + + vniversaliter super quod + innixe + in nixeto + in nixeto + nixeto + inuise + in mese + + + + + extenduntur + coextenduntur + coextenditur + . Uel + per + + iugum + intelligit + intelligitur + + + sinzeusim siue + + + + + + + sinzeus in siue + Initeus in sui + + + coniunctionem + coniunctioni + coniunctione + coniectionem + + + duorum + duarum + duo + + + tetracordarum + + cetera cordarum + retrocordorum + + + in + et + mese, ut videbitur + .44 + in + .44. + innixe + coexuntur + .

+

+ + Deinde. + + + MERITO. + QUARE MERITO. + QUINTO. + + + Concludit + Ostendit + + tertio intentum, + dicens + + + quare non immerito + secularium + + + + ipsius ypates + ypates ipsius + + unus ypates + ipsius compates + + + uel + seu + + + condeterminatio + cum determinatio + conterminatio + confirmatio + + + seu + uel + siue + finis, solent enim musici, et + maxime + + + + psallentes + + + psallentis + , + in diuinis + + + + in fine + + + + dicere + + seculorum amen. Est maius + et diutius + in diuinis + perdurans + quam + + + + secularium + secularum + seculorum + secularus + reliquarum cordarum, + quapropter + quam propter + per + + + reliquis sicut + sicut reliquis + reliquas sicut + reliquis sic + + + ipsis + ipsius + + existentibus breuis motus + in + + ypate + longi + longum + longa + longe + longius + + + neatem + neate + neatem diutius permanet + + + omnium + oppositum + + + conterminatur + conterminantur + in + ipsam + ipsa + . Et ideo + eam solam + solam eam + in eam solam + accidit subsonare, + ut componatur + huius + huiusmodi + sermo. + Ipsa + + illa + ista + ita + corda videtur + sola subsonare + subsonare sola + + subsonare + + + + + + seu + siue + + + post + per + alias + resonare + cordas sonare + sonare + + + , cuius neate diutius + permanet + permaneat + post cessationem aliarum + neates + neatis + , + talis quidem + quidem talis + tales quidem + talis quod + , + ut declaratum est, ypate + ut declaratum est est, ypate + ypate sonum, ut declaratum est + ut declaratum est, ypate est + ut declaratum, etiam in ypate + .

+

Nosce quod potest + causa huius + causa huiusmodi + causa eius + hoc causa + eam huius + + + breuitatis + breuiter + + + assignari + talis assignari + asignari talis + signari + , + quia + quod + + + ypate + Parypate + + + sonum reddit + reddit sonum + sonum reddat + grauem, + qui + que + + + extenditur + extendit + secundum longum + latum et + profundum + profunditatem + , + reliqua + relique + uero ad ipsam + acutum + accidit + , qui secundum longum + + , + ut + ceu + seu + sicut + + + uisum est + uisum e + uisum + + + + xia + prius + . + Ps.Arist. + Prob. + XI.16, 900b ll. 17–25 + Tardius + autem + aut + + + + quietatur + quietatus + comoratur + commutatur + + + sonus + sonum + aeris secundum plures moti dimensiones + quam secundum + unam + unum + cum + dictum etiam sit + etiam dictum sit + dictum etiam sit quod + etiam sit + dictum est etiam + + + graue + graue et + tarde et multum moueri + acutum + acuta + acutum uero + + + econtra + + , + ut + + + + uisum est sepius antea + uisum sepius antea + + . + + etcetera. + sequitur 43. + problema 19e. particule. +

+
+ +
+ + Quadragesimumtertium + problema + 43m + quadragesimum tertium. + Quadragesimumtertium. + 42m. + problema. + + +

+ PROPTER QUID DELECTABILE + + PROPTER QUID DELECTABILE UNIUS CANTUS EST SI AD LYRAM ET FISTULAM + CANTANT? + AUT QUIA OMNE DELECTABILE MIXTUM DELECTABILI UNUM + EST? + FISTULA ENIM DELECTABILIUS EST LYRA, QUARE ET CANTUS HOC MIXTO LYRA DELECTABILIUS + UTIQUE ERIT, QUONIAM MIXTUM IMMIXTO DELECTABILIUS EST, SI UTRORUNQUE SENSUM + ALIQUIS SIMUL ACCIPIAT. + UINUM ENIM DELECTABILIUS EST OXIMELLE. PROPTER ID + QUOD MIXTA SUNT MAGIS IPSIS QUE A NATURA MIXTA QUAM QUE A NOBIS, EST ENIM ET + UINUM QUOD EST MIXTUM EX ACUTO ET DULCI HUMORE. MANIFESTANT AUTEM ET GRANATA + UOCATA MUZA. + CANTUS QUIDEM IGITUR ET FISTULA MISCENTUR SIBI + IPSIS PROPTER SIMILITUDINEM, SPIRITU ENIM UTRAQUE FIUNT. SONUS AUTEM LYRE, + QUONIAM AUTEM NON SPIRITU FIT. + AUT MINUS SENSIBILE QUAM QUI EST FISTULE + INCOMMIXTIBILIS EST UOCE? FACIENS AUTEM DIFFERENTIAM SENSUI MINUS DELECTAT, + QUEMADMODUM IN SAPORIBUS DICTUM EST. + AMPLIUS FISTULA QUIDEM MULTA SUO SONO ET + SIMILITUDINE OCCULTAT PECCATORUM QUE SUNT CANTUS. LYRE AUTEM SONI, EXISTENTES + TENUES ET INCOMMIXTIBILES UOCI SECUNDUM SE CONSIDERATI ET EXISTENTES SIBI + IPSIS MANIFESTUM FACIUNT CANTUS PECCATUM, QUEMADMODUM REGULE EXISTENTES + IPSORUM. INIUSTIS AUTEM IN CANTU CULPATIS, COMMUNE EX UTRISQUE NECESSARIE PEIUS + FIERI + . + + Problema .43m. + etcetera. + + + Quare + Querit quare + cantus vnius + cum altero + altero est + + + mixtus + nuptus + + + uel cantus vnicus + uel cantus unius + uel cantus uel + uel cantus + + + + delectabilis + delectabilius + laudabilis + + + et suauis existit + existit et suauis + uel suauis existit + , puta, si + fuerit aliquis + aliquis fuerit + + + cantans + cantus + + + in + in in + sono lyre uel fistule? + Et + + adhuc delectabilior + est + cum + + + cantus fistule + sonus fistule siue cantus + + + quam + uel + lyre, + et + + per + se + et + + + + + + coniectus + coniunctus + + + cantui + + , ita ut triplex + fiat + fiat cantus + comparatio: puta, cantus simplicis + ad + ad cantus + + + compositum, et simplicis ad simplicem + compositum, et simplicitatem + simplicem + , + ut + et + non + + + fistule ad lyram, et + compositi + compositum + ad compositum, + sicut + ut + non + ac + + + + fistule et cantus ad lyram + et cantum.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit et primo assignat + causam quare + causam et quare + quia + cantus + vnius + vnus + cum sono alterius + uel + velut + cantus + vnicus + + musicus + + + sit + fit + delectabilis, + dicens prius + prius dicens + dicens primo + causam esse quoniam delectabile + omne + esse + etiam + + + commixtum est + + + quod mixtum est + , et + vnitum + vnicum + mixtum + ex diuersis, ut declaratum + est + + + + .38 + .18 + prius + . Quod autem + sit + sic + + + + delectabile + delectabilis dicens prius causam + vnum existit, + cum tunc + tamen tunc + cum tamen + cum causa + cum + + + vniformius + + uniformis + + + sensum moueat + moueat sensum + .

+

+ + Deinde. + + + FISTULA ENIM. + FISTULA. + Comparat 2° fistulam + ad lyram + penes + ponens + + + delectationem + delectationem et + . + Secundo + primo + assignat + causam + aliam causam + quare sonus fistule + est + sit + + delectabilior + eo qui + eo quod + est quod + quam + lyre. + Secunda + Secunda + ibi + Ibi secunda + Ibi + : + AUT. + + autem + āt + + + + Dicit + dicens + + + ergo + igitur + enim + + + + primo + + + quod fistula est + delectabilius instrumentum + auditu + auditui + quam lyra. + + Unde + + etiam cantus + commixtus + + + + ex + cum + uoce et fistula + + est + erit + + + iocundior + ioculoxior + + + commixto ex + + cum mixto et + uoce et lyra + + + + . Et hoc quia illud + quod + + + + est mixtum + mixtum est + mixtum + + est conmixtum + + + delectabilius + delectabilius est + + + eo quod + eo quod est + simplex + et + + + + immixtum + + + , + dummodo mixtura + + utrorumque + mixtibilium + + sensibilium mixtibilium + sentiatur + utcunque + utrumque + utique + existens + tamen + + in quadam + conmixtione + coniunctione + soni notione + .

+

+ + Deinde. + + + UINUM. + UNUM. + VNDE. + Declarat + secundo id in + id .2°. + in + 2° illud in + 2° + in + + + mixtione + + + + nature et artis + nature id est artis + nature naturis + , dicens quod + vinum quod + unum quod + vnumquodque + illud quod + est simplex + arte + erit + , + conmixtum + + + + tamen + cum + + + natura + anima + , + est delectabilius + delectabilius est + + + oximelle + exmilleus + ex melle + + + seu + ceu + + + acetimelle + + + aceto melle + accetimellis + aceti + aceti et melle + , quod + est + est in + arte + constructum + constrictum + constructionem + conmixtum + ex + melle + melle et + + + aceto + + et + aqua + quia + . Propter quod + vino + vinum + + modo + ipsi sunt amplius + mixta + + conmixta + ea que sunt + nature + natura + uere + + + quam + quod + in + mixtione + + commixtione + artificiali per nos + constructa + considerata + , sicut + illa + ea + que + oximellis + oximelle + ex mellis + . In priori + causa + enim + + + uera extat + extat uera + extat natura + existat vera + + + mixtio + commixtio + in + oximelle + + oximello + exmellere + , + uero + nature + uero secundum + + + sensualis + sensibilis + sensum + + tantum. Nam + vinum, quod + vnumquodque + est + mixtum quoddam + + quoddam mixtum + + + nature + naturale + , + componitur + compositum + compositio + ex humore acuto et dulci + mixtione + commixtione + + + sufficienter + sufficienti + . + Circa + Certa + Causata + quod + manifestant + manifestat + + + granata + grauata + generata + nominata + musa seu + + muza se + muca seu + + + + messa + + musa + , id est media, sunt + enim + + + tria specie: dulcia, + acida, et + acida + acuta, et + media ( + conmixta + + commixti + + + ex + et + dulci et + acetoso + + sapore). Et + ideo + + magis delectant + quando + quam + in vno tertio + + facta + certam + sunt + natura talia + naturalia + quam si + miscerentur + ministrantur + + + arte + aere + dulcia + cum + + + + + acidis + acetosis + . + Quidam + Quidem + quoque + habet + habent + + + + ex melle + oximelle + + loco + eius + est + quod + + expositum + expositum est + est expositum + + + ex melle + eximelle + oximelle + melle + , quod non + sic + sit + + + + approbo + ambo + , + quamuis id + quam id + quamuis sic + quamuis + licet + + + + + exposuerim + exposueram + exposuerint + expositum sit + + + quandoque + quoniam + .

+

+ + Deinde. + + CANTUS. Applicat ad propositum + concludendo + + , dicens + itaque + itaque quod + ita + + cantus + in + et + fistula + commiscetur + commiscentur + + + sibi + sub + ipsis propter similitudinem quam + habent + habent in + ad inuicem. Quod ostenditur + quia + quoniam + quando + ex + utrique, + ut + scilicet + cantus et fistule, soni perficiuntur flatu ex ore, + namque + enim + prodeunt. + Sed + Quod + + sonus lyre + non + non construitur + , + sed + + + + potius + + tactu + perficitur + construitur + instruitur + rotatio. Que autem similia sunt ad inuicem delectant amplius, cum + delitia + delitie + delectatio + + + causentur + causetur + causantur + tenetur + ex coniunctione conuenientis cum + conueniente + conuenienti + conueniente ut + + + 4° + de <app> + <lem wit="#γ #κ #Ea">accidenti</lem> + <rdg wit="#π #Py #m #v" ana="#morphological">accidente</rdg> + </app>. + Gal. + De morbo et acc. + IV.6 (The Greek original which d'Abano is here paraphrasing occurs in + bk. I of the treatise called De symptomatum causis) +

+

+ Nosce + Notandum + + + quod mixtio + quam connixtio + + + vini + vni + + + proportionatur sono + sono proportionatur + composito + + et + + + + facto ex fistula + ex fistula facto + et uoce, + que + quod + autem + ex oximellis + + + oximellis + oximell + oximelli + oximel + ex melle + + + simplici + simplicis + + + aut + autem + + + composito + compositi + + + ex uoce et + lyra + lyra composito + , respectu alterius + qui + que + + + ex + est + fistula.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit + assignans + assignando + et assignat + + + causam + aliam causam + causam duplicem + quare sonus lyre non + ut qui fistule est + ut qui fistule + est ut qui fistule + ut que fistule est + delectabilis. + Secunda: AMPLIUS. + Secunda + ibi: AMPLIUS. + Ibi secunda: + AMPLIUS. + + + + Dicit + Dicens + + + + primo + prius + + + id + ideo + + id prius + esse quoniam sonus lyre minus + est + + + + sensibilis + sensui + quam + sonus + + fistule, + quam minus + quare minus + quamuis + , + enim + eius + ein + + + componibilis + ponibilis + comparabilis + possibilis + est cum uoce, + habet + hec + enim + differentiam + differentia + dicta + , ut + iam + + visum + est + + ad ipsam. + + Ex illo autem + Ex isto autem + Ex illo + Et ideo + quod differentiam + et + diuersitatem + diuersitate + ad sensum habet + et diuersitatem habet ad sensum + habet et diuersitatem ad sensum + diuersitatem + minor sentitur delectatio, sicut + apparuit + apparet + + + in + + saporibus arte + et natura mixtis + et natura in mixtis + et natura compositis + commixtis et natura + .

+

+ + Deinde. + + + AMPLIUS. + AMPLIUS. Amplius + Assignat + causam secundam + secundam causam + causam dicens + secundam. + causam duplam + , + dicens + dicit + quod fistula propter suum + sonum + motum + et eius similitudinem, + quia + ut + sua fortitudine soni + extollit + + excellit + excedit + uocem + cantantis + + , + obtegit multa peccata + peccata multa obtegit + in + cantu + cantu cantu + contingentia. Sed soni + lyre + lyres + lyri + , + quia + + subtiles sunt et parui et + incommiscibiles + + + + + + uoci + uoces + , cum + secundum + per + se + considerantur + consideratur + considerentur + , + prout + cum + + + in seipsis + + + + extant + extent + + et non in aliis, + quibus + in quibus + qui hiis + + + occultentur + occultantur + , + manifestum est quod + manifestum quod + manifestum + aliam quam + Minor quia + circa ipsos + peccatum + peccant + + + accidit + accidunt + in cantu, + nam + non + in ipso, + sicut + sic + in aliis + scientiis + sonis + sunt + canones + canonem + quidam per quos armonice canitur, a quibus + + cum + dum + + + receditur + recedatur + contingit in cantu peccare. Quare subditur quod + + accidit + acutum + + + iniustis + + in musicis + in instrumentis + in tristis + in istis + non recte predictos canones + obseruantes + obseruantibus + + + alia + ac + littera + multis ac + multis hac + multis autem + + melior, ut peccent et + culpentur + culpent + cohientur + in cantu. Quod enim commune + existit + ex istis + , + ut ex + ex + + + + utrisque + utriusque + + + confectum + cum factum + , puta uoce + et + non + instrumento sicut lyra, + necessarie + necesse est + necessa est + uocem + deterius perfici eorum + consonantia + dissonantia + discordantia + distantia + , + contra + circa + + + regulas + duas + + + armonicas + armonice + canonicas + factum. + + et cetera + sequitur 44m. + problema 19e. particule. +

+
+ +
+ + Quadragesimumquartum + problema + 44m + Quadragesimumquartum. + quadragesimumquartum. + 43m. + problema. + + +

+ PROPTER QUID SEPTEM + + PROPTER QUID SEPTEM QUIDEM MEDIA + UOCATUR, OCTO AUTEM NON EST MEDIUM? + AUT QUIA SEPTEM CORDARUM FUERUNT ANTIQUITUS CONSONANTIE, SEPTEM AUTEM HABET MEDIUM? + AMPLIUS EORUM QUE SUNT IN MEDIO EXTREMITATUM, + MEDIUM SOLUM PRINCIPIUM QUODDAM EST, EST ENIM ALTERA EXTREMITATUM DECLINANTIUM IN ALIQUA DISTANTIA PER MEDIUM + QUOD PRINCIPIUM EST: HOC EST MEDIUM. QUONIAM AUTEM ULTIMA MEDIUM EST + CONSONANTIE NEATE ET YPATE, HORUM AUTEM IN MEDIO RELIQUI SONI, QUORUM MEDIA + UOCATA SOLA PRINCIPIUM EST ALTERIUS TETRACORDI, IUSTE MEDIA APPELLATUR. + EORUM AUTEM QUE SUNT IN MEDIO QUARUNDAM + EXTREMITATUM MEDIUM ERAT PRINCIPIUM SOLUM + . + + Problema .44m. etcetera. + + + Repetit + Quare repetit + + 25° + + et + + + + utcunque + utrunque + + + + 33m. + + , + dicens + + + + quare + + + + .7. + a + dicitur + habere medium etcetera + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit + + et + primo assignat + assignat primo + causam, + et iam + et inde + que iam + unde + + + apparuit + apparente + + 2°. + Quia + mentionem fecerat + + fecerat mentionem + de medio, + ostendit + dicit + + + quomodo + quomodo autem + + + accipiatur medium + medium accipitur + accipitur medium + accipiuntur medium + + + cum + dicitur + + + .7. habere medium + + cuius + gratia problema + problema gratia + + + repetiit + repetit + .

+

+ Secunda + Secunda ibi + Ibi secunda + Ibi + + AMPLIUS. + + Dicit + Dicens + + + igitur + igitur primo + + quod vno modo + dicitur medium + medium dicitur + + + quoddam principium + principium quoddam + + + existens medium + inter duo extrema nam + illud principium per quamdam distantiam equaliter declinat ab utroque + extremorum dicitur medium + + inter duo extrema, nam illud principium + quod + + per quandam + distantiam + distantia + equaliter + declinat + determinat + + ab utroque extremorum dicitur + medium, + sicut in aliqua consonantia est dare + sicut aliqua consonantia est dare + sicut in alia consonantia est dare + sicut in alico sonantia est dare + inter + + duo + + ultima + extrema sicut in alia distantiam est dare .2. extrema + + + ut + quod + vnus + sit sonus + sonus sit + + + cantus + + causatus + ab ypate fortis existens, + secundus + secundo + alius + a + neate siue + + + + nete + a nete + , inter quos est dare plures sonos medios + distantes ab extremis + ab extremis distantes + secundum + maius + magis + et minus, + ceu + seu + + + inter vnum + introductum + et septem + + que intermedia + + inter que ueniunt media + que alias inter inde cum media + 5. + intermedia + quia inde cum media + + + ut + et + + + .5. reliqua + dicantur + dicatur + dicuntur + + + media + mediam + .

+

+ Notandum + Nota + quod + huius + huiusmodi + + + medium dicitur principium + medium dicitur + principium medium dicitur principium + eo quod + est + + + + habitus + + quidam virtutis + qui + que + principium extat + actuum + actium + acutiuum + acutum + , cum sit diuisibile habens quantitatem. + Est et + Est etiam + aliud medium + uere + + + + indiuisibile + indiuisibile natura + ; quale medium + dicitur + dicuntur + + + solum illa habere + solum habere illa + solum illi habere + illa + sola habere + quorum + medium est principium alterius + tetracordi + + + + + tetracorda + . Quod non appellatur uere principium, sed + + medium magis, + sicut + sic + positis .7. cordis, quarta, + quidem + quidam + ut mese, repetita cum tribus + + superioribus + et inferioribus + + + + etiam + ea + + tribus + inferioribus et tribus superioribus + , + constituuntur + constituitur + constituetur + constituunt + + + duo + + + + tetracorda + + + + + tunc mese utrobique + uere + + medium extat. + + verbi gratia + verbi gratia si ordinantur + + + + Ypate. + + + + Parypate. + primum tetracordum. + + + Lychanos. + + + + Mese. + + + + Paramese. + + + + Paranete. + secundum + + tetracordum. + retracordium + + + + + Nete. + + +
+ + Primum retrocordum + + + + Et + + + + huius + huiusmodi + + + duo quidem + quidem duo + secundo quidem + duo + .20. + quidem + illius quidem + + + tetracorda + + + + secundum + sinzeusim ordinantur + + + sinzeusim + , + + + + cum + autem + + + + fuerint + fuerit + + + .8. + quatuor + corde secundum + dyazeusim + + + + + + + + computantur. + + + +

+

+ + Deinde. + + EORUM. + + Tunc + Nunc + repetit medium prius horum, + et + etiam + apparet sic igitur medium est + duplex + + : + vnum + + quidem geometricum + siue + ceu + quo ad nos + aut + autem + aliud + + + per abnegationem + + paranegomon + extremorum, + aliud vero + aliud uero aliud vero + + arismetricum + seu + secundum + + + rei + rei uel + uel + in uel secundum + + + per + pre + + indiuisibilem + equidistantiam + + ab extremis.

+

Apparet denique quod secundum + primum + plurimum + + + medium + modum + potest dici + dyaocto + + + + . Unde + primo + musice: + in + octocordo + + + sexto + corde + + + due semper + duo + semper + + + medie + + reperiuntur, + et + etiam + + + non + + vna + media + + potest inueniri. + Boeth. + De inst. mus. + Ι.20 (Friedlein p. 208, ll. 8–10) + + + etcetera. + sequitur 45. + problema. +

+
+ +
+ + Quadragesimumquintum + problema + 45m + quadragesimumquintum. + Quadragesimumquintum. + 44m. + problema. + + +

+ PROPTER QUID MULTI + PROPTER QUID MULTIPLICANTES + + PROPTER QUID MULTI CANTANTES SALUANT MAGIS RITHIMUM QUAM PAUCI? + AUT QUIA MAGIS AD UNUM, AUT ET RECTOREM, INTENDUNT + ET TARDIUS INCIPIUNT, QUARE FACILIUS IPSUM ADIPISCUNTUR? IN UELOCI QUIDEM + IGITUR MAGIS FIT PECCATUM. + ACCIDIT AUTEM DUCI INTENDERE MULTOS. APPROPRIATUS + AUTEM NULLUS UTIQUE IPSORUM ILLUSTRABITUR, ELEUANS MULTITUDINEM. IN PAUCIS + AUTEM MAGIS ILLUSTRANTUR, PROPTER QUΟD SECUNDUM SE IN SE IPSIS MAGIS + EXERCITANTUR QUAM APUD DUCEM + . + + Problema .45m. + etcetera. + Repetit + .22m + .22m. + problema + 21m + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit et primo assignat causam + et iam visum est + ut iam visum + + . Secundo + + declarat + declarat in + + + assignando + et assignat + + + differentiam + differentias + + + inter + + habentes ducem in cantu + et + et inter + + non + habentes + habentem + . Cuius + causa + causam + + + reiterauit + reiterat + sermonem: + 2a + 2a ibi + ibi + + + ACCIDIT + ante + . + Dicit + Dicens + + + 2° + hoc + contingere + quod + quia + + multi ad ducem + attendant + attendunt + ut eorum cantus + saluetur + saluentur + per amplius, quoniam cum + fuerint + fiunt + + + multi + + , nullus + ipsorum + eorum + determinatur, + ut + in + + + eleuando + + uocem + suam + + propter multitudinem, non paruam + poterit + + + + illustrari + illuxiari uel illustrari + + et super + aliorum + alios + + + uoces + uocem + uocens + + + suam extollere + suas extollere + suam vocem extollere + suam attollere + suam excellere + , + cum + quia + plurimi magis ualeant quam vnus + appropriatus + adappriatus + . Sed in paucis cantantibus + id + illud + + + + poterit + potest + sufficienter contingere, quare pauci cantantes plus + secundum + + semet ipsos + exercitantur + excitantur + et + singulariter + similliter + vniformiter + + + apparent + apparet + in cantu suo + illustrari + illustrati + quam + qui + que + + + + apud + + ducem plures cantantes + existunt + existent + + , + + non enim + enim + + + + singulatim + sigillatim + sed ad ducem + exercitantur + + . + + + et cetera + amen + dooo . + + + Problema 46 + + + huius precessit expositio .26°. + et uerita illic iam apparuit cuiusdam apparentis contrarietatis inter .27m. et istud cum dictum sit ibidem difficilius + acute cantare quam grauiter. hic autem videtur contrarium dici. sequitur 47. problema 19e. particule. +

+
+ +
+ + Quadragesimumsextum + problema + 46m + quadragesimum.sextum. + Quadragesimumsextum. + 44m. + problema. + + +

+ PROPTER QUID IN ACUTUM + PROPTER QUID IN ACUTIS + + + PROPTER QUID IN ACUTUM DISSONANT PLURIMI? + AUT QUIA FACILIUS ACUTUM DIMITTERE + QUAM GRAUE? + CANTANT IGITUR ACUTE MAGIS, ET IN QUO CANTANT + PECCANT + . + + + Huius + Huiusmodi + Cuius + Huius problematis + + + precessit + + + + expositio + expositio ex + + .26°.. Et ueritas + illic iam + iam illic + illic + hic iam + + + apparuit + apparet + + + cuiusdam + + + + apparentis + apparente + contrarietatis inter + .37m + .27m. + , et + istud + + illud + + + cum + tamen + dictum sit + ibidem + ibi + difficilius esse + acute cantare + cantare acute + quam grauiter. Hic + autem + + videtur contrarium + dici + dicere + . + + et cetera + +

+
+ +
+ + Quadragesimumseptimum + problema + 47m + quadragesimum septimum + Quadragesimumseptimum. + 45m. + problema. + + +

+ PROPTER QUID ANTIQUI + + PROPTER QUID ANTIQUI, SEPTEM + CORDARUM FACIENTES CONSONANTIAS, RELIQUERUNT YPATEM, SED NON NITEM + RELINQUERUNT? + AUT NON YPATEM, SED NUNC PARAMESEN APPELLATAM, + ABSTULERUNT ET TONILEM DISTANTIAM. UTEBANTUR AUTEM ULTIMA MEDIA DENSI IN + ACUTUM, PROPTER QUOD ET MEDIAM IPSAM APPELLAUERUNT. + AUT QUIA ERAT SUPERIORIS TETRACORDI FINIS, + INFERIORIS AUTEM PRINCIPIUM, ET MEDIAM HABEBAT PROPORTIONEM TONO + EXTREMITATUM + ? + + Quadragesimumseptimum problema etcetera. + + + Repetit + Repetit quoddam problema predictum + + + 7m, et + apparuit iam + iam apparuit + apparet iam + + + eius + + + + expositio + propositio + expositio propositio + + et apparuit iam ex ipso 7 + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + + Soluit + Soluit assignans + + + dupliciter + causam dupliciter + , + aliter tamen + aliter causam + et aliter + quam prius, dicens + primo + + quod non abstulerunt + + de 7 cordo + de 7º + corde + de 7 + cordis + de a cordo + decacordo + + + ypatem + + , sed non pro neque cordam + appellatam + dictam + + + paramese + paramesem + seu + tritem + + trite + cetere + . Sed abstulerunt + + #Vc also omits this passage + , ut + propositum + dictum + est, + nitem + + nitem uel netem + et per consequens + toni + tonum + thonum + communi + + + distantiam + distantia + , + que + qui + + + attenditur + + ab vna corda in aliam + siue + seu + + + ab + + vna voce in + alteram + aliam + , + ceu + seu + sicut + + + ut re + ut 20. + . + + Constituunt + Constituit + + enim due + uoces + tonum + + ita quod vna corda + cassata + causata + cessata + + + tollitur uox vna + tollitur vna uox + tolleri uox vna + + coller + coll'. + mox una + , + et + + per consequens + tonus + + totius + , cum ex duabus + + constet + + uocibus. + Auferentes + + + autem + nete + nete quia + nete qua + netem + , + ne + ut + + + armonie + armonice + + + destruerentur + destruentur + , cum media corda + paramese + + , + puta + + primo + modo medii + modo media + + + dicto + dicta + dicte + + + .44., + supplebant + supplebunt + supplebantur + + + defectum + + + + nete + uocis + + + sublate + + + + . + Utebantur + Putabantur + + + enim + enim cum + + media, + scilicet paramese + + paramese scilicet + , loco + ultime + ultimo + , + scilicet nete + videlicet nete + paranete scilicet + , quod + erat + + + + cum + quod + + + extendebant + extendant + + + eam + eum + + + in tantum + tantum + + ut sonum + redderet + reddent + rediret + + + acutum + + + , + ad modum + ut + nete, ita quod + cum + + + + ypate + ypatem + + + constituerent + constituerunt + construerent + dyapason, sicut cum nete preexistente. Et merito quoniam + corda + + + + extensior acutiorem reddit sonum + extensior reddit sonum acutiorem + exterior acutiorem reddit sonum + extentiora tuciorem reddit sonum + , + grauior + grauiorem + + + autem + uero + tardiorem, quare + mediam + + medium + appellauere, eo quod medium + habet virtutem + uirtutem habet + tenet virtutem + + + extremi + extremorum + + + ad ipsum comparatum + + comparatum ad ipsum + . + Si + Scilicet + + + namque + enim + autem + + + minus + uidetur + + + extensa + tensa + plus tenet locum medii, amplius uero extremi, aut + erat + erit + + + + policordum + + pollicordum dum + policordium uel policorniam + + + diegeugeneum + + + + + + + + + + + + , id est + disiunctum + + + disiectum + districtum + , ubi + cordarum + corde + + + reiterantur alique + alique + alique reiterantur + uel duplantur, ut + apparuit + apparebit + apparebat + apparente + + + 3° + problemate 3º + 30 + .13 + .

+

+ + Deinde. + + AUT. Assignat + aliam causam + causam aliam + , + dicens + scilicet + + + quia + quod + media + corda + cordarum + , + ut + uel + paramese virtute + quidem + quadam + + + et + ut + non distantia, ut tactum + + est + , erat + finis tetracordi superioris et principium + alterius + + + finis + inferius + + + tetracordi + + + tetracordandi + tractandi + + + inferioris + differens + , ut + uisum + + dictum est uel uisum + + + est + + . + Que + Quia + , secundum quod + existit media + media existit + existit mediam + ex illic media + est media + , + habet + habent + proportionem ad + extremitates + extremitatem + ambas suo tono, secundum quod + fuerit + fuerint + + + + isti + viri + + extremorum + comparata + comparata ad extrema + uel + alteri + alter + alterius + . Nam medium comparatum + ad + + + + extrema + extremum + vnum extremorum + + videtur alterum, .5. + + phisicorum + + , aut + ordinabatur + ordinabitur + ordinabam + paramese + ante mese + ante mesem + quoniam mese + aut in mese + , ut + distantia + destructa + + + etiam + + fere + sit + fit + sic + media. + Sic + Sicut + + igitur + quia + + paramese habet + uicem + nitem + uocem + extremorum ut medium, et quia + per eam + per eum + postea + ambo + constituuntur + constituunt + + + tetracordi + + + + tetracorda + + + virtute + uirtute autem + + + saltem + saltim + . + Siue + Sine + Seu + + + nete + + dubitatur, quia dictum est in septimo quod non + abstulerunt + abstulerit + + + nitem + + nete + + , + sed + secundum + scilicet + + tertiam + + id est tritem + + id est trite + ut tritem + id est netem + siue paramese.

+

Dicendum quod antiquitus + fuit primitus + fuit inuentus + fuit prius + + paramese quam nete + inuenta + inuentam + , + ceu + seu + sicut + + + pretactum + tractum + + + est + est in + + + 13°. + deinde + Demum + + + superueniens + superuenientis + preueniens + perueniens + veniens + + + tripandius + + + , extrahens tertiam + cordam ut + paramese + paramesem + paramesen + paramese est + + + a + + cordarum ordine, + netem + nete + uel netem + neque + loco + illius + ipsius + adiunxit ita + ut + + primitus non + fuerit + fuit + nete, postea uero + adinuenta + adiuncta + extiterit. Et sic + utrunque + + utraque + + + uerificabitur + uerificatur + + + particula + problema + . + + etcetera + sequitur 48. + problema 19e. particule. + + + verbi gratia + + ypate + + + + paripate + primum tena + cordum + + + lychanos + + + + mese + + + + paramese + 45 + + + Paramete + + + + nete + + +
Et huius 3us quidem cetra corda 2m. sinzeusim +

+
+ +
+ + Quadragesimumoctauum + problema + 48m + Quadragesimumoctauum + Quadragesimumoctauum. + 46m. + problema. + + +

+ PROPTER QUID IN TRAGEDIA + PROPTER QUID IN TRAGEDIA CHORI + + PROPTER QUID IN TRAGEDIA CHORI NON YPODORISTIUM NEQUE YPOFRIDISTIE + CANTANT? + AUT QUIA CANTUM MINIME HABENT HEE CONSONANTIE, QUO + INDIGENT MAGIS CHORO? + CONSUETUDINEM AUTEM CONSONANTIAM QUE QUIDEM EST + YPOFRIDISTIUM OPERATIUUM, PROPTER QUOD ET IN GERIONEM + EXITUS ET DEARMATIO IN HAC FACIEBANT. + YPODORISTIUM AUTEM MAGNIFICUM ET STABILE, PROPTER + QUOD ET CITHARISTISSIMA EST CONSONANTIARUM. + HEC AUTEM UTRAQUE CHORO QUIDEM IN CONSONANTIA, EIS + AUTEM QUE SUNT A SCENA MAGIS PROPRIA. ILLI ENIM HEROUM MUTATIUI, HII AUTEM + DUCES ANTIQUORUM SOLI FUERUNT. + PROPRII AUTEM HOMINES QUORUM EST CHORUS. PROPTER + QUOD ET CONUENIT IPSI LAMENTABILIS ET QUIETUS MOS ET MELOS, HUMANA ENIM. + + HEC AUTEM HABENT ALIE CONSONANTIE, MINUS AUTEM + ILLIS QUE EST YPOFRIGISTIUM, DIUINA UEL FURIOSA AUTEM ET BACHICHA. SECUNDUM + HANC QUIDEM PATIMUR ALIQUID, PASSIUI AUTEM IMBECILLES MAGIS FORTIBUS SUNT, + PROPTER QUOD ET IPSA CONUENIT CHORIS. SECUNDUM AUTEM EAM QUE EST YPODORISTIUM + ET YPOFRIDISTIUM OPERAMUR QUOD NON EST PROPRIUM CHORO. + EST AUTEM CHORUS CURATOR INOPERABILIS, + BENIUOLENTIAM ENIM SOLUM PREBET QUIBUS ADEST + . + + Problema .48m. + etcetera. + Repetit + 30m + 30. + problema + .3°. + + + ut amplius + exponat + apponat + + + + + dicens + + + quare chori + secundum tragediam + secundum tragedia + sicut tragedia + secundum trocordia + non cantant + cantum + + + + ypodoristium + + + + + + + et multo minus + et multo minus et + et multo minus et multo + minus + + + + ypofrigium + + + ypostigium + upotragium + ? Que + autem + autem sint + ista + exposita sunt + exposita + expositum est + + + .30°. + .3°. + + + antea + antea sunt + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit et primo in communi + dicens + + dicit + causam esse quia + huius + huiusmodi + consonantie, puta + ypodoristie + + + + + + + + + ac + et + + + ypofrigie + + ypofrigistice + + + , non + habent + fiunt + modum cantandi quo amplius indigent cantantes cantu chorico. + + Alie + Alia + + + namque + enim + consonantie proportione + indigent + indiget + + + chori + proportione + , et + alie + alia + + + leges + lege + + + comedice + + comete + , sub quibus + ypofrigius + + + + + + continetur + continentur + continet + continere + + cantus + et + ex + + + ypodoricus + + + , ut apparuit + .15 + 5º + .

+

+ + Deinde. + + + CONSUETUDINEM. + CONSUETUDINE. + + + Solutionem declarat secundo + Secundo declarat solutionem + solutionem declarat + 2° declarat + in + speciali + + + speciali + spali + et + spirituali + , + postea + + primo + notificat quid + sit + + chorus. + Secunda + Secunda ibi + ibi Secunda + + + EST AUTEM + EST AUTEM CHORUS + . + + Adhuc + Ad hoc + + + ostendit + .2°. + ostendit + primo + ostendit + + + quales + qualis + + + sint + sunt + cantus + ypodoristii + + + ypodoristum + ypodorium + yporistii + et + ypofrigii + + + + + , et + quorum + chorum + + + + secundo + 2a + + + chorici + chorico + qui chorici + . + Secunda + Secunda + ibi + Ibi secunda + Ibi + + + + PROPRII AUTEM + PROPRIA AUTEM + . + + Dicit + dicens + primo quod ex consuetudine longa est + consonantiam + consonantia + quandam + percipere in cantu + in cantu percipere + ab infantia, enim mox audiuntur. + Et + ideo + non + leges cantus + quidam fuerunt + quidem fuerunt + appellati, ut visum + est + + + 28. Que quidem consonantia + consuetudinaria secundum cantum + ypodoristium + + + ypodoristi + et + ypofrigium + + + + + + attenditur + + + artem dicitur + + + maxime + maxima + , cum + operatiuus + operatiuis + operatiuum + existat. + + Ipso + Ipsi + enim laborantes + incitantur + exitantur + excitantur + exercitantur + ad opus, ut + apparet + patet + in sono quem emittunt + antennas + + + + + anthoras + ante nos + in malos + eleuantes + + + . Et ideo cantus + qui + + fuere + fuerunt + + + antiquitus + antiquatenus + apud + gerionem + + genortem + et gentem + darmaticam + + + + + + + + + faciebant + fatiebant + exitus tandem + et + + + + terminationes + terminantes + terminationem + + + in consonantia + in consonantiam + consonantiam in + + + ypofrigiam + + + + + , sicut et + ditirambi + + + + + + dyterambus + dyachitambum + dicti rambi. + + + demum + + deinde + + + concidunt + decidunt uel concidunt + + + in ipsam + ipsam + in ipsa + , ut uisum + est + + + + 30° + 3° + .

+

+ + Deinde. + + + YPODORISTIUM. + YPODORISTI + YPODORISTUS. + Ostendit secundo qualis + sit + + cantus + + ypodoristium. Dicit quod + + + ypodoricis. Dicit quod + ypodoristus, dicens quod + ypodorisi, dicens quod + dicens ypodoristium + + ypodorum + + + + cantus + + + + ypodoristius + + + + ypodoristicum + ypodoristium + + + + + + est + est est + fit + + + magnificus laudabilis uirilis stabilis + laudabilis magnificus uirilis stabilis + magnificus uirilis laudabilis stabilis + magnificus laudabilis et uirilis + laudabilis magnificus stabilis et + virilis + . Unde inter + ceteras + + consonantias + est + + forte + citaricissimus + + + + + cicurrissimus + ticurrissimus + acutissimus + . + + Existit + + + + quod propter + propter quod + quam propter + lidium + dictum sit + sit dictum + ut + uisum est + uisum + apparet + + + 30° + 3° + , + et + + in + hiis + + + + indicatur + duacatur + + + sue rationis maior + rationis sue maior + rationis sui maior + sue rationis maius + sue + .

+

+ + Deinde. + + + HEC AUTEM. + + HIC AUTEM. + HUC AUTEM. + HOC AUTEM. + HUIC AUT. + CUM AUTEM. + NON AUTEM. + Ostendit qualis sit cantus choricus + subdens + + minorem, + dicens + + quod hec utraque consonantia, + puta + + + + ypofrigium + + + ypophrygius + ypofrigia + ypophigia + ypofrigii + ypofori + ypoforis + et + ypodoristium + + ypodoristia + ypodoristica + ypodorius + ypodoris + ypodotis + , + relatione + ratione + cantus chorici + est + + + + uelut + ualde + ultima + universaliter + verus + + + + in + + + + consonantia + consonantiam + consonantias velud consonantia + + . Unde + est + est in + + + illis + istis + ipsis + extranea, sed magis + propria + pro + + + duobus predictis + duabus predictis + predictis duobus + duobus + primis + + + cantandi modis + modis cantandi + est consonantia + ascema dicta, existens + + + dicta ascema, existens + + ut visum + est + + prius + mutatiua + mutata + mutatam + mutam + . Et + huius + huiusmodi + quidem + consonantia + consonantie + consonant + modi appellati + commutatiui + + comutatum + + + erant + + in + vsu + vsi + uisu + + + apud + + amplius + + + hereos + + + + , ipsi enim + soli + solum + fuerunt duces et gubernatores antiquorum, + + incitantes + incitando + excitantes + ipsos in actus + huius + huiusmodi + cantibus, ut in bellum uel aliud. + Et proprie + Et proprie in + Et proprium + + + + ypofrigium + + + ypophrygius + ypifrigis + ypofrigii + + ypofri + , + operatiui + operatim + + + enim + enim sunt + est + magis.

+

+ + Deinde. + + + PROPRII. + PROPRII AUTEM. + + + Ostendit + dicit + + + qualis + que qualis + et quorum + sit + sic + cantus choricus, dicens primo quod homines + singulares et priuati sunt + illi + + quorum cantus est choricus, et + propterea + + propter hoc + propter + + + fruuntur + finitur + formatur + fortiter + + + hiis + iis + illis + + + que + quem + ipsius. + Sibi namque + Si enim + + + conuenit + competit + ut + sit + + + + lamentabilis + + lemdabilis + , + inducens + + ut ducens + + + + in pietatem + in pietates + impietatem + homines, + etiam + et et + + + + agrestes + + , + et + + quietus more + in + + + et + + + + honestus + honesti + omestus + et + melodiosus + + + melodiosos + maxime, hec enim humana sunt et mansueta. Et + ideo + + + + amatores tali + amatores tale + amatorabtali + admonitores tali + + + genere cantandi + cantandi genere + vtuntur + in demulciendo + + + + et demulciendo + inde multitudo + + + dominarum primitus animos suarum + agrestes + primitus agrestes animos suarum dominarum + primitus dominarum animos suarum agrestes + primitus dominarum animos agrestes suarum + primitus dominarum animos suos + agrestes + dominarum primitus animas suarum agrestes + .

+

+ + Deinde. + + + HIC + HEC + HOC + + + AUTEM. + ETIAM. + Ostendit + 2° + + quod talia minus insunt + ceteris + + aliis + + + consonantiis + consonantia + + + achorica + + a chorico + , dicens quod + relique + reliqua + consonantie + prefate + prefacte + pretacte + minus participant + cum + + predictis, nam + ypofrigia + + + + est diuina + seu + et + legalis, ut apparuit .15. + + et + + uel + + + .28. + .24. + .18º. + .26. + , uel + furiosa + + furiosam + furioso + incitans + homines + + + + in + ad + tumultum + + et + uel + + + furiam + + . + Est autem + Aut est + + aut + + + bachica + + + + + brachia + + + praua + puta + biana + + + solida + solido + stolida + solitu + + , iuxta + illud + + + + noni + + 30e, + 30e + 4º, + .34e, + regule, + + + propter quod + propter quid + + + bachici + + + + + arthici + artifices ut + frequenter + frequentetur + sunt mali. + Ps.Arist. + Prob. + XXX.10, 956b ll. 11–12 + Iuxta siquidem + huius + huiusmodi + consonantiarum + imperfectarum + dictarum + frigiarum + factarum + fictarum + + + modum + modo + modos + + + patimur + patiuntur + + + aliquid, cum autem patimur + + + + imbecilliores + + + imbecilles + , amplius fortibus + reddimur + + redduntur + . + Et + + ideo non possumus + cantum tenere + tenere cantum + tantum cantum tenere + choricum, sed leges + facimus + facilius + + + et + ut + aut + + + ascema + + , ut tactum + est + + + + .15° + .55° + . Sed quia hiis opposite + sumus dispositi + dispositi sumus + sumus disposite + + + cum + ut + + + cantus + cantus cantus + est + lamentabilis + delectabilis + + + etcetera + + , + tunc + tunc .3. + tamen + competit dispositio nostra + et + potentia cantibus + predicta cantantibus + procantibus + + + choricis + choricum + . + Potest + Poterit + enim ipsos + seruare + conseruare + , + quamuis + quam + licet + cum + + + + extent + extant + existunt + exterit + sint + laboriosi, non + autem + enim + + + conuenit + cum nec + + + ut + sicut + + + dictum + + + + est + + + + ypofrigiam + ypofrigia + + + proprie + propria + ipsis, + operatiua + operatam + operatiam + operava + temperatera + + + namque + enim + , sicut expositum + est + + .

+

+ + Deinde. + + EST AUTEM. Ultimo + manifestat + monstrat + quid + sit + est + + + + + chorus + choris + , + dicens quod + et dicit quod + + + + chorus est + uelut quidam + uelut quod + uniuersaliter quidam + sicut quidam + quidam ualde + + + curator + curat + , + + studet + studens + enim + remouere + remouetur de + curas et + sollicitudines + + solicitudinem + ab audientibus. Est + et + etiam + + + + inoperabilis + incomparabilis + , non + enim + enim non enim + eos + eam + + + incitat + excitat + ad + actus + actum + + + ut + et + + + ypofrigium + + + ypofrigius + ypofrigii + ypofrigia + , + sed + licet + + + solum + + sonum + actum + + + beniuolentiam et complacentiam + benuolentiam + inducit quibus auditu + incurrit + + occurrit + occurat + . + Nihil + + enim post factum + relinquit + reliquid + cum + solum + sono + + + animos + animas + demulcere + laboret + laborat + labores + . + + etcetera + sequitur 49m. + problema 19e. particule. +

+
+ +
+ + Quadragesimumnonum + problema + 49m + xl. Nonum. doooo + Quadragesimumnonum. + 47m. + problema. + + +

+ PROPTER QUID SONORUM + + PROPTER QUID, SONORUM FACIENTIUM CONSONANTIAM, IN GRAUIORI EST + MOLLIOR? + AUT QUIA IN MELODIA SUA UOCE MOLLIS EST ET QUIETA, EA AUTEM QUE EST RITHIMI MISTIONE + ASPERA ET MOTIUA? + QUONIAM AUTEM GRAUIS QUIDEM SONUS MOLLIS ET + QUIETUS EST, ACUTUS AUTEM MOTIUUS, ET HABENTIBUS IDEM MELOS, ERIT UTIQUE + MOLLIOR GRAUIOR IN EODEM MELOS MAGIS. ERAT AUTEM MELOS IPSI MOLLE + . + + Problema .49m. + etcetera. + + + Quare + Querit quare + consonantia ex grauibus + causata + canta + + + sonis + sonus + est + mollior + melior + + + et delectabilior + + ac delectabior + + + + quam ex acutis + + + acutis + + + constructa + constituta + ?

+

+ + Deinde. + + AUT QUIA. Soluit, + primo ostendens + primo ostendit + et primo ostendit + + + quare + quod + consonantia + uocis + vocum + + + grauioris + grauiori + grauiore + grauior + est + mollior + + melior + . 2° adaptat + ad eam que sonorum + eam que sonorum + que sonorum ad ea + + + illic + ibi + . QUONIAM + AUTEM + + . + + Dicit causam + + Dicit primo causam + Dicens causam + Assignat causam dicens + + + + esse + + quoniam huius + huius esse quoniam + esse huius quoniam + esse quoniam huiusmodi + esse quia huiusmodi + + + consonantia + consonantiam + + + in + est + + + melodia + + melius + propter + suam uocem + vocem suam + suam + + + delectabilem + delectationem + laudabilem + + + ex qua + ex qui + in qua + + + construitur + constituitur + astruitur + mollis + est et + et + est + quieta, iuxta illud quod + prius dictum est + dictum est prius + dictum est + dictum prius + de cantu chorico. Sed fere per oppositum + consonantia + consonantie + + + rithimica ob suam + mixtionem + + minus + consonam + consona + + + + + aspera existit + asperexerit + aspera + , + pungens auditum + auditum pungens + + + et immutans + + et mutans + + + mox + subiecta + subiuncta + subita + , quasi + alteratione + alteratiua + + + nature + uero + + + preliatiua + + preliata + preliatam + .

+

+ + Deinde. + + + QUONIAM. + QUONIAM AUTEM. + QUANDO AUTEM. + Applicat ad sonum, dicens + similiter + simpliciter + + + esse + est + omne + + + in sono + + + quoniam grauis, ut dictum + est + + de uoce mollis, + est + + + + quietus et + et quietus + quietus est et + et quietus et + amenus, sed acutus + asper est + asper + et + conmotiuus + commotus + commutiuus + comonens + . + Unde + + Ui Unde + vnde + + posito quod + extat utrobique eadem + utrobique extat eadem + extet utrobique eadem + melodia illa que + est grauior + grauior est + erit grauior + erat grauior + + + mollior et + et mollior + melior est et + + + delectabilior + delectabilior erit + in + eadem + eodem + melodia + magis + ea que est grauior + , + nam + non + + + melos + + + + ipsius est + ipsi est + ipsius + + + molle + melle + + + quasi + id est + dulce.

+

+ Nota + Notandum + quod + cetera + certa + omnis + ita + circa + et altera + + consonantia debet constare ex acuto et graui. + Mollior tamen est + amenior + et amenior + et suauior + amor + et amor + et a motu + cum + in + + graue + tendit + cedit + + + quam + quem + antea + + + quando + cum + in acutum. + + etcetera + sequitur 50m. + problema 19e. particule. +

+
+ +
+ + Quinquagesimum problema + Ultimum problema + 50m + Quinquagesimum. + Quinquagesimum. + 48m. + problema. + + +

+ PROPTER QUID EQUALIUM + + PROPTER QUID EQUALIUM DOLIORUM ET SIMILIUM SIQUIDEM ALTERUM UACUUM FUERIT, + ALTERUM UERO AD MEDIUM PLENUM, DYAPASON CONSONAT ECHO? + AUT QUIA DUPLEX FIT ET QUE EST EX MEDIO EIUS QUE + EST EX UACUO? + QUID ENIM DIFFERT HOC QUAM IN FISTULIS? UIDETUR + ENIM UELOCIOR MOTUS ACUTIOR ESSE, IN MAIORIBUS AUTEM TARDIUS AER OBUIAT. ET IN + DUPLICIBUS TANTUM, ET IN ALIIS PROPORTIONALE. CONSONAT AUTEM DYAPASON ET + DUPLEX ITER AD MEDIUM + . + + Problema .50m. + etcetera. + + + Quare + Querit quare + + + si + cum + aliquis accipiat + duo + et + dolia eiusdem + + mensure + materie + + + + quantitatis + quantitatum + + + et + + + + figure et + + + et + + + vniuersaliter + vniuersalis + similitudinis omnis, in omnibus + enim + + + + sit + sunt + equalitas nisi + in hiis in + in iis in + in + in hiis nisi in hiis in + + quibus + fit + sit + comparatio, + ut visum est + ut visum + + + .5°. + + + 25°, + et 5º, + + + Pietro expresses this idea in his commentary on problem 10 of particula 15. + His reference to 5/25 is obscure. + puta quod + vnum sit + sit vnum + vnum est + + + omnino + omnis + + + corpore + + + + solido + + solito + ut liquore + aliquo + acuto + + + + + vacuum + vacuo + + + plenum, tamen aere + aere tamen plenum + plenum, tamen aer + + + , + + idem + namque + enim + tamen + + + apud vulgus est + est apud uulgum + amplius uulgus est + + + uacuum + et plenum aere + et aere plenum + plenum tamen aere + + , + .7°. + <app> + <lem wit="#α #κ #Pp #Pu #Pz #Vo #m #v">topicorum</lem> + + </app>, + Arist. + Top. + VII.1, 152b, l. 20 + + + et + + alterum sit semiplenum, et + percutiantur + percutiatur + etiam + equaliter + aliqualiter + + + quocunque + quoque + + + modo + uel + + + ambo + + , + uel + ut + + + clametur + clauetur + in ipsis; tunc + echo + + + resultans + ex + in + + + hiis + ipsis + + + per refractionem + per fractionem + prefatis + ad parietes reddit + simphoniam + + + + dyapasonicam + + + dyapason sonicam + dyapason solidam + dyapason eam + dyapason causa + dyapason + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit + et + + + + dicit primo causam + + primo dicit causam + id primo causam + primo dicens causam + esse quia sonus causatus ex uacuo + uase + + + + se habet + habet se + + + + ad sonum causatum + ex + a + semipleno + in + et + + + dupla + + proportione + in proportione dupla ad sonum causatum a semipleno + , continet + enim + omni + bis + eius + + + + totum + tonum + + + quod + quidem + uacuum + omne + esse + id quod + semiuacuum + + semimatium + semiatiuum + soni uacuum + . Dictum est + autem + enim + + + + .13° + 30. + .20. + quod dyapason ex numero duplici nascitur.

+

+ + Deinde. + + + QUID + QUOD + + + ENIM. + IGITUR + + + Secundo + + remouet + dubitationem + dubium alias dubitationem + dubium + , + quia crederet aliquis + + + + quod + + ex sonis talium non + resultaret + resonaret + + + simphonia + + + sicut ex sonis + aliorum + aliarum + . Et ideo + subdit + subdiderit + quod non est aliqua differentia + + quin + quando + quare + quasi + ex + sonis + sono + + + istorum + istarum + istis + istorum non + + + constituatur + causetur + + + dyapason consonantia + dyapason secundum + consonantiam + , + ceu + seu + sicut + + ex sono fistularum et + huius + huiusmodi + instrumentorum + motorum + + spiritu + seu + ceu + tactu. Quod ostendit + inuentio + inuentor + inuentorum + musice + malleorum + + + soni proportione, ut dictum + est + est in + + + + primo + prius + , quod siquidem + contingere bene + potest + contingere potest bene + bene contingere potest + considero vnde ponit + + + cum + eam + + + ubique + + in talibus ratio + semper proportionis duplicis + proportionis duplicis semper + semper proportionis dupliciter + + + obseruetur + bene obseruetur + . Quod ostenditur + quia + quia a + quod + dyapason + causatur + + + + ex + ab + + + acuto et graui + graui et acuto + acuto + quod + hic + huius + huic + accidit, + nam + est iam + motus uelocior factus in + semipleno + angustia loci + percipitur + percipere + + + esse + + acutior, in maiori autem tardius mouetur et obuiat + aer + aeri + + resistenti, + propter + propter uel + + + plurimam + plurima + multam + + + quantitatem ipsius + ipsius quantitatem + + + motam + motum + et per longam distantiam ut visum + est xia + xia est + xia + est + 41 + , ita + quod + ut + in + + hiis + iis + que sunt dupla + + ad inuicem + in ad inuicem + et + in + + + + + + etiam + aliis + aliis etiam + + + que + quod + aliquam proportionem + numeralem habent + habent numeralem + habent + numeralem + inter se consonat et + efficitur + conficitur + + + penes + + + + duplicia + + duplaria + dyapason. Cadit enim duplex + iter + inter + + + + et + est + + + + distantia + distantiam + + + extremi + et fini + ad medium, + ut in pleno, + vnum autem + vni autem + vini aut + verum autem + autem numeri + + + in + + + + semiuacuo + + + , cum alterum + contineat + continet + + + + pleni + pleni pleni + medietatem. Secundum uero + epitrica + + epitricam + + + dyatesseron + et dyatesseron + et + emiola + + + + emioligi + dyapente + et cetera + et illic + , ut + monstratum + + + manifestum + + + est + + + .13°.

+

+ Ex + Et + hiis + utique + itaque + + + quam + quamuis + + + breuius + breuiter + vermis + + + prodierunt + prodierint + producunt + in + lucem + latem + + + utcunque + utrunque + circa liberales artes, et + maxime circa + maxime + + + + + mathematica + + mathematicam + mathematicas + methaphysica + + + problemata + probabilis + proposita + + problemata mathematica + , grandi + textuali + + + + caligine + caligere + cum eius + corruptione + corrupta + + + inuoluta quandoque + quandoque inuoluta + inuoluta quando + . + In quibus etiam + In pluribus etiam + In quibusdam etiam + quia plurimis + extranea + extra ea + non + grandis + grandi + + + utilitas + utilitatis + subtilitas + que + hodie + a plurimis + + + appetitur + apparetur + + + summe reperitur + reperitur + + , quare + ipsa + in ipsa + ea + + + + celerius + + + + percurri + precucurri + precurri + precurrari + precucari + procurari + . + Nunc + Non + + + autem + + + + deinceps + + circa + reliquas + + aliquas + + + partes + partes cum + partes si + + + physice + + , + naturalemque + naturalisque + naturalesque + naturaleque + naturaliaque + maxime, problemata tam circa + composita + quam + quam circa + simplicia + existentia + + + + tractabuntur + tractabunt + . + + et cetera. + + + + sequitur + amen. Deo gratias amen + Explicit decimanona particula. + Explicit particula 19a deo gratias + Explicit particula xixa. sequitur .xx.ma +

+
+
+
+ + + +
+ Back Matter + +
+ List of persons mentioned by Pietro + + Historical figures + + AlAlexander + Aphrodisiensis + + + ArAristoteles + + + AxAristoxenus + Tarentinus + + + AvAvicenna + + + BoBoethius, + Anicius + Manlius + Severinus + + + CoHestiaeus + Colophonius + + + DamJohannes + Damascenus + + + GaGalenus, + Claudius + + + GArGuido + Aretinus + + + HipHippocrates + + + HorHoratius Flaccus, + Quintus + + + IsIsidorus + Hispalensis + + + MacMacrobius + Ambrosius + Theodosius + + + MuMusaeus + Atheniensis + + + NiNicomachus + Gerasenus + + + OvOvidius Naso, + Publius + + + PhilPhiloxenus + Cytherius + + + PhrPhrynichus (tragicus) + + + PlPlato + + + PtPtolemaeus, + Claudius + + + PythPythagoras + + + TerTerpander + Antissenis + + + ThTheophilus + Antiochenus + + + TiTimaeus + Locrus + + + TyTimotheus + Milesius + + + + Mythical figures + + CayCain + + + JuJupiter + + + MemMemoria + + + MerMercurius + + + MosMoses + + + OrOrpheus + + + TorTorebus, filius + Atys + + + TubTubal Cain + + +
+ + + + + +
+ List of titles cited by Pietro, with editions supplied + + d'Abano 1504 + d'Abano, Pietro. Conciliator differentiarum + philosophorum. Venetiis: n.p., + 1504. URL: + AlPr + Pseudo-Alexander of Aphrodisias. + Problemata. Ed. Robert W. Sharples and Sophia + Kapetanaki as Pseudo-Aristoteles (Pseudo-Alexander), Supplementa + Problematorum: A new edition of the Greek text with introduction and annotated + translation. Berlin: De Gruyter, + 2006; trans. Pietro d'Abano in + Vatican Biblioteca Apostolica reg. lat. 747, ff. 62r–104r, URL: + Arist. De an. + Aristotle. De anima. Ed. J. Decorte + and J. Brams as De Anima. Aristoteles Latinus Database + XII.1 URL: + Arist. Cael. + Aristotle. De caelo Ed. + F. Bossier as De caelo et mundo. Aristoteles Latinus Database + VIII URL: + Arist. Eth. Nic. + Aristotle. Liber ethicorum ad Nicomachum. Ed. + R.A. Gauthier as Analytica posteriora (Iacobi + Venetici translationis recensio). Aristoteles + Latinus + XXVI.1–3. Leiden and + Bruxelles: Brill and Desclée De Brouwer, + 1972–1974, URL: + Arist. Metaph. + Aristotle. Metaphysica. Ed. G. + Vuillemin-Diem as Metaphysica, lib. I-XIV. Recensio et + Translatio Guillelmi de Moerbeka. Aristoteles + Latinus + XXV.3. Leiden, New York, and + Köln: E.J. Brill, 1995, URL: + An. Post. + Aristotle. Analytica posteriora. Ed. L. + Minio-Paluello and B. G. Dod as Analytica + posteriora (Iacobi Venetici translationis recensio). Aristoteles Latinus + IV.1–4. Bruges and + Paris: Desclée De Brouwer, 1968, URL: + + Arist. Int. + Aristotle. Peri hermeneias. Ed. L. + Minio-Paluello and G. Verbeke as Periermenias (Peri hermeneias) (uel De Interpretatione). Aristoteles Latinus + II.2. Bruges and + Paris: Desclée De Brouwer, 1965, URL: + + Arist. Ph. + Aristotle. Physica. Ed. F. Bossier + and J. Brams as Physica (translatio + 'uetus'). Aristoteles Latinus + VII. Leiden and New + York: E.J. Brill, 1990, URL: + Arist. Pol. + Aristotle. De politicorum. Ed. Franciscus + Susemihl as Aristotelis Politicorum libri octo cum vetusta + translatione Guilelmi de Moerbeka. Leipzig: + Teubner, 1872. + Arist. Top.Aristotle. + Topica. Ed. L. Minio-Paluello as Topica. Translatio Boethii, Fragmentum Recensionis Alterius et Translatio + Anonyma. Aristoteles Latinus + V.1–3. Bruges and + Paris: Desclée De Brouwer, 1969, URL: + + ArPr + Pseudo-Aristotle. Problemata physica. Ed. + Carolus Ruelle, Hermannus Knoellinger and + Iosephus Klek as Aristotelis quae feruntur + Problemata physica. Leipzig: + Teubner, 1922. + AvCa + Avicenna. Canon medicinae. Trans. Gerardus Cremonensis as Avicennae Arabum + medicorum principis, Canon medicinae. Venice: + Iuntas, 1608. + BoAr + Anicius Manlius Severinus Boethius. De institutione + arithmetica. Ed. Godofredus Friedlein in Anicii Manlii Torquati Severini Boetii De institutione arithmetica libri duo, De + institutione musica libri quinque, 1–173. Leipzig: Teubner, + 1868. + BoMu + Anicius Manlius Severinus Boethius. De institutione + musica. Ed. Godofredus Friedlein in Anicii + Manlii Torquati Severini Boetii De institutione arithmetica libri duo, De + institutione musica libri quinque, 175–371. Leipzig: + Teubner, 1868. + GaAc + Galen. De morbo et accidenti. Ed. C. G. + Kühn as De symptomatum causis libri iii in Claudii Galeni opera omnia, vol. + 7, 83–272. + Leipzig: Knobloch, + 1824. + GaPu + Galen. De differentia pulsuum libri iv. Ed. C. + G. Kühn in Claudii Galeni opera omnia, vol. 8, 493–765. Leipzig: Knobloch, + 1824. + GaSa + Galen. De sanitate tuenda libri vi. Ed. K. + Koch in Corpus medicorum Graecorum + 5.4.2, 3–198. Leipzig: + Teubner, 1923. + HipAph + Hippocrates. Aphorismi. Ed. É. Littré + in Oeuvres complètes d'Hippocrate, vol. 4, 458–608. Paris: Baillière, + 1844. + IsEt + Isidore of Seville. Etymologiae. Ed. W. M. + Lindsay in Isidori Hispalensis Episcopi Etymologiarum sive + originum libri xx, vol. 1. + Oxford: Clarendon Press, + 1911. + MacSS + Macrobius Ambrosius Theodosius. Commentarium in somnium + Scipionis. Ed. Franciscus Eyssenhardt in Macrobius, 465–570. + Leipzig: Teubner, + 1868. + MasAph + Yuḥannā ibn Māsawaiyh. Aphorismorum libri. Ed. + Danielle Jacquart and Gérard Troupeau as Yuhannà ibn Màsawayh (Jean Mésué), Le livre des Axiomes médicaux + (Aphorismi), édition du texte arabe et des versions latines avec traduction + française et lexique. Geneva: + Droz, 1980. See also Biblioteca Apostolica vat. + lat. 2460, f. 39r–42r, URL: + + NiGer + Nichomachus (Dramatist). Geryones. Concerning this lost play, see URL: + Psalm + Liber psalmorum. Ed. Robertus Weber in Biblia sacra iuxta vulgatam versionem, 767–955. Stuttgart: + Deutsche Bibelgesellschaft, 1994. + PtHar + Claudius Ptolemy. Harmonica. Ed. I. + Düring as Die Harmonielehre des Klaudios + Ptolemaios in Göteborgs Högskolas Arsskrift + 36, 2–111. Göteborg: + Elanders, 1930. + SePr + Pseudo-Hermes Trismegistus. De sex rerum principiis. + Ed. Paolo Lucentini and Mark D. Delp in Corpus Christianorum, Continuatio Mediaeualis + 142. Turnhout: + Brepols, 2006. Sometimes + attributed to Gilbert of Poitiers. + +
+ +
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(revised: 202?)} +\def\TheID{\makeatother } +\def\TheDate{202?} +\title{Expositio problematum Aristotelis, Particula XIX: De harmonia} +\author{Pietro d’Abano}\makeatletter +\makeatletter +\newcommand*{\cleartoleftpage}{% + \clearpage + \if@twoside + \ifodd\c@page + \hbox{}\newpage + \if@twocolumn + \hbox{}\newpage + \fi + \fi + \fi +} +\makeatother +\makeatletter +\newcommand*{\cleartorightpage}{% + \clearpage + \if@twoside + \ifodd\c@page\else + \hbox{}\newpage + \if@twocolumn + \hbox{}\newpage + \fi + \fi + \fi +} +\makeatother +\makeatletter +\thispagestyle{empty} +\markright{\@title}\markboth{\@title}{\@author} +\renewcommand\small{\@setfontsize\small{9pt}{11pt}\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@ +\belowdisplayskip \abovedisplayskip +\abovedisplayshortskip \z@ plus2\p@ +\belowdisplayshortskip 4\p@ plus2\p@ minus2\p@ +\def\@listi{\leftmargin\leftmargini + \topsep 2\p@ plus1\p@ minus1\p@ + \parsep 2\p@ plus\p@ minus\p@ + \itemsep 1pt} +} +\makeatother +\fvset{frame=single,numberblanklines=false,xleftmargin=5mm,xrightmargin=5mm} + +% Fancy headers and footers. +\usepackage{fancyvrb} +\usepackage{fancyhdr} +\fancyhf{} +\setlength{\headheight}{14pt} +\fancyhead[LE]{\thepage} +\fancyhead[CE]{\nouppercase{\leftmark}} +\fancyhead[RO]{\thepage} +\fancyhead[CO]{\rightmark} +\fancyfoot[RO]{} +\fancyfoot[CO]{} +\fancyfoot[LO]{\TheID} +\fancyfoot[LE]{} +\fancyfoot[CE]{} +\fancyfoot[RE]{\TheID} +\fancypagestyle{plain}{\fancyhead{}\renewcommand{\headrulewidth}{0pt}} + +% For blank pages +\newcommand{\blankpage}{ + \clearpage + \fancypagestyle{empty}{ + \fancyhf{} % Clear header and footer + \renewcommand{\headrulewidth}{0pt} % Remove header rule + \renewcommand{\footrulewidth}{0pt} % Remove footer rule + } + \thispagestyle{empty} +} + +\usepackage[linktoc=all,colorlinks=true,linkcolor=black,anchorcolor=black,citecolor=black,filecolor=black,menucolor=black,runcolor=black,urlcolor=black,breaklinks]{hyperref} +\hypersetup{citebordercolor=0.75 0.75 0.75,linkbordercolor=0.75 0.75 0.75,urlbordercolor=0.75 0.75 0.75,bookmarksnumbered=true} +% Set the font for URLs to the regular font for the document. +\urlstyle{same}\makeatother +\begin{document} +\let\tabcellsep& +\thispagestyle{empty} +\vspace*{\fill} + +\begin{center} +This PDF is formatted to accommodate printing two pages per sheet in landscape mode. +\end{center} + +\vspace*{\fill} +\frontmatter +\thispagestyle{empty} +\begin{titlepage} % Suppresses headers and footers on the title page +\centering % Center everything on the title page + +%------------------------------------------------ +% Title +%------------------------------------------------ + +\rule{\textwidth}{1.6pt}\vspace*{-\baselineskip}\vspace*{2pt} % Thick horizontal rule +\rule{\textwidth}{0.4pt} % Thin horizontal rule + +\vfill +\begin{spacing}{1.5} +{\LARGE\uppercase{Expositio problematum Aristotelis, Particula XIX: De harmonia}} % Title +\end{spacing} +\vfill + +%------------------------------------------------ +% Editor(s) +%------------------------------------------------ + +Edited By + +\vfill + +{\Large Caleb Mutch} % Editor list + +\vfill +\rule{\textwidth}{0.4pt}\vspace*{-\baselineskip}\vspace{3.2pt} % Thin horizontal rule +\rule{\textwidth}{1.6pt} % Thick horizontal rule + +%------------------------------------------------ +% Series +%------------------------------------------------ +\vfill + +{\Large Medieval Academy of America}\\ +\vfill +{\large Library of Digital Latin Texts}\\ +\vfill +{\large Volume ?}\\ +\vfill % Whitespace between editor names and publisher logo + +%------------------------------------------------ +% Publisher +%------------------------------------------------ + + +\begin{figure}[h] % Position the logo here on the page. +\includegraphics[scale=0.50]{../images/DLL.eps} % Logo of DLL +\centering % Center the logo. +\end{figure} + +{\normalsize 202?} +\end{titlepage} +%---------------------------------------------------------------------------------------- +% Copyright Page +%---------------------------------------------------------------------------------------- +\begin{copyrightPage} +\thispagestyle{empty} +\vfill +\begin{figure}[h] % Position the logo here on the page. +\includegraphics[scale=0.50]{../images/DLL.eps} % Logo of DLL +\centering % Center the logo. +\end{figure} +\vfill +\centering +{\LARGE The Digital Latin Library}\\650 Parrington Oval, Carnegie Building 101, Norman, OK 73019, USA +\vfill + +\flushleft +\small +{The Digital Latin Library} publishes the \textit{Library of Digital Latin Texts} under the authority of The University of Oklahoma. Individual volumes are reviewed and sponsored by the Society for Classical Studies, the Medieval Academy of America, or the Renaissance Society of America, depending on the era of the text(s). + +\vfill + +Volumes are published under the Creative Commons Attribution-ShareAlike 4.0 International Licence (CC BY-SA 4.0): \url{https://creativecommons.org/licenses/by-sa/4.0/legalcode}. + +\vfill + +\textcopyright \thinspace Caleb Mutch, 202?. + +\vfill +\end{copyrightPage} +\cleardoublepage + +\blankpage + +\begin{acknowledgmentsPage} + +{\LARGE Acknowledgments} + +\begin{itemize} +\item TEI XML encoding:: Caleb Mutch. +\item TEI XML encoding:: Samuel J. Huskey. + +\end{itemize} + +\end{acknowledgmentsPage} + + +\blankpage + +\frontmatter +\pagenumbering{roman} + +\cleardoublepage +\tableofcontents +\blankpage +\cleardoublepage +\thispagestyle{plain} + +\setcounter{page}{5} + +\thispagestyle{plain} + +\newpage +\thispagestyle{plain} +\section{Preface} + +\pagestyle{fancy} + +\subsection{I. Pietro d’Abano’s \textit{Expositio problematum Aristotelis} } + +\subsubsection{1.1 General} +\par +The pseudo-Aristotelian \textit{Problems} is an extensive collection of questions and proposed answers concerning a wide range of subjects, including biology, mathematics, and physics, divided topically into thirty-eight sections. The nineteenth of these sections preserves the first substantial account of ancient Greek music making and theorizing to have been rediscovered in the medieval period. This material held great promise for medieval thinkers seeking to learn more about the foreign world of ancient Greek music, whose legendary emotional power had been lamentedly lost, and the text’s attribution to Aristotle imbued it with special authority. Yet the \textit{Problems} was also a challenging text to decipher. Not only was the subject manner often unfamiliar, the manuscript tradition of the Greek text is also corrupt in places. Furthermore, the first complete Latin translation, made by Bartholomew of Messina (fl. 1258–66), observed the common medieval practice of verbatim, indeed servilely literal, word-for-word translation. For all these reasons, potential readers of the \textit{Problems} were in sore need of orientation and explanation.\par +Into the breach strode Pietro d’Abano (c. 1257–1316), who was a professor of medicine with wide-ranging interests and expertise. Pietro composed his \textit{Expositio}, the first commentary on the entirety of the \textit{Problems} in the first decade of the fourteenth century, and there are more than twenty extant manuscripts of it, as well as multiple early print editions. His commentary also attracted the attention of his contemporaries, most notably Jean de Jandun (c. 1285–1328), a philosopher and theologian of considerable importance based at the University of Paris, who produced a revision of the entire \textit{Expositio}. Moreover, Pietro’s commentary on the problems of section XIX, in particular, was the first widely circulated medieval attempt to interpret and assimilate rediscovered knowledge about music in the ancient world, and his explanations consequently became a touchstone for later generations of music scholars who referred to the \textit{Problems}, including Franchino Gaffurio, Girolamo Mei, and Francisco de Salinas. Most recently, Claude Palisca has called attention to Pietro’s anticipation of Renaissance modes of scholarship (1985), and David E. Cohen has demonstrated that Pietro’s idiosyncratic interpretations of some of the problems concerning music played an important role in the development of the music-theoretical concept of harmony (2012). Yet despite the inherent interest of Pietro’s commentary as a site of cross-cultural engagement and its historical significance to later music theorizing, his commentary on section XIX, on music, has been inaccesible to scholars, for until recently it had not been published in any form since the sixteenth century’s sadly unreliable print editions. Even that recent publication (Meyer 2022), however, does not provide a proper critical edition of the text, as it is based on a sixteenth-century print edition, only considers half the extant manuscripts, and fails to distinguish between Pietro's first version of his commentary and his later revision (see section 2.1). The present critical edition rectifies that situation, establishing a base text informed by a stemmatic hypothesis of the complete manuscript tradition. Furthermore, this edition is openly accessible, and it presents a semantically encoded version of the text, allowing readers to select the types of variants they wish to consider. As a result, it provides a better informed version of Pietro's commentary and makes it more widely available than ever before. +\subsubsection{1.2 Structure} +\par +Each of the pseudo-Aristotelian problems follows a set structure. First, a question is posed, such as at the start the first problem: ``Why do those who are suffering and those who are rejoicing have pipes played for them?'' (\textit{Propter quid dolentes et gaudentes fistulantur}?) Then one or more possible reasons are proposed, often accompanied by additional explanation. For instance, the first problem continues: ``Is it so that the former mourn less, but the latter rejoice more?'' (\textit{Aut ut hii quidem minus tristentur, alii autem ut magis gaudeant}?) In his commentary Pietro follows a similar pattern. He first paraphrases the opening question, and then addresses the remainder of the problem, dividing it into between one and seven parts, depending on its length. He signals the beginning of each successive division of the text with its first word or two, followed by a partial or complete paraphrase. Given the unidiomatic Latin of Bartholomew of Messina’s translation and the common occurrence of obscure vocabulary, Pietro’s paraphrases provide an important means of ingress to the text on their own. He often supplements these paraphrases with additional explanatory material, both his own and by authors from antiquity. In the latter case, he often provides cross-references to other pertinent passages within the \textit{Problems} (from both section XIX and other sections), and he also inserts abbreviated quotations, most often from the Aristotelian and medical corpora. +\subsection{II. The Textual Tradition} + +\subsubsection{2.1 Introduction} +\par +Establishing the best text of Pietro d’Abano’s commentary is no simple task, for it survives in several different forms. By analyzing variants in the introduction with which Pietro starts his commentary on the \textit{Problems}, Gijs Coucke has demonstrated that Pietro produced a revised version of his commentary after the initial version was complete (2008, vol. 2, xlii–xliv). About a quarter of the extant manuscripts derive from the initial version, another quarter from the revision, and the remaining half of the manuscripts descend from the revision made by Jean de Jandun (concerning which see Swaenepoel 2009). While these latter manuscripts do not aid in the reconstruction of the text(s) Pietro himself wrote, they provide important testimony as to the work’s reception in the Parisian university scene, and consequently I have recorded variants from five selected manuscripts in the critical apparatus. Coucke notes that “all manuscripts appear to have the identical explicit, which refers to 1310 as the year in which Peter finished his \textit{Expositio}” (2008, vol. 2, xliv)—that presumably being the date when the initial version was completed.\par +Further complicating matters, some of the manuscripts change affiliations partway through the lengthy work. As Joan Cadden has observed, manuscript P\textsuperscript{z} ``contains the first half of Pietro’s version and the second half of Jean’s,'' and manuscript E\textsuperscript{a} has the converse arrangement (2013, 228). Additionally, in his edition of section IV of the \textit{Expositio}, Coucke identifies manuscript V\textsuperscript{b} as deriving from Pietro’s revised version, whereas by section XIX it hews more closely to the initial version. (Furthermore, manuscript P\textsuperscript{q} contains Jean’s version in sections IV and XIX, but by section XXVII it appears to have changed to Pietro’s version [Coucke 2008, vol. 2, xxvi].) As a result, I have preserved Coucke’s manuscript sigils, but not his labeling of families and conjectured sub-types. For instance, Coucke labels Pietro’s first and second versions \textit{P\textit{a}} and \textit{P\textit{b}}, respectively whereas I call them α and κ. (This change is made in part to avoid the confusing use of letters in Coucke’s \textit{Conspectus siglorum}, where the manuscripts elsewhere labeled as \textit{P\textit{b}} are listed under heading A, and those as \textit{P\textit{a}} under heading B.)\par +In classifying the manuscripts I used Coucke’s findings on section IV as a point of departure. I collated all the manuscripts’ versions of section XIX’s tenth problem to test the validity of Coucke’s findings to section XIX. Then I collated all the manuscripts representing solely either Pietro’s first or his second version (with the exception of M\textsuperscript{b}, to be discussed below), along with manuscripts E\textsuperscript{a} and P\textsuperscript{z} (since their classification differs between sections IV and XIX), and four representative manuscripts from the Jean de Jandun redaction. +\subsubsection{2.2 List of Sources} + +\paragraph{Manuscripts}\label{bibliography-manuscripts} + +\vspace{1.5em} + +{\large{Pietro's first version (α)}} +\begin{msitemlist}{1} +\bibitem [β]{β} Consensus of N\textsuperscript{u} and P\textsuperscript{y}, where N\textsuperscript{u} is extant +\begin{msitemlist}{1} + \bibitem [N\textsuperscript{u}]{Nu} Nuremberg, Stadtbibliothek, Cent. III.38, \textbf{ff. 61v–64v}: before 1389 + \bibitem [P\textsuperscript{y}]{Py} Paris, Bibliothèque Nationale man. lat. 6541 (accessed 2022-01-03), \textbf{ff. 179v–91v}: fourteenth century. \url{http://gallica.bnf.fr/ark:/12148/btv1b9068411m.r=6541} +\end{msitemlist} + +\bibitem [γ]{γ} \textit{Consensus of V\textsuperscript{a} and V\textsuperscript{b}} +\begin{msitemlist}{1} + \bibitem [V\textsuperscript{a}]{Va} Vatican, Biblioteca Apostolica lat. 2174 (accessed 2022-01-03), \textbf{ff. 72r–77r}: fourteenth century. \url{https://digi.vatlib.it/view/MSS\textunderscore Vat.lat.2174} + \bibitem [V\textsuperscript{b}]{Vb} Vatican, Biblioteca Apostolica lat. 2175 (accessed 2022-01-03), \textbf{ff. 107–16r}: fifteenth century. \url{https://digi.vatlib.it/view/MSS\textunderscore Vat.lat.2175} +\end{msitemlist} + +\bibitem [E\textsuperscript{a}]{Ea} Erfurt, Bibliothek Amploniana fol. 15, \textbf{ff. 136v–47r}: early fourteenth century +\end{msitemlist} + +\vspace{1.5em} + +{\large{Pietro's revised version (κ)}} +\begin{msitemlist}{1} +\bibitem [P\textsuperscript{x}]{Px} Paris, Bibliothèque Nationale man. lat. 6540 (accessed 2022-01-03), \textbf{ff. 154v-64v}: Fourteenth century. Italy. \url{http://gallica.bnf.fr/ark:/12148/btv1b90684121.r=6540} +\bibitem [λ]{λ} Consensus of M\textsuperscript{a}, V\textsuperscript{m}, and V\textsuperscript{z} +\begin{msitemlist}{1} + \bibitem [M\textsuperscript{a}]{Ma} Cesena, Malatestiana D.XXIV.2 (accessed 2022-01-03), \textbf{ff. 96v–104r}: before 1381. \url{http://catalogoaperto.malatestiana.it/elenco-libri/libro/?saggioid=DX.24.02} + \bibitem [V\textsuperscript{m}]{Vm} Venice, Biblioteca Nazionale Marciana, lat. VI. 126, \textbf{ff. 95r–100r}: fifteenth century + \bibitem [V\textsuperscript{z}]{Vz} Venice, Biblioteca Nazionale Marciana, lat. Z. 263, \textbf{ff. 48v–70r}: ca. fourteenth century, or after 1451 on the basis of watermark. On paper, in one column + \bibitem [M\textsuperscript{b}]{Mb} Cesena, Malatestiana S.VI.2/3 (accessed 2022-01-03), \textbf{S.VI.3, ff. 38v–56r}: 1381. \url{http://catalogoaperto.malatestiana.it/elenco-libri/libro/?saggioid=SX.06.03}A copy of M\textsuperscript{a} +\end{msitemlist} + +\end{msitemlist} + +\vspace{1.5em} + +{\large{Jean de Jandun's redaction}} +\begin{msitemlist}{1} +\bibitem [π]{π} Collated manuscripts +\begin{msitemlist}{1} + \bibitem [G\textsuperscript{u}]{Gu} Ghent, Bibliothéek van de Rijksuniversiteit, ms. 72 (accessed 2022-01-03), \textbf{ff. 234r–49v}: fourteenth century. \url{http://lib.ugent.be/catalog/rug01:000802948} + \bibitem [P\textsuperscript{p}]{Pp} Paris, Bibliothèque Nationale man. lat. 6542 (accessed 2022-01-03), \textbf{ff. 183v–94v}: 1385. \url{http://gallica.bnf.fr/ark:/12148/btv1b10721259d/f1.item.r=6542} + \bibitem [P\textsuperscript{u}]{Pu} Paris, Bibliothèque de l'Université 122, \textbf{114v–23r}: fifteenth century + \bibitem [P\textsuperscript{z}]{Pz} Paris, Bibliothèque Nationale man. lat. 6541A (accessed 2022-01-03), \textbf{ff. 179r-92r}: fourteenth century. \url{http://gallica.bnf.fr/ark:/12148/btv1b90680829/f2} + +\textit{Hands} +\begin{itemize} +\item P\textsuperscript{z2} is responsible for the header, and writes in an ink that has faded significantly. It may be the same scribe who wrote the large initials which begin each problem. +\end{itemize} + \bibitem [V\textsuperscript{o}]{Vo} Vatican, Biblioteca Apostolica Ottobon. lat. 1764, \textbf{ff. 147r–57v}: fourteenth century +\end{msitemlist} + +\bibitem Other manuscripts from the Jean de Jandun redaction +\begin{msitemlist}{1} + \bibitem [C\textsuperscript{a}]{Ca} Cambridge, Peterhouse 79, \textbf{ff. 76r–81v}: fourteenth century + \bibitem [P\textsuperscript{a}]{Pa} Paris, Bibliothèque Arsenal, 723, \textbf{ff. 183v–97r}: fourteenth century + \bibitem [P\textsuperscript{q}]{Pq} Paris, Bibliothèque Nationale man. lat. 15454, \textbf{ff. 127r–36r}: fifteenth century + \bibitem [S\textsuperscript{c}]{Sc} Seville, Biblioteca Colombina, 7.7.9, \textbf{ff. 121r ff.}: fourteenth to fifteenth century + \bibitem [V\textsuperscript{c}]{Vc} Vatican, Biblioteca Apostolica lat. 2176 (accessed 2022-01-03), \textbf{ff. 62r–65r}: fourteenth century. \url{https://digi.vatlib.it/view/MSS\textunderscore Vat.lat.2176} +\end{msitemlist} + +\end{msitemlist} + +\paragraph{Editions: Witnesses}\label{bibliography-early-editions} + +\begin{bibitemlist}{1} + + \bibitem [m]{m} Illarius, Stephanus. \textit{Expositio succinta problematum Aristotelis quam Petrus edidit Paduanus} (accessed 2022-01-03). Mantua: Paulus de Butzbach, 1475. \url{http://daten.digitale-sammlungen.de/\textasciitilde db/0006/bsb00068444/images/} + \bibitem [v]{v} Anonymous. \textit{Expositio preclarissimi atque eximii artium ac medicine doctoris Petri de Ebano Patauini in librorum problematum Aristotelis} (accessed 2022-01-03). [Venice]: Johannes Herbort, 1482. \url{http://daten.digitale-sammlungen.de/\textasciitilde db/0005/bsb00058463/images/}\end{bibitemlist} +\subsubsection{2.3 Pietro d’Abano’s First Version} +\par +The first version of Pietro’s commentary on section XIX of the \textit{Problems}, which I label α, is found in five manuscripts: N\textsuperscript{u}, P\textsuperscript{y}, V\textsuperscript{a}, V\textsuperscript{b}, and E\textsuperscript{a}. Manuscripts N\textsuperscript{u} and P\textsuperscript{y} usually carry the best version of this text. Unfortunately, N\textsuperscript{u}’s codex has lost a number of pages, resulting in total loss of the text from a point partway into problem 9 through problem 15, and again from the end of problem 38 through the end of the section.\par +Manuscripts V\textsuperscript{a} and V\textsuperscript{b} are associated by shared error. The most salient of these occurs in problem 20, where they repeatedly mistake discussion of the Greek language (\textit{oratio greca}) for “grammatical speech” (\textit{oratio gramatica}). The scribe of manuscript V\textsuperscript{a} evidently prioritized speed over neatness of script and also had very idiosyncratic orthography, regularly doubling single consonants or omitting one where they are normally doubled. Given the ubiquity of these variants, I have omitted them from the critical apparatus unless they are shared by other manuscripts. In his edition of section IV, Coucke finds that V\textsuperscript{b} contains the second version of Pietro’s commentary, but by section XIX there is little evidence of V\textsuperscript{b} sharing readings characteristic of that second version. In addition, the sub-family represented by V\textsuperscript{a} and V\textsuperscript{b} is particularly important for the commentary’s reception history since the incunable editions of the text align most closely with them.\par +The situation is more complicated with manuscript E\textsuperscript{a}. Coucke assigns manuscript E\textsuperscript{a} to the Jean de Jandun redaction, and in section XIX the manuscript adopts many (though not all) of the omissions that characterize that redaction, and it sometimes shares readings with P\textsuperscript{z}. Nonetheless, in non-omitted passages E\textsuperscript{a}’s text more closely resembles the manuscripts transmitting Pietro’s first version. As a result, I primarily affiliate it with that family of texts, with the proviso that the scribe of E\textsuperscript{a} evidently consulted a P\textsuperscript{z}-related manuscript from the Jandun redaction as well. +\subsubsection{2.4 Pietro d’Abano’s Second Version} +\par +The second version of Pietro’s commentary, which I label κ, is also found in five manuscripts: P\textsuperscript{x}, V\textsuperscript{m}, V\textsuperscript{z}, M\textsuperscript{a}, and M\textsuperscript{b}. With respect to the fourth section, Coucke hypothesized that manuscripts P\textsuperscript{x} and V\textsuperscript{b} (which in section IV transmits Pietro’s second version) most closely follow the original form of the second version, that a further revised form of the second version was the model for manuscripts M\textsuperscript{a}, M\textsuperscript{b}, and P\textsuperscript{z}, and that manuscript V\textsuperscript{m} shares common error with these latter three (Coucke 2008, vol. 2, xxxix). Only some of Coucke’s observations hold true in section XIX, however. I agree that a revised version, which I call λ, was the model for many of these manuscripts. As mentioned above, however, manuscript V\textsuperscript{b} has switched its affiliation and now follows Pietro’s first version, and P\textsuperscript{z} likewise has shifted to Jean of Jandun’s redaction. Additionally, Coucke does not consider V\textsuperscript{z}, since it does not contain section IV.\par +The resulting picture is that P\textsuperscript{x} follows the original form of the second version, and that M\textsuperscript{a}, M\textsuperscript{b}, V\textsuperscript{m}, and V\textsuperscript{z} derive from λ, a revised version thereof. Coucke’s hypothesis of a further revised source for M\textsuperscript{a}, M\textsuperscript{b}, and P\textsuperscript{z} (but not V\textsuperscript{m}) is not supported in section XIX, since there is good reason to believe that M\textsuperscript{b} is copied either directly from M\textsuperscript{a} or from another copy of M\textsuperscript{a}. For instance, in problem 2 the scribe of M\textsuperscript{a} erroneously wrote ``unaa'' instead of ``una,'' and M\textsuperscript{b}’s scribe wrote ``unaa'' before deleting the superfluous a. Still stronger evidence of copying is found in problem 3’s table of Greek note names, where M\textsuperscript{b}’s scribe was consulting a manuscript that breaks the word ``prollabamenos'' (\textit{recte: proslambanomenos}) into ``prolla'' and ``bamenos,'' as M\textsuperscript{a} does. We can tell this because M\textsuperscript{b}’s scribe evidently thought the line break divided two distinct words: in M\textsuperscript{b}, following ``prolla'' the rest of the line (about six characters’ worth) is left blank, before the table of note names begins at the top of the next column with ``bamenos.'' Furthermore, in problem 6 M\textsuperscript{b}’s scribe follows the word \textit{magnatis} with the superfluous phrase \textit{uel huius est inequale non eundem seruans tenorem} ahead of where it should occur in the text, and then repeats it in the correct place, following \textit{excellentis}. In this case of homeoteleuton the -\textit{tis} endings of \textit{magnatis} and \textit{excellentis} are nearly aligned in two successive lines of M\textsuperscript{a} (f. 97v), so it is very likely that M\textsuperscript{b}’s scribe’s eyes skipped from the end of \textit{magnatis} down a line to \textit{excellentis}, and then erroneously copied the words that followed. In sum, because my collation of M\textsuperscript{b} across the first ten problems revealed no meaningful discrepancies with M\textsuperscript{a}, but rather signs of direct copying, I conclude that it is not useful for establishing the best text of Pietro’s second version.\par +Of the remaining manuscripts in sub-family λ, V\textsuperscript{m} often preserves better readings than M\textsuperscript{a} and V\textsuperscript{z}. Zanetti dates V\textsuperscript{z} to about the fourteenth century (1741, 121), but it may have been copied later, as it is written on paper and is the only extant manuscript to be copied in a single column. I have examined its watermark, which is a bellflower with a five-petalled bell, two leaves that curl up, and a stem that curves sharply; it closely resembles watermark DE4620-PO-127158, which has been dated to 1447, in Rome, though its bell is straighter. Nonetheless, the manuscript's unique readings are not obviously inferior to those of M\textsuperscript{a}, so I have included its variants in the critical apparatus throughout. +\subsubsection{2.5 Jean de Jandun’s Redaction} +\par +The redaction undertaken by Jean de Jandun necessarily cannot help reconstruct the best text of Pietro’s commentary, but it is still of some interest. This is in part because ``Jandun is one of the most important thinkers in the Latin Averroist tradition ''(South 2002, 372), and consequently his understanding of the \textit{Problems} and Pietro’s commentary merits attention. Furthermore, due to the significant circulation of Jean’s redaction in the environs of the University of Paris it is valuable for understanding the \textit{Problems}’ reception. As a result, I have included readings from selected manuscripts of Jean’s redaction in my critical edition, but have also tagged them so that readers may filter out readings only found in that redaction.\par +Three broad feature of Jean’s redaction identified by Coucke in section IV also occur in section XIX. First, the redaction is most saliently characterized by omissions that ``either cover well defined text-units (paragraphs, or entire (subordinate) clauses), or entail the removal of repetitive or superfluous speech'' (2008, vol. 2: xxvii). Second, as a whole the manuscripts of Jean’s redaction largely agree with those of Pietro’s first version, but on occasion they follow his second version instead, as Coucke found (xxx–xxxi). Third, as in section IV manuscript Vo appears to be most valuable for establishing the text of the redaction (xxxiii). It has almost no unique errors of any importance, but a brief passage in problem 9 (\textit{utrobique existente. Et hoc quia in cantu}), which it alone omits, indicates that it cannot be the direct (or at least the sole) model for the rest of the redaction’s manuscripts.\par +Beyond these broad characteristics, however, further clarity is elusive. Whereas Coucke found that manuscripts P\textsuperscript{p} and V\textsuperscript{c} are “contaminated,” since in section IV they complete the omissions which are otherwise characteristic of Jean’s redaction (xxxi–xxxii), in section XIX P\textsuperscript{p} never does so and V\textsuperscript{c} only sometimes does. Coucke then goes on to note of section IV (and he observes that Delaurenti’s [then]-in-progress edition of section VII confirms the same), that: + +\begin{quote}The other representatives of J [Jean’s redaction], however, are hardly differentiated, and among them the relations are volatile and changing. Yet, the samples allow for a division of the manuscripts along two main branches: (1) one of them is built around V\textsuperscript{o}, C\textsuperscript{a} and E\textsuperscript{a}; (2) another unites the distinct pair P\textsuperscript{q} P\textsuperscript{u} (xxxii).\end{quote} + Broad outlines of these relations among manuscripts are still present in section XIX: in the first branch, C\textsuperscript{a} and V\textsuperscript{o} are still closely related, but E\textsuperscript{a} now aligns better with Pietro’s first version. In the second branch, moreover, frequent agreements of P\textsuperscript{q} with G\textsuperscript{u} and P\textsuperscript{u} with P\textsuperscript{p} also emerge. The remaining manuscripts, V\textsuperscript{c}, P\textsuperscript{a}, and S\textsuperscript{c}, do not clearly align with either branch.\par +Given that Jean’s redaction cannot help to establish Pietro’s text, I have not included all its manuscripts in the apparatus. I follow Coucke (xxxiv) in selecting manuscripts V\textsuperscript{o}, due to its paucity of errors, and G\textsuperscript{u}, because of its careful preparation and occasional unique variants. I also selected manuscript P\textsuperscript{z}, on account of its interest as it switches from Pietro’s second version to Jean’s redaction. Because Coucke identified manuscripts P\textsuperscript{u} and P\textsuperscript{q} as constituting a differentiated branch in section IV, I selected manuscript P\textsuperscript{u}, since by section XIX P\textsuperscript{q} closely matches G\textsuperscript{u}. And finally I included manuscript P\textsuperscript{p} to help establish the second branch’s readings. (Other manuscripts from Jean’s redaction are also occasionally cited when they support variants that would otherwise appear unique.) +\subsubsection{2.6 Stemmatic Hypothesis} +\par +\noindent\includegraphics[width=\textwidth]{images/Stemma.png} +\subsection{III. Pietro d’Abano’s Practices of Quotation} +\par +In section XIX of his commentary Pietro employs quotations in the same two ways observed by Coucke in section IV: more literal quotations, which come immediately after the source’s reference (usually cited by the work’s author, title, and book number, when applicable), and loose paraphrases, which precede the reference (2008 vol. 2, lxi). To this general pattern we may add a more specific observation: in section XIX Pietro’s more literal quotations draw exclusively on Boethius and Isidore, and he uses them to lay out background information about the discipline of music’s terminology and its received history. He does this most prominently in problem 1, but also later, too, for example in problems 3, 7, and 16. Pietro uses paraphrases, by contrast, largely to support or exemplify his interpretive claims, and they come from a significantly wider range of sources, as will now be addressed.\par +The sources with which Pietro engages in section XIX fall into three main categories: the Aristotelian corpus, medical texts, and late-Antique writings on music. Pietro cites sources from the first category most frequently. Cross-references abound to passages within the \textit{Problems}, from both section XIX and other sections, and Pietro also cites other Aristotelian works that were well known in his day, especially book VIII of the \textit{Politics}. (Other Aristotelian works with which Pietro engages in medical-focused sections of the \textit{Problems}, such as the \textit{De generatio animalium} and \textit{De historia animalium} [Coucke 2008, vol. 2, lxii], make no appearance here.)\par +Given section XIX’s dedication to the subject of music, the extent to which Pietro incorporates medical sources, the second category, undoubtedly speaks to his training as a physician. Three of these treatises are by Galen, whom Claude Palisca misidentified as ``an otherwise unknown author Balienus'' in a chapter on Pietro (1985, 55). The other medical sources range from the better known, such Avicenna’s \textit{Canon medicinae}, to the obscure, for instance the \textit{Aphorismi} of Yuḥannā ibn Māsawaiyh, which Pietro attributes to John of Damascus.\par +The number of texts in the third category, writings on music, is very small. While Pietro makes reference to Macrobius and Ptolemy, he demonstrates first-hand knowledge of only Boethius’s \textit{De institutione harmonica} and the section (III.15–23) of Isidore’s \textit{Etymologies} which concerns music. He also has at least passing familiarity with some aspects of medieval music theory, as he makes reference to the ``Guidonian tradition'' (\textit{traditio Guidonis}) in problem 1 and on occasion employs solmization syllables, but he displays no further awareness of music-theoretical writing from after late Antiquity. (He is, however, certainly aware of his day’s musical culture, as he discusses antiphonal singing and medieval instruments, which are unmentioned in Boethius or Isidore.) +\subsection{IV. Principles of Edition} + +\subsubsection{4.1 Latin Translation by Bartholomew of Messina} +\par +The textual tradition of Bartholomew of Messina’s Latin translation of the pseudo-Aristotelian text is largely independent of Pietro’s commentary, as only six of the twenty extant medieval manuscripts of Pietro’s commentary include the entirety of Bartholomew’s translation. Furthermore, sixty manuscripts contain part or the entirety of Bartholomew’s text, compared to only around thirty for the commentary (Coucke 2008 vol. 1, xxxvi; vol. 2, xxiii). As a result, a critically established text of the Latin translation of section XIX is beyond the scope of this edition. For readers’ convenience, though, I have included as a variant a reconstruction of the version of Bartholomew’s translation which Pietro likely consulted. This reconstruction is based on a critical edition of that text, which I am preparing for publication, along with alterations to the base text reflecting readings found in Pietro's commentary. +\subsubsection{4.2 The \textit{Expositio problematum} by Pietro d’Abano} +\par +To constitute the text and the critical apparatus I have accounted for all the manuscripts containing Pietro’s first and second versions of the commentary (except for manuscript M\textsuperscript{b}, since it is a copy of M\textsuperscript{a}). I have also included a selection of manuscripts from Jean of Jandun’s recension: V\textsuperscript{o}, G\textsuperscript{u}, P\textsuperscript{p}, and P\textsuperscript{z}. Furthermore, readings from the two incunable editions are mentioned when they agree on a unique reading or with variants found in other manuscripts.\par +In the edition’s text I aim to reconstruct Pietro’s second version of the commentary, and consequently readings shared by manuscript P\textsuperscript{x} and family λ are preferred. Where their readings diverge, if either P\textsuperscript{x} or λ agree with multiple manuscripts from Pietro’s first version, I prefer that shared text. Where the surviving manuscripts of Pietro’s second version are corrupt, manuscript P\textsuperscript{y} (and N\textsuperscript{u}, when not lacunate) is generally preferred.\par +With respect to orthography, I have largely preserved medieval spellings, rather than changing them to classical Latin standards. (The most prominent exceptions are that words ending with -cio, -cia, and the like have been changed to –tia, etc., and the –ij and –ijs endings to –ii and –iis.) Because the digital critical edition allows readers to choose whether to view orthographical variants, I have recorded most spelling variances in the apparatus. Certain commonly occurring differences have been silently normalized, however: \begin{itemize} +\item E\textsuperscript{a}, G\textsuperscript{u}, P\textsuperscript{p}, P\textsuperscript{z}, and V\textsuperscript{z}’s armoniac* emended to armonic* +\item N\textsuperscript{u}'s duppl* emended to dupl* +\item P\textsuperscript{p} and N\textsuperscript{u}'s mellodi* emended to melodi* +\item P\textsuperscript{z}'s sinegengium emended to sinezengium +\item G\textsuperscript{u}, P\textsuperscript{y}, nd V\textsuperscript{z}'s sesqui* emended to sexqui* +\item M\textsuperscript{a} and V\textsuperscript{a}'s hi* emended to hii* +\item P\textsuperscript{x}'s fati* emended to faci* +\item P\textsuperscript{x} and P\textsuperscript{y}'s sicud emended to sicut +\item P\textsuperscript{z}, P\textsuperscript{x} and P\textsuperscript{y}'s velud emended to velut +\item V\textsuperscript{a}'s ubiquitous unique orthographical variants ignored +\item All: adinuicem emended to ad inuicem +\item All: probleuma* emended to problema* +\item All: lira* emended to lyra* +\item All: standardized spellings of rithim*, chor*, and antiphon* +\item All: standardized spellings of dyatesseron, dyapente, and dyapason +\item All: standardized spellings of lychanos, mese, and paramese +\item G\textsuperscript{u}’s *ypote emended to *ypate\end{itemize} All contractions have been silently expanded, including the ampersand and Tironian \textit{et}, and tall s ( s ) has been changed to round s. I have ignored all changes of hand and/or ink for the marginal numbering of the problems.\par +Punctuation varies widely among the manuscripts. I initially adopted manuscript P\textsuperscript{x}’s punctuation, which is relatively sparse. Thereafter I added further punctuation in keeping with modern practice, especially where it was lacking at points of significant syntactic divisions. I followed a similar practice with paragraph divisions, basing them on those found in P\textsuperscript{x}, and adding others at moments clearly signaled by the text (such as new thoughts introduced by \textit{nosce quod, notandum,} and the like).\par +Relatedly, it should be noted that in section XIX manuscript V\textsuperscript{a} and the incunable editions mark the beginnings of new paragraphs with \textit{deinde}. In section IV, however, Coucke shows while that the manuscripts of Pietro’s second version (excepting V\textsuperscript{b}, which Coucke assigns to the second version) use \textit{deinde} in that way, the remaining manuscripts do not. The change of practice in V\textsuperscript{a} is easily explained: a new copyist takes over at f. 47r, at which point that use of \textit{deinde} to mark new paragraphs begins. In the manuscripts from Pietro’s second version, by contrast, that use of \textit{deinde} gradually fades away, and seems largely to disappear after problem 15 of section 11. +\subsection{V. Bibliography} + +\begin{bibitemlist}{1} +\bibitem [Cadden 2013]{Cadden2013} Cadden, Joan. \textit{Nothing Natural is Shameful: Sodomy and Science in Late Medieval Europe.} Philadelphia: University of Pennsylvania Press, 2013. +\bibitem [Cohen 2012]{Cohen2012} Cohen, David E.. \textit{Harmonic Mediation and the Triad: Gaffurio, Zarlino, Lippius and Pietro d’Abano’s Commentary on the Pseudo-Aristotelian \textit{Problems}.} Paper presented at the annual conference of the {\orgName Music Theory Society of New York State}. New York, N.Y., March 31, 2012. +\bibitem [Coucke 2008]{Coucke2008} Coucke, Gijs. \textit{Philosophy between Text and Tradition The Reception of Aristotle's \textit{Problemata} in the Middle Ages: Peter of Abano's \textit{Expositio Problematum} }. Leuven: Ph.D. dissertation, Katholieke Universiteit Leuven, 2008. +\bibitem [Coucke 2009]{Coucke2009} Coucke, Gijs. \textit{Needle in the Haystack: In Search of the Model of Peter of Abano's \textit{Expositio Problematum} }. \textit{Revue d'histoire des textes} 4 (2009): 179–213 +\bibitem [Klek 1922]{Klek1922} Klek, Joseph, Knoellinger, Hermann, Ruelle, Charles Emanuel, Pseudo-Aristotle. \textit{Aristotelis quae feruntur problemata physica} Leipzig: Teubner, 1922. +\bibitem [Kuksewicz 1985]{Kuksewicz1985} Kuksewicz, Zdzislaw. \textit{Les \textit{Problemata} de Pietro d'Abano et leur 'Rédaction' par Jean de Jandun}. \textit{Medioevo} 11 (1985): 113–37 +\bibitem [Leemans and Coucke 2011]{LeemansCoucke2011} Leemans, Pieter De, and Coucke, Gijs. \textit{\textit{Sicut vidi et tetigi}...: Ego-statements and Experience in Pietro d'Abano's \textit{Expositio Problematum Aristotelis} }. In \textit{Expertus sum: l'éxperience par les sens dans la philosophie naturelle médiévale, ed. Thomas Bénatouïl and Isabelle Draelants , 405–26. Florence, SISMEL, Edizioni del Galluzzo, 2011.} +\bibitem [Meyer 1922]{Meyer2022} Meyer, Christian, d'Abano, Pietro. \textit{Expositio problematum (XIX): Édition, introduction et notes critiques et explicatives} Leuven: Leuven University Press, 2022. +\bibitem [Palisca 1985]{Palisca1985} Palisca, Claude. \textit{The Earliest Musical Humanists: Pietro d’Abano}. Chap. 3 in \textit{Humanism in Italian Renaissance Musical Thought. New Haven, Yale University Press, 1985.} +\bibitem [Siraisi 1970]{Siraisi1970} Siraisi, Nancy. \textit{The \textit{Expositio Problematum Aristotelis} of Peter of Abano}. \textit{Isis} 61, no. 2 (1970): 321–39 +\bibitem [South 2002]{South2002} South, James B. \textit{John of Jandun}. In \textit{A Companion to Philosophy in the Middle Ages, ed. Jorge Gracia and Timothy Noone , 372–76. Malden, Mass., Blackwell, 2002.} +\bibitem [Swaenepoel 2009]{Swaenepoel2009} Swaenepoel, Tine. \textit{Les deux versions des «\textit{Problemata}» de Pierre d'Abano}. \textit{Filologia mediolatina} 16 (2009): 215–45 +\bibitem [Zanetti 1741]{Zanetti1741} [Zanetti, Anton Maria]. \textit{Latina et italica D. Marci Bibliotheca codicum manu scriptorum per titulos digesta}. [Venice]: Apud Simonem Occhi Bibliopolam, 1741. + +\end{bibitemlist} + +\mainmatter +\cleardoublepage +\pagenumbering{arabic} + +\def\endstanzaextra{\pstart\centering-\-\-\-\-\-\-\-\-\skipnumbering\pend} +\thispagestyle{plain} + +\beginnumbering + +\newpage +\thispagestyle{plain} +\section[{Expositio problematum Aristotelis, Particula XIX: De harmonia}]{\centering\uppercase{\so{Expositio problematum Aristotelis, Particula XIX: De harmonia}}}\label{edition-text} +\vspace{2\baselineskip} % Whitespace + +\pagestyle{fancy} + + +\fancyhead[C]{Particula XIX: De harmonia} +\pstart +\edtext{\subsection {\supplied{Incipit}}\label{edition-text book-19a}}{\lemma{Incipit} \Cfootnote[nosep]{\textit{γN\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}} | Incipit decimanona particula. \textit{mv} | «Incipit decimanona particula etcetera» (in mg.) De problematibus Aristotelis que sunt circa Musicam l'armoniam particula .19a. \textit{P\textsuperscript{z}} | «xix» (in mg.) \textit{E\textsuperscript{a}} | Sequitur xviiii. \textit{P\textsuperscript{y}} | «20a» (in mg.) \textit{P\textsuperscript{p}} | «20a particula» (in mg.) \textit{P\textsuperscript{u}} | Incipit particula 20a de armonia continens problemata 47 \textit{P\textsuperscript{q}} | Aristotelis \textit{problemata} de hiis que sunt circa armoniam particula 20m. Capitulum primum \textit{G\textsuperscript{u}} | de \textit{problematibus} arestotelis que sunt circa armoniam uel musicam particula 19a. \textit{M\textsuperscript{a}M\textsuperscript{b}}}} +\pend + +\pstart +\edtext{\subsubsection {Primum problema}\label{edition-text book-19a part1}}{\lemma{Primum problema} \Cfootnote[nosep]{\textit{G\textsuperscript{u}mv} | \textit{om}. \textit{αE\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | «.1.» (in mg.) \textit{M\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{z}} | problema primum \textit{M\textsuperscript{b}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DOLENTES}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | PROPTER QUID DOLENTES ET GAUDENTES \textit{V\textsuperscript{o}} | PROPTER QUID DOLENTES FISTULANTUR \textit{P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{V\textsuperscript{b}} | \textsuperscript{1}PROPTER QUID DOLENTES ET DELECTANTES FISTULANTUR?\textsuperscript{2}AUT UT HII QUIDEM MINUS TRISTENTUR? ALII AUTEM MAGIS GAUDEANT \textit{G\textsuperscript{u}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Propter quid dolentes etcetera.Propter quid dolentes et gaudentes fistulantur etcetera Determinatis problematibus circa \edtext{mathematicam}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}P\textsuperscript{y}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}mv} | mathematica \textit{M\textsuperscript{a}M\textsuperscript{b}N\textsuperscript{u}V\textsuperscript{m}} | methaphysica \textit{E\textsuperscript{a}} \textit{metha\textsuperscript{ca} a.c.} | metha\expan{physi}cam \textit{(orig. \textup{metha\textsuperscript{cam}})} \textit{P\textsuperscript{z}}}} et orationes, determinat \edtext{nunc}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} problemata circa \edtext{armonicam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | armoniam \textit{P\textsuperscript{z}}}} uel \edtext{musicam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | musica \textit{V\textsuperscript{a}}}}, eo quod in \edtext{ipsa}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{q}mv} | ipso \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}P\textsuperscript{u}V\textsuperscript{o}}}} est \edtext{quidam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} amor sermonis, ut \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{priori}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}mv} | posteriori \textit{P\textsuperscript{y}}}} particula. Et primitus ad \edtext{huius}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | huiusmodi \textit{V\textsuperscript{b}}}} \edtext{maiorem}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | amorem \textit{V\textsuperscript{a}} | \textit{om}. \textit{π}}} expositionem \edtext{premittantur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}} | premittuntur \textit{P\textsuperscript{y}mv}}} quedam \edtext{communia}{\Cfootnote[nosep]{\textit{αλπmv} | coloris \textit{P\textsuperscript{x}}}}, \edtext{sicut}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}mv} | scilicet \textit{πV\textsuperscript{b}}}} \edtext{quid}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{z}mv} | quidem \textit{V\textsuperscript{m}}}} est musica et que \edtext{ipsius}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | sint ipsius species \textit{V\textsuperscript{z}} | prius \textit{P\textsuperscript{z}}}}? \edtext{Que}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} secundum ‘ \edtext{boecium \textit{musice} 5°}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}V\textsuperscript{b}mv} | boecium \textit{musice} 4° \textit{λ} | boecium \textit{musicce} \textit{V\textsuperscript{a}} | boecium raritate 4° \textit{P\textsuperscript{x}} | boecium inprimo \textit{musice} \textit{π}}} \edtext{}{\Afootnote[nosep]{Boethius \textit{De inst. mus.} V. 2 (ed. Friedlein p. 352, ll. 4–5)}} \edtext{est armonica}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}} | armonica est \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | est armonice \textit{γP\textsuperscript{x}mv} | Armonia est \textit{G\textsuperscript{u}}}} facultas \edtext{differentias}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | differens \textit{P\textsuperscript{z}}}} \edtext{acutorum et grauium sonorum \edtext{sensu}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}mv} | sensum \textit{V\textsuperscript{b}}}} \edtext{et}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}} | ac \textit{γE\textsuperscript{a}N\textsuperscript{u}mv}}} ratione}{\Cfootnote[nosep]{\textit{ακmv} | acutorum sonorum et grauium sonorum ratione \textit{π}}} perpendens.’ Secundum \edtext{uero}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} ‘ysidorum \edtext{in}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ut \textit{P\textsuperscript{x}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{ \textit{ethymologiis} }{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{m}mv} | ethicis \textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}} \edtext{}{\Afootnote[nosep]{Isidore of Seville, \textit{Etym.} III .15 .1}} est peritia modulationis, \edtext{sono}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}πmv} | sonorum \textit{V\textsuperscript{b}} | \textit{om}. \textit{V\textsuperscript{a}}}} cantuque consistens.’ +\pend + +\pstart +\textbf{2} Dicitur etiam quod ‘sit scientia numeri ad sonos \edtext{proportionati}{\Cfootnote[nosep]{\textit{βγκmv} | proportionatos \textit{π} | \label{proport.}\textit{proportionatis} \textit{relati} \textit{E\textsuperscript{a}}}}.\edtext{}{\Afootnote[nosep]{Arist. \textit{An. post.} 90a , 14–23}}’ Que secundum ‘ \edtext{ysidorum}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{m}m} | yrodorum \textit{E\textsuperscript{a}}}} dicitur \edtext{a muso}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | autem misso \textit{P\textsuperscript{y}}}} \textit{ \edtext{quasi a querendo}{\Cfootnote[nosep]{\textit{γN\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | quasi acquirendo \textit{M\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | que acquerendo \textit{V\textsuperscript{m}} | id est acquirendo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} }, quia \edtext{per eam uis}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{a}} | per eam ius \textit{mv} | per ea uix \textit{V\textsuperscript{b}} | per ius \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | paruis \textit{P\textsuperscript{z}}}} \edtext{carminum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | corninum \textit{V\textsuperscript{o}}}} \edtext{querebatur}{\Cfootnote[nosep]{\textit{βγκmv} | queratur \textit{E\textsuperscript{a}} | acquiritur \textit{π}}}. Unde a poetis \hyperref[Ju]{iouis} et \hyperref[Mem]{ \edtext{memorie}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | uenem \textit{P\textsuperscript{u}}}} } \edtext{filias}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | philos \textit{P\textsuperscript{z}}}} \edtext{mutas}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | musas \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | unitas \textit{M\textsuperscript{a}}}} \edtext{esse}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} confictum \edtext{est}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | esse \textit{E\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{z}}}}, nam \edtext{memoria soni}{\Cfootnote[nosep]{\textit{κ} | soni memoria \textit{π} | si memoria soni \textit{P\textsuperscript{y}V\textsuperscript{b}mv}}} non \edtext{teneantur, pereunt}{\Cfootnote[nosep]{\textit{αmv} | teneatur, pereunt \textit{κ} | teneatur, perit \textit{π}}}, cum non \edtext{possint}{\Cfootnote[nosep]{\textit{βV\textsuperscript{b}V\textsuperscript{z}m} | possunt \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}v} | possit \textit{πE\textsuperscript{a}}}} scribi.\edtext{}{\Afootnote[nosep]{Isidore of Seville, \textit{Etym.}, III .15 .1–2}}’ \edtext{A nonnullis}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}mv} | Amat[?] nonnullis \textit{V\textsuperscript{b}} | nullus \textit{E\textsuperscript{a}} | Aut \textit{π}}} \edtext{uero dicitur}{\Cfootnote[nosep]{\textit{βγκmv} | dicitur uero \textit{E\textsuperscript{a}} | dicitur \textit{π}}} \edtext{a \textit{moys}}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | amois \textit{P\textsuperscript{x}}}} \textit{ \edtext{quod}{\Cfootnote[nosep]{\textit{αλπmv} | que \textit{P\textsuperscript{x}P\textsuperscript{z}}}} est aqua,} \edtext{quia}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{olim primitus}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}mv} | primitus olim \textit{V\textsuperscript{z}} | olim amicus \textit{C\textsuperscript{a}V\textsuperscript{o}} | olim tali primitus \textit{G\textsuperscript{u}}}} \edtext{inuenta fuit}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | fuit inuenta \textit{πV\textsuperscript{a}}}} \edtext{in illa}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | et illa \textit{P\textsuperscript{z}} | in aqua \textit{P\textsuperscript{p}}}}, et \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{ydriis}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv}}} siue \edtext{instrumentis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in instrumentis \textit{P\textsuperscript{p}}}} aquaticis \edtext{similiter}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | simpliciter \textit{V\textsuperscript{a}}}} \edtext{exercita}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ex certa \textit{P\textsuperscript{z}}}}. ‘ \edtext{Refert autem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | Refertur \textit{P\textsuperscript{z}}}} \edtext{\hyperref[Mos]{moyses} hanc}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | hanc \hyperref[Mos]{moyses} \textit{P\textsuperscript{z}}}} inuenisse \edtext{ \edtext{\hyperref[Tub]{tubal}}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}M\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | aabal \textit{P\textsuperscript{p}P\textsuperscript{u}} | \hyperref[Tub]{tubal} fratrem \hyperref[Cay]{cayn} \textit{P\textsuperscript{y}}}} de \edtext{stirpe}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv}}} \hyperref[Cay]{ \edtext{cayn}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}}}} } \edtext{ante diluuium}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}}.\edtext{}{\Afootnote[nosep]{Isidore of Seville, \textit{Etym.} III .16 .1}}’ \edtext{‘Sed \edtext{greci}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | gressi \textit{P\textsuperscript{z}}}}, ut apparet per macrobium et \edtext{boecium}{\Cfootnote[nosep]{\textit{βγλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | bonum \textit{P\textsuperscript{z}}}} , dicunt eam inuenisse’}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} ‘ \edtext{\hyperref[Pyth]{pytagori samium}}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | \hyperref[Pyth]{pictagorius samium} \textit{V\textsuperscript{b}} | \hyperref[Pyth]{pitagoram samium} \textit{M\textsuperscript{a}V\textsuperscript{z}} | \hyperref[Pyth]{pictagoram samium} \textit{V\textsuperscript{m}} | \hyperref[Pyth]{pictagoram} \textit{π} | pythagorici samium \textit{mv} | pitagorici \textit{V\textsuperscript{a}}}} sonitu \edtext{malleorum}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv}}}, \edtext{cum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | cum pro \textit{V\textsuperscript{a}}}} casu in \edtext{publicum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv}}} \edtext{exiret}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | iret \textit{V\textsuperscript{z}}}} \edtext{ad}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cum \textit{G\textsuperscript{u}}}} fabros, et cordarum \edtext{demum impulsione}{\Cfootnote[nosep]{\textit{βγλmv} | deinde impulsione \textit{P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{o}} | deinde pulsione \textit{G\textsuperscript{u}}}}.\edtext{}{\Afootnote[nosep]{Boethius, \textit{De inst. mus.} I .10 (Friedlein p. 196–7);}}\edtext{}{\Afootnote[nosep]{Macrobius, \textit{Comm. in somn. Scip.} II .1 (Eyssenhardt p. 572–575)}}’ +\pend + +\pstart +\textbf{3} \edtext{Diuiditur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Dicitur \textit{G\textsuperscript{u}P\textsuperscript{p}}}} autem musica \edtext{iuxta}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | secundum \textit{G\textsuperscript{u}}}} \edtext{eosdem}{\Cfootnote[nosep]{\textit{βγλπmv} | easdem \textit{E\textsuperscript{a}} | eo sedem \textit{P\textsuperscript{x}}}} in \edtext{mundanam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{b}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv}}}, \edtext{humanam}{\Cfootnote[nosep]{\textit{αλπmv} | habentiuam \textit{P\textsuperscript{x}}}}, \edtext{et}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} organicam \edtext{uel}{\Cfootnote[nosep]{\textit{αλπmv} | seu \textit{P\textsuperscript{x}}}} instrumentalem. \edtext{Mundana}{\Cfootnote[nosep]{\textit{βγG\textsuperscript{u}M\textsuperscript{b}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}mv} | mundanam \textit{E\textsuperscript{a}}}} \edtext{uero}{\Cfootnote[nosep]{\textit{βγκmv} | quidem \textit{π} | non \textit{E\textsuperscript{a}}}} \edtext{attenditur}{\Cfootnote[nosep]{\textit{γλG\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | intenditur \textit{E\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} in sono armonico, \edtext{quem}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | que \textit{V\textsuperscript{m}} | quam \textit{E\textsuperscript{a}}}} causant orbes celestes, secundum \edtext{\hyperref[Pyth]{pictagoram}}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | pithagoricos \textit{mv} | pictagoricos \textit{V\textsuperscript{b}} | pitagoricos \textit{V\textsuperscript{a}}}} cum aliis musicis, \edtext{differenter}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}P\textsuperscript{q}} | d\expan{iffe}r\expan{u}ntur \textit{(orig. \textup{drntur})} \textit{mv}}} \edtext{commotos}{\Cfootnote[nosep]{\textit{ακmv} | commoti \textit{π}}}. ‘ \edtext{Sonum}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{enim}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{armonicum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | organicum \textit{V\textsuperscript{z}}}} \edtext{causant}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | causatur \textit{V\textsuperscript{m}}}}, \edtext{sed}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | per \textit{V\textsuperscript{a}}}} \edtext{eum}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | eius \textit{P\textsuperscript{z}} | eum \surplus{sed eum} \textit{E\textsuperscript{a}}}} non \edtext{percipimus}{\Cfootnote[nosep]{\textit{ακmv} | percipimus ut \textit{π}}}, dicunt, \edtext{propter quod}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | propter hoc quod \textit{π} | propter ea quod \textit{P\textsuperscript{y}} | preterea \textit{M\textsuperscript{a}}}} \edtext{in auribus nostris a principio}{\Cfootnote[nosep]{\textit{βγκmv} | in auribus et nostris a principio \textit{E\textsuperscript{a}} | a principio nobis in auribus nostris \textit{π}}} \edtext{natiuitatis}{\Cfootnote[nosep]{\textit{ακmv} | natum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | notum \textit{V\textsuperscript{o}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακmv} | est et \textit{π}}} \edtext{complantatus}{\Cfootnote[nosep]{\textit{ακvv} | complantatur \textit{π}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{in eris apparet}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}} | apparet in eris \textit{P\textsuperscript{p}} | in eis apparet \textit{γE\textsuperscript{a}P\textsuperscript{z}mv}}} \edtext{malleatoribus}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | malleationibus \textit{P\textsuperscript{q}}}} strepitum \edtext{suum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{vix}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | vis \textit{V\textsuperscript{a}}}} percipientibus \edtext{consuetudine}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et ex consuetudine \textit{P\textsuperscript{p}}}} \edtext{quos}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}mv} | quod \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | quo \textit{P\textsuperscript{z}} | quorum \textit{V\textsuperscript{b}}}} \edtext{aristotelem impugnat \textit{celi et mundi} \edtext{}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}mv} | et \textit{P\textsuperscript{x}}}} 2°.}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}mv} | aristotelem impugnat 2° \textit{celi et mundi.} \textit{γλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | aristotelem in 2° \textit{celi et mundi} inpungnat. \textit{P\textsuperscript{z}}}} \edtext{}{\Afootnote[nosep]{Arist. \textit{De caelo}, II .9 , 290b , l. 25}}’ +\pend + +\pstart +\textbf{4} Musica uero \edtext{humana}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | mundana \textit{P\textsuperscript{y}}}} \edtext{dicitur}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{que}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | que est \textit{P\textsuperscript{y}}}} circa \edtext{concordantiam elementorum}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | concordantia elementorum \textit{V\textsuperscript{a}} | elementa \textit{π}}} \edtext{diuersorum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | diuersi \textit{N\textsuperscript{u}}}} ad inuicem \edtext{in vno composito}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | non composito \textit{P\textsuperscript{y}} | \textit{om}. \textit{πE\textsuperscript{a}}}} uel \edtext{compositionem}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | compositione \textit{P\textsuperscript{y}} | compositum \textit{P\textsuperscript{x}}}} corporis \edtext{uersatur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | similatur \textit{P\textsuperscript{y}}}}, per \edtext{eam}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{a}} | ea \textit{P\textsuperscript{x}V\textsuperscript{b}mv}}} enim natura spiritualis coniungitur \edtext{corpori et rationalis}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | corpori et in rationalis \textit{M\textsuperscript{b}} | rationalis \textit{P\textsuperscript{x}} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{concorditer}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | concordie \textit{mv}}} cum \edtext{irrationali}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | irrationabili \textit{E\textsuperscript{a}P\textsuperscript{z}} | rationali \textit{V\textsuperscript{z}}}} \edtext{coniungitur}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}. \edtext{Quod}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | erum[?] \textit{V\textsuperscript{m}}}} \edtext{videtur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | aristotelem \textit{P\textsuperscript{q}P\textsuperscript{u}}}} \edtext{a platonicis}{\Cfootnote[nosep]{\textit{αλπmv} | apolatonicis \textit{P\textsuperscript{x}}}} habitum ponentibus animam quandam armonicam \edtext{fore consistentiam}{\Cfootnote[nosep]{\textit{ακmv} | esse consistentiam \textit{π}}}. Vnde ‘ \edtext{datum in \textit{afforismis} }{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}} | dictum est in \textit{afforismis} \textit{γλmv} | damascenus in \textit{afforismis} \textit{π}}} \edtext{colligatio}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}} | colicgio \textit{V\textsuperscript{a}}}} \edtext{anime et corporis}{\Cfootnote[nosep]{\textit{κ} | corporis et anime \textit{απmv}}} secundum \edtext{ordinis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cordis \textit{P\textsuperscript{z}}}} naturalis consonantiam \edtext{facta}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | factam \textit{P\textsuperscript{q}P\textsuperscript{u}V\textsuperscript{c}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{q}}}}, ut \edtext{substat}{\Cfootnote[nosep]{\textit{κ} | subsistat \textit{απmv}}},\edtext{}{\Afootnote[nosep]{Yuḥannā ibn Māsawaiyh, \textit{Aph.}, (Vat. Lat. 2460, f. 39v, ll.7–8)}}’ quare \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}mv} | huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{o}}}} \edtext{musice}{\Cfootnote[nosep]{\textit{κ} | musice naturali \textit{αmv} | numeratione naturali \textit{π}}} \edtext{videntur scientie}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{z}mv} | scientie videntur \textit{V\textsuperscript{a}} | videntur hec scientie \textit{π} | numeri scientie \textit{V\textsuperscript{m}} | uidentur sane \textit{V\textsuperscript{b}}}} \edtext{supponi}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}}. +\pend + +\pstart +\textbf{5} Instrumentalis \edtext{uero}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} dicitur que quibusdam \edtext{exercetur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | exercet \textit{N\textsuperscript{u}}}} armonicis instrumentis, que \edtext{predicamentis videtur}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{q}V\textsuperscript{m}mv} | predicamentis videntur \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | videntur predicamentis \textit{P\textsuperscript{p}} | possunt uidetur \textit{P\textsuperscript{x}}}} \edtext{fore}{\Cfootnote[nosep]{\textit{ακmv} | esse \textit{π}}} \edtext{considerationis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv} | speculationis \textit{P\textsuperscript{y}} | c\expan{on}t\expan{rist}ationis \textit{(orig. \textup{\textsubscript{9}t[?]ātionis})} \textit{V\textsuperscript{b}}}} \edtext{existens duplex}{\Cfootnote[nosep]{\textit{γκmv} | existens d\expan{icendu}m \textit{(orig. \textup{dd'})} \textit{N\textsuperscript{u}} | existens dicendum \textit{P\textsuperscript{y}} | existens \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}}: \edtext{nam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} quedam exercetur instrumento naturali, ut \edtext{hominis}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | homines \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}}}} \edtext{uoce}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uoces \textit{G\textsuperscript{u}}}}, \edtext{cum reliquis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | reliquis cum \textit{P\textsuperscript{p}}}} organis \edtext{locutionis}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}} | locutiones \textit{V\textsuperscript{a}} | locutiuis \textit{M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}V\textsuperscript{o}}}}, \edtext{aut}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | an \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{artificiali}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | artificiale \textit{P\textsuperscript{z}}}}. Et \edtext{id}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | illud \textit{P\textsuperscript{p}P\textsuperscript{x}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{multipliciter}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{a}mv} | \surplus{multiplicatur aut artificiali et id} multipliciter \textit{V\textsuperscript{b}}}}: \edtext{aut}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | ut \textit{V\textsuperscript{a}}}} tactu \edtext{ut}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{viellis}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{o}} | vincul \textit{P\textsuperscript{z}}}}, \edtext{uel}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}V\textsuperscript{o}mv} | aut \textit{P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{z}}}} pulsu \edtext{ceu}{\Cfootnote[nosep]{\textit{βγκ} | seu \textit{E\textsuperscript{a}V\textsuperscript{o}mv} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{cimbalis}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}m} | ebalis \textit{E\textsuperscript{a}}}}, \edtext{uel}{\Cfootnote[nosep]{\textit{βγκπmv} | ut \textit{E\textsuperscript{a}}}} \edtext{flatu}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | flatum \textit{P\textsuperscript{p}} | flacio \textit{P\textsuperscript{x}V\textsuperscript{m}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{βγλP\textsuperscript{z}V\textsuperscript{o}mv} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | in \textit{E\textsuperscript{a}P\textsuperscript{x}}}} \edtext{tubis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | tibiis \textit{P\textsuperscript{z}}}}, aut quasi \edtext{omni modo}{\Cfootnote[nosep]{\textit{βπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}mv} | omnino \textit{V\textsuperscript{b}V\textsuperscript{z}}}} \edtext{sicut}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | ut \textit{πP\textsuperscript{y}}}} \edtext{fistulis}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv}}}. +\pend + +\pstart +\textbf{6} \edtext{Que}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{z}mv} | Qui \textit{P\textsuperscript{x}V\textsuperscript{m}} | Dicitur \textit{P\textsuperscript{y}}}} iuxta ‘ \edtext{ysidorum}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}}}} \edtext{diuiditur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}} | diuidetur \textit{mv} | dicitur \textit{P\textsuperscript{x}V\textsuperscript{m}}}} in \edtext{armonicam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | armonicam et \textit{P\textsuperscript{y}}}} metricam et \edtext{rithimicam}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | et rithimicam \textit{V\textsuperscript{z}} | rethoricam \textit{E\textsuperscript{a}}}}. \edtext{Quarum}{\Cfootnote[nosep]{\textit{βγκmv} | Quorum \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}} \edtext{armonica}{\Cfootnote[nosep]{\textit{αλπmv} | armonica metricam \textit{P\textsuperscript{x}}}} \edtext{graue in sonis et \edtext{acutum}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | acutis \textit{E\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | graue et acutum in sonis \textit{π} | graue in sonis acutum \textit{P\textsuperscript{y}}}} discernit. \edtext{Metrica}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | etricam \textit{E\textsuperscript{a}} | Matricam \textit{M\textsuperscript{a}P\textsuperscript{x}}}} \edtext{est}{\Cfootnote[nosep]{\textit{απmv} | etiam \textit{κ}}} que ratione probabili \edtext{cognoscit \edtext{mensuram}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}mv} | mensuras \textit{G\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | mensuram cognoscit \textit{V\textsuperscript{a}}}} diuersorum pedum ut \edtext{heroycum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{u}} | heronicam \textit{P\textsuperscript{x}}}} \edtext{iambicum}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | in abitio \textit{P\textsuperscript{x}}}} \edtext{et}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{heliacum}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}V\textsuperscript{m}V\textsuperscript{z}} | \textit{om}. \textit{E\textsuperscript{a}}}}. Rithimica \edtext{uero}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | uero est \textit{β} | est \textit{V\textsuperscript{a}}}} \edtext{que}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}V\textsuperscript{z}}}} uerborum \edtext{incursionem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | intercessionem \textit{P\textsuperscript{z}}}} \edtext{inquirit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | iungit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{αλπmv} | uerum \textit{P\textsuperscript{x}}}} \edtext{aut}{\Cfootnote[nosep]{\textit{γM\textsuperscript{b}} | autem \textit{P\textsuperscript{x}mv} | au\expan{t} \textit{(orig. \textup{aū})} \textit{M\textsuperscript{a}} | an \textit{βE\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | \textit{om}. \textit{π}}} suauiter \edtext{uel}{\Cfootnote[nosep]{\textit{απmv} | an \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | aut \textit{M\textsuperscript{a}}}} non suauiter sonus \edtext{cohereat}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | adhereat \textit{P\textsuperscript{q}}}}.\edtext{}{\Afootnote[nosep]{Isidore of Seville, \textit{Etym.} III .18 .1–2}}’ +\pend + +\pstart +\textbf{7} \edtext{Que}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Quasi \textit{P\textsuperscript{z}}}} \edtext{siquidem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quidem \textit{G\textsuperscript{u}} | quedam \textit{P\textsuperscript{z}}}} \edtext{tria}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | tripliciter \textit{γmv} | \textit{om}. \textit{P\textsuperscript{z}}}} ad genus \edtext{videntur concurrere}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}} | concurrere uidentur \textit{P\textsuperscript{y}} | videtur concurrere \textit{γM\textsuperscript{a}V\textsuperscript{m}mv} | videntur currere \textit{P\textsuperscript{p}P\textsuperscript{u}} | uidentur concinere \textit{P\textsuperscript{z}}}} \edtext{cantilene}{\Cfootnote[nosep]{\textit{βπM\textsuperscript{a}V\textsuperscript{z}mv} | ca\expan{n}tic\expan{u}le. \textit{(orig. \textup{caticlʼe})} \textit{V\textsuperscript{a}} | can\expan{tic}ule \textit{(orig. \textup{canule})} \textit{V\textsuperscript{b}} | causa mille \textit{P\textsuperscript{x}}}}, armonica tamen, ut \edtext{tactum}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}} | tactu \textit{V\textsuperscript{a}} | tactum est \textit{πM\textsuperscript{a}V\textsuperscript{m}mv} | dictum est \textit{V\textsuperscript{z}}}}, \edtext{consonantiam}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{a}V\textsuperscript{z}mv} | consonantia \textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}} grauis et \edtext{acuti}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | accuta \textit{V\textsuperscript{a}}}} \edtext{attendit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}}, \edtext{rithimica}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | rithimica uero \textit{β} | rithimicam ut tactum est \textit{P\textsuperscript{z}}}} \edtext{consonantiam}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | consonantia \textit{G\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}}}} \edtext{terminationum}{\Cfootnote[nosep]{\textit{βγκπmv} | durationum \textit{E\textsuperscript{a}}}}, metrica \edtext{uero}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | vel \textit{V\textsuperscript{o}}}} temporum ut apparet \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{traditione}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | traditionem \textit{E\textsuperscript{a}} | introductione \textit{γP\textsuperscript{z}}}} musice \edtext{\hyperref[GAr]{guidonis}}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}mv} | grauidons \textit{V\textsuperscript{b}} | gradionis \textit{P\textsuperscript{x}}}}. et circa \edtext{has}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} tres partes musice, et \edtext{maxime}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | maxime circa \textit{G\textsuperscript{u}}}} \edtext{duas}{\Cfootnote[nosep]{\textit{ακE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | duos \textit{P\textsuperscript{q}} | et \textit{P\textsuperscript{z}}}} \edtext{priores}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}}, \edtext{dubitat}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | dubitabit \textit{λ}}} ‘aristoteles \edtext{vtilitas}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | vnitas \textit{P\textsuperscript{y}} | volitas \textit{V\textsuperscript{o}}}} \edtext{uero}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} musice est,\edtext{}{\Afootnote[nosep]{Arist. \textit{Pol.} VIII .5 , 1339a , l. 11}}’ quia delectat \edtext{animos}{\Cfootnote[nosep]{\textit{κ} | animas \textit{απmv}}} \edtext{excitat, et}{\Cfootnote[nosep]{\textit{κN\textsuperscript{u}} | exercitas et \textit{V\textsuperscript{b}} | exercitat et \textit{P\textsuperscript{y}mv} | et exercitat \textit{V\textsuperscript{a}} | exitat et \textit{E\textsuperscript{a}} | et \textit{π}}} affectus mouet, \edtext{et}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{furiam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | furias \textit{V\textsuperscript{z}}}} placat, \edtext{siluestrem}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | siluestres \textit{V\textsuperscript{m}} | siluestre \textit{πP\textsuperscript{y}}}} \edtext{mansuescere}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | mansuestrem \textit{P\textsuperscript{z}}}} \edtext{facit}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}V\textsuperscript{m}}}}, ut apparet clangore, \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} tubarum et similium fortiores redduntur bellatores. Similiter \edtext{lassatos et exercitio}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}V\textsuperscript{b}mv} | et laxatos exercitio \textit{G\textsuperscript{u}} | lasatas et exercitio \textit{V\textsuperscript{a}} | laxatiuo et exercitio \textit{P\textsuperscript{y}} | laxatos exercitio \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}} | lassatos exercitio \textit{P\textsuperscript{q}}}} \edtext{laborioso}{\Cfootnote[nosep]{\textit{ακmv} | laborioso et \textit{π}}} \edtext{detentos}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | detento \textit{P\textsuperscript{z}}}} reddit \edtext{faciles}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | facille \textit{V\textsuperscript{a}} | facilius \textit{π}}} tollerare. Unde ‘ \edtext{ \textit{ \edtext{politicorum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}mv}}} } 8°:}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | 8° \textit{politicorum} \textit{G\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{m}} | \textit{palliticorum} duo \textit{P\textsuperscript{x}}}} musica habet delectationem naturalem propter quod omnibus etatibus et omnibus \edtext{moribus}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | et moribus \textit{V\textsuperscript{a}} | horis \textit{G\textsuperscript{u}P\textsuperscript{q}}}} usus ipsius est amicus.\edtext{}{\Afootnote[nosep]{Arist. \textit{Pol.} VIII , 1340a , ll. 3–5}}’ +\pend + +\pstart +\textbf{8} Recitat \edtext{etiam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | et \textit{V\textsuperscript{m}}}} ‘ \edtext{boecius}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | boecium \textit{G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}mv}}} \edtext{\hyperref[Pyth]{pictagoram}}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}V\textsuperscript{o}} | primae \hyperref[Pyth]{pyctoragam} \textit{P\textsuperscript{y}} | pythagoricos \textit{mv} | pictagoricas \textit{γ}}} \edtext{iuuenem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | in uenere \textit{P\textsuperscript{z}}}} \edtext{furentem}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} in \edtext{combustionem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}} | combustione \textit{πP\textsuperscript{y}mv}}} domus \edtext{riualis}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}mv}}} in qua \edtext{sortum}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}} | scortum \textit{λG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}mv}}} continebatur melodiis \edtext{musicis}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}mv} | musicum \textit{γ}}} eius animum \edtext{sedasse}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}}.\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} I .1 (Friedlein p. 185, l. 3)}}’ Cuius \edtext{vtilitatem}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{a}} | subtilitatem \textit{V\textsuperscript{b}mv}}} \edtext{tangit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | agit \textit{P\textsuperscript{z}}}} ‘ \edtext{ \textit{ \edtext{politicorum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{o}mv}}} } 8°}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | 8° \textit{politicorum} \textit{P\textsuperscript{z}} | aristotelis 8° \textit{politicorum} \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, \edtext{ponitur}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{m}mv} | ponuntur \textit{πV\textsuperscript{z}} | ponit \textit{β}}} enim \edtext{vnum quatuor}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}M\textsuperscript{b}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | quatuor \textit{P\textsuperscript{y}P\textsuperscript{z}} | ibi quatuor \textit{G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}} | quatuor ibi \textit{P\textsuperscript{p}}}} \edtext{que debet}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}v} | que debent \textit{P\textsuperscript{p}m} | quedam \textit{P\textsuperscript{x}}}} \edtext{adiscere}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{y}}}} \edtext{puer}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | pueri \textit{P\textsuperscript{p}} | \textit{om}. \textit{P\textsuperscript{x}}}}: que sunt \edtext{littere}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | littera \textit{G\textsuperscript{u}P\textsuperscript{q}} | lingue \textit{γmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{luctatiua}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | luctatio \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \surplus{luctatio} luctatio \textit{E\textsuperscript{a}} | licatio \textit{P\textsuperscript{x}} | iutatio \textit{V\textsuperscript{z}} | britatio \textit{P\textsuperscript{z}}}} musica et \edtext{protractiua}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | p\expan{ro}t\expan{r}act\expan{iu}a \textit{(orig. \textup{p't'actā})} \textit{N\textsuperscript{u}V\textsuperscript{a}} | protractura \textit{P\textsuperscript{p}} | pertractiua \textit{V\textsuperscript{b}} | porctiua \textit{P\textsuperscript{z}}}},\edtext{}{\Afootnote[nosep]{Arist. \textit{Pol.} VIII , 1337b , l. 23}}’ \edtext{ceu}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}V\textsuperscript{b}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}}}} \edtext{scribere}{\Cfootnote[nosep]{\textit{ακmv} | scriptura \textit{π}}} et pingere. +\pend + +\pstart +\textbf{9} Querit \edtext{igitur}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | ergo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{a}}}} \hyperref[Ar]{aristoteles} more \edtext{consueto}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | solito \textit{λC\textsuperscript{a}P\textsuperscript{q}}}} \edtext{problema, dicens}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}: \textit{Quare dolentes \edtext{et contristantes et}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}V\textsuperscript{z}} | contristantes et \textit{E\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | contristantes \textit{P\textsuperscript{y}V\textsuperscript{a}} | et tristantes et \textit{M\textsuperscript{a}P\textsuperscript{x}} | et contristantes sunt \textit{P\textsuperscript{p}}}} delectantes \edtext{gaudentesque}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | et gaudentes \textit{P\textsuperscript{p}V\textsuperscript{z}} | gaudentes \textit{P\textsuperscript{x}}}} \edtext{fistulas}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}} et \edtext{vniversaliter instrumenta}{\Cfootnote[nosep]{\textit{ακmv} | vniuersaliter omnia instrumenta \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{delectationem et gaudium inducentia}{\Cfootnote[nosep]{\textit{αV\textsuperscript{m}V\textsuperscript{z}mv} | delectationem inducentia et gaudium \textit{P\textsuperscript{x}} | delectationem inducentia \textit{M\textsuperscript{a}} | gaudium et letitiam inducentia \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | letitiam quod inducentia \textit{G\textsuperscript{u}}}} expedit audire?} Unde ‘ \edtext{alexander}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{}{\Cfootnote[nosep]{\textit{γκπmv} | in \textit{problematibus} \textit{β}}} \edtext{et maxime}{\Cfootnote[nosep]{\textit{βγκπmv} | \surplus{et maxime} et maxime \textit{E\textsuperscript{a}}}} \edtext{quantum}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{x}}}} \edtext{ad primam partem:}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | ad primam: \textit{P\textsuperscript{y}}}} Propter \edtext{quid}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{coram}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | corpora \textit{P\textsuperscript{z}}}} patientibus fistule \edtext{et}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aut \textit{G\textsuperscript{u}}}} \edtext{tympana.}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{o}} | tympane. \textit{V\textsuperscript{a}} | timpana etcetera. \textit{V\textsuperscript{b}}}} \edtext{}{\Afootnote[nosep]{Ps.-Alex. Aph., \textit{Prob.} I .78 (Vat. reg. lat. 747, f. 75v)}}’ +\pend + +\pstart +\textbf{10} \edtext{Nosce quod ‘ \edtext{omnes passiones}{\Cfootnote[nosep]{\textit{κ} | licet omnes passiones \textit{γmv} | licet omnes \textit{E\textsuperscript{a}} | omnes passiones licet \textit{P\textsuperscript{y}} | omnes passiones sint \textit{N\textsuperscript{u}}}} \edtext{sint coniuncti}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}} | sint coniuncte \textit{βγ} | sint coniecti \textit{mv} | sicut continetur \textit{κ}}}, 1° \textit{de anima} \edtext{}{\Afootnote[nosep]{Arist. \textit{De an.} I .1 , 403a , l. 25 ((Cf. 403a l. 16))}}’; \edtext{quedam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | quedam te \textit{P\textsuperscript{y}}}} \edtext{tamen se plus tenet}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | tamen se tenet \textit{E\textsuperscript{a}} | tamen se plus tenent \textit{V\textsuperscript{b}} | tamen plus se tenent \textit{β} | tamen plus tenent \textit{V\textsuperscript{a}} | se plus tenent \textit{M\textsuperscript{a}}}} ex parte \edtext{corporis, ut dolere et delectari, \edtext{alie uero ex parte}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}N\textsuperscript{u}mv} | exparte uero \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{αλmv} | \textit{om}. \textit{P\textsuperscript{x}}}} anime ut \edtext{gaudere}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | gaudium \textit{V\textsuperscript{m}}}} et tristari; ita \edtext{ut}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} per vnum expressum \edtext{aliud \hyperref[Ar]{aristoteles} audiat}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}N\textsuperscript{u}mv} | \hyperref[Ar]{aristoteles} audiat aliud \textit{P\textsuperscript{x}} | aliud audiat \hyperref[Ar]{aristoteles} \textit{P\textsuperscript{y}}}} \edtext{recitatum}{\Cfootnote[nosep]{\textit{γmv}}} }{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}. +\pend + +\pstart +\textbf{11} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}}}} } Soluit dicens causam esse \edtext{ut}{\Cfootnote[nosep]{\textit{αλπmv} | nisi \textit{P\textsuperscript{x}}}} \textit{ \edtext{qui}{\Cfootnote[nosep]{\textit{αλπmv} | quod \textit{P\textsuperscript{x}}}} tristantur \edtext{ac etiam}{\Cfootnote[nosep]{\textit{ακmv} | et \textit{π}}} \edtext{dolent}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | doleant \textit{E\textsuperscript{a}P\textsuperscript{z}}}} minus \edtext{contristentur}{\Cfootnote[nosep]{\textit{ακmv} | tristentur \textit{π}}} \edtext{et}{\Cfootnote[nosep]{\textit{αλπmv} | ac etiam \textit{P\textsuperscript{x}}}} doleant \edtext{propter}{\Cfootnote[nosep]{\textit{ακmv} | propter melodiam uel \textit{π}}} iocunditatem inductam ex sonitu \edtext{instrumenti}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | instrumenta \textit{P\textsuperscript{z}}}} }. In \edtext{oppositis}{\Cfootnote[nosep]{\textit{ακmv} | oppositis uero \textit{π}}} causa \edtext{extat}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}} | extet \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | existit \textit{π} | est \textit{mv}}} ut \textit{magis \edtext{gaudeant}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} et \edtext{delectentur}{\Cfootnote[nosep]{\textit{ακmv} | iocundentur \textit{π}}}, si enim \edtext{aliqui}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | alia \textit{V\textsuperscript{a}}}} sunt iocundi \edtext{addita}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | a dicta \textit{P\textsuperscript{z}}}} causa \edtext{iocunditatis}{\Cfootnote[nosep]{\textit{ακmv}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{P\textsuperscript{p}P\textsuperscript{u}} | scilicet \textit{G\textsuperscript{u}P\textsuperscript{q}}}} fistulationis \edtext{armonice}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | armonia \textit{C\textsuperscript{a}V\textsuperscript{o}}}} \edtext{amplius delectabuntur.}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | delectabuntur amplius. \textit{λ} | magis iocundabuntur. \textit{G\textsuperscript{u}P\textsuperscript{q}}}} } +\pend + +\pstart +\textbf{12} Nosce quod \edtext{id}{\Cfootnote[nosep]{\textit{ακ} | illud \textit{πmv}}} potest contingere quia idem \edtext{potest esse}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | est \textit{G\textsuperscript{u}P\textsuperscript{q}}}} causa diuersorum aut \edtext{ratione}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{u}P\textsuperscript{z}mv} | ratione diuersorum aut ratione \textit{C\textsuperscript{a}E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{c}V\textsuperscript{o}}}} dispositionis \edtext{susceptiui}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}mv} | susceptum \textit{E\textsuperscript{a}} | suscepti \textit{V\textsuperscript{m}} | susceptorum \textit{V\textsuperscript{z}} | subscopii \textit{P\textsuperscript{x}}}}; uel quia \edtext{diuersa}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}mv} | d\expan{ictu}m \textit{(orig. \textup{dm})} \textit{C\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{c}V\textsuperscript{o}} | diuersimode \textit{P\textsuperscript{p}} | dum \textit{P\textsuperscript{q}}}} \edtext{egeant}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}mv} | egeat \textit{V\textsuperscript{a}} | agat \textit{π}}} \edtext{eadem}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | eodem \textit{λN\textsuperscript{u}V\textsuperscript{b}mv} | eorum \textit{V\textsuperscript{a}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{uel}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | et \textit{P\textsuperscript{y}} | \textit{om}. \textit{πM\textsuperscript{a}}}} \edtext{ratione}{\Cfootnote[nosep]{\textit{αλπmv} | idem \textit{P\textsuperscript{x}}}} eius \edtext{quod}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} per se \edtext{aut}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{q}mv} | an \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | et \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} per accidens \edtext{extat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | existat \textit{P\textsuperscript{z}}}}, ‘ut \edtext{nauta}{\Cfootnote[nosep]{\textit{βγκπmv}}} per \edtext{sui}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | suam \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{presentiam}{\Cfootnote[nosep]{\textit{βγκπmv} | presentia \textit{E\textsuperscript{a}}}} \edtext{causa}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | causa est \textit{G\textsuperscript{u}V\textsuperscript{b}mv} | est causa \textit{P\textsuperscript{z}V\textsuperscript{a}}}} salutis nauis, \edtext{eius}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | enim \textit{P\textsuperscript{y}}}} uero \edtext{absentia}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | absentiam \textit{P\textsuperscript{p}P\textsuperscript{u}} | absentia causa \textit{P\textsuperscript{q}} | \textit{om}. \textit{P\textsuperscript{y}}}} submersionis \edtext{2° \textit{ \edtext{physicorum}{\Cfootnote[nosep]{\textit{λG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}}}} } }{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | \textit{physicorum} 2° \textit{P\textsuperscript{y}V\textsuperscript{a}}}}.\edtext{}{\Afootnote[nosep]{Arist. \textit{Phys.} II .3 , 195a , l. 13}}’ \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{u}V\textsuperscript{z}} | sequitur 2m. problema. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Secundum problema}\label{edition-text book-19a part2}}{\lemma{Secundum problema} \Cfootnote[nosep]{\textit{γG\textsuperscript{u}mv} | «2m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{Secundum} Secundum \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID LONGIUS}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID LONGIUS AUDITUR \textit{P\textsuperscript{q}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID LONGIUS IDEM EADEM UOCE AUDITUR CUM ALIIS CANTANS ET CLAMANS QUAM SOLUS? \textsuperscript{2}AUT QUIA COADUNATE ALIQUID FACERE, AUT REPRIMERE AUT IMPELLERE, NON TANTA PROPE SUNT QUANTUS NUMERUS. \textsuperscript{3}SED SICUT LINEA BIPEDALIS NON DUPLUM SED QUADRUPLUM ALIQUID SCRIBIT, ITA COMPOSITA PLUS POSSUNT, AUT SECUNDUM NUMERUM AUT QUANDO FUERINT DIUERSA. \textsuperscript{4}COADUNATIS IGITUR EXISTENTIBUS UNA FIT UOCIS FORTITUDO ET SIMUL IMPELLIT AEREM. QUARE MULTIPLICITER PREIT, \textsuperscript{5}ETENIM EX OMNIBUS UOX UNIUSCUIUSQUE MULTIPLEX \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}mv}}}.} Secundum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{m}mv} | Querit quare \textit{λ}}} vnus et \edtext{idem}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | idem \surplus{Secundum} \textit{P\textsuperscript{y}}}} numero \edtext{eadem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}P\textsuperscript{q}P\textsuperscript{u}}}} \edtext{similiter}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | simpliciter \textit{P\textsuperscript{z}}}} uoce cantans \edtext{et}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} \edtext{uociferans}{\Cfootnote[nosep]{\textit{βγκπmv} | uociferaret \textit{E\textsuperscript{a}}}} \edtext{ \edtext{remotius auditur}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | auditur remotius \textit{V\textsuperscript{m}}}} quando cum aliis \edtext{vna cantat et}{\Cfootnote[nosep]{\textit{βγV\textsuperscript{z}mv} | una uoce cantat et \textit{M\textsuperscript{a}V\textsuperscript{m}} | una uoce cantant uel \textit{P\textsuperscript{x}}}} clamat quam si solus \edtext{tantum}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} cantaret \edtext{aut}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | an \textit{V\textsuperscript{m}}}} uociferaret}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}}?} Non tamen \edtext{adeo}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{distantur}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | distantantes \textit{G\textsuperscript{u}} | distante \textit{V\textsuperscript{a}} | distant \textit{P\textsuperscript{y}} | distanter \textit{P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | \textit{om}. \textit{E\textsuperscript{a}}}}, \edtext{sicut}{\Cfootnote[nosep]{\textit{αλπmv} | sint \textit{P\textsuperscript{x}}}} vnus post alium \edtext{ordinatus}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | ordinatus uero \textit{P\textsuperscript{y}}}} distantia \edtext{uociferaret}{\Cfootnote[nosep]{\textit{ακmv} | uociferat \textit{π}}} \edtext{ut in}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ut \textit{κ} | in \textit{P\textsuperscript{y}} | et in \textit{P\textsuperscript{z}}}} \edtext{proicientibus}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{a}V\textsuperscript{z}mv}}} lapidem \edtext{successiue}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{m}mv}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}mv}}} } Soluit \edtext{dicens primo causam esse}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | dicens causam esse primo \textit{M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{m}} | primo dicens causam esse \textit{G\textsuperscript{u}P\textsuperscript{q}} | dicens causam esse \textit{P\textsuperscript{x}}}} \textit{quia \edtext{coniunctim}{\Cfootnote[nosep]{\textit{βλG\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | coniuncti \textit{V\textsuperscript{b}} | coniunctum \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}} | coniunctus \textit{P\textsuperscript{z}}}} \edtext{aliquid}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{o}mv} | aliquod \textit{P\textsuperscript{p}} | ad \textit{P\textsuperscript{p}}}} agere, puta \edtext{est reprimere}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | reprimere est \textit{V\textsuperscript{z}} | reprimere \textit{πP\textsuperscript{y}M\textsuperscript{a}}}} \edtext{coangustante}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}mv} | coangustantem \textit{V\textsuperscript{m}} | coangustare \textit{βM\textsuperscript{a}} | coangustando \textit{π} | angustatis \textit{V\textsuperscript{z}}}} \edtext{an}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | aut \textit{απM\textsuperscript{a}mv}}} \edtext{impellere}{\Cfootnote[nosep]{\textit{ακmv} | repellere \textit{G\textsuperscript{u}P\textsuperscript{q}} | compellere \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{contendendo}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | continendo \textit{P\textsuperscript{z}}}}, uel \edtext{aliquid}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | aliquod \textit{P\textsuperscript{u}} | adeo \textit{P\textsuperscript{q}}}} \edtext{singulariter}{\Cfootnote[nosep]{\textit{ακ} | simile \textit{π} | simpliciter \textit{mv}}} tale, non \edtext{tamen}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | tantum \textit{λE\textsuperscript{a}P\textsuperscript{p}} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{potest}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{per se vnumquodque}{\Cfootnote[nosep]{\textit{ακmv} | vnum per se \textit{π}}},} \edtext{sicut quando plura}{\Cfootnote[nosep]{\textit{ακmv} | quantum quando duo simul \textit{π}}} coniunguntur \edtext{numerum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | vnum \textit{P\textsuperscript{z}}}} \edtext{constituentia}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | constituentia ut \textit{V\textsuperscript{m}}}}, \edtext{dummodo}{\Cfootnote[nosep]{\textit{ακmv} | dum tamen \textit{π}}} \edtext{ordinentur}{\Cfootnote[nosep]{\textit{βπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}} | ordinetur \textit{V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv}}} in vnum \edtext{ut}{\Cfootnote[nosep]{\textit{βγκmv} | velut \textit{π} | uel \textit{E\textsuperscript{a}}}} nauis \edtext{tractus}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} ostendit. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{SED SICUT.}{\Cfootnote[nosep]{\textit{αλπmv} | \surplus{SED} SED SICUT. \textit{P\textsuperscript{x}}}} } Declarat secundo dicens \edtext{quod}{\Cfootnote[nosep]{\textit{αλπmv} | quia \textit{P\textsuperscript{x}}}} \edtext{istud}{\Cfootnote[nosep]{\textit{ακ} | illud \textit{πmv}}} \edtext{apparet}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | apparens \textit{N\textsuperscript{u}}}} ex tali simili quoniam \textit{sicut linea duorum pedum non \edtext{solum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | solum est \textit{V\textsuperscript{m}}}} \edtext{duplum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | dupliciter \textit{G\textsuperscript{u}}}}, sicut est potest \edtext{figurare}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | significare \textit{P\textsuperscript{y}} | firmare \textit{π}}} \edtext{intellecta moueri, sed}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | intellecta mouere, sed \textit{P\textsuperscript{y}} | intellectum ymmo etiam \textit{π}}} quadruplum et octuplum}, secundum quod diuersimode \edtext{ \edtext{mensurando}{\Cfootnote[nosep]{\textit{βP\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}mv} | infundo \textit{M\textsuperscript{a}V\textsuperscript{m}} | commensurando \textit{V\textsuperscript{a}}}} \edtext{applicatur}{\Cfootnote[nosep]{\textit{αβP\textsuperscript{x}V\textsuperscript{m}mv} | applicantur \textit{M\textsuperscript{a}V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{ακmv} | applicatur mensurando \textit{π}}}, \textit{ \edtext{ita}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{o}mv}}} ut \edtext{super}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}} | per \textit{V\textsuperscript{z}} | semper \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{plurem numerum habeat}{\Cfootnote[nosep]{\textit{βP\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{z}} | plurem numeri habeat \textit{M\textsuperscript{a}V\textsuperscript{m}} | pluralem numerum habeat \textit{V\textsuperscript{b}mv} | plures vnam habeant \textit{π}}} potentiam, similiter \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | in \textit{V\textsuperscript{m}}}} \edtext{ad inuicem etiam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | ad inuicem et \textit{G\textsuperscript{u}P\textsuperscript{q}} | ad inuicem \textit{P\textsuperscript{y}V\textsuperscript{a}mv}}} in \edtext{quibuscunque}{\Cfootnote[nosep]{\textit{βγλmv} | quibusdam \textit{πE\textsuperscript{a}} | quibusdamcunque \textit{P\textsuperscript{x}}}} aliis.} Cum \edtext{autem}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}} | aut \textit{γE\textsuperscript{a}N\textsuperscript{u}mv}}} plura \edtext{fuerint}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | fuerunt \textit{G\textsuperscript{u}P\textsuperscript{p}mv}}} \edtext{numero amplius possunt}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | numero moueri amplius possunt \textit{G\textsuperscript{u}}}}, \edtext{uel}{\Cfootnote[nosep]{\textit{ακmv} | uel quam \textit{π}}} cum diuisa fuerint quocunque \edtext{alio}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | alio modo \textit{P\textsuperscript{z}} | \textit{om}. \textit{M\textsuperscript{b}}}} distinguente dummodo vnum \edtext{proportionaliter compossit}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{z}} | proportionaliter compos sit \textit{V\textsuperscript{m}} | proportionaliter composcit \textit{mv} | proportionaliter possit \textit{π}}} \edtext{alteri}{\Cfootnote[nosep]{\textit{ακmv} | alteri coadunari \textit{π}}}. +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{COADUNATIS.}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} } \edtext{Concludit tertio}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | 3º concludit \textit{M\textsuperscript{a}}}} \edtext{quod quando}{\Cfootnote[nosep]{\textit{ακmv} | quod \textit{π}}} \textit{ \edtext{aliqua}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | antequam aliqua \textit{P\textsuperscript{z}}}} plura numero \edtext{uel}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aut \textit{G\textsuperscript{u}}}} specie \edtext{aut}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | uel \textit{M\textsuperscript{a}}}} qualitercunque diuisa \edtext{coniungantur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | coniunguntur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} ad inuicem \edtext{uirtute}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | virtutem \textit{P\textsuperscript{q}} | uirtute cum \textit{G\textsuperscript{u}} | uirtute quod quantum \textit{mv}}}, \edtext{utpote}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{o}mv} | ut potentia \textit{V\textsuperscript{a}} | ut puto \textit{P\textsuperscript{x}}}} \edtext{in uoce una}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | in uoce \textit{M\textsuperscript{a}} | voce vna \textit{mv} | in uoce sua \textit{G\textsuperscript{u}}}} ex \edtext{omnibus}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | hominibus \textit{N\textsuperscript{u}}}} \edtext{contingit}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}mv} | contingitur \textit{N\textsuperscript{u}} | contingit simul \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{uocum}{\Cfootnote[nosep]{\textit{ακmv} | uocis \textit{π}}} \edtext{fortitudo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fortificando \textit{P\textsuperscript{p}P\textsuperscript{q}}}} \edtext{simul}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uel \textit{P\textsuperscript{y}} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{impellens}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | implens \textit{P\textsuperscript{z}}}} \edtext{aerem}{\Cfootnote[nosep]{\textit{ακmv} | aera \textit{π}}}. Et ideo \edtext{ualde amplius}{\Cfootnote[nosep]{\textit{απmv} | amplius ualde \textit{P\textsuperscript{x}V\textsuperscript{z}} | amplius \textit{M\textsuperscript{a}V\textsuperscript{m}}}} \edtext{potest}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv} | potest amplius \textit{V\textsuperscript{m}} | ponit \textit{V\textsuperscript{z}}}} preire \edtext{et}{\Cfootnote[nosep]{\textit{κ} | et in \textit{απmv}}} \edtext{longinquius}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv}}} audiri quam uox vnius} quod ostenditur. Nam ex uoce \edtext{uniuscuiusque}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv}}} uox \edtext{quedam}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quidem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}}}} una constituitur \edtext{multiplicium}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | multiplicem \textit{V\textsuperscript{z}}}} \edtext{habens}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | habet \textit{V\textsuperscript{a}}}} potentiam, \edtext{ceu}{\Cfootnote[nosep]{\textit{βγκmv} | seu \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{tractus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | tractum \textit{P\textsuperscript{z}} | tracti \textit{V\textsuperscript{b}}}} optime \edtext{una}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} et \edtext{diuisim}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | diuisius \textit{N\textsuperscript{u}}}} \edtext{denotat nauis}{\Cfootnote[nosep]{\textit{ακmv} | ostendit nauis \textit{π}}}. \edtext{Et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} hoc \edtext{quidem}{\Cfootnote[nosep]{\textit{βγκπmv} | quidem denotat uoce uniuscuiusque uox quedam una constituitur multiplicium habens potentiam seu tractus potime una et diuisim denotat nauis. Et hoc quidem \textit{E\textsuperscript{a}}}} problema \edtext{partim}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | partium \textit{P\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{pertinet}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | pertinet enim \textit{V\textsuperscript{o}} | partini enim \textit{P\textsuperscript{z}}}} ‘ \edtext{.xie. ut uisum particule}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}} | .xie. ut visum est particule \textit{λV\textsuperscript{a}mv} | .xie. particule, ut uisum est particule \textit{P\textsuperscript{u}} | ut uisum est particule \textit{P\textsuperscript{z}V\textsuperscript{o}} | .xie. ut visum est \textit{V\textsuperscript{b}} | .5e. particule, ut visum est \textit{G\textsuperscript{u}P\textsuperscript{p}}}} \edtext{}{\Afootnote[nosep]{Ps.-Arist. \textit{Prob.} XI}}’ \edtext{partimque isti}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{a}mv} | partimque pertinet isti \textit{V\textsuperscript{b}}}}. \edtext{}{\Cfootnote{etcetera. \textit{V\textsuperscript{b}V\textsuperscript{z}} | sequitur 3a. problema 19. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Tertium problema}\label{edition-text book-19a part3}}{\lemma{Tertium problema} \Cfootnote[nosep]{\textit{γG\textsuperscript{u}mv} | «3m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{tertium} Tertium \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID PARYPATEM}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}V\textsuperscript{o}} | PROPTER QUID MAGIS FRANGITUR \textit{P\textsuperscript{q}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID PER YPATEM CANTANTES MAXIME RUMPIMUS NICHILOMINUS QUAM NITEM ET SUPERIORA, CUM DISTANTIA PLURI? \textsuperscript{2}AUT QUIA DIFFICILLIME HANC CANTANT, ET IPSA EST PRINCIPIUM? \textsuperscript{3}ID AUTEM DIFFICILE PROPTER ELEUATIONEM ET DEPRESSIONEM UOCIS. IN HIIS AUTEM LABOR, LABORANS AUTEM MAGIS CORRUMPITUR \textit{G\textsuperscript{u}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Tertium problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} \edtext{cum cantamus}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}M\textsuperscript{b}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | cantamus \textit{E\textsuperscript{a}V\textsuperscript{m}} | quando cantamus \textit{P\textsuperscript{y}} | causa cantamus \textit{P\textsuperscript{x}} | cum caneamus \textit{m} | cum teneamus \textit{v} | cantantes \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} secundum \edtext{notam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uocem \textit{P\textsuperscript{y}P\textsuperscript{z}}}} quam \edtext{illa}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{o}mv} | ista \textit{C\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}}}} corda representat que uocatur \edtext{ypotes}{\Cfootnote[nosep]{\textit{κV\textsuperscript{a}}}} potissime \edtext{interrumpimus}{\Cfootnote[nosep]{\textit{αλπmv} | interrumpitur \textit{P\textsuperscript{x}}}} cantum, non \edtext{potentes}{\Cfootnote[nosep]{\textit{αλπmv} | potens \textit{P\textsuperscript{x}}}} \edtext{ipsum continuare}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | continuare ipsum \textit{P\textsuperscript{y}} | ipsum continere \textit{P\textsuperscript{p}}}} sicut \edtext{accepimus}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}M\textsuperscript{b}V\textsuperscript{m}mv} | accipimus \textit{P\textsuperscript{x}V\textsuperscript{z}} | incepimus \textit{π}}} \edtext{pre sui}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | pro sui \textit{V\textsuperscript{a}} | prefui \textit{mv}}} difficultate. Et in nullo \edtext{minus}{\Cfootnote[nosep]{\textit{ακπ} | videtur \textit{mv}}} \edtext{ymmo}{\Cfootnote[nosep]{\textit{βπP\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}}}} \edtext{ \edtext{in omnibus}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | in \textit{P\textsuperscript{u}} | etiam \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{magis frangimus}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | frangimus magnum \textit{V\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | magis in omnibus frangimus \textit{V\textsuperscript{z}}}} \edtext{cantum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | totis \textit{P\textsuperscript{z}}}} \edtext{propter}{\Cfootnote[nosep]{\textit{κ} | per \textit{απmv}}} ipsam quam \edtext{per}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | propter \textit{V\textsuperscript{z}}}} \edtext{nitem}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}mv} | nucem \textit{V\textsuperscript{a}} | uitem \textit{P\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{c}V\textsuperscript{o}}}} \edtext{siue netem}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}mv} | seu netem \textit{πV\textsuperscript{b}} | uel nectere \textit{V\textsuperscript{a}}}}. \edtext{Et}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} vniversaliter magis \edtext{frangitur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}} \edtext{cantus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} et difficilius \edtext{seruatur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | seruatur quam \textit{P\textsuperscript{z}}}} quando \edtext{vtitur}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{m}mv} | vtuntur \textit{π} | utimur \textit{V\textsuperscript{z}}}} \edtext{notis}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | votis \textit{V\textsuperscript{a}} | motis \textit{P\textsuperscript{z}}}} per cordas \edtext{superiores}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{a}mv} | superioribus \textit{V\textsuperscript{b}}}} \edtext{denotatis}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | denotatur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}}}}, et precipue quando distant inter se \edtext{maxime}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}.} Hoc autem \edtext{fit}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}m} | fit in \textit{P\textsuperscript{y}V\textsuperscript{z}} | fit instans \textit{γ} | sit \textit{E\textsuperscript{a}V\textsuperscript{m}v}}} instrumentis \edtext{cantando \edtext{aut}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{b}mv} | ac \textit{V\textsuperscript{a}}}} per notas illas que sunt in instrumentis}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{proportionatas.}{\Cfootnote[nosep]{\textit{γN\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | proportionatis. \textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}} | proportionate. \textit{mv}}} +\pend + +\pstart +\textbf{2} \edtext{Notandum}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{o}mv} | Notandum quod \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}} | Nota \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{ad}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} intellectum \edtext{eius quod}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{hic}{\Cfootnote[nosep]{\textit{αλmv} | hic dicitur \textit{π} | huius \textit{P\textsuperscript{x}}}} et \edtext{multorum}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} in hac particula \edtext{dicendorum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | contentorum et dicendorum \textit{P\textsuperscript{y}}}} quod antiquitus \edtext{a \hyperref[Pyth]{pictagora} inuentum fuit instrumentum dictum monocordum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{m}V\textsuperscript{o}} | inuentum fuit a \hyperref[Pyth]{pictagora} instrumentum dictum menocordum \textit{P\textsuperscript{z}} | a pictagoricis inuentum fuit instrumentum dictum monocordum \textit{V\textsuperscript{b}} | a pitagoricis instrumentum inuentum fuit dictum monocordum \textit{V\textsuperscript{a}} | a pithagoricis inuentum fuit instrumentum monocordum \textit{mv}}}, eo quod vnam \edtext{solam cordam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | cordam solam \textit{P\textsuperscript{u}V\textsuperscript{m}} | solam \textit{M\textsuperscript{a}}}} haberet \edtext{taliter formatum}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}M\textsuperscript{b}V\textsuperscript{m}mv} | talem formatum \textit{V\textsuperscript{a}V\textsuperscript{z}} | formatum taliter \textit{πE\textsuperscript{a}} | taliter et formatum \textit{P\textsuperscript{x}} | taliter proportionatum \textit{V\textsuperscript{b}}}} \edtext{in}{\Cfootnote[nosep]{\textit{ακπ} | etiam \textit{mv}}} quo proportiones musice \edtext{.5e. cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | 53 \textit{V\textsuperscript{a}} | 59. \textit{P\textsuperscript{z}}}} \edtext{tonis}{\Cfootnote[nosep]{\textit{βγλπmv} | rationes \textit{P\textsuperscript{x}} | \textit{om}. \textit{V\textsuperscript{a}}}} simplices prius cognosci \edtext{iubebat}{\Cfootnote[nosep]{\textit{αλ} | iubeat \textit{P\textsuperscript{x}} | iubebant \textit{mv} | uidebantur \textit{π}}} secundum diuersitatem \edtext{loci}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | loci et \textit{β}}} \edtext{instrumenti tacti}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | in fritanti \textit{P\textsuperscript{y}}}} \edtext{representante.}{\Cfootnote[nosep]{\textit{βP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | representantem. \textit{M\textsuperscript{a}P\textsuperscript{x}mv} | representatis. \textit{V\textsuperscript{a}} | r\expan{e}p\expan{rese}ntat\expan{is} \textit{(orig. \textup{r'pn'tat'})} \textit{P\textsuperscript{z}} | representare. \textit{G\textsuperscript{u}V\textsuperscript{b}}}} \edtext{Deinceps}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Deinde \textit{G\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{q}}}} \edtext{inuenta sunt instrumenta}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | instrumenta inuenta sunt \textit{V\textsuperscript{a}} | sunt instrumenta \textit{N\textsuperscript{u}} | inuenta fuerunt instrumenta \textit{κ}}} cum pluribus cordis: \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | ut cum \textit{P\textsuperscript{p}} | et \textit{P\textsuperscript{z}}}} duabus \edtext{ceu rubeba}{\Cfootnote[nosep]{\textit{βλV\textsuperscript{a}} | seu rubeba \textit{P\textsuperscript{z}} | seu reubeba \textit{E\textsuperscript{a}} | seu rubeda \textit{V\textsuperscript{o}} | sicut rubeba \textit{P\textsuperscript{q}P\textsuperscript{u}} | sicut rubeda \textit{G\textsuperscript{u}} | sicut rubula \textit{P\textsuperscript{p}}}} que similiter organum \edtext{introductum}{\Cfootnote[nosep]{\textit{γκmv} | introductorium \textit{βP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | introductorum \textit{G\textsuperscript{u}P\textsuperscript{p}}}} existit. \edtext{Denique}{\Cfootnote[nosep]{\textit{κ} | Deinde \textit{G\textsuperscript{u}P\textsuperscript{p}} | Deindeque \textit{V\textsuperscript{b}mv} | Demumque \textit{βP\textsuperscript{q}P\textsuperscript{u}V\textsuperscript{a}} | Demum quia \textit{E\textsuperscript{a}} | Deinde quia \textit{P\textsuperscript{z}V\textsuperscript{o}}}} paulatim sunt cetere \edtext{adinuente}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | inuente \textit{G\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{x}V\textsuperscript{b}} | aduenientes \textit{P\textsuperscript{z}}}}. Unde ‘1° \textit{musice} \edtext{ait}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} boecius \edtext{\hyperref[Ni]{nichomacum}}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{z}mv} | nichoantum \textit{P\textsuperscript{x}} | intomarum \textit{P\textsuperscript{z}} | inchoantum \textit{E\textsuperscript{a}P\textsuperscript{y}} | inchoatam \textit{M\textsuperscript{a}}}} dicere musicam \edtext{in principio fuisse}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | fuisse in principio \textit{P\textsuperscript{y}} | in principio fore \textit{V\textsuperscript{a}}}} \edtext{simplicem}{\Cfootnote[nosep]{\textit{αλπmv} | simpliciter \textit{P\textsuperscript{x}}}} \edtext{in}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} tantum quod tota constabat \edtext{ex}{\Cfootnote[nosep]{\textit{ακπ} | in \textit{mv}}} quatuor cordis. Quod \edtext{durauit}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | durabat \textit{V\textsuperscript{a}}}} vsque ad \hyperref[Or]{ \edtext{orphei}{\Cfootnote[nosep]{\textit{βπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{z}}}} } \edtext{tempus}{\Cfootnote[nosep]{\textit{βγκπmv} | tempore \textit{E\textsuperscript{a}}}} \edtext{puta, quod}{\Cfootnote[nosep]{\textit{βγκE\textsuperscript{a}mv} | puta ex \textit{E\textsuperscript{a}} | ex \textit{π}}} \edtext{prima}{\Cfootnote[nosep]{\textit{ακmv} | prima quidem \textit{π}}} et quarta corda \edtext{constitueret}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}M\textsuperscript{b}N\textsuperscript{u}V\textsuperscript{m}mv} | constituerent \textit{P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}} | constabat \textit{π}}} \edtext{consonantiam duplam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}} | consonantiam dupla \textit{mv} | consonantiam \textit{P\textsuperscript{y}} | consonantia dupla \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{o}}}} dyapason \edtext{dictam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}mv} | dicta \textit{P\textsuperscript{z}V\textsuperscript{o}}}}. Medie \edtext{quidem}{\Cfootnote[nosep]{\textit{ακmv} | vero \textit{π}}} \edtext{harum ad se inuicem}{\Cfootnote[nosep]{\textit{βγκmv} | harum ad inuicem \textit{πE\textsuperscript{a}}}} tonum constituebant, \edtext{ \edtext{et}{\Cfootnote[nosep]{\textit{βγπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} ad \edtext{extremas}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | extremas partes \textit{V\textsuperscript{b}mv}}} comparate}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} dyapente \edtext{et}{\Cfootnote[nosep]{\textit{βγκπmv} | id est \textit{E\textsuperscript{a}}}} dyatesseron, ut apparebit .13., \edtext{ita ut in}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | ita in \textit{N\textsuperscript{u}mv} | ita ut \textit{P\textsuperscript{p}P\textsuperscript{z}}}} hiis quatuor cordis \edtext{nichil}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}}}} dissonum \edtext{existeret}{\Cfootnote[nosep]{\textit{βλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | existere \textit{V\textsuperscript{b}} | existerit \textit{P\textsuperscript{x}} | existiterit \textit{P\textsuperscript{u}}}} ad \edtext{imitationem}{\Cfootnote[nosep]{\textit{λP\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | mutationem \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{x}} | immutationem \textit{E\textsuperscript{a}V\textsuperscript{b}}}} \edtext{mundane musice}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | musice mundane \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} antedicte que ex quatuor \edtext{constat ut tactum elementis}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}} | ut tactum constat elementis \textit{P\textsuperscript{y}} | constat elementis ut tactum est \textit{π} | constat ut tactum est elementis \textit{V\textsuperscript{a}V\textsuperscript{m}mv} | constat ut dictum est elementis \textit{V\textsuperscript{z}}}}. Quarum quatuor \edtext{cordarum}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | cordarum ut \textit{P\textsuperscript{y}} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{dicitur \hyperref[Mer]{mercurium} inuentorem}{\Cfootnote[nosep]{\textit{ακmv} | dicitur mercurius inuentor \textit{π}}} fuisse. \edtext{Unde}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Ut \textit{P\textsuperscript{z}}}} adhuc \edtext{aliqua instrumentorum}{\Cfootnote[nosep]{\textit{βγV\textsuperscript{z}mv} | aliquo instrumentorum \textit{P\textsuperscript{x}} | aliquod instrumentorum \textit{π} | alia instrumentorum \textit{M\textsuperscript{a}V\textsuperscript{m}} | aliud instrumentorum \textit{E\textsuperscript{a}}}} \edtext{videmus}{\Cfootnote[nosep]{\textit{ακmv} | vidimus \textit{π}}} \edtext{tantum}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} quatuor cordas \edtext{habere}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | habentia \textit{V\textsuperscript{z}} | \textit{om}. \textit{V\textsuperscript{a}}}} ut \edtext{citaram}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}} et \edtext{zigam}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | zita \textit{V\textsuperscript{a}} | zigam uel mygam \textit{V\textsuperscript{b}}}}. \edtext{quintam}{\Cfootnote[nosep]{\textit{αλπmv} | quantum causa \textit{P\textsuperscript{x}}}} vero cordam \edtext{chorebus}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}mv} | thozebus \textit{V\textsuperscript{o}} | ciozebus \textit{P\textsuperscript{p}P\textsuperscript{u}} | zozebeth \textit{G\textsuperscript{u}} | tozobus \textit{P\textsuperscript{z}}}} \edtext{achis filius}{\Cfootnote[nosep]{\textit{βγκmv} | ac is filius \textit{E\textsuperscript{a}} | ac hiffilius \textit{π}}} \edtext{lidorum}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | lindorum \textit{V\textsuperscript{a}}}} \edtext{rex}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | regis \textit{V\textsuperscript{a}}}} \edtext{adiunxit}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{a}mv}}}, \edtext{hiagris}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{z}} | yagris \textit{γ} | \textit{"According to Clement, Strom. 1. 76. 5, Agnis (Hyagnis) the Phrygian—a legendary prehistoric figure—invented 'the trichord and the diatonic scale'; but it is not entirely clear whether 'trichord' here is adjectival, referring to a type of scale, or a noun, the instrument that bore [the name 'trichord']" (M. L. West, Ancient Greek Music [Oxford: Clarendon Press, 1992], 173, n. 43).}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}mv} | quidam \textit{P\textsuperscript{p}P\textsuperscript{q}} | quid \textit{P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{phirs}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | furix \textit{G\textsuperscript{u}P\textsuperscript{q}} | firix \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{a}} | sirix \textit{V\textsuperscript{o}P\textsuperscript{u}} | phinix \textit{mv}}} \edtext{sextam}{\Cfootnote[nosep]{\textit{αλπmv} | 6ta \textit{P\textsuperscript{x}}}} \edtext{apposuit}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | apponit \textit{M\textsuperscript{a}V\textsuperscript{m}} | a \textit{P\textsuperscript{y}}}}. \edtext{Septimam}{\Cfootnote[nosep]{\textit{γλN\textsuperscript{u}P\textsuperscript{q}mv} | Aliam \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}}}} uero \edtext{\hyperref[Ter]{terpanterius lesbius}}{\Cfootnote{crepander nilesbius \textit{P\textsuperscript{y}} | epauctus lesbius \textit{G\textsuperscript{u}}}} \edtext{inuenit}{\Cfootnote[nosep]{\textit{αλπmv} | \surplus{inuenit} inuenit \textit{P\textsuperscript{x}}}} \edtext{planetarum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | ad planetarum \textit{V\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{septem}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{similitudinem}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}} | similitudine \textit{γG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}}. Inter quas grauissima erat, \edtext{ypate dicta}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | ypate dictas \textit{P\textsuperscript{p}} | ypatem dictam \textit{M\textsuperscript{a}}}} \edtext{quasi}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} maior \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{honorabilior}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | honorabilis \textit{P\textsuperscript{u}} | honor \textit{M\textsuperscript{a}P\textsuperscript{x}}}} vnde et \hyperref[Ju]{iouem} \edtext{ypaton uocant}{\Cfootnote[nosep]{\textit{βP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | ypate uocant \textit{P\textsuperscript{x}} | ypatem vocat \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{id est}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | scilicet \textit{G\textsuperscript{u}} | et \textit{V\textsuperscript{a}} | autem in \textit{P\textsuperscript{x}}}} \edtext{supremum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}mv}}} et \edtext{consulem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | consilem \textit{P\textsuperscript{z}}}} eodem \edtext{nomine nuncupantes}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | nomine \textit{G\textsuperscript{u}}}} propter \edtext{dignitatis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | dignitatem \textit{P\textsuperscript{z}}}} excellentiam. Septem uero \edtext{fuisse cordas}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | cordas fuisse \textit{V\textsuperscript{a}}}} antiquitus \edtext{testatur}{\Cfootnote[nosep]{\textit{κ} | testabitur \textit{N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | testabatur \textit{γG\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | detestabatur \textit{E\textsuperscript{a}}}} .25. \edtext{et 32.}{\Cfootnote[nosep]{\textit{βλ} | et 33 \textit{γG\textsuperscript{u}mv} | et 34° \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | 232 \textit{P\textsuperscript{x}} | et 25. et 24. \textit{P\textsuperscript{z}} | 252. 32. \textit{E\textsuperscript{a}}}} \edtext{Et}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{attributa}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}} fuit \edtext{is}{\Cfootnote[nosep]{\textit{κV\textsuperscript{a}} | hiis \textit{V\textsuperscript{b}} | hec \textit{βπE\textsuperscript{a}} | ea \textit{mv}}} saturno propter \edtext{tarditatem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} motus et grauitatem soni. \edtext{Parypate}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | Parypaten \textit{M\textsuperscript{a}}}} uero \edtext{2a}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | 2o \textit{M\textsuperscript{a}} | \textit{om}. \textit{V\textsuperscript{a}}}} quasi iuxta \edtext{ypatem}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv}}} collocata. \edtext{Lychanos 3a. \edtext{ideo quia}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ideoque \textit{G\textsuperscript{u}} | quia \textit{P\textsuperscript{x}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} lychanos \edtext{digitus dicitur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | dicitur digitus \textit{β}}} \edtext{quem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | quod \textit{P\textsuperscript{z}V\textsuperscript{z}}}} latini indicem \edtext{uocant}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | notant \textit{V\textsuperscript{z}}}}; greci uero \edtext{a lingendo lychanos}{\Cfootnote[nosep]{\textit{αV\textsuperscript{a}mv} | a ligendo liginos \textit{M\textsuperscript{a}} | a lingendo diginos \textit{V\textsuperscript{m}} | alligendo lychanos \textit{P\textsuperscript{x}} | a ligando lychanos \textit{π}}}. Et \edtext{quia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} in \edtext{cantando}{\Cfootnote[nosep]{\textit{κ} | cantando ad \textit{απmv}}}, \edtext{hanc}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | hac \textit{V\textsuperscript{b}}}} cordam \edtext{tertiam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}}}} ab \edtext{ypate}{\Cfootnote[nosep]{\textit{βγG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | ypatem \textit{M\textsuperscript{a}P\textsuperscript{z}}}}, \edtext{digitus}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | digiti \textit{V\textsuperscript{b}}}} \edtext{hic}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} pertingit, quare ab \edtext{ipso}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | illo \textit{λ}}} lychanos appellatur. Quarta uero \edtext{dicitur mese}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}mv} | meser dicitur \textit{G\textsuperscript{u}}}} \edtext{quasi}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | que \textit{P\textsuperscript{y}} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{media quia}{\Cfootnote[nosep]{\textit{γN\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | quia media \textit{πE\textsuperscript{a}} | media \textit{M\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{y}}}} inter primam et \edtext{septimam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | aliam \textit{P\textsuperscript{y}}}} \edtext{uere}{\Cfootnote[nosep]{\textit{γλG\textsuperscript{u}E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vera \textit{P\textsuperscript{x}} | vero \textit{P\textsuperscript{p}V\textsuperscript{c}}}} \edtext{media est quarta}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quarta est media \textit{P\textsuperscript{p}}}}. \edtext{Quinta}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | 5a vero \textit{C\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{q}} | 5a est \textit{P\textsuperscript{p}}}} paramese \edtext{quasi}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | id est \textit{G\textsuperscript{u}P\textsuperscript{q}}}} iuxta mediam \edtext{collocata}{\Cfootnote[nosep]{\textit{αλπmv} | collocatam \textit{P\textsuperscript{x}}}}. \edtext{Septima quidem dicitur}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Septima dicitur \textit{V\textsuperscript{a}} | Septima dicitur quidem \textit{G\textsuperscript{u}} | 6a uero dicitur \textit{V\textsuperscript{b}}}} \edtext{nete}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | siete \textit{P\textsuperscript{p}}}} \edtext{quasi neate id est inferior. \edtext{Inter quam et paramese}{\Cfootnote[nosep]{\textit{βP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}} | Inter quam parame \textit{M\textsuperscript{a}} | et parame \textit{V\textsuperscript{a}} | quasi et parame \textit{V\textsuperscript{b}} | quasi paramese \textit{mv}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} est sexta dicta \edtext{paranete}{\Cfootnote[nosep]{\textit{βγκπmv}}} quasi iuxta \edtext{netem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{sita}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | sitam \textit{E\textsuperscript{a}} | posite \textit{V\textsuperscript{z}} | \textit{om}. \textit{G\textsuperscript{u}}}}. \edtext{Paranese}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | Paramese \textit{N\textsuperscript{u}V\textsuperscript{a}} | Parapiese \textit{P\textsuperscript{y}}}} autem quia \edtext{3a}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} est a nete \edtext{eodem}{\Cfootnote[nosep]{\textit{αλπmv} | eadem \textit{P\textsuperscript{x}}}} uocabulo \edtext{trite}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | tricte \textit{P\textsuperscript{z}} | trite \surplus{id est trite} \textit{V\textsuperscript{a}}}} \edtext{id est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | quasi \textit{V\textsuperscript{o}}}} \edtext{tertia}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | entia \textit{P\textsuperscript{y}}}} dicitur.\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} I .20 (Friedlein pp. 205–6, ll. 28–9)}}’ Fiat \edtext{igitur}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | ergo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}mv}}} \edtext{talis cordarum}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | cordarum talis \textit{P\textsuperscript{u}P\textsuperscript{y}} | talis \textit{λ}}} \edtext{parygrafia}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}V\textsuperscript{b}}}} secundum \hyperref[Ty]{ \edtext{thimotheum}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{x}V\textsuperscript{z}}}} } ‘\label{quote-3.1-Ar}precipuum \edtext{in}{\Cfootnote[nosep]{\textit{βγκπmv} | et \textit{E\textsuperscript{a}}}} \edtext{hac}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | hic \textit{P\textsuperscript{z}} | ac \textit{V\textsuperscript{a}}}} \edtext{arte}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} virum: ut \edtext{apparet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | patet \textit{G\textsuperscript{u}P\textsuperscript{q}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{2°}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}mv} | in 2° \textit{C\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{c}V\textsuperscript{o}} | 4° \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \textit{methaphysice} \edtext{}{\Afootnote[nosep]{Arist. \textit{Met.} II .1 , 993b , ll. 15–17}}’, incipiendo a superiori cordarum uocem grauissimam \edtext{ \edtext{reddenti}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | reddente \textit{V\textsuperscript{z}}}} \edtext{ad inferius}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} descendendo \edtext{ut}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | usque \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | et \textit{V\textsuperscript{m}}}} ad ultimam acutissimam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} representantem: {\small \par \par +\begin{longtable}{P{0.41157894736842104\textwidth}P{0.438421052631579\textwidth}} +Hypate\tabcellsep prima.\\ +Parypate\tabcellsep secunda.\\ +Lychanos\tabcellsep tertia.\\ +Mese\tabcellsep quarta.\\ +Paramese\tabcellsep quinta.\\ +Paranete\tabcellsep sexta.\\ +Nete\tabcellsep septima.\end{longtable} \par} + +\pend + +\pstart +\textbf{3} \edtext{Et}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | Est \textit{V\textsuperscript{a}} | \textit{om}. \textit{π}}} \edtext{iste}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | istis \textit{V\textsuperscript{a}}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | siquidem \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{septem \edtext{videntur}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | numeri \textit{V\textsuperscript{m}}}} \edtext{esse ceteris essentialiores}{\Cfootnote[nosep]{\textit{κN\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | ceteris esse essentialiores \textit{V\textsuperscript{a}} | ceteris essentialiores esse \textit{E\textsuperscript{a}} | ceteris essentialiores \textit{P\textsuperscript{y}P\textsuperscript{z}}}} et necessariores}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | essentialiores et necessariores septem videntur esse \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, ita ut \hyperref[Ar]{aristoteles} \edtext{ \edtext{supra}{\Cfootnote[nosep]{\textit{βγκmv} | ergo \textit{E\textsuperscript{a}}}} \edtext{ipsas}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} non \edtext{tangat}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | tangit \textit{γM\textsuperscript{b}P\textsuperscript{y}mv}}} ut apparebit ullam}{\Cfootnote[nosep]{\textit{ακmv} | ipsas solas tangat non nulli tamen \textit{π}}}, \edtext{fueruntque}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | fueritque \textit{P\textsuperscript{x}P\textsuperscript{y}} | fuerunt \textit{E\textsuperscript{a}M\textsuperscript{a}} | fuerunt quia \textit{V\textsuperscript{a}} | fuerunt qui \textit{π}}} consequenter \edtext{8 .9. et .10.}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}m} | .8. .9. .10. \textit{βv} | octo nouem et decem dixerunt \textit{π}}} iuxta \edtext{illud}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | istud \textit{P\textsuperscript{y}}}} ‘ \edtext{psalmiste}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | psal\expan{mist}e. \textit{(orig. \textup{psa\textsuperscript{le}.})} \textit{P\textsuperscript{x}V\textsuperscript{m}} | psalmi \textit{P\textsuperscript{z}}}} in \edtext{psalterio}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | altero \textit{P\textsuperscript{z}}}} \edtext{decacordo}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | decacordo psallam tibi \textit{P\textsuperscript{y}}}}.\edtext{}{\Afootnote[nosep]{ \textit{Psalm} 143 :9 (Psalm 144:9 in English translations)}}’ Et \edtext{deinceps}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | inde \textit{V\textsuperscript{a}} | deinde \textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}} | demum \textit{P\textsuperscript{u}}}} \edtext{in tantum}{\Cfootnote[nosep]{\textit{ακmv} | iterum \textit{π}}} \edtext{creuit numerus}{\Cfootnote[nosep]{\textit{κ} | excreuit numerus \textit{βP\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{o}mv} | numerus excreuit \textit{G\textsuperscript{u}P\textsuperscript{q}} | exercuit numerus \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}} | ex trite ut numerus \textit{P\textsuperscript{u}}}} ut \edtext{\hyperref[Bo]{boecius} 18 cum}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}} | \hyperref[Bo]{boecius} cum \textit{πE\textsuperscript{a}V\textsuperscript{b}mv} | \hyperref[Bo]{boecius} 7 \textit{V\textsuperscript{a}}}} reiteratione \edtext{ipsarum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | ipsorum \textit{G\textsuperscript{u}P\textsuperscript{y}} | ipsas \textit{V\textsuperscript{a}}}} \edtext{enumeret}{\Cfootnote[nosep]{\textit{αλπmv} | nuetur \textit{P\textsuperscript{x}}}} sub \edtext{dyatonico melo}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | dyacomcouiclo \textit{P\textsuperscript{z}} | ydyacomicomelo \textit{P\textsuperscript{p}}}} et \edtext{totidem}{\Cfootnote[nosep]{\textit{αλπmv}}} sub \edtext{cromatico}{\Cfootnote[nosep]{\textit{λN\textsuperscript{u}V\textsuperscript{a}}}} \edtext{ac \edtext{18}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | .xxviii. \textit{mv} | etiam \textit{P\textsuperscript{y}}}} sub enarmonico}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}M\textsuperscript{b}}}} \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quasi \textit{P\textsuperscript{z}}}} \edtext{uariatione}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | \surplus{ua} uariatione \textit{N\textsuperscript{u}}}} \edtext{quadam}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | quedam \textit{E\textsuperscript{a}V\textsuperscript{o}}}} \edtext{communi}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | communis \textit{M\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{sine zeugnum}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{et diateuzeugnum}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}} | et \surplus{dyateuzegnu} dyateuzeugnum \textit{P\textsuperscript{y}} | et dyageogimini \textit{mv} | \textit{om}. \textit{E\textsuperscript{a}}}}. Non enim \edtext{plura tribus sunt}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | plura sunt tribus \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | sunt plura tribus \textit{G\textsuperscript{u}}}} genera \edtext{melorum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv}}} quibus \edtext{omnis}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | omnes \textit{V\textsuperscript{a}} | omnibus \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{contexitur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{cantilena.}{\Cfootnote[nosep]{\textit{αλπmv}}} \edtext{Cuius hec est descriptio}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}mv} | Cuius est huius descriptio \textit{E\textsuperscript{a}G\textsuperscript{u}V\textsuperscript{m}} | Quibus hec est descriptio \textit{βP\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}} | Cuiusmodi est huiusmodi descriptio \textit{V\textsuperscript{b}}}} \edtext{\begin{itemize} +\item \edtext{dyatonici}{\Cfootnote[nosep]{\textit{κV\textsuperscript{b}mv} | dyacommunia \textit{E\textsuperscript{a}}}} +\item \edtext{proslabanomenos}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} +\item \edtext{ypate ypaton}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv}}} +\item \edtext{parypate ypaton}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | parypatem ypaton \textit{M\textsuperscript{a}} | \textit{om}. \textit{γmv}}} +\item \edtext{lychanos ypato dyatonici}{\Cfootnote[nosep]{\textit{βγκmv}}} +\item \edtext{ypate meson}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | meson \textit{mv}}} +\item \edtext{parypate meson}{\Cfootnote[nosep]{\textit{βγP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} +\item \edtext{lychanos meson dyatonici}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{b}mv} | diacenos meson diatonici \textit{V\textsuperscript{a}}}} +\item \edtext{mese}{\Cfootnote[nosep]{\textit{βγκmv} | me――――sem \textit{E\textsuperscript{a}}}} +\item \edtext{trite sinezeugnum dyatonici}{\Cfootnote[nosep]{\textit{V\textsuperscript{z}} | trite sinezeugium \textit{βE\textsuperscript{a}} | trite sinezeugmen \textit{V\textsuperscript{b}} | trite sinegeumen \textit{mv} | trite sinezeuium paramese trite diazeuium paramete \textit{V\textsuperscript{a}}}} +\item \edtext{paranete sinezeugium}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}} | paranete sinezeumen diatonici \textit{V\textsuperscript{b}} | permete sinegeumen dyatonici \textit{mv} | paranete sinezeugnum dyatonici \textit{V\textsuperscript{z}} | paranete sine ceugnum dyatonici \textit{M\textsuperscript{a}V\textsuperscript{m}} | paramete inmeazegium dyatonici \textit{E\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{y}V\textsuperscript{a}}}} +\item \edtext{nete sunezeugium}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{x}V\textsuperscript{a}}}} +\item \edtext{paramese}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} +\item \edtext{trite diezeugium}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}} | trite diazeuium paramete \textit{V\textsuperscript{a}} | Ededie zeugium \textit{P\textsuperscript{x}} | \textit{om}. \textit{V\textsuperscript{b}}}} +\item \edtext{paranete dyezeugium dyatonici}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}}}} +\item \edtext{nete dyezeugnum}{\Cfootnote[nosep]{\textit{V\textsuperscript{z}}}} +\item \edtext{trite yperboleon dyatonici}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}V\textsuperscript{z}} | trite ypereboleon \textit{V\textsuperscript{b}} | trite yperboleon \textit{βV\textsuperscript{a}mv}}} +\item \edtext{paranete yperboleon dyatonici}{\Cfootnote[nosep]{\textit{α}}} +\item nete yperboleon.\end{itemize} }{\Cfootnote[nosep]{\textit{ακmv} | \textit{"Of the 'moveable' notes whose positions varied in different genera, Lychanos was treated as especially diagnostic of genus, and as a note-name it is sometimes augmented or replaced by enharmonios, chrōmatikē, or diatonos, depending on its actual station. The same happens more rarely with Paranētē" (M. L. West, Ancient Greek Music [Oxford: Clarendon Press, 1992], 222).}}} Similis autem per omnia \edtext{figuratio extat}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | extat figuratio \textit{E\textsuperscript{a}} | est figuratio \textit{π} | figuratio \textit{P\textsuperscript{y}}}} in \edtext{cromatico}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | orematico \textit{γmv}}} \edtext{melo ac consimilis}{\Cfootnote[nosep]{\textit{αV\textsuperscript{z}mv} | melon ac consimilis \textit{V\textsuperscript{a}} | melo et consimilis \textit{π} | melcoris similis \textit{P\textsuperscript{x}} | melo et cuius similis \textit{M\textsuperscript{a}} | melo ac minus similis \textit{V\textsuperscript{m}}}} in \edtext{enarmonico}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | armonico \textit{P\textsuperscript{z}V\textsuperscript{a}}}}, excepto \edtext{quod ut}{\Cfootnote[nosep]{\textit{πN\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}} | quod \textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{m}mv}}} in \edtext{prima}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | primam \textit{P\textsuperscript{p}}}} \edtext{subscribitur}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | describitur \textit{M\textsuperscript{a}M\textsuperscript{b}} | scribitur \textit{βπ}}} \edtext{dyatonici}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | dyatonicum \textit{G\textsuperscript{u}P\textsuperscript{q}} | dyatonicis \textit{C\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{c}} | dyaconitus \textit{P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{ita}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | ita ut \textit{γmv} | \textit{om}. \textit{V\textsuperscript{z}}}} in secunda \edtext{cromaticon}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | tromaticus \textit{P\textsuperscript{z}} | cromatico \textit{M\textsuperscript{b}P\textsuperscript{x}} | cormanticon \textit{V\textsuperscript{b}} | cormanticum \textit{V\textsuperscript{a}mv}}} et in tertia \edtext{enarmonicum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | ermonicum \textit{V\textsuperscript{a}}}}, ita ut omnes coniuncte \edtext{liiii.}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quinque \textit{P\textsuperscript{z}}}} \edtext{sunt}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}} | sint \textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} corde. Moderni autem in aliquibus ultra lxiiii. \edtext{apposuere}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | apponunt \textit{P\textsuperscript{y}} | apposuerunt \textit{π}}} ut medius \edtext{canon}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | canono \textit{V\textsuperscript{z}} | canon dictus \textit{απmv}}} ostendit. \begin{itemize} +\item dyatonici +\item proslabanomenos +\item ypate ypaton +\item parypate ypaton +\item lychanos ypato dyatonici +\item ypate meson +\item lychanos meson +\item Mese +\item Trite sinezengium +\item Paranete sinezengium dyatonici +\item Nete sinezengium +\item Paramese +\item Trite dyazengium +\item paranete dyezengium dyatonici +\item zeze dyezengium +\item trite yperboleon dyatonici +\item Nete yperboleon\end{itemize} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} +\pend + +\pstart +\textbf{4} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | AUT QUIA. \textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv}}} } Soluit \edtext{dicens}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}m} | dicit \textit{P\textsuperscript{z}}}} causam esse \textit{quia \edtext{cum}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{πV\textsuperscript{z}}}} difficultate \edtext{ampliori}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}E\textsuperscript{a}V\textsuperscript{o}} | amplior \textit{mv} | \textit{om}. \textit{γP\textsuperscript{z}}}} cantus \edtext{fit}{\Cfootnote[nosep]{\textit{βγκπmv} | sit \textit{E\textsuperscript{a}}}} secundum \edtext{ypatem}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | ypate \textit{P\textsuperscript{x}}}}. Ipsa \edtext{enim est}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}} | est enim \textit{N\textsuperscript{u}} | est \textit{γmv} | enim \textit{P\textsuperscript{x}}}} principium} \edtext{incipiendo}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{κ} | incipiendo a \textit{G\textsuperscript{u}P\textsuperscript{q}}}} superius, ut \edtext{prescriptum}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}} | prescriptum est \textit{γλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | descriptum est \textit{G\textsuperscript{u}P\textsuperscript{q}}}} ad quam. Si \edtext{perueniri debet}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}mv} | debet perueniri \textit{V\textsuperscript{z}} | perueneriet debet \textit{V\textsuperscript{b}}}} uocem \edtext{oportet}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} eleuare et \edtext{ab}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | ad \textit{V\textsuperscript{o}}}} \edtext{ipsa}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | ipsam \textit{V\textsuperscript{m}V\textsuperscript{o}}}} uersus \edtext{netem}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | noctem \textit{V\textsuperscript{a}}}} \edtext{deuenire}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | peruenire \textit{G\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{x}} | uenire \textit{P\textsuperscript{y}V\textsuperscript{z}}}}, cum cantus perficiatur \edtext{sonorus}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | sonorum \textit{G\textsuperscript{u}P\textsuperscript{x}mv}}} ex contrariis eleuando et \edtext{deprimendo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | descendendo \textit{P\textsuperscript{p}}}} uocibus. +\pend + +\pstart +\textbf{5} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ID AUTEM.} \edtext{Contingit}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}V\textsuperscript{b}} | Concludit \textit{V\textsuperscript{a}mv} | Dicitur \textit{πP\textsuperscript{x}}}} propter hoc \edtext{quod}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}mv} | quia \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} contraria \edtext{sunt subitam}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | subitam sunt \textit{P\textsuperscript{y}} | sunt subiecta \textit{M\textsuperscript{a}} | sunt subicita \textit{V\textsuperscript{m}V\textsuperscript{z}} | sunt subtila \textit{P\textsuperscript{p}}}} \edtext{inducentia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | inducentiam \textit{P\textsuperscript{z}}}} alterationem. \textit{In hoc \edtext{uero}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{intercidit}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | interdicit \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} labor et difficultas, \edtext{ubi autem huius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}} | ubi huius \textit{mv} | ubi autem hoc \textit{M\textsuperscript{a}V\textsuperscript{z}} | ubi autem huiusmodi \textit{γG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}}}} magis accidit corrumpi} sicut etiam \edtext{in}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} aliis apparet potentiis. \textit{Et \edtext{ideo}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{agonizantes}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv}}} cantant leges et non \edtext{choros}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | choros ut \textit{M\textsuperscript{a}}}} } 15°. Per alias \edtext{uero}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} cordas et proprie \edtext{medias}{\Cfootnote[nosep]{\textit{αλπmv} | motas \textit{P\textsuperscript{x}}}} per oppositum \edtext{cum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | \textit{om}. \textit{N\textsuperscript{u}}}} difficultate cantatur \edtext{minime.}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} +\pend + +\pstart +\textbf{6} \edtext{Circa predicta dubitatur}{\Cfootnote[nosep]{\textit{ακ} | Dubitatur circa dicta \textit{π} | Dubitatur \textit{mv}}} quoniam videmus \edtext{plura}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{y}mv} | plurima \textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} instrumenta habentia multo plures cordas \edtext{quam}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv} | que \textit{γE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}}}} \edtext{pretacte}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | pretacte sunt \textit{P\textsuperscript{p}}}}. \edtext{Rota}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | Corda \textit{V\textsuperscript{a}}}} enim habet xliiii. \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} .22.as \edtext{in vno}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} latere et in \edtext{reliquo}{\Cfootnote[nosep]{\textit{αλπmv} | aliquo \textit{P\textsuperscript{x}}}} \edtext{totidem}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{medius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | melius \textit{P\textsuperscript{z}}}} uero \edtext{canon.}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}mv} | canorum \textit{V\textsuperscript{o}}}} lxiiii. et de \edtext{aliis}{\Cfootnote[nosep]{\textit{ακmv} | reliquis \textit{π}}} \edtext{similiter}{\Cfootnote[nosep]{\textit{κ}}}. Dicendum quod \edtext{ille}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | illi \textit{G\textsuperscript{u}P\textsuperscript{q}}}} plures reducuntur \edtext{ad}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quid \textit{G\textsuperscript{u}}}} minores \edtext{prius}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | prius ut \textit{M\textsuperscript{a}}}} \edtext{institutas}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | institutos \textit{V\textsuperscript{a}mv}}}. \edtext{Quatuor}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | 4 enim \textit{π} | Qua eticorum \textit{P\textsuperscript{y}}}} superadditarum \edtext{sumuntur}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{m}mv} | sumentur \textit{P\textsuperscript{y}}}} pro vna \edtext{priorum}{\Cfootnote[nosep]{\textit{βγG\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | priorum et \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}}, ita ut \edtext{xxviii.}{\Cfootnote[nosep]{\textit{ακmv} | 24 \textit{π}}} \edtext{cadant}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} in .vii. notiores, \edtext{et}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | \textit{om}. \textit{γmv}}} \edtext{.xliiii.}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | 24. \textit{P\textsuperscript{z}} | 28. \textit{V\textsuperscript{m}} | .10. et .44. \textit{V\textsuperscript{z}}}} \edtext{redeant}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | redeunt \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} in \edtext{.xi.}{\Cfootnote[nosep]{\textit{ακmv} | 12 \textit{π}}} et \edtext{.lxiiii.}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | 68. \textit{V\textsuperscript{m}}}} in \edtext{.xvi.}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | .18. \textit{V\textsuperscript{z}}}} Et similiter \edtext{ \edtext{de}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | in \textit{P\textsuperscript{u}}}} aliis taliter \edtext{uariatis}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uariatus \textit{P\textsuperscript{x}}}}. Sicut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{namque}{\Cfootnote[nosep]{\textit{ακ} | enim \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} ‘ \edtext{quatuor positi sunt gradus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{o}} | positi sunt quatuor gradus \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}} | 4or. sunt positi gradus \textit{N\textsuperscript{u}} | sunt positi quatuor gradus \textit{G\textsuperscript{u}P\textsuperscript{q}} | positi sunt gradus \textit{mv} | sunt gradus \textit{P\textsuperscript{z}}}} \edtext{medicinarum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | mediarum \textit{P\textsuperscript{p}}}} \edtext{prius in tegni, }{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | prius integri, \textit{V\textsuperscript{z}}}} \edtext{}{\Afootnote[nosep]{Avic. \textit{Can. med.} I , fen 2 , 2 .15}}’ \edtext{deinde quoque}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | deindeque \textit{βγmv} | deinde \textit{E\textsuperscript{a}π}}} \edtext{quinto simplicium vnusquisque}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | 4or simplicium vnusquisque \textit{V\textsuperscript{z}} | 5° simplicium \textit{π}}} \edtext{diuisus est}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}mv} | est diuisus \textit{V\textsuperscript{b}} | diuisus est quilibet \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{in}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} tres mansiones, ut \edtext{agnoscatur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}} | agnoscantur \textit{V\textsuperscript{b}} | cognoscatur \textit{mv}}} quantum \edtext{possibile}{\Cfootnote[nosep]{\textit{ακmv} | possibile est \textit{π}}} \edtext{particularius}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | particularis \textit{V\textsuperscript{a}} | per particularius \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{complexio}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | con\expan{iu}n\expan{cti}o \textit{(orig. \textup{con\textsuperscript{no}})} \textit{P\textsuperscript{z}}}} \edtext{medicine}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | meclicine \textit{P\textsuperscript{z}} | medie \textit{βE\textsuperscript{a}}}}. \edtext{Ita}{\Cfootnote[nosep]{\textit{αλπmv} | Ita ut \textit{P\textsuperscript{x}}}} \edtext{posteriores}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | posterioris \textit{V\textsuperscript{o}}}} \edtext{musici}{\Cfootnote[nosep]{\textit{βγκπmv} | minus \textit{E\textsuperscript{a}}}} non solum cordis \edtext{fuere}{\Cfootnote[nosep]{\textit{ακmv} | fuerunt \textit{π}}} \edtext{contenti}{\Cfootnote[nosep]{\textit{αλπmv} | contempti \textit{P\textsuperscript{x}}}} quibus essentialiores et \edtext{integraliores}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | irregulariores \textit{γmv}}} \edtext{denotarentur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | denotaretur \textit{P\textsuperscript{z}}}} proportiones. Verum ut \edtext{sonum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | solum \textit{V\textsuperscript{a}mv}}} amplius \edtext{melodiosum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv}}} \edtext{construerent}{\Cfootnote[nosep]{\textit{βκ} | constituerent \textit{γπE\textsuperscript{a}mv}}} \edtext{inter}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | in \textit{V\textsuperscript{a}}}} \edtext{priores}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} principaliores alias \edtext{adiunxere}{\Cfootnote[nosep]{\textit{ακmv} | adiuxerunt \textit{π}}}, ne inter eas \edtext{magna}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{permanerent}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | permanerem \textit{V\textsuperscript{a}} | permaneret \textit{V\textsuperscript{b}mv}}} \edtext{interstitia}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{b}} | tristitia \textit{V\textsuperscript{a}} | in tristitia \textit{G\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{c}mv}}}. \edtext{}{\Cfootnote{etcetera \textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}} | sequitur 4m problema. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Quartum problema}\label{edition-text book-19a part4}}{\lemma{Quartum problema} \Cfootnote[nosep]{\textit{γG\textsuperscript{u}mv} | «4m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{Quartum problema} Quartum \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID SECUNDUM HANC}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | PROPTER QUID SECUNDUM PARYPATEN \textit{V\textsuperscript{m}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID SECUNDUM HANC DIFFICULTER YPATEN, FACILE ETIAM DIUISIO ALTERIUS? \textsuperscript{2}AUT QUIA CUM REMISSIONE YPATE ET SIMUL POST DIUISIONEM LEUE SURSUM PROICERE? \textsuperscript{3}PROPTER HOC AUTEM UIDETUR ET QUE DICUNTUR AD VNAM AD HANC QUAM CIRCA NITEM. \textsuperscript{4}OPORTET ENIM CUM DIMISSIONE ET REMISSIONE UALDE PROPRIA CONSUETUDINI AD UOLUNTATEM. \textsuperscript{5}HUIUS AUTEM UTIQUE CONSONANTIA QUEDAM CAUSA \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}mv}}}.} Quartum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} secundum \edtext{istam}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{z}} | illam \textit{M\textsuperscript{a}V\textsuperscript{m}mv} | hanc \textit{π} | primam \textit{V\textsuperscript{b}}}} cordam puta \edtext{ypatem}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv}}} \edtext{difficulter}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv}}} \edtext{cantatur}{\Cfootnote[nosep]{\textit{ακπ} | cantetur \textit{mv}}}?} Et ideo \edtext{dictum est}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}mv} | dictum \textit{βP\textsuperscript{x}}}} \edtext{antea}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ante \textit{π} | anima \textit{V\textsuperscript{z}}}} \textit{ \edtext{secundum}{\Cfootnote[nosep]{\textit{κ} | secundum eam \textit{απ}}} interruptionem cantus \edtext{peruenire}{\Cfootnote[nosep]{\textit{αP\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}mv} | peruenirem \textit{P\textsuperscript{x}} | prouenire \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} } et \textit{licet cum difficultate} \edtext{cantetur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | canta \textit{P\textsuperscript{z}}}}. \textit{Tamen diuisio siue distinctio \edtext{istius}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | ipsius \textit{V\textsuperscript{b}}}} corde a \edtext{quacunque}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}} \edtext{alia}{\Cfootnote[nosep]{\textit{βγκπ} | aliam \textit{E\textsuperscript{a}} | \textit{om}. \textit{mv}}} est facilis et manifesta et \edtext{proprie}{\Cfootnote[nosep]{\textit{αλπmv} | prope \textit{P\textsuperscript{x}}}} ab inferioribus}, ut \edtext{nete}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | ratione \textit{P\textsuperscript{y}}}} \edtext{ac}{\Cfootnote[nosep]{\textit{αλπmv} | et \textit{P\textsuperscript{x}}}} \edtext{ei}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}mv} | ea \textit{C\textsuperscript{a}V\textsuperscript{o}} | eis \textit{P\textsuperscript{x}V\textsuperscript{a}} | etiam \textit{V\textsuperscript{m}}}} propinquis. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv}}} } Soluit \edtext{et prius}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} ad \edtext{id}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | illud \textit{E\textsuperscript{a}P\textsuperscript{z}}}} quod \edtext{subdictum}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}} | subdictum est \textit{P\textsuperscript{z}V\textsuperscript{a}m} | subditum est \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}} | subditum \textit{βE\textsuperscript{a}M\textsuperscript{a}M\textsuperscript{b}} | subductum \textit{V\textsuperscript{z}}}} \edtext{secundo}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{dicens}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | dicit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}}}} \textit{ \edtext{illud}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}mv} | id \textit{λN\textsuperscript{u}V\textsuperscript{b}} | ideo \textit{πP\textsuperscript{y}}}} \edtext{esse}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} quia faciendo remissionem et quasi quandam \edtext{interpollationem}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}}}} cum cantus fiat cum \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ypatem \textit{M\textsuperscript{a}}}} \edtext{simulque}{\Cfootnote[nosep]{\textit{ακmv} | simul que \textit{π}}} \edtext{fere}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ferre \textit{P\textsuperscript{z}}}} statim post durationem \edtext{uel}{\Cfootnote[nosep]{\textit{βγκmv} | et \textit{πE\textsuperscript{a}}}} \edtext{diuisionem}{\Cfootnote[nosep]{\textit{γκπmv} | dimissionem \textit{βE\textsuperscript{a}}}} \edtext{intonationis}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | intonantis \textit{M\textsuperscript{a}}}} grauem, \edtext{leue}{\Cfootnote[nosep]{\textit{ακπmv} | leuem \textit{V\textsuperscript{a}}}} \edtext{fit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | sit \textit{P\textsuperscript{z}}}} \edtext{uocem}{\Cfootnote[nosep]{\textit{αλπmv} | uoce \textit{P\textsuperscript{x}}}} sursum emittere,} cum iam \edtext{aliqualiter cantans}{\Cfootnote[nosep]{\textit{λπN\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | cantans aliqualiter \textit{P\textsuperscript{y}} | aliter cantans \textit{V\textsuperscript{a}} | cum nam aliqualiter cantus \textit{E\textsuperscript{a}}}} \edtext{quieuerit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | quieuit \textit{V\textsuperscript{a}} | conuenerit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} emittendo spiritum et \edtext{attrahendo}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | mittendo \textit{G\textsuperscript{u}} | emittendo \textit{π}}} sufficienter in uocis \edtext{organa}{\Cfootnote[nosep]{\textit{βγκπmv} | organe \textit{E\textsuperscript{a}}}}. \edtext{Et ideo}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | Et ideo non \textit{G\textsuperscript{u}} | Et ideo in \textit{V\textsuperscript{a}} | Ideo \textit{E\textsuperscript{a}}}} percipi videtur \edtext{discretio}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | distinctio \textit{P\textsuperscript{z}V\textsuperscript{a}}}} in cantu \edtext{facto}{\Cfootnote[nosep]{\textit{ακmv} | facta \textit{π}}} per \edtext{ypatem}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{m}mv}}} cum alia sibi opposita. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{PROPTER HOC.}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | PROPTER. \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} } \edtext{Assignat}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}} causam \edtext{prioris}{\Cfootnote[nosep]{\textit{βγκπmv} | priores \textit{E\textsuperscript{a}}}} \edtext{premissi}{\Cfootnote[nosep]{\textit{ακmv} | dicti \textit{π}}} dicens \textit{ \edtext{id}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{z}V\textsuperscript{o}} | illud \textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv}}} \edtext{fore}{\Cfootnote[nosep]{\textit{ακmv} | esse \textit{π}}} quia melodie \edtext{que}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{referuntur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}} | feruntur \textit{P\textsuperscript{y}mv}}} ad unam cordam, puta ad illam que est circa \edtext{netem}{\Cfootnote[nosep]{\textit{αλπmv} | uenem \textit{E\textsuperscript{a}} | uene \textit{P\textsuperscript{x}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{ακmv} | aut \textit{π}}} \edtext{paranetem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | paranete \textit{P\textsuperscript{z}}}} \edtext{ac etiam paramese}{\Cfootnote[nosep]{\textit{βγκmv} | aut etiam paranete \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}} \edtext{facilime}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | faciliter \textit{G\textsuperscript{u}P\textsuperscript{z}}}} \edtext{cantantur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | cantatur \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}}}},} eo quod non interuenit multa diuersitas \edtext{uocum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | uocis \textit{G\textsuperscript{u}P\textsuperscript{u}}}} secundum \edtext{acutum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | auctum \textit{V\textsuperscript{m}}}} et \edtext{grauem}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}} | graue \textit{πE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv}}}, \textit{ \edtext{sed tamen}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sed cum \textit{P\textsuperscript{p}P\textsuperscript{q}} | et inde \textit{P\textsuperscript{x}}}} \edtext{licet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sit est cum \textit{G\textsuperscript{u}}}} \edtext{per ypatem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | parypatem \textit{P\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{u}V\textsuperscript{o}}}} cantetur \edtext{difficulter}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv}}} propter \edtext{grandem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | gradem \textit{V\textsuperscript{a}} | magnam \textit{P\textsuperscript{y}} | grauem \textit{G\textsuperscript{u}}}} notarum \edtext{distantiam}{\Cfootnote[nosep]{\textit{ακmv} | differentiam \textit{π}}}. \edtext{Cum}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{tamen}{\Cfootnote[nosep]{\textit{αλπmv} | causa \textit{P\textsuperscript{x}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{fit}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv} | sit \textit{E\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{z}}}} ut \edtext{tactum est}{\Cfootnote[nosep]{\textit{γκπmv} | tactum \textit{βE\textsuperscript{a}}}} quadam \edtext{dimissione}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | diuisione \textit{P\textsuperscript{z}}}} et \edtext{remissione}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | reuersione \textit{γmv}}} \edtext{quasi pausando}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | pausando quasi \textit{G\textsuperscript{u}}}} ita \edtext{ea reddatur}{\Cfootnote[nosep]{\textit{ακmv} | ea redditur \textit{π}}} propria \edtext{ualde}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | uelut \textit{P\textsuperscript{y}}}} consuetudini \edtext{per uoluntatem \edtext{acquisite}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | aquisittam \textit{V\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{b}}}},} \edtext{quis enim \edtext{sic}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | sint \textit{P\textsuperscript{x}}}} eligit, \edtext{tunc utique}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | nunc atque \textit{P\textsuperscript{z}}}} consuetudine}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | «per uoluntatem acquisite. Quis enim sic eligit tunc utique consuetudine» (in mg.) \textit{M\textsuperscript{b}}}} inducta in cantando per \edtext{ypatem}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}}. \edtext{Secundum}{\Cfootnote[nosep]{\textit{ακπ} | Per \textit{mv}}} talem \edtext{dimissionem et remissionem}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | remissionem et demissionem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | remissionem[?] ad omissione \textit{V\textsuperscript{o}} | dimmisionem \textit{V\textsuperscript{z}} | dimisoonem \textit{V\textsuperscript{a}}}} licet de se cantetur difficilime \edtext{illo}{\Cfootnote[nosep]{\textit{ακmv} | illa \textit{π}}} autem \edtext{modo}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} minime, \edtext{quoniam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | quod \textit{V\textsuperscript{o}} | quia \textit{mv} | quando \textit{P\textsuperscript{y}}}} consuetudo difficilima \edtext{etiam alleuiat}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | alleuiat etiam \textit{P\textsuperscript{p}} | etiam illeuiauit \textit{P\textsuperscript{y}}}} \edtext{ \edtext{cuncta}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}V\textsuperscript{a}mv} | puncta \textit{V\textsuperscript{b}} | cetera \textit{P\textsuperscript{x}}}} iuxta \edtext{illud}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | istud \textit{P\textsuperscript{y}}}} ‘ \edtext{ypocratis \textit{afforisticis} }{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}} | ypo. affirmatio \textit{mv} | yporetis \textit{amforisticis} \textit{P\textsuperscript{y}} | iporcratis anpho. \textit{V\textsuperscript{a}} | ypoti. amplias[?] \textit{P\textsuperscript{x}}}} assueti assuetos ferre labores et \edtext{reliqua}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}} | ceteram \textit{V\textsuperscript{a}mv}}}.\edtext{}{\Afootnote[nosep]{Hipp. \textit{Aph.} II .49}}’}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}Dicit autem uoluntatem quia ‘ \edtext{consuetudo proprie}{\Cfootnote[nosep]{\textit{ακmv} | proprie consuetudo \textit{π}}} in habentibus rationem \edtext{acquiritur}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}mv} | aquirimus \textit{E\textsuperscript{a}} | requiritur \textit{V\textsuperscript{a}}}} \edtext{apparens}{\Cfootnote[nosep]{\textit{ακmv} | ut apparet \textit{π} | \textit{om}. \textit{E\textsuperscript{a}V\textsuperscript{a}}}} \edtext{ \textit{ethycorum} secundo}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | secundo \textit{ethicorum} \textit{π}}}.\edtext{}{\Afootnote[nosep]{Arist. \textit{Eth. Nic.} II , 1103a l. 17}}’ +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{HUIUS AUTEM.}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | HUIUSMODI AUTEM \textit{M\textsuperscript{a}V\textsuperscript{b}mv} | HUIUS ERGO \textit{G\textsuperscript{u}P\textsuperscript{q}}}} } \edtext{Subdit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{o}mv} | Concludit \textit{P\textsuperscript{p}P\textsuperscript{u}}}} tertio quod \textit{ \edtext{etiam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | illud \textit{C\textsuperscript{a}V\textsuperscript{o}}}} consonantia est \edtext{aliqua}{\Cfootnote[nosep]{\textit{βγπP\textsuperscript{x}V\textsuperscript{o}mv} | alia \textit{λE\textsuperscript{a}}}} causa \edtext{eius}{\Cfootnote[nosep]{\textit{ακmv} | huius \textit{π}}},} \edtext{quod}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{z}}}} \edtext{per ypatem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}mv} | parypatem \textit{κP\textsuperscript{u}V\textsuperscript{o}}}} cantus \edtext{sepe}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} non \edtext{reputatur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | reputata \textit{V\textsuperscript{a}}}} \edtext{difficilius}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | difficilimus \textit{P\textsuperscript{p}mv} | difficilior \textit{V\textsuperscript{b}} | difficilis \textit{M\textsuperscript{a}} | difilis \textit{V\textsuperscript{a}}}} nam consonantia \edtext{fessa}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | fesse \textit{P\textsuperscript{z}} | falsa \textit{G\textsuperscript{u}V\textsuperscript{c}}}} \edtext{restaurantur}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | restauratur \textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}mv}}} \edtext{ut visum et}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}} | et \textit{π} | ut uisum est \textit{γmv} | ut uisum est et \textit{E\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | ut uisum eius \textit{P\textsuperscript{x}}}} \edtext{uigorantur}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | vigorantur det \textit{V\textsuperscript{a}} | uigoratur \textit{G\textsuperscript{u}M\textsuperscript{a}V\textsuperscript{b}mv}}} \edtext{debilitata}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}} | debilitatem \textit{P\textsuperscript{z}} | et debilitata \textit{V\textsuperscript{b}} | et debilitatur \textit{mv}}}. \edtext{ \edtext{Εt}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{ideo quesitum}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}mv} | ideo quiritur \textit{V\textsuperscript{z}} | queritur ideo \textit{M\textsuperscript{a}}}} ‘quare \edtext{coram}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | cum \textit{P\textsuperscript{y}}}} \edtext{infirmis}{\Cfootnote[nosep]{\textit{αλmv} | interimus \textit{P\textsuperscript{x}}}} \edtext{secundum \edtext{alexander}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv}}} ``fistule ac \edtext{tympana}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | tympana etcetera \textit{P\textsuperscript{y}}}}.''}{\Cfootnote[nosep]{\textit{βγκmv} | secundum \textit{E\textsuperscript{a}}}} \edtext{}{\Afootnote[nosep]{Ps.-Alex. Aph. \textit{Prob.} I .78 (Vat. reg.lat. 747, f. 75v)}}’}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{ \edtext{Sic}{\Cfootnote[nosep]{\textit{βγλπmv} | Sicut \textit{P\textsuperscript{x}}}} \edtext{igitur}{\Cfootnote[nosep]{\textit{βγλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ergo \textit{G\textsuperscript{u}P\textsuperscript{x}}}} \edtext{licet de se}{\Cfootnote[nosep]{\textit{βλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | \surplus{de se} licet de se \textit{P\textsuperscript{z}} | licet se \textit{P\textsuperscript{x}} | ita de se \textit{V\textsuperscript{a}}}} \edtext{difficulter}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{m}mv} | difficiliter \textit{P\textsuperscript{x}V\textsuperscript{z}}}} cantetur \edtext{ypate}{\Cfootnote[nosep]{\textit{βγπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | parypatem \textit{M\textsuperscript{a}}}} per}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} accidens, \edtext{tamen non}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | non tamen \textit{P\textsuperscript{y}}}} in tantum. Puta \edtext{uel}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} ratione consuetudinis \edtext{interuenientis}{\Cfootnote[nosep]{\textit{αλπmv} | interueniente \textit{P\textsuperscript{x}}}} \edtext{aut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | ac \textit{P\textsuperscript{u}}}} \edtext{delectabilis}{\Cfootnote[nosep]{\textit{ακmv} | delectationis \textit{π}}} \edtext{ipsius}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} armonie, cum \edtext{fuerit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{amicius}{\Cfootnote[nosep]{\textit{V\textsuperscript{z}} | ac amicius \textit{P\textsuperscript{x}} | animi eius \textit{γE\textsuperscript{a}mv} | cum eius \textit{M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | cum eis \textit{G\textsuperscript{u}} | eius \textit{P\textsuperscript{y}} | \textit{aicius was likely mistaken for amici eius}}} \edtext{adiecta}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}mv} | adicta \textit{V\textsuperscript{b}} | adiuncta \textit{πE\textsuperscript{a}}}} \edtext{opposita, et \edtext{quod}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | quia \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}}}} distinctio}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} maxime apparet in \edtext{eo}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{qui}{\Cfootnote[nosep]{\textit{αλπmv} | quod \textit{P\textsuperscript{x}}}} secundum ipsam \edtext{cantu}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}V\textsuperscript{b}mv} | cantum \textit{P\textsuperscript{x}} | cantat \textit{V\textsuperscript{a}} | causatur \textit{π}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 5a. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Quintum problema}\label{edition-text book-19a part5}}{\lemma{Quintum problema} \Cfootnote[nosep]{\textit{γG\textsuperscript{u}mv} | «5m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}V\textsuperscript{z}} | \surplus{quintum problema.} Quintum. \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DELECTABILITER}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID HABENTES ALIQUAM NOTITIAM \textit{P\textsuperscript{q}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID DELECTABILITER AUDIUNT CANTANTES QUOSCUMQUE, UTIQUE PRESCIENTES ADIPISCUNTUR CANTUS, QUAM QUOS NESCIUNT? \textsuperscript{2}UTRUM QUIA MAGIS MANIFESTUS ADIPISCENS SICUT INTENTIONEM QUANDO COGNOSCUNT QUOD CANITUR? HOC AUTEM DELECTABILE CONSIDERARE, QUIA DELECTABILE DISCERE. HUIUS AUTEM CAUSA HOC QUIDEM ACCIPERE SCIENTIAM. HOC UERO UTI ET RECOGNOSCERE IPSAM. \textsuperscript{3}ADHUC AUTEM ET CONSUETUM DELECTABILE MAGIS INCONSUETO \textit{G\textsuperscript{u}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Quintum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} cum \edtext{delectatione}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | delectatio \textit{V\textsuperscript{m}}}} maiori \edtext{audiunt}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | audiuntur \textit{β}}} homines cantatores \edtext{ac}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aut \textit{G\textsuperscript{u}}}} etiam \edtext{sonatores}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | senatores \textit{G\textsuperscript{u}} | subatores \textit{P\textsuperscript{y}}}} cantantes omnes \edtext{illos cantus}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | cantus illos \textit{V\textsuperscript{a}} | istos cantus \textit{P\textsuperscript{p}P\textsuperscript{u}}}} quorum \edtext{preaudientes}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | audientes \textit{P\textsuperscript{y}} | plaudientes \textit{C\textsuperscript{a}V\textsuperscript{o}}}} \edtext{habuere}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}V\textsuperscript{b}} | habuerant \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | habuerunt \textit{G\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{x}P\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{prius}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} aliquam cognitionem?} Siue \edtext{sit}{\Cfootnote[nosep]{\textit{βγP\textsuperscript{x}V\textsuperscript{m}mv} | sint \textit{M\textsuperscript{a}M\textsuperscript{b}V\textsuperscript{z}} | \textit{om}. \textit{πE\textsuperscript{a}}}} secundum verba, \edtext{ut}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | aut \textit{V\textsuperscript{a}mv} | ita \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}mv} | quid \textit{M\textsuperscript{a}N\textsuperscript{u}}}} \edtext{aliquid}{\Cfootnote[nosep]{\textit{ακmv} | aliqui \textit{π}}} de \edtext{ystoria}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}m}}} \edtext{gesti}{\Cfootnote[nosep]{\textit{βγκmv} | gesta \textit{πE\textsuperscript{a}}}} iam \edtext{audiuerint}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}} | audierint \textit{V\textsuperscript{a}mv} | audiuerit \textit{V\textsuperscript{b}} | audierunt \textit{π}}}, uel \edtext{demum}{\Cfootnote[nosep]{\textit{κ} | de modo \textit{απmv}}} \edtext{cantandi}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}}, \edtext{eo quod}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | eos quod \textit{V\textsuperscript{z}}}} \edtext{audiuerint}{\Cfootnote[nosep]{\textit{αV\textsuperscript{o}} | audiuerunt \textit{λG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | audierit \textit{P\textsuperscript{x}} | audiuerit \textit{V\textsuperscript{b}}}} alias, \edtext{illum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | illud \textit{V\textsuperscript{a}}}} \edtext{et}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}} | \textit{om}. \textit{γP\textsuperscript{y}mv}}} \edtext{consuetudinem aliquam inde acceperunt}{\Cfootnote[nosep]{\textit{κ} | acceperunt consuetudinem aliquam inde \textit{V\textsuperscript{b}mv} | consuetudinem inde acceperunt \textit{πE\textsuperscript{a}} | acceperunt aliquam consuetudinem inde \textit{V\textsuperscript{a}} | consuetudinem aliquam acceperunt \textit{β}}} quam illos \edtext{cantus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv}}} quorum \edtext{audientes}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} nullam \edtext{habuerunt}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | habuerint \textit{P\textsuperscript{y}V\textsuperscript{m}}}} \edtext{precognitionem}{\Cfootnote[nosep]{\textit{ακπ} | cognitionem \textit{P\textsuperscript{a}mv}}} omnino. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{UTRUM.} Soluit \edtext{et prius}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | et primo \textit{P\textsuperscript{y}} | primo \textit{P\textsuperscript{z}}}} \edtext{probabilius magis}{\Cfootnote[nosep]{\textit{αλ} | probabile magis \textit{P\textsuperscript{x}mv} | magis probabiliter \textit{π}}} dicens \edtext{illud}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}} | id \textit{βλV\textsuperscript{a}} | hoc \textit{mv} | ideo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} esse \textit{ \edtext{quoniam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | quia \textit{M\textsuperscript{a}}}} quando homo aliquam prescientiam \edtext{habuerit}{\Cfootnote[nosep]{\textit{αλπmv} | habuerunt \textit{P\textsuperscript{x}}}} circa cantum \edtext{quem}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | \surplus{quem} quem \textit{P\textsuperscript{y}} | quam \textit{C\textsuperscript{a}E\textsuperscript{a}V\textsuperscript{o}}}} \edtext{audiuit}{\Cfootnote[nosep]{\textit{ακmv} | audit \textit{π}}}, adipiscitur \edtext{et attingit ei quod est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{y}} | et adtingerit ei quod est \textit{N\textsuperscript{u}} | et attingit ei quod \textit{mv} | ei quod est \textit{π}}} \edtext{sibi}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | igitur \textit{P\textsuperscript{z}}}} \edtext{magis}{\Cfootnote[nosep]{\textit{ακπ} | magis est \textit{mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{manifestum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uisum \textit{P\textsuperscript{z}}}}.} Et hoc declarat \edtext{quemadmodum}{\Cfootnote[nosep]{\textit{ακmv} | q\expan{ua}m \textit{(orig. \textup{qm})} \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | quod diu \textit{P\textsuperscript{z}} | q\expan{uo}d\expan{am}m\expan{odo} \textit{(orig. \textup{qdm})} \textit{V\textsuperscript{o}}}} quando aliquis habuerit intentionem gesti quod cantatur \edtext{et hystoriam}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} eius \edtext{quodammodo}{\Cfootnote[nosep]{\textit{αλπmv} | quodam \textit{P\textsuperscript{x}}}} \edtext{sciuit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}} | sciuerit \textit{βγmv} | presciuit \textit{π}}}, tunc \textit{ \edtext{hoc}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}mv} | huic \textit{β} | hunc \textit{λ}}} \edtext{intendere est}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | est intendere \textit{P\textsuperscript{y}} | intende est \textit{P\textsuperscript{p}} | intendetur est \textit{E\textsuperscript{a}}}} delectabile \edtext{precognoscentibus}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | precognoscentiam \textit{E\textsuperscript{a}} | precognitionibus \textit{P\textsuperscript{a}P\textsuperscript{z}}}}, eo quod iocundum est \edtext{discere}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | dicere \textit{M\textsuperscript{a}}}} \edtext{aliquid}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aliquod \textit{P\textsuperscript{p}} | adhuc \textit{P\textsuperscript{y}}}} cuius non \edtext{perfecte habetur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | habetur perfecte \textit{G\textsuperscript{u}P\textsuperscript{p}}}} \edtext{cognitio}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | precognitio \textit{P\textsuperscript{p}}}} }, \edtext{quod fit}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | ut fit \textit{G\textsuperscript{u}P\textsuperscript{q}} | quod sit \textit{E\textsuperscript{a}P\textsuperscript{x}} | quare sit \textit{V\textsuperscript{m}}}} \edtext{iterum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | iterum \surplus{Iterum} \textit{P\textsuperscript{z}}}} audiendo \edtext{uel}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ut \textit{P\textsuperscript{p}}}} \edtext{considerare}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | considerando \textit{V\textsuperscript{z}}}}, ut \edtext{continetur}{\Cfootnote[nosep]{\textit{ακmv} | continetur in \textit{π}}} .xl., ubi \edtext{id}{\Cfootnote[nosep]{\textit{κ} | illud \textit{E\textsuperscript{a}} | hoc \textit{βγπmv}}} \edtext{repetitur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | repetetur \textit{V\textsuperscript{a}mv}}}. \edtext{Que}{\Cfootnote[nosep]{\textit{βγκπmv} | Quod \textit{E\textsuperscript{a}}}} duo interueniunt cum quis habet cognitionem \edtext{gesti}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | gesta \textit{P\textsuperscript{z}}}} aliquam, \edtext{nam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | iam \textit{G\textsuperscript{u}}}} \edtext{ipse}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ipsa \textit{P\textsuperscript{z}}}} \edtext{discit}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}mv} | discet \textit{P\textsuperscript{z}} | adiscit \textit{P\textsuperscript{x}} | dicit \textit{E\textsuperscript{a}} | dixit \textit{V\textsuperscript{b}V\textsuperscript{m}}}} in eo quod \edtext{accipit scientiam cantus}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | scientiam cantus accipit \textit{P\textsuperscript{y}}}} \edtext{illius}{\Cfootnote[nosep]{\textit{αλπmv} | ipsius \textit{P\textsuperscript{x}}}}, eo quod gestum \edtext{illud licet}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}} | illud hoc \textit{N\textsuperscript{u}} | illud \textit{P\textsuperscript{y}mv}}} \edtext{aliqualiter}{\Cfootnote[nosep]{\textit{αλπmv} | aliqua \textit{P\textsuperscript{x}}}} \edtext{esset}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | est \textit{P\textsuperscript{x}V\textsuperscript{a}} | erat \textit{G\textsuperscript{u}} | fuit \textit{P\textsuperscript{p}}}} \edtext{scitum}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{z}mv} | situm \textit{V\textsuperscript{m}} | scituti \textit{V\textsuperscript{b}}}} ab eo. Non \edtext{tamen}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{per modum melodie}{\Cfootnote[nosep]{\textit{απmv} | promotionem die \textit{M\textsuperscript{a}V\textsuperscript{m}} | toto omni die \textit{V\textsuperscript{z}} | per motionem die \textit{P\textsuperscript{x}}}} utitur \edtext{autem}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} et \edtext{considerat}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | considerant \textit{V\textsuperscript{z}} | consitus \textit{P\textsuperscript{z}}}} \edtext{in}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} eo quod \edtext{audit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | audiat \textit{P\textsuperscript{p}}}} gestum cuius \edtext{habuit}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}N\textsuperscript{u}mv} | habet \textit{πP\textsuperscript{x}} | prius habuit \textit{P\textsuperscript{y}}}} cognitionem. Et ideo \edtext{videmus}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} homines ut plurimum \edtext{cum}{\Cfootnote[nosep]{\textit{ακmv} | quando \textit{π}}} uolunt \edtext{amplius}{\Cfootnote[nosep]{\textit{ακmv} | in \textit{π}}} \edtext{cantu}{\Cfootnote[nosep]{\textit{βγλπmv} | cantum \textit{E\textsuperscript{a}P\textsuperscript{x}}}} \edtext{delectari}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}} \edtext{facere}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | faciunt facere \textit{P\textsuperscript{z}}}} \edtext{sibi}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ubi \textit{G\textsuperscript{u}}}} \edtext{ystoriam}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}m}}} gesti \edtext{enarrare}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | enarari \textit{V\textsuperscript{a}} | numerare \textit{P\textsuperscript{z}}}}, tunc enim \edtext{dupliciter}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | dicitur \textit{P\textsuperscript{y}} | dicit dupliciter dicitur \textit{P\textsuperscript{x}}}} \edtext{delectantur}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{z}mv} | delectatur \textit{C\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{c}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{}{\Cfootnote[nosep]{\textit{κ} | et melodia et ystoria et siquidem cum habuerint \textit{απmv}}}. \edtext{Triplex enim \edtext{tunc}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{dilectatio}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}}}} concurrit}{\Cfootnote[nosep]{\textit{κ}}} \edtext{consuetudinem}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | consuetudine \textit{M\textsuperscript{a}}}} audiendi \edtext{predictum cantum}{\Cfootnote[nosep]{\textit{ακmv} | cantum predictum \textit{π}}} \edtext{aliquando \edtext{in}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}} | ita \textit{mv}}} amplius}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | amplius aliquando \textit{P\textsuperscript{y}}}} \edtext{delectantur}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}mv} | delectatur \textit{C\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{c}V\textsuperscript{o}}}} triplex enim tunc delectatio concurrittriplex enim delectatio tunc concurittriplex enim delectatio concurrit, \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} unde secundo confirmat causam \edtext{prefatam}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | prefactam \textit{P\textsuperscript{z}V\textsuperscript{a}}}}. +\pend + +\pstart +\textbf{3} \textit{ \edtext{ADHUC AUTEM}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{z}V\textsuperscript{o}} | AD HOC AUTEM \textit{P\textsuperscript{x}mv} | ADHUC \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} .} \edtext{Dicit}{\Cfootnote[nosep]{\textit{κ} | Dicens \textit{απmv}}} quod amplius ad hoc facit \edtext{si quod}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | si quid \textit{M\textsuperscript{a}} | que si \textit{P\textsuperscript{y}} | sicut \textit{π}}} \edtext{auditur fuerit consuetum,}{\Cfootnote[nosep]{\textit{βV\textsuperscript{b}mv} | auditur fuit consuetum, \textit{V\textsuperscript{a}} | auditur fuerit \textit{κE\textsuperscript{a}} | audiui \textit{π}}} \edtext{quia}{\Cfootnote[nosep]{\textit{βγmv} | \textit{om}. \textit{κπE\textsuperscript{a}}}} \textit{consuetum magis \edtext{delectat}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | delectant \textit{V\textsuperscript{a}}}} quam oppositum,} \edtext{cum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | quam \textit{V\textsuperscript{b}}}} sit \edtext{factum}{\Cfootnote[nosep]{\textit{κ} | facta \textit{απmv}}} natura \edtext{quedam}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{a}P\textsuperscript{x}mv} | quadam \textit{E\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}}}} et \edtext{nobis}{\Cfootnote[nosep]{\textit{κN\textsuperscript{u}V\textsuperscript{b}mv} | a nobis \textit{P\textsuperscript{y}} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{conuenientia}{\Cfootnote[nosep]{\textit{βγπP\textsuperscript{x}V\textsuperscript{z}mv} | conuenientiam \textit{E\textsuperscript{a}V\textsuperscript{m}} | conuenientius \textit{M\textsuperscript{a}}}}. Quod autem ‘ \edtext{et}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | etiam \textit{V\textsuperscript{z}} | et quomodo \textit{απmv}}} \edtext{consueta}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{b}mv} | consuete \textit{E\textsuperscript{a}} | co\expan{n}ue\expan{nien}tia \textit{(orig. \textup{coue\textsuperscript{tia}})} quod autem et quomodo consuetta \textit{V\textsuperscript{a}}}} \edtext{delectent}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}mv} | delectant \textit{βπ} | delectentur \textit{P\textsuperscript{x}}}}, \edtext{ostensum est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{z}mv} | \surplus{ostensum} ostensum \textit{P\textsuperscript{y}} | ostensum \textit{N\textsuperscript{u}P\textsuperscript{u}} | ostensum est in \textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}}}} \edtext{sexto 18e.}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | sexto 16e. \textit{G\textsuperscript{u}P\textsuperscript{q}} | 3e 18e. sexto \textit{P\textsuperscript{y}} | sexto et octaue \textit{mv}}},\edtext{}{\Afootnote[nosep]{Ps.-Arist. \textit{Prob.} 18 .6 , 917a ll. 6–17}}’ et per oppositum \edtext{quid agant}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | quod agant \textit{E\textsuperscript{a}P\textsuperscript{z}} | agant \textit{V\textsuperscript{z}} | quod agunt \textit{P\textsuperscript{p}P\textsuperscript{u}} | quando audiunt \textit{G\textsuperscript{u}P\textsuperscript{q}}}} opposita, \edtext{et ideo}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} \edtext{audientes}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | audiente \textit{V\textsuperscript{a}}}} qui \edtext{vnius}{\Cfootnote[nosep]{\textit{ακmv} | videntur \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | vuius[?] \textit{P\textsuperscript{p}}}} \edtext{lingue sunt}{\Cfootnote[nosep]{\textit{γκmv} | lingue \textit{βπE\textsuperscript{a}}}} \edtext{cantum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | tantum \textit{V\textsuperscript{b}}}} \edtext{alterius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | anterius \textit{P\textsuperscript{q}P\textsuperscript{u}} | alterius auertimus \textit{G\textsuperscript{u}}}} minime \edtext{nisi}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{consueti}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | consuete \textit{G\textsuperscript{u}}}} \edtext{delectantur}{\Cfootnote[nosep]{\textit{βγκπmv} | delectentur \textit{E\textsuperscript{a}}}}, cum neque \edtext{ystoriam neque}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{m}} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{modum cantandi precognouerint}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{z}} | modum cantandi precognouerit \textit{V\textsuperscript{m}} | modum cantandi precognouerunt \textit{V\textsuperscript{a}mv} | modum precognouerunt \textit{P\textsuperscript{x}} | modum precantandi cognouerit \textit{V\textsuperscript{b}} | modum precanendi cognouerint \textit{β} | cantandi modum precognouerunt \textit{P\textsuperscript{p}} | cantandi precognouerunt \textit{G\textsuperscript{u}P\textsuperscript{q}} | cantandi precognouerint \textit{P\textsuperscript{z}V\textsuperscript{o}} | precantandi cognouerunt \textit{P\textsuperscript{u}}}}. In opposito \edtext{autem secus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | autem cetus \textit{C\textsuperscript{a}P\textsuperscript{a}V\textsuperscript{c}V\textsuperscript{o}}}}, \edtext{ceu}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}P\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}} | cum \textit{P\textsuperscript{y}}}} \edtext{mihi}{\Cfootnote[nosep]{\textit{mv} | nichil \textit{P\textsuperscript{y}}}} \edtext{contingit}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}V\textsuperscript{o}mv} | contigit \textit{M\textsuperscript{a}} | conuenit \textit{P\textsuperscript{p}}}} \edtext{per omne}{\Cfootnote[nosep]{\textit{ακmv} | parisius \textit{π}}} cum ad \edtext{gallos}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv}}} me \edtext{transtuli}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv}}}. Ut \edtext{autem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | aut \textit{P\textsuperscript{q}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{id}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | illud \textit{E\textsuperscript{a}P\textsuperscript{z}}}} \edtext{repetitum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | repetitur \textit{V\textsuperscript{z}} | reperietur \textit{P\textsuperscript{z}} | repente \textit{C\textsuperscript{a}V\textsuperscript{o}}}} \edtext{.xl.}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | 48°. \textit{P\textsuperscript{p}} | quarto \textit{E\textsuperscript{a}}}} \edtext{exponatur}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | exponitur \textit{γG\textsuperscript{u}mv}}} \edtext{omne}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ore \textit{G\textsuperscript{u}} | esse \textit{P\textsuperscript{x}}}}, \hyperref[Ar]{aristoteles} \edtext{talem}{\Cfootnote[nosep]{\textit{βγκπmv} | et aliam \textit{E\textsuperscript{a}}}} addit \edtext{causam}{\Cfootnote[nosep]{\textit{απE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{dicens}{\Cfootnote[nosep]{\textit{αλπmv} | dicit \textit{P\textsuperscript{x}}}} \edtext{ideo esse}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | id esse \textit{P\textsuperscript{y}P\textsuperscript{z}} | \textit{om}. \textit{V\textsuperscript{a}}}} quoniam \edtext{ille qui}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | illi qui \textit{V\textsuperscript{a}} | illud qui \textit{P\textsuperscript{z}} | ille \textit{P\textsuperscript{q}}}} \edtext{cantantem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cantant \textit{G\textsuperscript{u}} | cantationem \textit{P\textsuperscript{z}}}} \edtext{compatitur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | audit compatitur \textit{P\textsuperscript{y}}}} ipsi et ab \edtext{ipso}{\Cfootnote[nosep]{\textit{βγκπmv} | illo \textit{E\textsuperscript{a}}}} \edtext{afficitur}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | efficitur \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{z}}}}, propter uoces quas \edtext{exprimit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | exprimunt \textit{C\textsuperscript{a}P\textsuperscript{z}}}} \edtext{que}{\Cfootnote[nosep]{\textit{αλπmv} | qui \textit{P\textsuperscript{x}}}} \edtext{audienti}{\Cfootnote[nosep]{\textit{βγκmv} | auditui \textit{πE\textsuperscript{a}}}} \edtext{videntur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | numeri \textit{V\textsuperscript{m}}}} denotare \edtext{gaudium}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | cantum \textit{V\textsuperscript{a}}}}, et ideo \edtext{consonat sibi}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | sibi consonat \textit{P\textsuperscript{y}}}} \edtext{id quod}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}} | illud quod \textit{γP\textsuperscript{y}mv} | quod \textit{π}}} ille \edtext{cantat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | cantant \textit{P\textsuperscript{p}} | qui cantant \textit{P\textsuperscript{z}}}}. \edtext{Et}{\Cfootnote[nosep]{\textit{ακπ} | cum \textit{mv}}} \edtext{quadam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | quandam \textit{V\textsuperscript{a}}}} naturali inclinatione \edtext{ad delectationem \edtext{mouetur}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | mouentur \textit{V\textsuperscript{z}}}} in \edtext{seipso ceu}{\Cfootnote[nosep]{\textit{βγκmv} | se seu \textit{E\textsuperscript{a}}}} ille mouetur}{\Cfootnote[nosep]{\textit{ακmv} | mouetur ad delectationem in se seu ille mouetur \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | in se mouetur ad delectationem \textit{P\textsuperscript{p}}}}. \edtext{Quando}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Quoniam \textit{P\textsuperscript{z}}}} \edtext{enim}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | ei \textit{V\textsuperscript{m}}}} \edtext{natura}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | natatur \textit{P\textsuperscript{u}} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{vnius}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | unus \textit{V\textsuperscript{b}} | minus \textit{P\textsuperscript{z}}}} \edtext{percipit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | perficit \textit{P\textsuperscript{y}}}} naturam alterius \edtext{congaudere}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | gaudere \textit{E\textsuperscript{a}V\textsuperscript{b}} | congaudet \textit{G\textsuperscript{u}P\textsuperscript{q}} | cum gaudere \textit{C\textsuperscript{a}P\textsuperscript{z}}}} \edtext{ \edtext{aut}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | et \textit{V\textsuperscript{z}} | uel \textit{V\textsuperscript{a}}}} tristari uel \edtext{se}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{purgare}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | purgalis \textit{P\textsuperscript{z}}}}, natura etiam \edtext{illius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ipsius illius \textit{P\textsuperscript{p}}}} \edtext{ad hoc mouetur}{\Cfootnote[nosep]{\textit{βκmv} | mouetur ad hoc \textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}} | mouetur ad se hoc \textit{C\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{c}V\textsuperscript{o}}}} agendum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, ut \edtext{declaratum est}{\Cfootnote[nosep]{\textit{γκπmv} | declaratum \textit{βE\textsuperscript{a}}}} \edtext{septima}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}}. \edtext{Quare}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Aut quare \textit{G\textsuperscript{u}}}} subdit in \edtext{eius}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{verificationem sermonis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}} | sermonis uerificationem \textit{P\textsuperscript{y}} | verificatione sermonis \textit{γmv}}} quod omnis \edtext{cantans}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cantus \textit{G\textsuperscript{u}P\textsuperscript{q}}}} consonat sibi et alium reddit consonum et \edtext{affectum}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}E\textsuperscript{a}V\textsuperscript{o}} | affectantem \textit{V\textsuperscript{b}mv} | effectum \textit{P\textsuperscript{z}V\textsuperscript{c}} | affectione \textit{V\textsuperscript{a}}}}, dummodo illum \edtext{cantum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | cantu \textit{M\textsuperscript{a}}}} non \edtext{exprimat}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | exponat \textit{M\textsuperscript{a}}}} propter \edtext{necessitatem}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | ueritatem \textit{P\textsuperscript{z}}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | aut \textit{G\textsuperscript{u}}}} \edtext{sperans}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}} | superans \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} \edtext{ita}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{y}mv} | ita ut \textit{N\textsuperscript{u}} | inde \textit{π}}} \edtext{victum}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | uitum \textit{E\textsuperscript{a}N\textsuperscript{u}}}} lucrari \edtext{ceu}{\Cfootnote[nosep]{\textit{βγκmv} | seu \textit{E\textsuperscript{a}} | ut \textit{π}}} \edtext{ystriones}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}m}}} aut metu \edtext{pene}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | pone \textit{V\textsuperscript{a}}}} uel \edtext{tristitia}{\Cfootnote[nosep]{\textit{αλπmv} | tristitiam \textit{P\textsuperscript{x}}}}, et \edtext{huius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | huiusmodi \textit{G\textsuperscript{u}M\textsuperscript{b}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{y}V\textsuperscript{b}mv}}} \edtext{propter que talia}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{z}} | propter que talia tam \textit{M\textsuperscript{a}} | propter talia que \textit{P\textsuperscript{y}} | propter quod talia \textit{P\textsuperscript{x}} | propter talia \textit{mv}}} \edtext{cantantes}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{non}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | nec \textit{V\textsuperscript{b}}}} \edtext{magne}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{a}mv} | magis \textit{πV\textsuperscript{b}}}} \edtext{consonant}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | consonans \textit{V\textsuperscript{m}V\textsuperscript{z}} | consonat \textit{P\textsuperscript{z}} | consonas \textit{P\textsuperscript{x}}}} aliis \edtext{et}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{x}}}} maxime \edtext{extraneis}{\Cfootnote[nosep]{\textit{βγκπmv}}} ab illo cantu \edtext{et sibimet ipsis}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} minime. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}} | sequitur 6m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Sextum problema}\label{edition-text book-19a part6}}{\lemma{Sextum problema} \Cfootnote[nosep]{\textit{γG\textsuperscript{u}mv} | «6m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{sextum.} Sextum. \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID PARYPATE}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID RATIONABILE EST \textit{P\textsuperscript{q}} | \textit{om}. \textit{βλE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID PAR YPATE SECUNDUM RATIONEM IN CANTIBUS TRAGICUM. \textsuperscript{2}AUT PROPTER INEQUALITATEM? PASSIUUM ENIM INEQUALE, ET IN MAGNITUDINE FORTUNE AUT TRISTITIE. EQUALE AUTEM MINUS PLORABILE UEL ULULABILE \textit{G\textsuperscript{u}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Sextum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} rationabile \edtext{existit}{\Cfootnote[nosep]{\textit{ακmv} | est \textit{π}}} quod \edtext{genus cantandi tragicum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | genus cantandi traycum \textit{P\textsuperscript{y}} | genus tragicum \textit{π}}} \edtext{per ypatem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}m} | per ypate \textit{V\textsuperscript{a}} | parypatem \textit{P\textsuperscript{u}P\textsuperscript{z}v}}} cantetur?} \edtext{Nosce quod}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | Notandum quod \textit{mv} | Nosce \textit{πM\textsuperscript{a}}}} \edtext{circa}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} genus \edtext{armonicum}{\Cfootnote[nosep]{\textit{ακmv} | armoniarum uel armonicum \textit{π}}} \edtext{quodcumque}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}mv} | quod t\expan{alis} \textit{(orig. \textup{t'})} \textit{P\textsuperscript{q}} | \textit{om}. \textit{G\textsuperscript{u}}}} duplicem maneriem cantandi constare, \edtext{quedam enim}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | quidem enim \textit{P\textsuperscript{p}} | que \textit{V\textsuperscript{a}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{comedia}{\Cfootnote[nosep]{\textit{ακmv} | comedia et \textit{π}}} altera tragedia. Est autem comedia \edtext{canticum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{o}mv} | cantus \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} agreste \edtext{que}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} res priuatarum \edtext{et humilium personarum}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | personarum et humilium \textit{P\textsuperscript{z}} | et humilium \textit{G\textsuperscript{u}} | et habilium personarum \textit{γ}}} \edtext{comprehendit}{\Cfootnote[nosep]{\textit{ακmv} | comprehendens \textit{π}}}, et dicitur \edtext{a cosmos}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{z}mv} | acosinos \textit{P\textsuperscript{x}} | a cosinos \textit{M\textsuperscript{a}} | a camos \textit{P\textsuperscript{y}}}} quod est \edtext{villa uel laus}{\Cfootnote[nosep]{\textit{βγκmv} | villa \textit{πE\textsuperscript{a}}}} secundum aliquos. Grece \edtext{tamen}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | tantum \textit{V\textsuperscript{a}}}} \edtext{mundus}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} et \edtext{odi}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | odos \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} cantus \edtext{quasi}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quia \textit{P\textsuperscript{p}}}} \edtext{mundanus}{\Cfootnote[nosep]{\textit{απM\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | uel \textit{V\textsuperscript{z}}}} vulgaris \edtext{cantus}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cantatus \textit{E\textsuperscript{a}}}}, \edtext{de rebus enim}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}mv} | enim de rebus \textit{V\textsuperscript{a}} | de rebus \textit{M\textsuperscript{a}V\textsuperscript{m}}}} vulgaribus tractat et \edtext{affinibus}{\Cfootnote[nosep]{\textit{ακπ} | affinibus et \textit{mv}}} \edtext{ \edtext{cotidiane}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}P\textsuperscript{x}m}}} \edtext{locutionis}{\Cfootnote[nosep]{\textit{κ} | locutioni \textit{πE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv}}} }{\Cfootnote[nosep]{\textit{ακπmv} | locutioni cotidiane \textit{V\textsuperscript{b}}}}. Vel \edtext{dicitur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{a commessatione}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | a conmiseratione \textit{P\textsuperscript{x}} | a commensuratione \textit{V\textsuperscript{m}} | a commesatione \textit{V\textsuperscript{z}} | a commensatione \textit{M\textsuperscript{a}} | a commessatione quia \textit{π} | accessatione \textit{N\textsuperscript{u}} | accensatione \textit{E\textsuperscript{a}}}} post cibum, \edtext{enim}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{homines solebant}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | solebant homines \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}}}} \edtext{ad}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{eam audiendam}{\Cfootnote[nosep]{\textit{αλπmv} | audiendam eam \textit{P\textsuperscript{x}}}} \edtext{conuenire}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | pervenire \textit{V\textsuperscript{a}}}}. Tragedia uero \edtext{est modus carminis}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | est modus carminum \textit{β} | cantans \textit{P\textsuperscript{z}}}} quo poete in \edtext{luctibus}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv}}} regum utebantur. \edtext{Dicta}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | Dictus \textit{π} | Dictum \textit{P\textsuperscript{y}}}} a \edtext{tragos}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | treges \textit{V\textsuperscript{a}}}} quod \edtext{est}{\Cfootnote[nosep]{\textit{απV\textsuperscript{z}mv} | dicitur \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}} \edtext{yrcus}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv}}} et \edtext{odi}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | odos \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}}}} \edtext{cantus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}mv} | quod est cantus \textit{C\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{quasi}{\Cfootnote[nosep]{\textit{κ} | in \textit{P\textsuperscript{z}} | et \textit{V\textsuperscript{a}} | inde \textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv}}} \edtext{hyrcinus}{\Cfootnote[nosep]{\textit{βV\textsuperscript{o}} | yranus \textit{P\textsuperscript{x}mv}}} cantus. Et quia materia erat \edtext{tristis}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | tristis et \textit{λ}}} \edtext{feda}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}} | fetida \textit{V\textsuperscript{z}} | seda \textit{βγG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}mv}}}, \edtext{huiusmodi}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}} | huius \textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv}}} \edtext{animal}{\Cfootnote[nosep]{\textit{ακπ} | animalis \textit{mv}}} \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uel \textit{P\textsuperscript{z}}}} \edtext{yrcum}{\Cfootnote[nosep]{\textit{κV\textsuperscript{b}E\textsuperscript{a}} | yrcus \textit{G\textsuperscript{u}mv} | hircus \textit{P\textsuperscript{q}P\textsuperscript{u}} | hincus \textit{P\textsuperscript{p}}}} \edtext{pro munere}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}mv} | perminuere \textit{P\textsuperscript{z}} | provire \textit{V\textsuperscript{a}} | pro numero \textit{C\textsuperscript{a}V\textsuperscript{c}V\textsuperscript{o}}}} \edtext{poematis}{\Cfootnote[nosep]{\textit{βγκmv} | poanatis \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}} \edtext{accipiebant}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}mv} | accipiebantur \textit{V\textsuperscript{o}} | recipiebant \textit{V\textsuperscript{a}}}} \edtext{additur. Et}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | additur. Etiam \textit{πN\textsuperscript{u}} | quod dicitur in \textit{P\textsuperscript{y}}}} \edtext{maneries a quibus 3°}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}mv} | maneries a quibusdam 3a \textit{πM\textsuperscript{a}N\textsuperscript{u}}}} \edtext{satira}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}}}} dicta \edtext{que}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | in \textit{P\textsuperscript{y}}}} carmine \edtext{construitur}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | constituitur \textit{γP\textsuperscript{z}}}} \edtext{reprehensorio}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}mv} | reprehensoris \textit{C\textsuperscript{a}P\textsuperscript{a}V\textsuperscript{c}V\textsuperscript{o}} | reprehensorior \textit{P\textsuperscript{u}} | reprehensionis \textit{P\textsuperscript{z}}}} \edtext{ceu}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{c}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{modus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | motus \textit{P\textsuperscript{z}V\textsuperscript{c}}}} \edtext{\hyperref[Hor]{oratii} fuit}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | fuit oratii \textit{απmv}}} maxime. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | AUT QUIA. \textit{G\textsuperscript{u}mv}}} } Soluit dicens \edtext{causam esse sumptam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | causam esse causam sumptam \textit{P\textsuperscript{y}}}} \textit{ab \edtext{inequalitate}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | equalitate \textit{P\textsuperscript{y}}}}, vtrobique \edtext{enim}{\Cfootnote[nosep]{\textit{κπ} | scilicet \textit{mv} | uidelicet \textit{βγ} | uidet \textit{E\textsuperscript{a}}}} inest quedam inequalitas}, ut in cantu \edtext{tragico}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}mv}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{per ypatem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | parypaten \textit{M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}}}} facto, \edtext{propter}{\Cfootnote[nosep]{\textit{αλπmv} | per \textit{P\textsuperscript{x}}}} \edtext{eius esse}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | esse eius \textit{M\textsuperscript{a}M\textsuperscript{b}} | eam esse \textit{π} | eius at esse \textit{V\textsuperscript{a}}}} \edtext{supremum}{\Cfootnote[nosep]{\textit{ακmv} | supremam \textit{π}}}. Nam in \edtext{vnoquoque}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vtroque \textit{G\textsuperscript{u}P\textsuperscript{q}}}} istorum est quedam passio et difficultas, \edtext{quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | earum \textit{P\textsuperscript{z}}}} autem \edtext{tale}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{o}mv} | tale est \textit{λG\textsuperscript{u}P\textsuperscript{q}}}}, \edtext{siue}{\Cfootnote[nosep]{\textit{ακmv} | seu \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | ceu \textit{P\textsuperscript{z}} | Inequale seu \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{sit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}}}} \textit{in magnitudine \edtext{ \edtext{fortune}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}} | fortitudine \textit{γP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} ceu cantus magne letitie alicuius \edtext{magnatis}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | magnatis aut \textit{P\textsuperscript{y}} | magnatis et \textit{γN\textsuperscript{u}mv} | magnatis \surplus{uel huius est inequale non eundem seruans tenorem} \textit{M\textsuperscript{b}}}} probitatis, siue in \edtext{magnitudine}{\Cfootnote[nosep]{\textit{βγλmv} | magnitudine letitie \textit{P\textsuperscript{x}}}} }{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} tristitie}, \edtext{sicut}{\Cfootnote[nosep]{\textit{βγκπmv} | sum \textit{E\textsuperscript{a}}}} mortis alicuius excellentis \edtext{uel}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | \textit{om}. \textit{πE\textsuperscript{a}P\textsuperscript{y}}}} \edtext{huiusmodi}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}mv} | huius \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | ut nuper domini ubertim dicens carraria uel hoc \textit{P\textsuperscript{y}}}}, est \edtext{inequale}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | equale \textit{P\textsuperscript{y}}}}, \edtext{non eundem seruans tenorem. Quod \edtext{autem}{\Cfootnote[nosep]{\textit{αλπ} | aut \textit{mv} | \textit{om}. \textit{P\textsuperscript{x}}}} est \edtext{inequale}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | in eis uale \textit{P\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} et dissonum \edtext{rationabile est}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}} | rationabile erit \textit{mv} | rationale est \textit{V\textsuperscript{m}V\textsuperscript{z}} | est rationale \textit{V\textsuperscript{a}}}}, ut \edtext{cantu}{\Cfootnote[nosep]{\textit{αλπmv} | cantum \textit{P\textsuperscript{x}}}} exprimatur \edtext{huiusmodi}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}} | huius \textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et huius \textit{V\textsuperscript{a}}}}, ut pondus \edtext{meloticum}{\Cfootnote[nosep]{\textit{βγP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | meloticus \textit{P\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{q}}}} \edtext{configeretur}{\Cfootnote[nosep]{\textit{γN\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}mv} | cum figeretur \textit{M\textsuperscript{a}} | contingeretur \textit{P\textsuperscript{x}} | velociter configeretur \textit{P\textsuperscript{q}} | uelociter consigneretur \textit{G\textsuperscript{u}}}} rei de qua \edtext{existit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | extitit \textit{P\textsuperscript{z}}}}. Tunc cantus consurgit ‘\label{quote-6.1-Gal} \edtext{eurithimus}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | onrichimius \textit{P\textsuperscript{z}} | enrichimus \textit{(\textup{\sic{in rich enrichimus}} a.c.)} \textit{P\textsuperscript{y}}}} \edtext{sicut de huius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | sicut huius de \textit{V\textsuperscript{z}} | sicut de huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}mv}}} \edtext{pulsu scribitur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | pulsi scribitur \textit{P\textsuperscript{y}} | cantu scribitur \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{ \textit{de differentiis pulsuum} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | 8 \textit{differentiis pulsuum} et \textit{P\textsuperscript{z}}}} \edtext{a}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \surplus{a} a \textit{G\textsuperscript{u}}}} \edtext{galeno}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv}}}. \edtext{}{\Afootnote[nosep]{Gal. \textit{De diff. puls.} I .8 (I.12 in Latin trans. by Burgundio of Pisa) \edtext{}{\Bfootnote[nosep]{Cf. \textit{Conciliator} diff. 83}}}}’ \edtext{Ceu}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{u}mv} | Seu \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}}}} in \edtext{bellis}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | becillis \textit{P\textsuperscript{y}V\textsuperscript{z}}}} \edtext{tubarum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | tuban[?] \textit{P\textsuperscript{z}}}} clangor bellantes concitat in furorem, in oppositis autem \edtext{ut}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} in \edtext{choreis}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | choris \textit{V\textsuperscript{a}}}} \edtext{oppositum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | compositum \textit{P\textsuperscript{z}}}} \edtext{expetitur}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}} | experitur \textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | eproexperitur \textit{P\textsuperscript{z}}}}, ac similiter \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} mortuorum lamentatione. Et \edtext{id}{\Cfootnote[nosep]{\textit{κV\textsuperscript{b}mv} | illud \textit{α} | hoc \textit{π}}} est \edtext{quod}{\Cfootnote[nosep]{\textit{αλπmv} | quod est equale \textit{P\textsuperscript{x}}}} \edtext{subditur}{\Cfootnote[nosep]{\textit{βγκmv} | subdit \textit{πE\textsuperscript{a}}}} a contrariis probando \edtext{pretactum}{\Cfootnote[nosep]{\textit{ακπ} | pretactam \textit{mv}}}, \edtext{inquiens}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in conueniens \textit{G\textsuperscript{u}P\textsuperscript{q}}}} quod \textit{ \edtext{illud}{\Cfootnote[nosep]{\textit{αλπmv} | id est \textit{P\textsuperscript{x}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} est \edtext{equale}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | inequale \textit{V\textsuperscript{z}}}} in cantu et vnum conseruans tenorem non \edtext{est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{plorabile}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | proportionabile \textit{γmv}}} \edtext{aut}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | seu \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{ululabile}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}mv} | amabilabile \textit{E\textsuperscript{a}} | lamentabile \textit{π}}} }, cum \edtext{non sit quid}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sit quid non \textit{P\textsuperscript{p}}}} passiuum, \edtext{propter quod non est \edtext{conueniens}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | inconueniens \textit{V\textsuperscript{z}}}} ipsum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{parypatem}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}v} | per ypatem \textit{βγG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}V\textsuperscript{z}m}}} cuius est \edtext{inequalitatem}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | inequalitas \textit{V\textsuperscript{a}}}} tenere \edtext{sed}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | super \textit{P\textsuperscript{y}}}} per alias \edtext{cordarum}{\Cfootnote[nosep]{\textit{βλV\textsuperscript{a}mv} | cordas \textit{πP\textsuperscript{x}V\textsuperscript{b}}}} \edtext{mitiores}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}v} | anteriores \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} exponere. +\pend + +\pstart +\textbf{3} \edtext{Nosce}{\Cfootnote[nosep]{\textit{ακπ} | Notandum \textit{mv}}} quod ‘pondus est \edtext{illud}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | illud quod \textit{P\textsuperscript{z}}}} in \edtext{quo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}mv} | quod \textit{C\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{o}} | quid \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}}}} proportiones \edtext{secundum auicenna }{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{cadunt musice}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | musice cadunt \textit{π} | cadunt musice et \textit{P\textsuperscript{y}}}}.\edtext{}{\Afootnote[nosep]{Avic. \textit{Can. med.} Book I , fen 2 , 3 (p. 141 of 1608 ed.)}}’ Hoc autem pondus \edtext{rebus expedit}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}N\textsuperscript{u}mv} | rebus expetit \textit{P\textsuperscript{y}} | rebus accidit \textit{P\textsuperscript{x}} | expedit conformari rebus \textit{π}}} circa quas \edtext{extat}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{z}V\textsuperscript{o}mv} | extant \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | extitat \textit{P\textsuperscript{x}}}} \edtext{configurari}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}, \edtext{cum eo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quod eo \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}V\textsuperscript{c}}}} \edtext{exprimantur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | exprimatur \textit{P\textsuperscript{z}}}} passiones que sunt in anima.‘ \edtext{Voces \edtext{enim}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | autem \textit{G\textsuperscript{u}}}} \edtext{sunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} note passionum \edtext{que sunt}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} in \edtext{ea}{\Cfootnote[nosep]{\textit{ακmv} | anima \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{ακC\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{c}mv} | \textit{om}. \textit{P\textsuperscript{q}V\textsuperscript{o}}}} illeque rerum \edtext{primo}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | id est \textit{V\textsuperscript{a}}}} \textit{ \edtext{peryarmenias}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | pergere \textit{V\textsuperscript{a}}}}.} \edtext{}{\Afootnote[nosep]{Arist. \textit{Peri herm.} I .1 , 16a ll. 5–6}}’ Unde si res \edtext{fuerit}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | fuit \textit{V\textsuperscript{z}}}} \edtext{alta}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | altera \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}}}} \edtext{in signis}{\Cfootnote[nosep]{\textit{αλπmv} | insignis \textit{P\textsuperscript{x}}}} \edtext{contingit tragedia}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{o}mv} | tragedia contingit \textit{G\textsuperscript{u}P\textsuperscript{q}} | conuenit tragedia \textit{M\textsuperscript{a}P\textsuperscript{z}} | conuenit tregedia \textit{N\textsuperscript{u}} | querit tragedi \textit{V\textsuperscript{z}}}} \edtext{ipsam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{exprimere.}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | exponere. \textit{M\textsuperscript{a}}}} Si autem econtra \edtext{comedia}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}} ut modus \edtext{coaptetur}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | coagiretur \textit{P\textsuperscript{z}V\textsuperscript{c}} | coitetur \textit{V\textsuperscript{a}}}} \edtext{rei}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ei \textit{M\textsuperscript{a}}}} \edtext{ceu}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} \edtext{proprietas}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | proprietas approprietur \textit{G\textsuperscript{u}}}} subiecto. \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{z}V\textsuperscript{z}} | sequitur 7m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Septimum problema}\label{edition-text book-19a part7}}{\lemma{Septimum problema} \Cfootnote[nosep]{\textit{γG\textsuperscript{u}mv} | «7m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{Septimum.} Septimum \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID ANTIQUI}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID ANTIQUI CONSTITUENTES \textit{P\textsuperscript{q}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID ANTIQUI SEPTEM CORDARUM FACIENTES ARMONIAM YPATEM, SED NON NITEM RELIQUERUNT? \textsuperscript{2}UTRUM HOC MENDACIUM, UTRAMQUE ENIM RELIQUERUNT, TERTIAM UERO ELEUAUERUNT? \textsuperscript{3}AUT NON, SED QUIA GRAUIOR FORTIFICAT ACUTIORIS SONUM, QUARE MAGIS YPATE REDDIT ANTIFONUM QUAM NITE? \textsuperscript{4}QUIA ACUTUM POTENTIA MAGIS, GRAUE AUTEM FACILIUS CANTATUR \textit{G\textsuperscript{u}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Septimum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} est quod antiquitus \edtext{constituentes}{\Cfootnote[nosep]{\textit{βγG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{o}V\textsuperscript{z}mv} | constitutos \textit{E\textsuperscript{a}P\textsuperscript{u}} | constun[?]entes \textit{P\textsuperscript{z}} | constitutiones \textit{P\textsuperscript{x}V\textsuperscript{m}}}} armoniam musicalem ex septem cordis \edtext{diuiserunt}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}} | dimiserunt \textit{λE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv}}} ypatem \edtext{non}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{auferentes}{\Cfootnote[nosep]{\textit{βλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv}}} \edtext{ipsam}{\Cfootnote[nosep]{\textit{ακmv} | eam \textit{π}}} ab armonia, non autem \edtext{relinquerunt}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv}}} \edtext{nete}{\Cfootnote[nosep]{\textit{κ} | neten \textit{P\textsuperscript{z}} | netem \textit{γE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uocem \textit{P\textsuperscript{y}}}},} \edtext{uerum}{\Cfootnote[nosep]{\textit{ακmv} | uelut \textit{π}}} \edtext{inde abstulerunt}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | namque abstulerunt \textit{G\textsuperscript{u}} | inabstulerunt \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}}? +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{UTRUM.} Soluit et \edtext{prius}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | primo \textit{πV\textsuperscript{a}V\textsuperscript{z}}}} \edtext{problema}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | problemas \textit{V\textsuperscript{m}} | probatur \textit{β} | probabiliter \textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}mv}}} dicens \textit{ \edtext{id}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{o}mv} | illud \textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}} | illico \textit{G\textsuperscript{u}}}} \edtext{ \edtext{non esse uerum}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}} | non uerum \textit{γmv}}} }{\Cfootnote[nosep]{\textit{απmv} | esse uerum \textit{κ}}} quod \edtext{premissum est}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}} | premissum \textit{βP\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv}}}, quoniam non \edtext{seruauerunt solum}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | solum seruauerunt \textit{π} | seruauerunt \textit{V\textsuperscript{a}}}} \edtext{ \edtext{ypatem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv}}}, \edtext{ymmo}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{z}}}} \edtext{utramque}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | utraque \textit{β}}} \edtext{puta}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | pia[?]ta \textit{G\textsuperscript{u}}}} ypatem}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | ypatem \textit{V\textsuperscript{a}}}} et \edtext{netem}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | nete \textit{M\textsuperscript{a}P\textsuperscript{q}}}}. \edtext{Sed}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | Si \textit{V\textsuperscript{z}}}} \edtext{quam}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | quem \textit{P\textsuperscript{y}} | quid \textit{M\textsuperscript{a}}}} abstulerunt fuit tertia, \edtext{ut}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{G\textsuperscript{u}}}} paramese \edtext{uel}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} lychanos, \edtext{utraque}{\Cfootnote[nosep]{\textit{βγκπmv} | utramque \textit{E\textsuperscript{a}}}} enim est tertia \edtext{eius}{\Cfootnote[nosep]{\textit{ακmv} | huius \textit{π}}} quod est \edtext{ \edtext{septem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | 7a. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{esse}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}mv} | circa \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | esse 7 \textit{λ}}} cordas.} Unde 32° \edtext{dicetur}{\Cfootnote[nosep]{\textit{βγκπmv} | unde dicetur \textit{E\textsuperscript{a}}}} quod \textit{\hyperref[Ter]{ \edtext{tripandius}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} } extrahens tertiam cordam a \edtext{septicordo}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cordo \textit{P\textsuperscript{y}}}} \edtext{netem}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}mv} | nutio \textit{P\textsuperscript{x}}}} \edtext{apposuit}{\Cfootnote[nosep]{\textit{απmv} | apponit \textit{M\textsuperscript{a}} | apponunt \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}}.} Sic \edtext{ergo}{\Cfootnote[nosep]{\textit{κ} | igitur \textit{απmv}}} \edtext{per}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | per 4 \textit{P\textsuperscript{z}}}} \edtext{interemptionem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | interpretationem \textit{β} | intentionem \textit{V\textsuperscript{a}}}} soluit. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT NON.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | AUT. \textit{P\textsuperscript{p}P\textsuperscript{u}} | AUT QUIA. \textit{G\textsuperscript{u}}}} } Soluit \edtext{ \edtext{magis}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{y}}}} ad \edtext{orationem}{\Cfootnote[nosep]{\textit{κN\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | oratio \textit{E\textsuperscript{a}} | rationem \textit{G\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}}}} \edtext{secundo}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}V\textsuperscript{b}} | 2a. \textit{P\textsuperscript{x}} | \textit{om}. \textit{πV\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{ακπ} | secundo magis ad orationem \textit{mv}}} \edtext{dicens}{\Cfootnote[nosep]{\textit{βγG\textsuperscript{u}M\textsuperscript{a}mv} | dicit \textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{nichil}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}E\textsuperscript{a}V\textsuperscript{o}} | alias \textit{P\textsuperscript{z}} | hoc \textit{γmv}}} esse quod dicitur ut quod \edtext{abstulissent}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | abstulissetur \textit{P\textsuperscript{p}}}} \edtext{netem}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv}}} et \edtext{dimisissent}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | dimisissentur \textit{P\textsuperscript{p}} | ad misissent \textit{E\textsuperscript{a}}}} \edtext{stare}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{ypatem}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv}}}. Sed hoc dictum \edtext{ \edtext{fortassis}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}N\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{ex hoc}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{pullulauit}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{q}V\textsuperscript{b}V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}mv} | ex hoc pullulauit fortassis \textit{P\textsuperscript{y}}}}, quia \textit{sonus \edtext{cordis}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | corde \textit{βγπM\textsuperscript{a}V\textsuperscript{z}mv}}} grauis \edtext{vigorat}{\Cfootnote[nosep]{\textit{ακmv} | fortificat \textit{G\textsuperscript{u}} | figurat \textit{P\textsuperscript{p}P\textsuperscript{q}V\textsuperscript{o}} | fiat \textit{P\textsuperscript{u}} | sumitur[?] \textit{P\textsuperscript{z}}}} sonum acutioris.} Suo enim multo tempore et duratione graue \edtext{substentat}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}m}}} \edtext{acutum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | acutam \textit{P\textsuperscript{y}}}} \edtext{ne}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{o}mv} | non \textit{N\textsuperscript{u}} | ut \textit{P\textsuperscript{z}}}} cito \edtext{pereat}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | periat \textit{P\textsuperscript{p}} | persat \textit{P\textsuperscript{y}}}} \edtext{cum breui tempore feriat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}. \textit{Propter \edtext{quod}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{ypate}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ypatem \textit{M\textsuperscript{a}} | ypaton \textit{P\textsuperscript{y}}}} \edtext{longo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{tempore}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{aere}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | aera \textit{mv} | aerem \textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} percutiente \edtext{quam}{\Cfootnote[nosep]{\textit{βκπ} | quem \textit{γmv} | quod \textit{E\textsuperscript{a}}}} \edtext{nete}{\Cfootnote[nosep]{\textit{λG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{b}mv} | uite \textit{P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{reddat}{\Cfootnote[nosep]{\textit{βγλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | redeat \textit{E\textsuperscript{a}} | reddit \textit{G\textsuperscript{u}}}}, \edtext{ob eius}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | ab eius \textit{P\textsuperscript{x}} | propter eius \textit{P\textsuperscript{y}} | \hspace{1em} \textit{V\textsuperscript{a}}}} acuitatem, que \edtext{potentia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | ponitur \textit{C\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} uel fortitudine indiget in cantando, \edtext{difficile namque}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | difficilime namque \textit{V\textsuperscript{b}} | difilime namque \textit{V\textsuperscript{a}} | difficile enim \textit{G\textsuperscript{u}P\textsuperscript{q}mv}}} \edtext{acutum}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{b}mv} | acuta \textit{V\textsuperscript{a}}}} cantare \edtext{sed graue facilius,}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}}}} } \edtext{sicut pluries dicetur. Sic \edtext{itaque}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | ergo \textit{G\textsuperscript{u}P\textsuperscript{q}}}} quia grauis corda sonum fortificat \edtext{acute et ad se}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{x}mv} | acute et a se \textit{V\textsuperscript{z}} | acute et acute a se \textit{P\textsuperscript{z}}}} conuertit. et \edtext{quia}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | \surplus{quia} quia \textit{V\textsuperscript{a}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{difficile acutum cantare}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}} | acutum cantare \textit{βG\textsuperscript{u}P\textsuperscript{z}} | difficilime acutam est cantare \textit{V\textsuperscript{a}} | difficilime est acutum cantare \textit{V\textsuperscript{b}} | difficilime acutum cantare est \textit{mv}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}}}}, quis credidit ex hoc \edtext{cum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | causa \textit{V\textsuperscript{b}}}} \edtext{nete}{\Cfootnote[nosep]{\textit{γP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv} | nitem \textit{P\textsuperscript{x}V\textsuperscript{m}} | netem \textit{M\textsuperscript{a}} | voce \textit{G\textsuperscript{u}} | intensum \textit{V\textsuperscript{z}}}} sonum \edtext{non}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{perciperet}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | percipet \textit{P\textsuperscript{x}V\textsuperscript{a}} | percipiet \textit{M\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{z}}}} \edtext{proprium}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | cum \textit{V\textsuperscript{m}}}} esset \edtext{sublata}{\Cfootnote[nosep]{\textit{αλπmv} | sublato \textit{P\textsuperscript{x}}}}? Et fortassis aliquis leget \edtext{illud}{\Cfootnote[nosep]{\textit{βπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | istud \textit{E\textsuperscript{a}V\textsuperscript{z}} | illud ut tactum multe \textit{γmv}}} \textit{ \edtext{QUIA ACUTUM.}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} } quod aliam solutionem \edtext{subiungat.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | subiungit. \textit{P\textsuperscript{q}} | subiunget. \textit{G\textsuperscript{u}}}} +\pend + +\pstart +\textbf{4} \edtext{Nosce}{\Cfootnote[nosep]{\textit{ακπ} | Notandum \textit{mv}}} quod ‘ \edtext{armonia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | armoniam \textit{P\textsuperscript{u}}}} que \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | est in \textit{P\textsuperscript{y}}}} vna trium \edtext{partium ut tactum est musice}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}} | partium ut tactum musice \textit{E\textsuperscript{a}N\textsuperscript{u}} | partium musice ut tactum est \textit{π} | partium \textit{γmv}}}, proprie pertinet ad \edtext{comedos}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | comedias \textit{P\textsuperscript{z}} | comedras \textit{P\textsuperscript{p}}}} \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | uel \textit{V\textsuperscript{z}}}} \edtext{tragedos}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv}}} uel choros, et omnino ad eos \edtext{qui}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | que \textit{P\textsuperscript{u}P\textsuperscript{z}}}} precipue uoce cantant. Ex ea \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} \edtext{causatur}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | causatur talis \textit{βπE\textsuperscript{a}} | cantatur talis \textit{M\textsuperscript{a}}}} armonia que \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{uocis}{\Cfootnote[nosep]{\textit{γκmv} | uocum \textit{βπE\textsuperscript{a}}}} modulatio \edtext{ \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | a \textit{P\textsuperscript{z}}}} concordia plurium \edtext{sonorum}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}mv} | \surplus{plurium} sonorum \textit{P\textsuperscript{y}}}} \edtext{uel}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{coaptatio}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | coadapatatio \textit{V\textsuperscript{m}} | coactio \textit{P\textsuperscript{z}}}}. \edtext{Simphonia}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv}}} est \edtext{uocis}{\Cfootnote[nosep]{\textit{γκmv} | uocum \textit{βπ}}} modulatio}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} temperata ex graui et \edtext{acuto accordantibus}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | acuto concordantibus \textit{V\textsuperscript{z}} | acuto a cordantibus \textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}} sonis, \edtext{cuius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | suis \textit{P\textsuperscript{z}}}} quidem \edtext{contraria}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | contraria est \textit{π} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{dyaphonia}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{o}mv}}}. \edtext{Euphonia}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv}}} est suauitas \edtext{uocis}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | uocum \textit{βM\textsuperscript{a}V\textsuperscript{m}}}}, \edtext{hec}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | hoc \textit{V\textsuperscript{a}}}} autem melos \edtext{a melle et}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{a}} | amelo et \textit{P\textsuperscript{x}} | a melos a mellis \textit{V\textsuperscript{b}} | a melle \textit{V\textsuperscript{a}} | a mellis \textit{mv}}} \edtext{suauitate}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | suauitatis \textit{P\textsuperscript{z}}}} dicta. \edtext{Dyastema}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{x}} | Dyafema \textit{P\textsuperscript{z}} | Dyaphonia \textit{P\textsuperscript{p}}}} est \edtext{uocis}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}V\textsuperscript{z}mv} | uocum \textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{u}}}} spatium ex duobus uel pluribus sonis \edtext{coaptatum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | coaptant \textit{P\textsuperscript{p}P\textsuperscript{u}} | coadaptatum \textit{M\textsuperscript{a}V\textsuperscript{m}}}}. \edtext{Dyesis}{\Cfootnote[nosep]{\textit{βπM\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{m}mv}}} est \edtext{spatia}{\Cfootnote[nosep]{\textit{βγκmv} | spatium \textit{πE\textsuperscript{a}}}} \edtext{quedam}{\Cfootnote[nosep]{\textit{ακmv} | quoddam \textit{π}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{deducens}{\Cfootnote[nosep]{\textit{κV\textsuperscript{b}mv} | deductiones \textit{βπE\textsuperscript{a}V\textsuperscript{a}}}} \edtext{modulandi}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} et \edtext{vergendi}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | turgendi \textit{P\textsuperscript{z}}}} \edtext{de vno}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} in alterum \edtext{sonum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | solum \textit{G\textsuperscript{u}}}}.\edtext{}{\Afootnote[nosep]{Isidore of Seville, \textit{Etym.}, III .20 .1–6}}’ ‘ \edtext{Boecius autem}{\Cfootnote[nosep]{\textit{βγκπmv} | Bouus autem \textit{E\textsuperscript{a}}}} \edtext{dyesim dicit}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}M\textsuperscript{a}M\textsuperscript{b}V\textsuperscript{a}V\textsuperscript{m}mv} | dicit Dyesim \textit{π}}} \edtext{vnius fore}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}mv} | fore unius \textit{P\textsuperscript{y}} | minus fore \textit{πE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}} | fore \textit{V\textsuperscript{z}}}} \edtext{semitonii}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | semitonium \textit{M\textsuperscript{b}}}}.\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} II .28 (Friedlein p. 260, ll. 21–24)}}’ ‘Tonus \edtext{est}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | est autem \textit{C\textsuperscript{a}G\textsuperscript{u}} | autem \textit{V\textsuperscript{o}}}} \edtext{acuta uocis}{\Cfootnote[nosep]{\textit{αmv} | uocis acuta \textit{P\textsuperscript{x}V\textsuperscript{z}} | uox acuta \textit{M\textsuperscript{a}} | acuta \textit{V\textsuperscript{m}} | aucta acuta vocis \textit{V\textsuperscript{o}} | arta uocis \textit{G\textsuperscript{u}} | alta uocis \textit{P\textsuperscript{z}} | acuta arta uocis \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{enunciatio}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv}}}. \edtext{Αrsis}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | Resis \textit{mv}}} quidem uocis eleuatio, \edtext{tesis}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}mv} | enthesis \textit{P\textsuperscript{y}}}} \edtext{depressio}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}}.\edtext{}{\Afootnote[nosep]{Isidore of Seville, \textit{Etym.}, III .20 .7, 9}}’ Sic \edtext{igitur}{\Cfootnote[nosep]{\textit{αλπmv} | ergo \textit{P\textsuperscript{x}}}} ex \edtext{symphonia}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}}}} potest \edtext{haberi}{\Cfootnote[nosep]{\textit{ακπ} | habere \textit{mv}}} quod \edtext{antiphonum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}} | antiphonori \textit{P\textsuperscript{x}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{uel}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{antiphona}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | anthima \textit{G\textsuperscript{u}}}} sit quedam modulatio \edtext{uel}{\Cfootnote[nosep]{\textit{κ} | et \textit{απmv}}} intonatio \edtext{contra}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | circa \textit{M\textsuperscript{a}} | que \textit{P\textsuperscript{x}} | quam \textit{P\textsuperscript{z}}}} \edtext{simphoniam}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv}}}, ut \edtext{sonus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | sanus \textit{V\textsuperscript{o}}}} qui \edtext{post}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}mv} | potest \textit{P\textsuperscript{y}} | prius \textit{E\textsuperscript{a}}}} eam refrangitur auditum \edtext{demultiens}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}} | denuntians \textit{P\textsuperscript{z}} | de multotiens \textit{V\textsuperscript{z}}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 8m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Octauum problema}\label{edition-text book-19a part8}}{\lemma{Octauum problema} \Cfootnote[nosep]{\textit{γG\textsuperscript{u}mv} | «8m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{octauum problema.} Octauum. \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID GRAUIS}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID SONUS GRAUIS CORDE \textit{P\textsuperscript{q}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID GRAUIS ACUTE FORTIFICAT SONUM? \textsuperscript{2}AUT QUIA MAIUS HOC GRAUE? OBTUSO ENIM ASSIMULATUR, HOC UERO ACUTO ANGULO \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Octauum problema etcetera. \edtext{Quia}{\Cfootnote[nosep]{\textit{βγλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Quare \textit{E\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{x}P\textsuperscript{z}}}} \edtext{dixerat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | dixatur \textit{P\textsuperscript{u}} | distrahit \textit{P\textsuperscript{z}}}} \textit{grauem cordam \edtext{sonum fortificare}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fortificare sonum \textit{P\textsuperscript{p}}}} acute,} \edtext{causam siquidem querit huius}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{y}mv} | causa siquidem querit huius \textit{N\textsuperscript{u}} | querit causam huius \textit{π}}} dicens \textit{ \edtext{quare}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | quia \textit{β}}} grauis \edtext{corde}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | corda \textit{V\textsuperscript{a}mv} | cordas \textit{V\textsuperscript{b}}}} \edtext{sonus}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{uigorat}{\Cfootnote[nosep]{\textit{γκπmv} | uigilat \textit{β}}} eum \edtext{qui}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | quia \textit{V\textsuperscript{a}}}} acute?} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } Soluit \edtext{dicens causam esse}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | causam esse dicens \textit{G\textsuperscript{u}}}} \edtext{quoniam}{\Cfootnote[nosep]{\textit{βγκπmv} | quia \textit{E\textsuperscript{a}}}} \textit{illud quod est \edtext{graue}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{q}P\textsuperscript{u}}}} \edtext{maius}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | magis \textit{C\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}}}} \edtext{est}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}}}} et fortius. Quod ostenditur quoniam \textit{ \edtext{angulo}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | angulatio \textit{P\textsuperscript{y}}}} \edtext{simulatur}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | multiplicatur \textit{V\textsuperscript{a}} | si multiplicatio \textit{V\textsuperscript{b}} | si multiplicatur \textit{mv}}} \edtext{obtuso}{\Cfootnote[nosep]{\textit{ακ} | acuto \textit{π}}} trianguli, \edtext{qui}{\Cfootnote[nosep]{\textit{βγκπmv} | quod \textit{E\textsuperscript{a}}}} quidem maior \edtext{est et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | est est et \textit{P\textsuperscript{z}}}} fortior \edtext{etiam}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{uigore}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | minore \textit{M\textsuperscript{a}}}} acuto \edtext{acuto ut res \edtext{ostendunt}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | ostenduntur \textit{N\textsuperscript{u}} | ostendit \textit{P\textsuperscript{z}V\textsuperscript{a}}}} nature et artis, acutum uero \edtext{angulo}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | anguli \textit{V\textsuperscript{o}} | triangulo \textit{V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} proportionatur acuto}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}},} \edtext{ceu}{\Cfootnote[nosep]{\textit{βγκmv} | seu \textit{πE\textsuperscript{a}}}} minori et debiliori. Quod autem \edtext{maius}{\Cfootnote[nosep]{\textit{αλmv} | magis \textit{P\textsuperscript{x}} | minus \textit{P\textsuperscript{z}} | maius est \textit{π}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | est \textit{P\textsuperscript{z}}}} fortius uigorat \edtext{quod}{\Cfootnote[nosep]{\textit{βγπP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | quam \textit{M\textsuperscript{a}} | quia \textit{E\textsuperscript{a}}}} minus et debilius,} \edtext{huius}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}} | huiusmodi \textit{N\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv}}} quidem graue \edtext{acuti respectu}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | respectu acuti \textit{P\textsuperscript{z}}}}, quare ipsum uigorat, \edtext{ut .xii. etiam apparebit}{\Cfootnote[nosep]{\textit{βP\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | ut 12. apparebit \textit{E\textsuperscript{a}} | ut xii. at etiam apparebit \textit{V\textsuperscript{a}} | ut 13º etiam apparebit \textit{M\textsuperscript{a}} | \textit{om}. \textit{π}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 9m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Nonum problema}\label{edition-text book-19a part9}}{\lemma{Nonum problema} \Cfootnote[nosep]{\textit{γG\textsuperscript{u}mv} | «9m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{nonum problema.}Nonum. \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DELECTABILITER}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID DELECTABILIUS AUDIMUS \textit{P\textsuperscript{q}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID DELECTABILITER UNITATEM CANTUS AUDIMUS SI QUIS AD FISTULAM AUT LYRAM CANTAT ET AD CORDAS, ET EUNDEM CANTUM CANTANT UTROBIQUE? \textsuperscript{2}SI ENIM ADHUC MAGIS IDEM, POTIUS OPORTEBAT AD MULTOS FISTULATORES ET ADHUC DELECTABILITER ESSE. \textsuperscript{3}AUT QUIA ADIPISCENS MANIFESTUS INTENTIONEM MAGIS QUANDO AD FISTULAM AUT LYRAM? QUOD UERO AD MULTOS FISTULATORES AUT LYRAS MULTAS NON EST DELECTABILE PROPTER ID QUOD DESTRUIT MELODIAM \textit{G\textsuperscript{u}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Nonum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} \edtext{cum delectatione}{\Cfootnote[nosep]{\textit{ακmv} | delectabiliter \textit{π}}} audimus \edtext{cantum vnitum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | unitum \textit{V\textsuperscript{o}} | tantum munentum \textit{P\textsuperscript{z}}}} seu \edtext{in}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} vnum \edtext{coniectum}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | coniunctum \textit{απM\textsuperscript{a}V\textsuperscript{m}mv}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{αλπmv} | in \textit{P\textsuperscript{x}}}} si quis \edtext{cantat}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | cantet \textit{M\textsuperscript{a}}}} in fistula \edtext{uel}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{P\textsuperscript{p}} | uel in \textit{P\textsuperscript{u}}}} lyra et vniuersaliter in cordis \edtext{ceu}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}mv} | seu \textit{πE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}}}} \edtext{in psalterio canone}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}V\textsuperscript{b}mv} | in pulsatio canone \textit{P\textsuperscript{x}} | in psaltero causam \textit{V\textsuperscript{a}} | psalterio canone \textit{βπ}}} et \edtext{huius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | huiusmodi \textit{βG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}mv}}} instrumentis \edtext{ex cordis multis}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{b}mv} | sex multis cordis \textit{V\textsuperscript{a}}}} compositis, dummodo utrobique \edtext{cantet}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | causet \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | esset \textit{P\textsuperscript{z}}}} eundem \edtext{cantum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | cantet \textit{V\textsuperscript{a}}}}?} Quoniam si vnus cantus \edtext{seu}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ceu \textit{V\textsuperscript{z}}}} \edtext{dantia}{\Cfootnote[nosep]{\textit{αP\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | concordantia \textit{P\textsuperscript{p}}}} \edtext{fieret in}{\Cfootnote[nosep]{\textit{V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}} | fieret \textit{βE\textsuperscript{a}V\textsuperscript{a}mv} | fieret in vno \textit{πP\textsuperscript{x}} | in \textit{M\textsuperscript{a}}}} \edtext{instrumento}{\Cfootnote[nosep]{\textit{βγκπE\textsuperscript{a}V\textsuperscript{b}mv} | instrumentum \textit{V\textsuperscript{a}}}} et \edtext{alius}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | alius in \textit{λ}}} uoce \edtext{cantantis}{\Cfootnote[nosep]{\textit{βπM\textsuperscript{a}} | causantis \textit{P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}} | canentes \textit{V\textsuperscript{b}} | canentis \textit{E\textsuperscript{a}V\textsuperscript{z}mv}}}, \edtext{in}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | etiam \textit{γ} | in etiam \textit{mv}}} \edtext{illo}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | illum \textit{G\textsuperscript{u}P\textsuperscript{q}}}} non \edtext{consurgeret}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | consurget \textit{M\textsuperscript{a}P\textsuperscript{y}}}} \edtext{propter dissonantiam delectatio}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | delectation propter dissonantia \textit{P\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{SI ADHUC.}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | SI ENIM ADHUC. \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}}}} } \edtext{Quasi}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | quare \textit{P\textsuperscript{z}}}} arguit in \edtext{contrarium}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | contraria \textit{V\textsuperscript{a}}}} dicens quod \textit{ \edtext{si unius}{\Cfootnote[nosep]{\textit{κ} | si huius \textit{P\textsuperscript{y}V\textsuperscript{a}} | si huiusmodi \textit{V\textsuperscript{b}N\textsuperscript{u}mv} | si talis \textit{π} | lilicius \textit{E\textsuperscript{a}}}} \edtext{delectatio}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{contingat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | contingit \textit{P\textsuperscript{z}}}} propter \edtext{vnitatem}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | raritates id est unitatem \textit{P\textsuperscript{y}}}} cantus et \edtext{ydemptitatem}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}m}}}, tunc \edtext{oportebit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv}}} magis delectari cum quis cantabit \edtext{cum multis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{fistulantibus uel lyrantibus}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | lyrantibus uel fistulantibus \textit{P\textsuperscript{x}} | fistulantibus et lyrantibus \textit{V\textsuperscript{a}} | fistulationibus uel lyris \textit{P\textsuperscript{z}}}},} cum magis \edtext{videantur}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}P\textsuperscript{y}mv} | uideatur \textit{N\textsuperscript{u}P\textsuperscript{x}}}} super vnum \edtext{opus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | corpus \textit{G\textsuperscript{u}}}} \edtext{unitari}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{b}mv} | imitari \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}} | mutari \textit{C\textsuperscript{a}P\textsuperscript{z}} | mundari \textit{E\textsuperscript{a}}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | vel \textit{mv}}} plures trahentes \edtext{nauem}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}} | nauim \textit{V\textsuperscript{b}mv}}} \edtext{imitantur}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{o}} | mutantur \textit{P\textsuperscript{z}V\textsuperscript{m}} | vnitantur \textit{M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}mv}}}, ut melius \edtext{trahant.}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | trahatur. \textit{V\textsuperscript{m}}}} +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{q}mv}}} } \edtext{Soluit dicens}{\Cfootnote[nosep]{\textit{βγκπmv} | Dicit \textit{E\textsuperscript{a}}}} causam esse \edtext{quia}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}P\textsuperscript{x}mv} | quoniam \textit{λP\textsuperscript{p}P\textsuperscript{u}}}} \textit{cum \edtext{aliquis cantat}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}mv} | aliquis cantet \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | aliquis cante \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}}}} \edtext{singulariter}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}} | signanter \textit{γmv} | singulariter cantat \textit{π}}} intentionem et maneriem cantus magis \edtext{vnitatur}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | vnitur \textit{G\textsuperscript{u}} | innitatur uel vnitatur \textit{V\textsuperscript{a}} | vnitatem \textit{P\textsuperscript{x}mv}}} \edtext{uox}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{cum sono}{\Cfootnote[nosep]{\textit{αλπmv}}} \edtext{instrumenti}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | instrumentis \textit{V\textsuperscript{a}}}} \edtext{quam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | quod \textit{N\textsuperscript{u}}}} \edtext{quando}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | cum \textit{πE\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{y}}}} cantaret in diuersis instrumentis}, \edtext{etiam}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | et \textit{P\textsuperscript{y}V\textsuperscript{z}}}} eodem cantu \edtext{utrobique existente. \edtext{Et hoc}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}mv} | Et hoc \surplus{et hoc} \textit{V\textsuperscript{a}} | Et \textit{E\textsuperscript{a}}}} quia in cantu}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{o}}}} \edtext{quedam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{y}mv} | quidem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | quid \textit{V\textsuperscript{c}V\textsuperscript{o}} | qui \textit{P\textsuperscript{z}}}} reseruantur proportiones ut dicetur \edtext{commensurate}{\Cfootnote[nosep]{\textit{αP\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | commemeratione \textit{P\textsuperscript{p}}}}. Quibus \edtext{obseruatis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | conseruatis \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{c}}}} \edtext{iocunda}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} \edtext{consurgit}{\Cfootnote[nosep]{\textit{ακmv} | consistit \textit{G\textsuperscript{u}V\textsuperscript{o}} | existit \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} \edtext{armonia}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | euphonia et armonia \textit{P\textsuperscript{y}}}}, que \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | proui \textit{P\textsuperscript{z}}}} \edtext{corrumpitur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | corrumpuntur \textit{V\textsuperscript{m}}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{indelectabilis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | indelectationes \textit{V\textsuperscript{a}}}} redditur cum \edtext{cantans}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv} | cantares \textit{V\textsuperscript{o}} | cantatis \textit{E\textsuperscript{a}}}} ad multa \edtext{cantauerit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cantauit \textit{P\textsuperscript{u}P\textsuperscript{z}}}} instrumenta. +\pend + +\pstart +\textbf{4} Quod autem \edtext{inductum}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}} | inductum est \textit{πM\textsuperscript{a}V\textsuperscript{m}mv} | aductum est \textit{V\textsuperscript{z}}}} \edtext{in}{\Cfootnote[nosep]{\textit{ακmv} | ad \textit{π}}} contrarium prius non valet quia licet \edtext{multi possint}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | possint multi \textit{V\textsuperscript{a}}}} \edtext{idem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | id \textit{P\textsuperscript{z}} | ratione \textit{P\textsuperscript{y}}}} cantare, non tamen eodem modo. \edtext{Non solum enim requiritur}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}} | Solum enim requiritur \textit{V\textsuperscript{z}} | Non enim solum requiritur \textit{E\textsuperscript{a}mv} | Non solum requiritur \textit{V\textsuperscript{a}} | Et non requitur solum \textit{π}}} \edtext{ydemptitas}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}m}}} \edtext{ex parte}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} illius quod cantatur et cuiuslibet cantantis \edtext{ad}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | ad id \textit{V\textsuperscript{b}}}} se ipsum \edtext{ymo}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}mv}}} \edtext{uniuscuiusque}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}P\textsuperscript{y}} | uniuscuiusque et \textit{γλE\textsuperscript{a}mv}}} ad \edtext{alium}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | aliud \textit{V\textsuperscript{a}}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} \edtext{ad}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} omnes, \edtext{ita quod}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | itaque \textit{V\textsuperscript{b}}}} ex omnibus \edtext{resultent}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | resultant \textit{P\textsuperscript{y}}}} proportiones debite in cantu. Quod autem \edtext{subditur}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | subdit \textit{V\textsuperscript{a}} | subiecit \textit{mv} | subicitur \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | subiecti \textit{E\textsuperscript{a}P\textsuperscript{x}} | subieci \textit{λV\textsuperscript{b}} | obicitur \textit{G\textsuperscript{u}P\textsuperscript{q}}}} de \edtext{nauis tractu}{\Cfootnote[nosep]{\textit{λ} | tractu nauis \textit{αmv} | tractu nauis uel ligni \textit{π}}} \edtext{non huic}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | huic non \textit{G\textsuperscript{u}} | non habet huic \textit{V\textsuperscript{a}} | non hoc \textit{V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{similatur}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | simulari \textit{V\textsuperscript{a}} | assimilatur \textit{π}}} dicto, quoniam \edtext{plurimi}{\Cfootnote[nosep]{\textit{αλπmv} | plurium \textit{P\textsuperscript{x}}}} \edtext{possunt simul idem}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | possunt idem simul \textit{π} | possint idem simul \textit{E\textsuperscript{a}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{P\textsuperscript{p}P\textsuperscript{q}}}} nauem eodem modo et \edtext{tempore}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv}}} trahere ut audientes \edtext{uocem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vocem vocem \textit{P\textsuperscript{p}}}} \edtext{rectoris}{\Cfootnote[nosep]{\textit{αλπmv} | retoris \textit{P\textsuperscript{x}}}} nauis. \edtext{Non}{\Cfootnote[nosep]{\textit{αλπmv} | Ut \textit{P\textsuperscript{x}V\textsuperscript{m}}}} autem talis \edtext{unitas}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ueritas \textit{P\textsuperscript{z}}}} potest in cantu plurium \edtext{obseruari}{\Cfootnote[nosep]{\textit{ακmv} | reseruari \textit{π}}} \edtext{armonico}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | armonica \textit{E\textsuperscript{a}} | armonia \textit{P\textsuperscript{z}}}}, cum \edtext{eum}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | enim \textit{C\textsuperscript{a}P\textsuperscript{a}V\textsuperscript{c}V\textsuperscript{o}} | quo \textit{P\textsuperscript{z}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}}}} \edtext{ex}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} pluribus \edtext{ \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} contrariis \edtext{oporteat}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | oportet \textit{P\textsuperscript{p}}}} \edtext{constituere}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}mv} | const\expan{r}uere \textit{(orig. \textup{ⳋst\textsuperscript{u}ere})} \textit{M\textsuperscript{a}V\textsuperscript{m}} | construere \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}P\textsuperscript{y}V\textsuperscript{z}}}} in \edtext{unum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}mv} | unam \textit{C\textsuperscript{a}P\textsuperscript{a}V\textsuperscript{o}} | unum tonum alias \textit{V\textsuperscript{a}} | unitatem \textit{P\textsuperscript{y}}}}. \edtext{Tandem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{redditur}{\Cfootnote[nosep]{\textit{V\textsuperscript{a}V\textsuperscript{z}mv} | reditur \textit{P\textsuperscript{x}} | reductis \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | redditis \textit{E\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{m}} | \textit{om}. \textit{P\textsuperscript{y}}}} quod \edtext{fit}{\Cfootnote[nosep]{\textit{λG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | sit \textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}}}} impossibile pluribus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{entibus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | existentibus \textit{P\textsuperscript{z}}}} \edtext{uocibus et}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uocibus in \textit{M\textsuperscript{a}V\textsuperscript{m}} | uocibus \textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}}}} instrumentis. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{z}V\textsuperscript{z}} | sequitur 10m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Decimum problema}\label{edition-text book-19a part10}}{\lemma{Decimum problema} \Cfootnote[nosep]{\textit{γG\textsuperscript{u}mv} | «10m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{decimum problema.} Decimum. \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID NON DELECTABILIS}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID DELECTABILIUS SIT \textit{V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID SI DELECTABILIS HOMINIS UOX QUE SINE SERMONE CANTANTIS NON DELECTABILE EST UT \label{uernare}\textit{UERNANTIUM}, SED FISTULA AUT LYRA? \textsuperscript{2}AUT NON ILLIC, SI NON IMMUTATUR, SIMILITER DELECTABILE? \textsuperscript{3}AT UERO SED PROPTER OPUS IPSUM. UOX ENIM DELECTABILIS QUE EST HOMINIS, PERCUSSIUA AUTEM MAGIS INSTRUMENTA ORIS. PROPTER QUOD DELECTABILIUS AUDIRE QUAM UERNARE \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}. PROPTER QUID SONANS ACUTIOR QUIA MINUS IMBECILLIOR EST FACTA.} Decimum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} \edtext{si}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sit \textit{G\textsuperscript{u}}}} uox \edtext{humana}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | humani \textit{V\textsuperscript{a}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} delectabilis \edtext{auditu}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}mv} | auditui \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} }, unde ‘ \edtext{\hyperref[Mu]{museus}}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}mv} | muscis \textit{E\textsuperscript{a}} | musicus \textit{γ} | dicitur \textit{π}}} \edtext{ \textit{ \edtext{politicorum}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}mv}}} } 8°}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | .8uo. \textit{politicorum} \textit{π} | \textit{policitorum} scilicet \textit{P\textsuperscript{x}} | \textit{politicorum} \textit{V\textsuperscript{a}}}} \edtext{delectabilissimum}{\Cfootnote[nosep]{\textit{αmv} | delectabili fine \textit{κ} | quod delectabilissimum \textit{π}}} est hominibus cantare,\edtext{}{\Afootnote[nosep]{Arist. \textit{Pol.} VIII , 1339b , l. 22}}’ \textit{cum \edtext{quis}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | qui \textit{V\textsuperscript{a}} | aliquis \textit{πE\textsuperscript{a}}}} cantat \edtext{etiam}{\Cfootnote[nosep]{\textit{αλmv} | et \textit{P\textsuperscript{x}} | \textit{om}. \textit{π}}} \edtext{non proferendo sermonem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | sermonem non proferendo \textit{V\textsuperscript{a}}}} \edtext{omnino}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} } aut \edtext{insignificatium}{\Cfootnote[nosep]{\textit{ακvm} | insignium \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | insignita \textit{G\textsuperscript{u}} | insignibus \textit{P\textsuperscript{z}}}}, \edtext{cur non est delectabilis}{\Cfootnote[nosep]{\textit{κ} | cur non delectabilis est \textit{α} | non delectabilis est \textit{π} | cur enim est delectabilis \textit{mv}}} \edtext{uox alicuius uernantium}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}mv} | uox uernantium \textit{P\textsuperscript{y}} | Videtur tamen \textit{π}}}, \edtext{cum sit}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cum non sit \textit{G\textsuperscript{u}} | crescit \textit{P\textsuperscript{x}}}} \edtext{hominis uox}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uox hominis \textit{G\textsuperscript{u}}}}, \edtext{et}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | eti \textit{P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | etiam \textit{γmv} | \textit{om}. \textit{P\textsuperscript{p}}}} lyre \edtext{et}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | etiam \textit{E\textsuperscript{a}}}} fistule sonus est delectabilis? \edtext{Qui}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{z}mv} | Que \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}}}} minorem \edtext{communicationem}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | communitatem \textit{M\textsuperscript{a}}}} \edtext{uidetur cum homine}{\Cfootnote[nosep]{\textit{ακmv} | cum homine videtur \textit{π}}} habere quam \edtext{uox ipsa}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | ipsa uox \textit{P\textsuperscript{y}}}} humana. In hiis \edtext{itaque}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} uerbis \edtext{\hyperref[Ar]{aristoteles}}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | eadem \textit{P\textsuperscript{z}} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{succincte tetigit}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}v} | tetigit succincte \textit{P\textsuperscript{x}} | succincte tangit \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{motiuum}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv}}} quesiti et confirmationem \edtext{eius}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | quesiti \textit{M\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{y}}}}. +\pend + +\pstart +\textbf{2} \edtext{Notandum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | Nota \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} quod \textit{uernare uocisuocumuocem} est \textit{expressionem facere in qua \edtext{non}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{manifestatur}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}V\textsuperscript{a}mv} | manifestetur \textit{λE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}}}} aliqua \edtext{sensibilis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | subtilitas \textit{π}}} diuersitas \edtext{extensione}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | expressione \textit{G\textsuperscript{u}P\textsuperscript{q}}}} et \edtext{depressione vocis}{\Cfootnote[nosep]{\textit{ακπ} | diuersione \textit{mv}}}, ita quod eius \edtext{remaneat}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | remanet \textit{P\textsuperscript{y}} | maneat \textit{V\textsuperscript{z}}}} equalitas,} \edtext{ad modum}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | aut modo \textit{E\textsuperscript{a}}}} quo \edtext{uer}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | ut \textit{V\textsuperscript{b}} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{equale ponitur a medicis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | ponitur equale a medicis \textit{π} | ponitur a medicis equale \textit{P\textsuperscript{y}}}}. Est enim quasi \edtext{illud quod dicitur}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | illud \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}} \edtext{bordonizare}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}mv} | bordonizare et \textit{P\textsuperscript{z}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} per se \edtext{minime uidetur}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | minime \textit{E\textsuperscript{a}} | minimam \textit{π}}} delectationem inducere. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{q}} | AUT HEC. \textit{P\textsuperscript{p}}}} } \edtext{Soluit}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | 8o \textit{E\textsuperscript{a}}}} et \edtext{prius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | primo \textit{G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}}}} respondet ad confirmationem, dicens quod \textit{illic scilicet in \edtext{fistula et lyra}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}mv} | fistulis et lyra \textit{π}}} non est \edtext{delectari}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | delectatia \textit{V\textsuperscript{b}}}}, \edtext{quoniam similiter}{\Cfootnote[nosep]{\textit{ακπ} | similiter \textit{mv}}} \edtext{in eis ita se habet ut}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | in eis ita se habet sicut \textit{M\textsuperscript{a}} | in eis similiter se habet ut \textit{E\textsuperscript{a}} | in eis se habet ut \textit{V\textsuperscript{z}} | in eis se habet \textit{P\textsuperscript{x}} | se habet ut \textit{V\textsuperscript{a}} | etiam se habet eis ut \textit{π}}} \edtext{in}{\Cfootnote[nosep]{\textit{γλP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}P\textsuperscript{x}}}} \edtext{uernante}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | uernanti \textit{V\textsuperscript{a}} | vernantem \textit{G\textsuperscript{u}P\textsuperscript{q}} | vernantis \textit{P\textsuperscript{z}} | t\expan{erm}i\expan{n}ate \textit{(orig. \textup{tiate})} \textit{P\textsuperscript{y}}}} }, \edtext{quia}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}mv} | quoniam \textit{λπ}}} si non \edtext{fiat}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fiet \textit{P\textsuperscript{z}} | fieret \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{immutatio}{\Cfootnote[nosep]{\textit{αλπmv} | mutatio \textit{P\textsuperscript{x}}}} soni secundum \edtext{ascensionem}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv} | assentionem \textit{E\textsuperscript{a}} | immutationem \textit{G\textsuperscript{u}P\textsuperscript{q}}}} et \edtext{depressionem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | descensionem \textit{V\textsuperscript{a}}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | et \textit{M\textsuperscript{a}}}} \edtext{inde}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}mv} | inde de \textit{V\textsuperscript{b}} | unde \textit{V\textsuperscript{a}} | m\expan{un}d\expan{um} \textit{(orig. \textup{mdʼ})} \textit{E\textsuperscript{a}}}} \edtext{consurgant}{\Cfootnote[nosep]{\textit{απmv} | surgant \textit{M\textsuperscript{a}} | desurgant \textit{V\textsuperscript{m}V\textsuperscript{z}} | desurgat \textit{P\textsuperscript{x}}}} debite proportiones armonice, non \edtext{contingit}{\Cfootnote[nosep]{\textit{κP\textsuperscript{q}P\textsuperscript{z}V\textsuperscript{b}mv} | conuenit \textit{G\textsuperscript{u}P\textsuperscript{p}}}} delectari ex \edtext{huius}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{z}mv} | huiusmodi \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}}}} instrumenti sono. \edtext{Sic}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Sicut \textit{λ}}} \edtext{igitur}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ergo \textit{G\textsuperscript{u}P\textsuperscript{x}}}} uernare non est \edtext{delectabile}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | delectatio \textit{mv}}}, eo quod \edtext{proportiones}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | non proportiones \textit{M\textsuperscript{b}}}} \edtext{non cadunt in ipso melite}{\Cfootnote[nosep]{\textit{γmv} | non cadunt mellite \textit{E\textsuperscript{a}} | in ipso mellite \textit{P\textsuperscript{x}V\textsuperscript{m}} | in ipso melite \textit{V\textsuperscript{z}} | non cadunt in ipso melodice \textit{P\textsuperscript{y}} | in ipso non sunt mellite \textit{M\textsuperscript{a}} | non cadunt multipliciter \textit{π}}} \edtext{auditum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | audientum auditum \textit{V\textsuperscript{b}}}} \edtext{demulcentes}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{z}mv} | demulceantes \textit{P\textsuperscript{x}V\textsuperscript{m}}}}. +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT UERO}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | AT UERO \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}} | AUT QUIA \textit{P\textsuperscript{z}}}}.} Respondet \edtext{motiuo}{\Cfootnote[nosep]{\textit{γλπP\textsuperscript{y}mv} | moto\expan{r}is \textit{(orig. \textup{moto\textsuperscript{is}})} \textit{E\textsuperscript{a}} | m\expan{o}t\expan{iu}o \textit{(orig. \textup{mto})} \textit{V\textsuperscript{m}} | mot\expan{iu}o \textit{(orig. \textup{moto})} \textit{V\textsuperscript{z}} | in \textit{P\textsuperscript{x}}}} \edtext{ipsius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | ipsi \textit{P\textsuperscript{p}} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{causam dando}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | dando causam \textit{π} | dando causi \textit{E\textsuperscript{a}} | di\expan{cen}do \textit{(orig. \textup{di.\textsuperscript{do}})} \textit{V\textsuperscript{a}}}} quare uox \edtext{humana}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | humani \textit{V\textsuperscript{a}}}} cantantis sit delectabilis. \textit{Hoc enim est propter operationem ex qua consequitur. \edtext{In}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} ipsa namque \edtext{magis}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} percutiuntur instrumenta \edtext{oris}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv}}} ordinata ad \edtext{formationem}{\Cfootnote[nosep]{\textit{ακπ} | formationes \textit{mv}}} \edtext{cantus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{delectabilis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | debilis \textit{V\textsuperscript{a}}}} \edtext{quam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quod \textit{P\textsuperscript{z}}}} \edtext{in}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | ex \textit{π} | \textit{om}. \textit{P\textsuperscript{y}}}} uernare. Ex \edtext{huius}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | huiusmodi \textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}}}} \edtext{namque}{\Cfootnote[nosep]{\textit{αλV\textsuperscript{z}} | nam \textit{P\textsuperscript{x}} | enim \textit{mv} | autem \textit{π}}} \edtext{maiori percussione}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{z}mv} | percussione maiori \textit{V\textsuperscript{m}} | maiore percussione \textit{P\textsuperscript{z}V\textsuperscript{o}}}} instrumentorum \edtext{oris que}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | horisque \textit{P\textsuperscript{y}}}} fit in cantu, nunc in \edtext{uocem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uoce \textit{P\textsuperscript{z}}}} \edtext{extollendo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | excellendo \textit{P\textsuperscript{z}}}} \edtext{nunc}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | tunc \textit{αV\textsuperscript{m}mv}}} in deprimendo,} modo uero medie conseruando \edtext{resultat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | resultet \textit{P\textsuperscript{p}}}} \edtext{cantus}{\Cfootnote[nosep]{\textit{ακmv} | modus \textit{π}}} armonicus suauis ualde. Et ideo \edtext{inquit}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}} | dicit \textit{mv} | in quid \textit{E\textsuperscript{a}}}} \textit{delectabilius \edtext{fore}{\Cfootnote[nosep]{\textit{ακmv} | esse \textit{π}}} uocem \edtext{ \edtext{hominis cantantis}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | cantantis hominis \textit{P\textsuperscript{p}} | etiam hominis cantantis \textit{M\textsuperscript{a}}}} audire, cum \edtext{hic huiusmodi}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}} | hic huius \textit{M\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{z}} | h\expan{i}c huius \textit{(orig. \textup{h\textsuperscript{c} hui\textsubscript{9}})} \textit{E\textsuperscript{a}} | hoc huius \textit{P\textsuperscript{u}P\textsuperscript{z}mv}}} \edtext{contingat}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | contingit \textit{V\textsuperscript{a}}}} quam vocem}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{vernantis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | mutatis \textit{P\textsuperscript{z}}}}, \edtext{ubi}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{minime}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | maxime minime \textit{P\textsuperscript{p}}}}.} Vox etiam \edtext{hominis delectabilis}{\Cfootnote[nosep]{\textit{αλπmv} | delectabilis hominis \textit{P\textsuperscript{x}} | delectabilis \textit{V\textsuperscript{z}}}} quia consueta et \edtext{quoniam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quia \textit{G\textsuperscript{u}}}} \edtext{potest}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | possunt \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{mutari}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | imitari \textit{P\textsuperscript{p}} | immitari \textit{P\textsuperscript{z}}}} \edtext{componi et contraponi}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | et contraponi \textit{P\textsuperscript{p}P\textsuperscript{u}} | et componi \textit{G\textsuperscript{u}} | et potest contraponi \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{facillime}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 11. problema 19. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Undecimum problema}\label{edition-text book-19a part11}}{\lemma{Undecimum problema} \Cfootnote[nosep]{\textit{γmv} | «11m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | Undecimum. \surplus{Undecimum problema} \textit{P\textsuperscript{y}} | \textit{om}. \textit{G\textsuperscript{u}M\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID SONANS}{\Cfootnote[nosep]{\textit{P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID SONANS ACUTIOR? \textsuperscript{2}AUT QUIA MINUS IMBECILLIOR FACTA EST \textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Undecimum problema etcetera.Propter quid sonans etcetera \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} aliquis sonans \edtext{sonitu}{\Cfootnote[nosep]{\textit{αλπmv} | sonitum \textit{P\textsuperscript{x}}}} uel uoce acutior redditur et per consequens \edtext{alius}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}mv} | alii \textit{V\textsuperscript{b}} | autem \textit{P\textsuperscript{y}}}} grauior?} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | QUIA. \textit{M\textsuperscript{a}}}} } Soluit dicens causam esse quia \edtext{hic}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}} | sicut \textit{P\textsuperscript{y}} | \textit{om}. \textit{γmv}}} sonans est \edtext{minus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | unius \textit{P\textsuperscript{z}}}} sonans \edtext{quam}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} illud \edtext{quod}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quid \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}}}} grauiter sonat. \textit{Quod autem \edtext{sit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fit \textit{G\textsuperscript{u}}}} minus ostenditur \edtext{quia}{\Cfootnote[nosep]{\textit{αλπmv} | quod \textit{P\textsuperscript{x}}}} \edtext{fit}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | sit \textit{E\textsuperscript{a}}}} \edtext{a virtute}{\Cfootnote[nosep]{\textit{αλπmv} | acute \textit{P\textsuperscript{x}}}} \edtext{que}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}mv} | quia \textit{P\textsuperscript{x}P\textsuperscript{y}}}} facta est \edtext{imbecillior}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}}}}.} Grauiter autem sonans a virtute \edtext{causatur fortiori}{\Cfootnote[nosep]{\textit{ακmv} | fortiori causatur \textit{π}}}, propter \edtext{quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quid \textit{P\textsuperscript{z}}}} \edtext{dictum}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}} | dictum est \textit{γλπE\textsuperscript{a}mv}}} ‘ \edtext{.xia.}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} quod \edtext{pueri femine}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | femine pueri \textit{P\textsuperscript{y}}}} \edtext{eunuchi}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | et eunuchi \textit{P\textsuperscript{z}} | eunuci et \textit{γmv}}} \edtext{infirmi}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} habent uoces acutas,\edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XI .16 , 900b , ll. 15–17}}’ oppositi \edtext{autem}{\Cfootnote[nosep]{\textit{ακmv} | vero \textit{π}}} graues \edtext{propter}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | per \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}}}} oppositum. \edtext{}{\Cfootnote{etcetera \textit{V\textsuperscript{b}V\textsuperscript{z}} | etcetera etcetera \textit{P\textsuperscript{z}} | sequitur 12m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Duodecimum problema}\label{edition-text book-19a part12}}{\lemma{Duodecimum + problema} \Cfootnote[nosep]{\textit{γG\textsuperscript{u}mv} | «12m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}} | \surplus{duodecimum problema}Duodecimum. \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID CORDARUM}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID CORDARUM GRAUIOR SEMPER SONUM ACCIPIT? SI ENIM OPORTET DIMITTERE QUE EST CIRCA MEDIAM PARAMESEM CUM ALIA MEDIA, FIT MEDIUM NIHILOMINUS. SI AUTEM MEDIA, UTRAQUE ALTA NON FUERIT. \textsuperscript{2}AUT QUIA GRAUE MAGNUM EST, QUARE FORTE? ET INEST IN MAGNO PARUUM, ET ASSUMPTIONE DUE NITE IN YPATE FIUNT \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Duodecimum problema. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Querit quare \textit{λ} | que \textit{P\textsuperscript{p}}}} de cordis \edtext{illa}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} que grauioris \edtext{extat}{\Cfootnote[nosep]{\textit{ακ} | est \textit{πmv}}} \edtext{toni}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | soni \textit{G\textsuperscript{u}P\textsuperscript{q}}}} semper accipit \edtext{sonum}{\Cfootnote[nosep]{\textit{αλmv} | tonum \textit{πP\textsuperscript{x}}}} } et representat \edtext{pre aliis ipsum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ipsum pre aliis \textit{V\textsuperscript{z}}}} ut \edtext{subiectum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sonum \textit{P\textsuperscript{p}} | so\expan{lu}m \textit{(orig. \textup{so\textsuperscript{m}})} \textit{P\textsuperscript{u}}}} \edtext{proprietatem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | proprietate \textit{V\textsuperscript{b}}}}, \edtext{dum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cum \textit{G\textsuperscript{u}P\textsuperscript{q}}}} tamen equaliter fiat percussio \edtext{et}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{ad hoc}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | adhuc \textit{πP\textsuperscript{y}V\textsuperscript{z}}}}, \textit{si oportet propter aliquam causam \edtext{ut}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv} | aut \textit{V\textsuperscript{z}} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{defectum ipsius}{\Cfootnote[nosep]{\textit{ακE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ipsius defectum \textit{P\textsuperscript{p}}}} \edtext{aut aliter}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}mv} | aliter \textit{E\textsuperscript{a}} | aut alteri \textit{M\textsuperscript{a}} | aliquando \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{p}}}} dimittere paramese que est iuxta mediam,} scilicet \edtext{iuxta}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | iusta \textit{V\textsuperscript{b}}}} mese \edtext{siue mediam uere}{\Cfootnote[nosep]{\textit{αmv} | siue mediam ipso \textit{P\textsuperscript{x}} | siue mediam ipse \textit{V\textsuperscript{m}} | siue mediam ipsa \textit{M\textsuperscript{a}V\textsuperscript{z}} | \textsuperscript{hec} \textit{E\textsuperscript{a}} | hec \textit{π}}}. \edtext{Namque}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Namque linea \textit{G\textsuperscript{u}}}} \edtext{septem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | id est \textit{V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{z}}}} cordarum \edtext{ut visum est media}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | ut visum media est \textit{M\textsuperscript{a}} | media ut uisum est \textit{V\textsuperscript{z}} | ut visum est \textit{mv}}} \textit{ \edtext{ \edtext{cum}{\Cfootnote[nosep]{\textit{ακ} | \textit{om}. \textit{mv}}} \edtext{alia}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}mv} | alio \textit{V\textsuperscript{a}} | aliqua \textit{V\textsuperscript{m}} | septima \textit{V\textsuperscript{b}}}} quodammodo \edtext{media existente}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | existente media \textit{P\textsuperscript{y}} | existente \textit{V\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{ακmv} | quodammodo cum aliquo existente \textit{π}}} } ut lychanos, ita quod ea \edtext{sonum}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}mv} | sonus \textit{M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}}}} \edtext{non}{\Cfootnote[nosep]{\textit{αλπ} | nisi \textit{P\textsuperscript{x}mv}}} \edtext{constituatur in}{\Cfootnote[nosep]{\textit{ακ} | constituat in \textit{πmv}}} armonia. \edtext{Nihilominus ex}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}} | Nihilominus in \textit{G\textsuperscript{u}P\textsuperscript{q}} | Nicomos ex \textit{V\textsuperscript{b}} | Nichilominus \textit{C\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | Lichanos ex \textit{mv}}} extremis \edtext{puta}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{ypate nete parypate}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | ypate parypate nete \textit{G\textsuperscript{u}} | ypatem nete parypatem \textit{M\textsuperscript{a}} | ypanete parypate \textit{P\textsuperscript{z}} | ypate \textit{P\textsuperscript{x}}}} \edtext{etiam et}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | et etiam \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | et \textit{G\textsuperscript{u}} | etiam \textit{P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{a}}}} \edtext{paranete}{\Cfootnote[nosep]{\textit{αλπmv}}}, \edtext{ \edtext{sicut}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | sic \textit{E\textsuperscript{a}}}} ex \edtext{illis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | hiis \textit{V\textsuperscript{b}}}} tribus \edtext{mediis}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | medicis \textit{V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} resultat quoddam medium \edtext{constitutiuum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | constitiuus \textit{P\textsuperscript{z}}}} armonie, in quo grauior cordarum sonum \edtext{preaccipit}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | accipit pro \textit{V\textsuperscript{a}}}} \edtext{aliis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{acutis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | totis. Deinde \textit{V\textsuperscript{a}}}}. \edtext{Communis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Cum minimis \textit{P\textsuperscript{z}}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | quidam \textit{P\textsuperscript{p}} | que \textit{P\textsuperscript{z}}}} \edtext{littera}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | habetur \textit{P\textsuperscript{z}}}} circa \edtext{mediam partem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}} | mediam partem habet \textit{πP\textsuperscript{y}} | mediam \textit{mv}}} \edtext{hoc tamen}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}V\textsuperscript{a}mv} | habet causam \textit{P\textsuperscript{z}} | tamen \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | \textit{om}. \textit{V\textsuperscript{b}}}} licet possit \edtext{tollerari series}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | series tollerari \textit{V\textsuperscript{b}}}} tamen iam exposita continens paramese \edtext{ \edtext{planior et sauior}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}} | sauior et planior \textit{P\textsuperscript{y}V\textsuperscript{a}} | planior suauior \textit{P\textsuperscript{z}} | planior et senior \textit{P\textsuperscript{x}V\textsuperscript{m}} | planior et sanior \textit{V\textsuperscript{z}} | planior est et uerior \textit{M\textsuperscript{a}}}}.}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} \textit{ \edtext{ \edtext{Sed si}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | Sed \textit{E\textsuperscript{a}} | Et si \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}}}} \edtext{utraque media}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | utreque medie \textit{V\textsuperscript{a}} | utraque medio \textit{G\textsuperscript{u}}}} \edtext{coniungantur}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{o}mv} | coniungatur \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}}}} ad inuicem \edtext{utpote}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | utputa \textit{P\textsuperscript{y}}}} dicatur \edtext{intermediarum}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | intermediorum \textit{P\textsuperscript{x}}}}, \edtext{sicut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | ut \textit{mv}}} \edtext{sunt}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | est \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} lychanos mese paramese}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} siue \edtext{trite}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | recte \textit{P\textsuperscript{z}}}}, non \edtext{constituitur}{\Cfootnote[nosep]{\textit{αλπmv} | constituit \textit{P\textsuperscript{x}}}} sonus \edtext{eleuatus}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}}, ita ut inde resultet grauis,} \edtext{tanquam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv}}} \edtext{corde}{\Cfootnote[nosep]{\textit{λπP\textsuperscript{y}} | cordis \textit{E\textsuperscript{a}V\textsuperscript{b}mv} | corda \textit{V\textsuperscript{a}}}} grauioris \edtext{reddentis}{\Cfootnote[nosep]{\textit{αλπmv} | reddente \textit{P\textsuperscript{x}}}} sonum grauiorem, \edtext{cum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | ut \textit{V\textsuperscript{b}}}} sonus \edtext{harum}{\Cfootnote[nosep]{\textit{ακmv} | earum \textit{π}}} \edtext{existat}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | existet \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | extat \textit{V\textsuperscript{a}V\textsuperscript{z}}}} \edtext{in medio}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | intermedius \textit{P\textsuperscript{y}}}} inter \edtext{graue}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{o}mv} | grauem \textit{λP\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}}}} et \edtext{acutum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | acutam \textit{P\textsuperscript{y}}}}. Sic \edtext{itaque}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | igitur \textit{V\textsuperscript{a}}}} \edtext{videtur duo}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | duo uidetur \textit{V\textsuperscript{b}}}} querere \edtext{puta}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | scilicet \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{quia}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | quare \textit{απM\textsuperscript{a}mv}}} grauior cordarum sonum preaccipiat et \edtext{cur ex}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv} | cum cur ex \textit{M\textsuperscript{a}} | cum ex \textit{E\textsuperscript{a}} | cum \textit{πV\textsuperscript{z}}}} \edtext{extremis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | exterius \textit{P\textsuperscript{z}}}} \edtext{concursus}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | concursis \textit{V\textsuperscript{a}mv} | cum cursus \textit{P\textsuperscript{x}}}} fiat in medium reddens grauem sonum \edtext{non autem}{\Cfootnote[nosep]{\textit{ακπv} | aut \textit{P\textsuperscript{z}}}} ex mediis. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{κP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | AUT QUIA. \textit{αG\textsuperscript{u}P\textsuperscript{p}mv}}} } Soluit dicens causam esse \edtext{quia}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | quod \textit{E\textsuperscript{a}} | quoniam \textit{P\textsuperscript{p}}}} \textit{ \edtext{id}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}} | illud \textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{quod}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | quod est \textit{P\textsuperscript{y}} | \textit{om}. \textit{π}}} graue magnum et forte \edtext{diuque}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | diu \textit{P\textsuperscript{z}}}} \edtext{perdurans}{\Cfootnote[nosep]{\textit{ακmv} | permanens seu perdurans \textit{π}}} preaccipit vigorem sui oppositi, talis siquidem est grauior \edtext{cordarum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cordam \textit{P\textsuperscript{z}}}} ad alias, \edtext{etiam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | et \textit{M\textsuperscript{a}V\textsuperscript{z}}}} in magno \edtext{continetur et}{\Cfootnote[nosep]{\textit{αλπmv} | continetur \textit{P\textsuperscript{x}} | continuo et \textit{V\textsuperscript{z}} | continuo \textit{M\textsuperscript{a}}}} \edtext{occultatur}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}mv}}} parvuum, sicut in \edtext{superiori}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | siteriorum \textit{V\textsuperscript{o}} | siteriori \textit{P\textsuperscript{a}}}}, taliter quod sonus duarum \edtext{nitarum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}} | neten \textit{P\textsuperscript{y}} | notarum \textit{V\textsuperscript{a}} | ninctarum \textit{P\textsuperscript{p}}}} assumptus est in sono vno \edtext{parypatem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | parametem \textit{P\textsuperscript{z}}}} \edtext{causato}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv}}}.} Ex quo habetur quod grauior cordarum \edtext{sonum preaccipit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | preaccipit sonum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, \edtext{et quod}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | et \textit{κP\textsuperscript{z}}}} \edtext{ex ultimis extremis}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | ex extremis ultimis \textit{π} | exultans extremis \textit{E\textsuperscript{a}}}} \edtext{medium potest}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | potest medium \textit{M\textsuperscript{a}}}} \edtext{resultare}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | resultari \textit{V\textsuperscript{a}} | representare \textit{G\textsuperscript{u}}}}, sicut apparebit \edtext{.23°}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | 22° \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | 12º \textit{C\textsuperscript{a}P\textsuperscript{a}V\textsuperscript{o}} | xxiii° doooo \gap{} \textit{P\textsuperscript{y}} | in 12° \textit{P\textsuperscript{z}}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 13m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Tertiumdecimum problema}\label{edition-text book-19a part13}}{\lemma{Tertiumdecimum + problema} \Cfootnote[nosep]{\textit{G\textsuperscript{u}V\textsuperscript{a}} | «13m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | Tredecimum. \surplus{Tredecimum problema} \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID IN DYAPASON}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID IN DYAPASON ACUTI QUIDEM ANTIFONUM FIT GRAUE, HUIUS AUTEM ACUTUM NON? \textsuperscript{2}AUT QUIA MAXIME QUIDEM IN AMBOBUS EST AMBORUM MELODIA? SI AUTEM NON, NON GRAUE, MAIUS ENIM EST \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Decimumtertium problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} in proportione \edtext{illa}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}V\textsuperscript{o}mv} | ista \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} \edtext{que}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | quo \textit{V\textsuperscript{z}}}} dicitur dyapason uel proportio dupla uel \edtext{totius, illud}{\Cfootnote[nosep]{\textit{ακmv} | tonus, illud \textit{π}}} quod \edtext{habet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | hec \textit{G\textsuperscript{u}}}} rationem \edtext{acuti}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | acute \textit{V\textsuperscript{a}}}} \edtext{plerumque}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | plerumique \textit{G\textsuperscript{u}} | plurium \textit{V\textsuperscript{m}}}} \edtext{pertransit}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}V\textsuperscript{m}mv} | transit \textit{πE\textsuperscript{a}P\textsuperscript{y}}}} in \edtext{grauem}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}mv} | graue \textit{γE\textsuperscript{a}}}}, \edtext{quod autem}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | quod autem hec \textit{E\textsuperscript{a}} | illud autem quod \textit{π}}} habet rationem \edtext{grauis non permutatur in acutum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | grauis non permutatur in acutum \surplus{grauis non permutatur in acutum} \textit{P\textsuperscript{y}}}}?} +\pend + +\pstart +\textbf{2} \edtext{Uidendum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | Videndum est \textit{πV\textsuperscript{a}}}} nunc \edtext{gratia eius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | eius gratia \textit{V\textsuperscript{a}} | gratia huius \textit{π}}} quod \edtext{dicitur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | dicit \textit{V\textsuperscript{a}}}} dyapason \edtext{quot}{\Cfootnote[nosep]{\textit{αλπmv} | quod \textit{P\textsuperscript{x}}}} et que \edtext{sunt}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}v} | sint \textit{γE\textsuperscript{a}V\textsuperscript{z}m}}} \edtext{proportiones}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | proportionales \textit{P\textsuperscript{z}}}} \edtext{musicales}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}} | musicale \textit{P\textsuperscript{x}} | musicales et \textit{γπP\textsuperscript{y}mv} | mussice \textit{V\textsuperscript{z}} | mutabiles \textit{E\textsuperscript{a}} | numeri \textit{M\textsuperscript{a}}}} \edtext{quomodo}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | penes quid \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{sumantur}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{z}mv}}}, \edtext{et}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{quia originantur}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | quia organantur \textit{V\textsuperscript{z}} | dico quod originantur \textit{π}}} ex proportionibus \edtext{arismetricis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}} \edtext{ \edtext{intuendum}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | intuendum est \textit{V\textsuperscript{a}}}} prius illas.}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} ‘ \edtext{ \edtext{Sunt autem secundum boecium in \edtext{primis}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{a}mv} | principiis \textit{V\textsuperscript{b}}}} \textit{arismetrice} }{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} et \textit{musice} }{\Cfootnote[nosep]{\textit{ακmv} | numeri \textit{π}}} quinque \edtext{sumpte}{\Cfootnote[nosep]{\textit{ακmv} | sumptis \textit{π}}} penes numerum inequalem. \edtext{Quarum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Quarum est \textit{P\textsuperscript{z}}}} tres sunt \edtext{simplices}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | simplices uel simpliciores \textit{V\textsuperscript{a}}}} \edtext{puta}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{multiplex et submultiplex}{\Cfootnote[nosep]{\textit{αmv} | multiplex submultiplex et \textit{P\textsuperscript{p}} | multiplex submultiplex \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | multiplex \textit{κG\textsuperscript{u}}}}, superparticularis \edtext{et}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{subsuperparticularis}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}mv} | \textit{om}. \textit{P\textsuperscript{z}V\textsuperscript{o}}}}, \edtext{superpartiens et subsuperpartiens}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv}}}. Due autem composite quarum prima componitur \edtext{ex}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | est \textit{P\textsuperscript{p}}}} multiplici \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{superparticulari}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | superari \textit{P\textsuperscript{z}} | subsuperparticulari \textit{V\textsuperscript{z}}}} \edtext{ \edtext{et ex}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | et \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{multiplici}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | supermultiplici \textit{γmv} | submultiplici \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{et subsuperparticulari}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | sup \textit{V\textsuperscript{z}} | et superparticulari \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | \textit{om}. \textit{E\textsuperscript{a}G\textsuperscript{u}V\textsuperscript{z}}}}, \edtext{secunda ex \edtext{multiplici superparticulari}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | multiplici et superparticulari \textit{V\textsuperscript{a}mv} | multiplici superpartiente \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}} | multiplici similiter particulari \textit{P\textsuperscript{z}} | multiplicitati \textit{V\textsuperscript{b}}}} et \edtext{submultiplici}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | submultiplici et \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}mv} | subsupermultipici et \textit{V\textsuperscript{b}}}} \edtext{subsuperparticulari}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | subsuperpartienti \textit{V\textsuperscript{b}} | subsuperpartiente \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | superparticulari \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | \textit{om}. \textit{G\textsuperscript{u}M\textsuperscript{a}}}}.\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} I .4 (Friedlein p. 191, ll. 6–10);}}\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. arith.} I .22 (Friedlein p. 46, ll. 6–17)}}’ +\pend + +\pstart +\textbf{3} Multiplex autem \edtext{est}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}M\textsuperscript{a}} | est quando \textit{απmv} | \textit{om}. \textit{V\textsuperscript{m}V\textsuperscript{z}}}} numerus maior minorem in se \edtext{continet}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | continens \textit{M\textsuperscript{a}V\textsuperscript{z}}}} pluries, ut \edtext{bis uel}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | bis \textit{G\textsuperscript{u}P\textsuperscript{p}} | \textit{om}. \textit{E\textsuperscript{a}}}} ter \edtext{aut}{\Cfootnote[nosep]{\textit{ακmv} | uel \textit{π}}} \edtext{quater}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | quater ter \textit{G\textsuperscript{u}} | quater uel multociens \textit{V\textsuperscript{a}}}} \edtext{et sic}{\Cfootnote[nosep]{\textit{ακπ} | aut \textit{mv}}} deinceps, ut \edtext{nichil}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uel \textit{P\textsuperscript{x}P\textsuperscript{z}}}} desit \edtext{nichilque}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{exsuperet}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv}}}. \edtext{Huius}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | Hec \textit{P\textsuperscript{y}} | Huiusmodi \textit{E\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{b}}}} autem species sunt duplex triplex quadruplex et sic in infinitum. Duplex \edtext{quidem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{cum vnus numerus alium}{\Cfootnote[nosep]{\textit{ακmv} | ut vnus numerus alium \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | cum vnum numerum \textit{G\textsuperscript{u}}}} bis continet que dicitur proportio dupla ut quatuor ad duo. \edtext{Triplex}{\Cfootnote[nosep]{\textit{αλπmv} | triplex numerus \textit{P\textsuperscript{x}}}} \edtext{cum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | tamen \textit{G\textsuperscript{u}}}} vnus numerus continet \edtext{alium totum tribus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}} | alium numerum tribus \textit{V\textsuperscript{o}} | alium tribus \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv} | alium numerum tribus totum \textit{V\textsuperscript{a}}}} \edtext{uicibus}{\Cfootnote[nosep]{\textit{ακπ} | modis \textit{mv}}} sicut \edtext{trinarius se habet ad vnitatem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | se habet trinarius ad vnitatem \textit{V\textsuperscript{a}} | trinarius ad vnitatem se habet \textit{π}}}. +\pend + +\pstart +\textbf{4} Proportio autem \edtext{secunda}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | + value="2/1">dupla secundum \textit{V\textsuperscript{b}} | dupla \textit{P\textsuperscript{p}}}} iuxta \edtext{aliam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | alia \textit{V\textsuperscript{z}} | alium \textit{P\textsuperscript{z}}}} inequalitatem, ut superparticularis cum \edtext{eius}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{opposita}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}} | oppositus \textit{V\textsuperscript{z}} | opponitur \textit{γV\textsuperscript{o}mv} | opposatur \textit{P\textsuperscript{x}} | oporteat \textit{M\textsuperscript{a}}}}, est cum maior \edtext{numerus}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} continet in se totum \edtext{semel}{\Cfootnote[nosep]{\textit{αλπmv} | solis \textit{P\textsuperscript{x}}}} \edtext{et}{\Cfootnote[nosep]{\textit{αλmv} | et adhuc \textit{π} | in \textit{P\textsuperscript{x}}}} \edtext{vnam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | unam in \textit{M\textsuperscript{a}}}} eius \edtext{insuper}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} partem, \edtext{ut aut}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | ut autem \textit{γ} | vltra ut aut \textit{P\textsuperscript{p}}}} \edtext{dimidia}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | dimidiam \textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} \edtext{uel}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | aut \textit{π} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{tertia}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | tertiam et \textit{απM\textsuperscript{a}mv}}} \edtext{ita}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sic \textit{P\textsuperscript{p}}}} deinceps. \edtext{Cuius}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | Huius \textit{γ}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | autem \textit{V\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{p}}}} proportionis modi sunt \edtext{sexquialtera}{\Cfootnote[nosep]{\textit{αλπmv}}}, \edtext{ \edtext{sexquitertia}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{y}} | sequitertia sexquiquinta \textit{V\textsuperscript{a}} | sexquiquinta \textit{mv}}} uel epitrita}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | sexquiquinta uel epitria \textit{V\textsuperscript{b}} | sexquinta uel epitrica \textit{M\textsuperscript{a}V\textsuperscript{z}} | sexquiinta uel epitrita \textit{V\textsuperscript{m}} | sexquiinta uel epuctria \textit{P\textsuperscript{x}} | sexquitertia \textit{π}}}, \edtext{sexquiquarta}{\Cfootnote[nosep]{\textit{αλπmv} | sexque quanta \textit{P\textsuperscript{x}}}} et \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}mv}}}. Sexquialtera \edtext{seu emiola}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}} | seu emialmlem \textit{V\textsuperscript{a}} | seu enumerale \textit{V\textsuperscript{b}mv} | seu enucha \textit{P\textsuperscript{z}} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} cum \edtext{quis}{\Cfootnote[nosep]{\textit{ακmv} | aliquis \textit{π}}} numerus alium semel continet et \edtext{insuper}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | super \textit{P\textsuperscript{z}}}} \edtext{eius mediam partem}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}mv} | partem eius mediam \textit{λ} | huius mediam partem \textit{P\textsuperscript{y}} | eius partem \textit{P\textsuperscript{x}}}}, \edtext{ut \edtext{ternarius se habet ad binariumbinare}{\Cfootnote[nosep]{\textit{αP\textsuperscript{z}V\textsuperscript{o}mv} | ternarius ad binarium se habet \textit{λ} | tria se habent ad duo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}. Sexquitertia \edtext{cum}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}} | est qui \textit{P\textsuperscript{y}} | \textit{om}. \textit{γmv}}} semel et eius \edtext{tertiam partem}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | partem tertiam \textit{P\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}}, ut \edtext{ \edtext{quaternarius}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | quaternarium \textit{P\textsuperscript{y}} | quaternarius \sout{ad}\textsuperscript{et} ternarius \textit{V\textsuperscript{z}}}} ad ternarium}{\Cfootnote[nosep]{\textit{ακmv} | quatuor ad tria \textit{G\textsuperscript{u}P\textsuperscript{u}} | sexquiquater numerus ad quaternarium \textit{P\textsuperscript{z}} | 4 se habent ad 3 \textit{P\textsuperscript{p}} | quaternarius ad quaternarium \textit{V\textsuperscript{o}}}}. +\pend + +\pstart +\textbf{5} \edtext{Superpartiens}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{z}mv} | Superparticularis \textit{G\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{x}}}} \edtext{est}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} \edtext{quando}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{a}mv} | quoniam \textit{V\textsuperscript{b}} | quare \textit{E\textsuperscript{a}}}} maior numerus continet minorem et \edtext{insuper}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | maxime \textit{P\textsuperscript{y}}}} \edtext{eius aliquas partes}{\Cfootnote[nosep]{\textit{ακm} | aliquas eius partes \textit{πv}}}, ut \edtext{duas}{\Cfootnote[nosep]{\textit{ακmv} | 3as \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | 3es \textit{P\textsuperscript{z}} | \textit{om}. \textit{G\textsuperscript{u}}}} tres etcetera. Cuius \edtext{species sunt}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | species \textit{V\textsuperscript{z}}}} \edtext{superbipartiens}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}V\textsuperscript{o}mv} | ter bipartiens \textit{P\textsuperscript{y}} | superbipartiens et \textit{P\textsuperscript{u}} | subyparicus \textit{P\textsuperscript{z}} | subbipartiens et \textit{G\textsuperscript{u}}}} \edtext{supertripartiens}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | triparties \textit{P\textsuperscript{x}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{etcetera}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | et sic \textit{E\textsuperscript{a}} | \textit{om}. \textit{G\textsuperscript{u}}}}. \edtext{Superbipartiens}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | subipartiens \textit{P\textsuperscript{z}}}} est cum \edtext{numerus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | minor numerus \textit{G\textsuperscript{u}}}} continet numerum \edtext{semel}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | si\expan{mu}l \textit{(orig. \textup{sil})} \textit{P\textsuperscript{z}}}} et \edtext{eius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | etiam \textit{G\textsuperscript{u}}}} duasdue \edtext{partes}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | partes vltra \textit{P\textsuperscript{p}}}}, ut \edtext{quinarius ad ternarium se habet}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | quinare ad ternare se habet \textit{E\textsuperscript{a}} | quinque ad tria se habet \textit{G\textsuperscript{u}} | 5 ad 3 se habent \textit{P\textsuperscript{p}P\textsuperscript{u}} | numerus + quinarius ad ternarium se habet \textit{P\textsuperscript{z}V\textsuperscript{o}}}}. \edtext{Supertripartiens}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}} | Supertripartiens est \textit{γmv} | Superquiertiens \textit{V\textsuperscript{o}} | Superpartiens \textit{E\textsuperscript{a}} | Tripartiens \textit{M\textsuperscript{a}}}} quando \edtext{semel continet}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | unus continet numerum semel \textit{P\textsuperscript{p}} | semel \textit{V\textsuperscript{a}}}} \edtext{totum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}mv} | \textit{om}. \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{eius}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{tres partes}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}mv} | tertiam partem \textit{γE\textsuperscript{a}}}}, ut septem \edtext{se habet ad}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | ad \textit{G\textsuperscript{u}P\textsuperscript{p}mv}}} quatuor. \edtext{Superquadripartiens}{\Cfootnote[nosep]{\textit{αλπmv} | Supertripartiens \textit{P\textsuperscript{x}}}} \edtext{etcetera, ut}{\Cfootnote[nosep]{\textit{ακmv} | etiam, sicut \textit{π}}} \edtext{.ix.}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | .ix. cum \textit{E\textsuperscript{a}}}} \edtext{se habet ad .5}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | ad 5 se habet \textit{V\textsuperscript{a}} | ad .5 \textit{π}}}. +\pend + +\pstart +\textbf{6} \edtext{Compositarum}{\Cfootnote[nosep]{\textit{ακmv} | Compositorum \textit{π}}} uero \edtext{multiplex}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | simplex \textit{E\textsuperscript{a}}}} superparticularis est \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{q}P\textsuperscript{u}}}} numerus \edtext{continet maior}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}} | maior continet \textit{πM\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}mv}}} \edtext{minorem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | numerum minorem \textit{G\textsuperscript{u}} | minorem numerum \textit{P\textsuperscript{z}}}} totum multotiens et insuper \edtext{aliquam}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | aliam \textit{πE\textsuperscript{a}}}} partem \edtext{eius}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}}, ut medietatem uel tertiam \edtext{et}{\Cfootnote[nosep]{\textit{αλπmv} | y.t. \textit{P\textsuperscript{x}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | huiusmodi \textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}}}}. \edtext{Huius}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}mv} | Huiusmodi \textit{P\textsuperscript{y}V\textsuperscript{b}}}} autem \edtext{species sunt}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{z}mv} | sunt species \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | sunt \textit{P\textsuperscript{y}}}} \edtext{duplex + sexquialtera}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{z}mv} | duplex sexquialtera \textit{(\textup{\sic{duplex sexquin alta duplex sexquialtera}} a.c.)} \textit{P\textsuperscript{x}} | sexquialtera \textit{G\textsuperscript{u}}}}, \edtext{ \edtext{duplex + sexquitertia}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | duplex + sexquitertia et \textit{λ} | duplex + sexquialtera \textit{V\textsuperscript{o}}}}, duplex sexquiquarta, etcetera,}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{et \edtext{id ratione}{\Cfootnote[nosep]{\textit{λP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | id rationem \textit{E\textsuperscript{a}V\textsuperscript{b}mv} | ideo ratione \textit{P\textsuperscript{z}} | rationem ratione \textit{P\textsuperscript{y}}}} duplicitatis;duplicis ex \edtext{parte}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{uero}{\Cfootnote[nosep]{\textit{λP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | uero uel \textit{E\textsuperscript{a}}}} triplicitatistriplicis}{\Cfootnote[nosep]{\textit{λP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{C\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}}}} \edtext{ \edtext{triplex sexquialtera,}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{λ}}} \edtext{triplex sexquitertia}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | triplex + sexquitertia duplex sexquitertia \textit{V\textsuperscript{m}V\textsuperscript{z}} | triplex quitertia \textit{E\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{x}}}}, \edtext{etcetera}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}mv} | triplex etcetera \textit{P\textsuperscript{y}} | triplex sexquiquarta \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}mv} | \textit{om}. \textit{C\textsuperscript{a}G\textsuperscript{u}V\textsuperscript{a}}}}. \edtext{Est}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} duplex sexquialtera \edtext{quando}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | est quando \textit{P\textsuperscript{y}P\textsuperscript{z}}}} maior \edtext{numerus}{\Cfootnote[nosep]{\textit{ακmv} | numerus bis \textit{π}}} \edtext{continet minorem totum}{\Cfootnote[nosep]{\textit{γπP\textsuperscript{y}} | minorem totum continet \textit{V\textsuperscript{z}} | minorem totum \textit{M\textsuperscript{a}V\textsuperscript{m}mv} | minorem \textit{E\textsuperscript{a}} | minorem se totum \textit{P\textsuperscript{x}}}} et insuper \edtext{eius partem mediam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | partem eius mediam \textit{V\textsuperscript{a}} | eius medium \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, ut \edtext{.5.quinariusquinarequinarium \edtext{se habet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | se habent \textit{G\textsuperscript{u}P\textsuperscript{u}} | \textit{om}. \textit{mv}}} ad \edtext{.2}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}mv} | binarium \textit{λP\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | binare \textit{E\textsuperscript{a}} | 3 \textit{P\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | 10 ad 4 \textit{P\textsuperscript{p}}}}. \edtext{Duplex + sexquitertia}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Duplex + sexquialtera 3a. \textit{P\textsuperscript{x}}}} \edtext{quando}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | est quando \textit{γmv} | quando ipsum \textit{π}}} continet totum et \edtext{ipsius}{\Cfootnote[nosep]{\textit{ακmv} | eius \textit{π}}} \edtext{tertiam partem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | partem 3am \textit{P\textsuperscript{z}V\textsuperscript{o}}}}, ut \edtext{septem se habet}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | septem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}mv}}} ad \edtext{.3}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | .3. iii \textit{P\textsuperscript{z}}}}. \edtext{Duplex sexquiquarta etcetera}{\Cfootnote[nosep]{\textit{γλP\textsuperscript{y}mv} | Duplex sexquiquarta \textit{πP\textsuperscript{x}}}}, \edtext{ut .ix. \edtext{se habet ad}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{z}} | habet se ad \textit{V\textsuperscript{m}} | ad \textit{πmv}}} quatuor. \edtext{Triplex + sexquialtera}{\Cfootnote[nosep]{\textit{αλmv} | Triplex sexquitertia \textit{π}}} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} quando \edtext{alter \edtext{alterum continet totum}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | alteram continet totam \textit{V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{ακmv} | alter continet alterum totum ter \textit{π}}} \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | ut \textit{P\textsuperscript{x}V\textsuperscript{m}}}} \edtext{adhuc}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv} | ad hoc \textit{E\textsuperscript{a}} | ad \textit{V\textsuperscript{m}}}} \edtext{eius tertiam}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | tertiam eius \textit{V\textsuperscript{a}}}} partem, \edtext{ut \edtext{decem}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | quatuor \textit{P\textsuperscript{x}}}} ad tria. \edtext{Triplex + sexquialtera}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | Triplex + sexquitertia \textit{V\textsuperscript{a}mv} | Quadruplex + sexquialtera \textit{P\textsuperscript{y}V\textsuperscript{b}} | Triplex sexquiquarta \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{quando}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{o}mv} | est quando \textit{γ}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{quartam partem continet}{\Cfootnote[nosep]{\textit{αλV\textsuperscript{o}mv} | partem 4am. continet \textit{G\textsuperscript{u}} | partem continet \textit{P\textsuperscript{u}P\textsuperscript{x}} | continet \textit{P\textsuperscript{z}} | continet minorem numerum ter et 4am. partem \textit{P\textsuperscript{p}}}} ultra \edtext{totum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}}, ut .13. ad quatuor. +\pend + +\pstart +\textbf{7} Multiplex \edtext{superpartiens}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | est superpartiens \textit{P\textsuperscript{x}} | superparticularis \textit{G\textsuperscript{u}}}} \edtext{est cum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | est quando \textit{V\textsuperscript{a}mv} | cum \textit{π}}} maior numerus continet \edtext{minorem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | minorem numerum \textit{P\textsuperscript{p}} | maiorem \textit{M\textsuperscript{a}M\textsuperscript{b}}}} plus quam semel uel multotiens \edtext{et}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | ut \textit{P\textsuperscript{y}}}} \edtext{ \edtext{pluries}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}} | plures \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv}}}, cum \edtext{hoc}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | hic \textit{G\textsuperscript{u}}}} \edtext{ipsius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | eius \textit{V\textsuperscript{z}}}} \edtext{partem}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | partes \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv}}} }{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | plures partes cum hoc ipsius \textit{V\textsuperscript{a}} | cum hoc plures eius partes \textit{P\textsuperscript{p}}}}. \edtext{Cuius}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | Et \textit{P\textsuperscript{y}}}} etiam \edtext{infinite sunt}{\Cfootnote[nosep]{\textit{ακmv} | sunt infinite \textit{π}}} species, ut \edtext{duplex superbipartiens, duplex supertripartiens, etcetera}{\Cfootnote[nosep]{\textit{mv} | duplex superpartiens, duplex supertripartiens, etcetera \textit{M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{m}} | duplex superpartiens, et desupertripartiens, etcetera \textit{V\textsuperscript{z}} | duplex superpartiens, triplex superpartiens, etcetera \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | duplex superpartiens etcetera, duplex supertripartiens etcetera \textit{γP\textsuperscript{y}} | duplex superpartiens, etcetera \textit{E\textsuperscript{a}P\textsuperscript{x}} | duplex superparticularis \textit{G\textsuperscript{u}}}} et \edtext{id}{\Cfootnote[nosep]{\textit{ακπ} | illud \textit{mv}}} \edtext{ratione}{\Cfootnote[nosep]{\textit{αλπmv} | ratio \textit{P\textsuperscript{x}}}} duplicitatis; ex parte \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}} | quidam \textit{P\textsuperscript{p}} | quid \textit{C\textsuperscript{a}P\textsuperscript{a}V\textsuperscript{o}} | uero \textit{mv}}} triplicitatis erunt \edtext{ \edtext{triplex + superbipartiens}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}mv} | triplex superpartiens \textit{M\textsuperscript{a}} | triplex subpartiens \textit{V\textsuperscript{m}} | triplex sibi partiens \textit{P\textsuperscript{x}}}}, \edtext{triplex + supertripartiens}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}mv} | triplex superpartiens \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | triplex superbipartiens triplex superbipartiens \textit{V\textsuperscript{o}}}}, \edtext{etcetera}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}. \edtext{Duplex + superbipartiens}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | Duplex superpartiens \textit{P\textsuperscript{u}} | Duplex supertiens \textit{V\textsuperscript{a}}}} est quando numerus maior \edtext{continet}{\Cfootnote[nosep]{\textit{ακmv} | continet bis \textit{π}}} minorem et insuper \edtext{duas}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} eius partes, ut octo \edtext{se habet}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}} | habet se \textit{V\textsuperscript{m}} | se habent \textit{π} | \textit{om}. \textit{mv}}} ad \edtext{triam}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}} | tria \textit{E\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{o}} | tres \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | .3. uel .2 \textit{V\textsuperscript{a}}}}. \edtext{Duplex + supertripartiens \edtext{est quando}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}} | est \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | etcetera \textit{αλmv}}}, \edtext{ut xi. \edtext{se habet}{\Cfootnote[nosep]{\textit{αλV\textsuperscript{o}} | se habent \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{mv}}} ad \edtext{.3}{\Cfootnote[nosep]{\textit{αλV\textsuperscript{o}mv} | quatuor \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}. \edtext{Quadruplex + superbipartiens}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}mv} | Triplex + superbipartiens \textit{V\textsuperscript{a}} | Triplex supertripartiens \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{est quando}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}V\textsuperscript{b}mv} | quando \textit{V\textsuperscript{a}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} etcetera, ut .15.}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | triplex \textit{P\textsuperscript{z}}}} \edtext{se habet}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}V\textsuperscript{o}} | se habent \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{p}mv}}} ad quatuor. \edtext{Hee}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}m} | Hec \textit{P\textsuperscript{z}V\textsuperscript{a}}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}mv} | quidam \textit{P\textsuperscript{p}} | qua \textit{C\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} sunt numerorum \edtext{inequalitates}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{z}mv} | inequales \textit{M\textsuperscript{a}V\textsuperscript{m}}}} ex quibus \edtext{quinque}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} resultant proportiones \edtext{arismetrice}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | arismetricas \textit{P\textsuperscript{z}}}} cum \edtext{suis oppositis}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | optis \textit{P\textsuperscript{y}}}} antedictis. +\pend + +\pstart +\textbf{8} Restat \edtext{quidem breuiter uidere secundo}{\Cfootnote[nosep]{\textit{κ} | breuiter quidem uidere secundo \textit{P\textsuperscript{y}V\textsuperscript{b}mv} | quidem breuiter uidetur secundo \textit{E\textsuperscript{a}} | breuiter 2° uidere \textit{πV\textsuperscript{a}}}}: \edtext{quot et que}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}mv} | que et quot \textit{V\textsuperscript{a}} | que et quot sunt \textit{π} | quod et que \textit{V\textsuperscript{m}}}} \edtext{ex hiis sint}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}mv} | sint ex hiis \textit{V\textsuperscript{z}} | ex hiis sunt \textit{E\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{m}} | ex istis sint \textit{P\textsuperscript{y}} | ex hiis \textit{π}}} \edtext{consonantie siue simphonie}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | consonantie \textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}} | consonauere \textit{P\textsuperscript{z}}}} musicales, \edtext{et}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} a \edtext{quibus}{\Cfootnote[nosep]{\textit{κ} | quibus proportionibus \textit{απmv}}} \edtext{sumantur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{z}mv} | summatur \textit{P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}} | sumuntur \textit{C\textsuperscript{a}V\textsuperscript{o}}}} \edtext{arismetricis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | arismetricum \textit{γG\textsuperscript{u}mv}}}. Secundum \edtext{quidem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | quod \textit{P\textsuperscript{x}} | quid \textit{C\textsuperscript{a}V\textsuperscript{o}} | \textit{om}. \textit{λ}}} \hyperref[Mac]{macrobium} et \hyperref[Bo]{boecium} ex omni \edtext{numerorum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | modorum \textit{P\textsuperscript{z}V\textsuperscript{c}}}} uarietate pauci \edtext{numeri}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{reperiuntur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} qui \edtext{conueniant sibi}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | conueniunt sibi \textit{M\textsuperscript{a}} | 9 aut 8 \textit{P\textsuperscript{z}}}} ad \edtext{consonantiam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | confouentiam \textit{G\textsuperscript{u}}}} musicalem \edtext{constituendam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | considerandam \textit{P\textsuperscript{z}} | custodiendam \textit{V\textsuperscript{b}}}}. Sunt \edtext{autem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}P\textsuperscript{z}}}} \edtext{hii}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | hiis \textit{P\textsuperscript{z}V\textsuperscript{a}}}} sex \edtext{omnes}{\Cfootnote[nosep]{\textit{ακmv} | omnis \textit{π}}} iuxta \edtext{quos}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | quas \textit{P\textsuperscript{x}} | quot \textit{V\textsuperscript{m}}}} \edtext{quinque consonantie}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | consonantie quinque \textit{P\textsuperscript{x}P\textsuperscript{z}}}} constituuntur, \edtext{et}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | ut \textit{V\textsuperscript{b}}}} \edtext{tonus}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}mv} | totus \textit{V\textsuperscript{a}} | totius \textit{E\textsuperscript{a}}}} \edtext{ex quo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | equo \textit{P\textsuperscript{z}}}} \edtext{constituunt}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | constituuntur \textit{V\textsuperscript{a}} | constituitur \textit{πV\textsuperscript{z}}}} \edtext{dyatonum}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}v}}}, scilicet epitricus, \edtext{emiolus, duplaris, triplaris}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | emi solus duplarum triplarum \textit{P\textsuperscript{z}}}}, quadruplarusquadruplumquadruplaris quadriplum, epodousepogdoiiepogdonium. +\pend + +\pstart +\textbf{9} Epitricus \edtext{uel}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | seu \textit{G\textsuperscript{u}P\textsuperscript{q}} | et \textit{P\textsuperscript{x}}}} \edtext{sexquitertius}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}v} | sex quinitus \textit{P\textsuperscript{x}}}} est \edtext{ut aliqualiter iam}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}mv} | unde iam aliqualiter \textit{V\textsuperscript{a}} | uel aliqualiter iam \textit{E\textsuperscript{a}}}} \edtext{patuit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | paruit \textit{P\textsuperscript{y}}}} cum maior numerus continet minorem totum et eius tertiam partem, ut quatuor \edtext{se habet ad}{\Cfootnote[nosep]{\textit{αλ} | se ad \textit{P\textsuperscript{x}} | ad \textit{πmv}}} tria. Ex quo \edtext{nascitur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}} \edtext{ \edtext{simphonia}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}mv}}} uel consonantia}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | consonantia seu symphonia \textit{G\textsuperscript{u}} | simphonia consonantia \textit{P\textsuperscript{x}}}} \edtext{dyatesseron dicta id est}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | dicta dyatesseron id est \textit{πmv} | dyatesseron dicta \textit{M\textsuperscript{a}}}} \edtext{per quatuor}{\Cfootnote[nosep]{\textit{αλπmv} | per quatuor et per 3am. \textit{P\textsuperscript{x}}}}, que in \edtext{sexquitertia proportione consistit}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | sexquitertia consistit proportione \textit{P\textsuperscript{z}V\textsuperscript{o}} | sexquitertiam proportionem consistit \textit{P\textsuperscript{x}}}}, ut \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} una uox in grauitate \edtext{uel}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | seu \textit{G\textsuperscript{u}P\textsuperscript{q}}}} acuitate \edtext{ \edtext{se habuerit ad aliam sicut}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | se habet ad aliam sicut \textit{P\textsuperscript{y}} | se habuerit ad \surplus{ad} aliam sicut \textit{P\textsuperscript{z}} | ad aliam se habuerit scilicet \textit{P\textsuperscript{p}}}} quatuor ad triatres}{\Cfootnote[nosep]{\textit{απmv} | se \textit{P\textsuperscript{x}} | se hii· \textit{V\textsuperscript{m}V\textsuperscript{z}} | sed hii \textit{M\textsuperscript{a}}}}. +\pend + +\pstart +\textbf{10} \edtext{Iuxta uero emiolam uel sexquialteram ut cum maior numerus}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} \edtext{minorem continet}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}mv} | continet minorem \textit{πV\textsuperscript{a}} | minorem \surplus{minorem} continet \textit{V\textsuperscript{b}}}} totum et \edtext{medietatem ipsius}{\Cfootnote[nosep]{\textit{γκmv} | ipsius medietatem \textit{π} | medietatem ipsi \textit{E\textsuperscript{a}} | medietatem \textit{P\textsuperscript{y}}}}, \edtext{ceu se habet}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | ceu se habent \textit{V\textsuperscript{z}} | ceu \textit{P\textsuperscript{z}mv} | ceu se habet \textit{E\textsuperscript{a}} | ut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | seu \textit{C\textsuperscript{a}V\textsuperscript{o}}}} tria ad \edtext{duo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | 3 \textit{P\textsuperscript{u}}}}. Oritur consonantia dicta dyapente uel \edtext{per}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{u}}}} \edtext{quinque}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{u}mv} | quandoque \textit{G\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}} | quecunque \textit{P\textsuperscript{z}} | communionem \textit{P\textsuperscript{p}}}} \edtext{in quinto enim loco \edtext{terminatur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | teminatur \textit{V\textsuperscript{b}}}} }{\Cfootnote[nosep]{\textit{ακmv} | in 5° loco terminatur \textit{π}}} in \edtext{monocordo}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{z}}}}, \edtext{sicut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | sic \textit{P\textsuperscript{z}}}} dyatesseron in \edtext{quatuor}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}} | quarta \textit{P\textsuperscript{p}P\textsuperscript{u}} | quarto \textit{γG\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | 8o \textit{V\textsuperscript{z}}}} \edtext{ceu}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv} | seu \textit{πE\textsuperscript{a}}}} \edtext{cum}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}mv} | ut \textit{P\textsuperscript{y}} | \textit{om}. \textit{P\textsuperscript{x}}}} una \edtext{vox}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} \edtext{se habuerit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} ad aliam \edtext{in}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{grauitate et leuitate}{\Cfootnote[nosep]{\textit{αλπmv} | leuitatem et grauitatem \textit{P\textsuperscript{x}}}} \edtext{etcetera}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{11} Secundum \edtext{siquidem}{\Cfootnote[nosep]{\textit{απmv} | quidem \textit{λ} | 44. quidem \textit{P\textsuperscript{x}}}} duplarem numerum \edtext{uel}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | secundum \textit{P\textsuperscript{y}}}} proportionem, ut quatuor \edtext{se habet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | se habent \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{mv}}} ad duo sumitur proportio dyapason siue \edtext{per}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} totum, terminat \edtext{enim et}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | et \textit{E\textsuperscript{a}} | enim uel \textit{π}}} continet \edtext{totum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{monacordum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}}}} et maxime primum cadit \edtext{enim}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cum \textit{P\textsuperscript{z}}}} super \edtext{octo}{\Cfootnote[nosep]{\textit{αλmv} | scilicet \textit{P\textsuperscript{x}} | 4 \textit{π}}} incipiens \edtext{a gama greco}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | a gama grece \textit{P\textsuperscript{z}} | in gama greco \textit{P\textsuperscript{p}} | agamo greco \textit{κ} | agamatrico \textit{V\textsuperscript{a}}}}. +\pend + +\pstart +\textbf{12} \edtext{Scilicet}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}} | .g. \textit{P\textsuperscript{z}} | \textit{om}. \textit{λV\textsuperscript{b}mv}}} iuxta \edtext{uero triplarem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | triplarem vero \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} numerum \edtext{seu}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | siue \textit{G\textsuperscript{u}P\textsuperscript{q}}}} proportionem, ut cum numerus \edtext{se habet}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | se habeat \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | habeat se \textit{V\textsuperscript{b}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{u}}}} ad numerum \edtext{ceu}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | seu \textit{E\textsuperscript{a}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | ut \textit{P\textsuperscript{p}}}} tria ad vnum, componitur enim ex multiplici et superparticulari \edtext{sicut se habet tria ad vnum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | sicut habet se tria ad unum \textit{P\textsuperscript{y}} | \textit{om}. \textit{π}}}, nascitur \edtext{simphonia}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}mv}}} \edtext{composita}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | et componitur \textit{V\textsuperscript{b}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{ακ} | ex \textit{πmv}}} \edtext{dyapente dyapason}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}} | dyapente et dyapason \textit{πV\textsuperscript{b}mv}}} ut quando \edtext{vna}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | vnam \textit{V\textsuperscript{a}} | \textit{om}. \textit{πE\textsuperscript{a}}}} uox excedit \edtext{alteram}{\Cfootnote[nosep]{\textit{ακπ} | aliam \textit{mv}}} etcetera. Iuxta uero numerum quadruplum, \edtext{cum}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vt cum \textit{G\textsuperscript{u}P\textsuperscript{q}} | est \textit{P\textsuperscript{x}}}} vnus alium \edtext{quater}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | quadruplum \textit{P\textsuperscript{x}} | quadrupliciter \textit{V\textsuperscript{m}}}} continet, ut quatuor \edtext{se habet}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | se habent \textit{P\textsuperscript{q}P\textsuperscript{u}} | \textit{om}. \textit{mv}}} ad vnum oritur \edtext{bis}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | hiis \textit{E\textsuperscript{a}}}} diapason. +\pend + +\pstart +\textbf{13} EpogdousEpogodus est \edtext{numerus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | unus \textit{P\textsuperscript{z}}}} qui \edtext{inter}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}} | intra \textit{λE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv}}} se minorem \edtext{concludit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | conclaudit \textit{V\textsuperscript{a}mv} | claudit \textit{V\textsuperscript{b}} | continet \textit{π}}} et insuper \edtext{octauam eius partem}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{m}mv} | eius octauam partem \textit{V\textsuperscript{z}} | 8 eius partem \textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | octauam \textit{P\textsuperscript{y}} | scilicet eius partem \textit{P\textsuperscript{x}}}}, \edtext{ceu}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | seu \textit{P\textsuperscript{z}V\textsuperscript{o}} | se \textit{E\textsuperscript{a}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} nouem \edtext{se habet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | se habent \textit{G\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{p}mv}}} ad octo. \edtext{Ex}{\Cfootnote[nosep]{\textit{αλπmv} | Et \textit{P\textsuperscript{x}}}} \edtext{hoc}{\Cfootnote[nosep]{\textit{ακmv} | quo \textit{π}}} quidem \edtext{numero}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | numerus \textit{P\textsuperscript{p}P\textsuperscript{z}}}} \edtext{ \edtext{sonus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{consurgit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | contingit uel consurgit \textit{G\textsuperscript{u}}}} \edtext{quem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | quam \textit{P\textsuperscript{z}} | quomodo \textit{M\textsuperscript{a}}}} musici \edtext{tonum uocant}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | uocant tonum \textit{P\textsuperscript{x}} | tonum uocarunt \textit{λ} | tonum uocauerunt \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | tonum uocarent \textit{V\textsuperscript{a}mv} | tonum \textit{P\textsuperscript{z}V\textsuperscript{b}}}}, \edtext{ \edtext{qui}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | quod \textit{P\textsuperscript{y}}}} \edtext{autem}{\Cfootnote[nosep]{\textit{λG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{tono minus}{\Cfootnote[nosep]{\textit{λG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | tono unus minus \textit{V\textsuperscript{a}} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{semitonum}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}}}} }{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{z}V\textsuperscript{b}}}} \edtext{dicitur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}}, quod \edtext{non}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | non est \textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{extimandum}{\Cfootnote[nosep]{\textit{ακmv} | existimandum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | ex utis \textit{P\textsuperscript{z}}}} tonum \edtext{uere fore}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | fere fore \textit{π} | fore fere \textit{E\textsuperscript{a}}}} sicut \edtext{neque}{\Cfootnote[nosep]{\textit{ακmv}}} semiuocalem in \edtext{litteris}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv}}}. \edtext{Non enim}{\Cfootnote[nosep]{\textit{ακmv} | Nam \textit{π}}} tonus \edtext{naturaliter}{\Cfootnote[nosep]{\textit{αλπmv} | universaliter \textit{P\textsuperscript{x}}}} in duo \edtext{equalia}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} potest diuidi, \edtext{cum}{\Cfootnote[nosep]{\textit{αλπmv} | et \textit{P\textsuperscript{x}}}} \edtext{constet}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | constat \textit{G\textsuperscript{u}P\textsuperscript{q}} | constans \textit{V\textsuperscript{a}} | stet \textit{E\textsuperscript{a}}}} ex \edtext{numero}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | numero cum \textit{V\textsuperscript{b}}}} nouenarionouenarumnouem, \edtext{quod}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | qui \textit{V\textsuperscript{a}V\textsuperscript{z}}}} \edtext{in duo}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | sono \textit{E\textsuperscript{a}}}} \edtext{diuidi minime potest equaliter}{\Cfootnote[nosep]{\textit{γmv} | diuidi minime potest \textit{κ} | diuidi minime equaliter potest \textit{πE\textsuperscript{a}} | equalia diuidi minime potest \textit{P\textsuperscript{y}}}}. \edtext{Unde et}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | Unde \textit{V\textsuperscript{z}} | Et \textit{V\textsuperscript{a}} | Et ideo \textit{π} | Ut \textit{E\textsuperscript{a}}}} \edtext{semitonium uocarunt}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | uocauerunt semitonum \textit{π}}} sonum \edtext{tono}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}} | tonum \textit{V\textsuperscript{a}mv}}} minorem. Est autem \edtext{semitonum}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}}}} duplex \edtext{maius scilicet}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | scilicet maius \textit{G\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{z}} | maius \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} et minus. \edtext{Maius \edtext{uidem}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{b}} | qui \textit{M\textsuperscript{a}}}} dicitur \edtext{apothomi}{\Cfootnote[nosep]{\textit{κ}}} }{\Cfootnote[nosep]{\textit{κV\textsuperscript{b}} | Minus quidem dicitur apothemi \textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | ampli[?]us quidem dicitur apothemi \textit{P\textsuperscript{p}} | Maius quidem dicitur \textit{V\textsuperscript{a}} | \textit{om}. \textit{G\textsuperscript{u}}}} apud \edtext{uero}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | nomen \textit{P\textsuperscript{z}}}} \hyperref[Bo]{ \edtext{boecium}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} } \edtext{decisio}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}, \edtext{minus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | nimis \textit{P\textsuperscript{z}}}} \edtext{autem}{\Cfootnote[nosep]{\textit{ακmv} | aut \textit{π}}} \edtext{dyesis}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}}}} uel \edtext{limes}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | lineis \textit{V\textsuperscript{a}}}}, \edtext{quod}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | quid \textit{P\textsuperscript{u}} | qui \textit{E\textsuperscript{a}}}} tam \edtext{paruo}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | paruum \textit{G\textsuperscript{u}V\textsuperscript{a}}}} distare a \edtext{tono}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}} | toto \textit{mv}}} \edtext{deprehensum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | depressum \textit{P\textsuperscript{z}}}} est quantum \edtext{hii}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} duo \edtext{numeri}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | numerus \textit{G\textsuperscript{u}}}} distant: \edtext{ut}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | \textit{om}. \textit{λ}}} \edtext{.243.}{\Cfootnote[nosep]{\textit{λG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | 242 \textit{P\textsuperscript{x}} | 283 \textit{E\textsuperscript{a}} | .343. \textit{P\textsuperscript{y}} | 2. 43. \textit{P\textsuperscript{z}} | 12. 143. \textit{V\textsuperscript{a}}}} \edtext{et 256}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | 256. \textit{P\textsuperscript{p}P\textsuperscript{y}} | 2256 \textit{γmv}}}. \edtext{Quorum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Quando \textit{P\textsuperscript{z}}}} quidem \edtext{vnusquisque}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quisque \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{constat}{\Cfootnote[nosep]{\textit{γλπP\textsuperscript{y}mv} | constant \textit{E\textsuperscript{a}} | constituit \textit{P\textsuperscript{x}}}} ex \edtext{duabus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | 29. \textit{P\textsuperscript{u}}}} \edtext{uocibus}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | uicibus \textit{V\textsuperscript{m}}}} \edtext{puta}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | prout \textit{P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{ακmv} | ut et \textit{π}}} mi, \edtext{est et}{\Cfootnote[nosep]{\textit{ακmv} | est etiam \textit{π}}} \edtext{ditonus}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{a}}}}, \edtext{ \edtext{qui}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | qui est \textit{P\textsuperscript{p}}}} \edtext{ex duobus consurgit perfectis tonis}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | ex duo consurgit perfectus tonus \textit{P\textsuperscript{z}} | consurgens ex duobus tonis perfectis \textit{P\textsuperscript{p}} | ex duobus perfectis consurgit sonis \textit{P\textsuperscript{y}}}}, \edtext{et}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}mv} | ut \textit{P\textsuperscript{y}}}} \edtext{semidytonus}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | semiditonis \textit{V\textsuperscript{a}} | semitonus \textit{λπv}}} qui ex duobus non \edtext{integris}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}mv} | integer \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}}. Ut \edtext{id autem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | id \textit{V\textsuperscript{a}} | id aut \textit{mv} | autem hec \textit{π}}} per amplius \edtext{appareat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}mv} | appareant \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | apparent \textit{C\textsuperscript{a}V\textsuperscript{o}}}} \edtext{parigraphia}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}}}} \edtext{conscribatur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | scribatur \textit{πP\textsuperscript{y}}}} \edtext{ista}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}mv} | ista videlicet \textit{V\textsuperscript{b}} | ista in ista t[?]olitua \textit{V\textsuperscript{a}} | talis \textit{π}}}. \edtext{\begin{longtable}{P{0.10688622754491017\textwidth}P{0.2214071856287425\textwidth}P{0.279940119760479\textwidth}P{0.24176646706586827\textwidth}} +\Panel{Γ.}{label}{1}{l}\tabcellsep 1296.\tabcellsep ut.\tabcellsep \\ +\Panel{}{label}{1}{l}\tabcellsep \tabcellsep \tabcellsep \\ +\Panel{a.}{label}{1}{l}\tabcellsep 1152.\tabcellsep re.\tabcellsep \\ +\Panel{b.}{label}{1}{l}\tabcellsep 1034.\tabcellsep mi.\tabcellsep dytonus.\\ +\Panel{c.}{label}{1}{l}\tabcellsep 972.\tabcellsep faut.\tabcellsep dyatesseron. \\ +\Panel{d.}{label}{1}{l}\tabcellsep 864.\tabcellsep solre.\tabcellsep dyapente. \\ +\Panel{e.}{label}{1}{l}\tabcellsep 768.\tabcellsep lami.\tabcellsep \\ +\Panel{f.}{label}{1}{l}\tabcellsep 739.\tabcellsep faut.\tabcellsep \\ +\Panel{g.}{label}{1}{l}\tabcellsep 648.\tabcellsep solreut.\tabcellsep dyapason.\\ +\Panel{a.}{label}{1}{l}\tabcellsep 576.\tabcellsep lamire.\tabcellsep \\ +\Panel{b.}{label}{1}{l}\tabcellsep 554.\tabcellsep mi.\tabcellsep \\ +\Panel{b.}{label}{1}{l}\tabcellsep 512.\tabcellsep fa.\tabcellsep \\ +\Panel{c.}{label}{1}{l}\tabcellsep 486.\tabcellsep solfaut.\tabcellsep dyatesseron dyapason.\\ +\Panel{d.}{label}{1}{l}\tabcellsep 432.\tabcellsep lasolre.\tabcellsep dyapente dyapason. \\ +\Panel{e.}{label}{1}{l}\tabcellsep 384.\tabcellsep lami.\tabcellsep \\ +\Panel{f.}{label}{1}{l}\tabcellsep 366.\tabcellsep faut.\tabcellsep \\ +\Panel{g.}{label}{1}{l}\tabcellsep 324.\tabcellsep solreut.\tabcellsep bis dyapason.\\ +\Panel{a.}{label}{1}{l}\tabcellsep 288.\tabcellsep lamire.\tabcellsep \\ +\Panel{b.}{label}{1}{l}\tabcellsep 277.\tabcellsep mi.\tabcellsep \\ +\Panel{b.}{label}{1}{l}\tabcellsep 256.\tabcellsep fa.\tabcellsep \\ +\Panel{c.}{label}{1}{l}\tabcellsep 243.\tabcellsep solfa.\tabcellsep \\ +\Panel{d.}{label}{1}{l}\tabcellsep 216.\tabcellsep lasol.\tabcellsep \\ +\Panel{}{label}{1}{l}\tabcellsep \tabcellsep \tabcellsep \end{longtable}}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv} | \gap{} \textit{V\textsuperscript{b}} | \textit{om}. \textit{V\textsuperscript{b}}}} +\pend + +\pstart +\textbf{14} Sunt itaque consonantie \edtext{quinque}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{scilicet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}}: dyatesseron, dyapente, dyapason, \edtext{dyapente dyapason, et}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | dyapente dyapason \textit{γP\textsuperscript{z}V\textsuperscript{o}mv} | dyatesseron et \textit{λ} | et \textit{P\textsuperscript{x}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}E\textsuperscript{a}}}} \edtext{bis dyapason}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | bisserer \textit{V\textsuperscript{a}}}}. \edtext{Que quidem}{\Cfootnote[nosep]{\textit{γλπP\textsuperscript{y}mv} | Qui quidem \textit{P\textsuperscript{x}} | Siquidem \textit{E\textsuperscript{a}}}} \edtext{hiis}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | hii \textit{V\textsuperscript{z}} | \textit{om}. \textit{V\textsuperscript{a}}}} tonis \edtext{et}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{semitonis}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv}}} \edtext{constituuntur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | constituitur \textit{V\textsuperscript{a}}}}, \edtext{dyatesseron}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | diatonici \textit{P\textsuperscript{x}V\textsuperscript{m}} | dyatri \textit{V\textsuperscript{z}}}} enim constat ex \edtext{duobusduabus \edtext{tonis}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv}}} \edtext{et}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cum \textit{P\textsuperscript{x}}}} \edtext{semitono}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{ \edtext{non}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}P\textsuperscript{z}}}} integro, dyapente \edtext{tribus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{o}mv} | 39 \textit{P\textsuperscript{u}}}} tonis et minore \edtext{semitono}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{κπV\textsuperscript{b}mv} | \textit{om}. \textit{P\textsuperscript{y}V\textsuperscript{a}}}}, \edtext{dyapason}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | dyapason ex \textit{G\textsuperscript{u}}}} quinque \edtext{tonis}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv}}} et \edtext{semitonis duobus minoribus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{a}} | duobus semitonis minoribus \textit{π} | semitoniis duobus \textit{P\textsuperscript{y}}}}, \edtext{neque}{\Cfootnote[nosep]{\textit{ακmv} | nullaque \textit{π}}} \edtext{peruenit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}m} | per peruenit \textit{v} | prouenit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | prout \textit{C\textsuperscript{a}V\textsuperscript{o}}}} ad \edtext{.vi.}{\Cfootnote[nosep]{\textit{ακmv} | quinque \textit{π}}} \edtext{tonos}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv}}} perfecte. Ex quibus apparet quod dyatesseron et \edtext{dyapente}{\Cfootnote[nosep]{\textit{απmv} | diapentesseron \textit{λ} | diapentesseran \textit{P\textsuperscript{x}}}} \edtext{consurgunt}{\Cfootnote[nosep]{\textit{ακmv} | consurgit \textit{π}}} in \edtext{dyapason}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{z}mv} | diapasseron \textit{P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | \textit{om}. \textit{π}}}. \edtext{Dyapente dyapason}{\Cfootnote[nosep]{\textit{αmv} | Dyapente dyapason que \textit{π} | Et in pentadyasson \textit{κ}}} ex .ix. \edtext{tonis}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv}}} \edtext{et ex}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | ex \textit{M\textsuperscript{a}} | et \textit{απmv}}} \edtext{semitono}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}V\textsuperscript{a}} | semitonis \textit{P\textsuperscript{z}}}} minori constat, \edtext{bis uero dyapason}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | sed ipsa bis dyapason \textit{π}}} ex .12. \edtext{perficitur}{\Cfootnote[nosep]{\textit{ακmv} | perfectis \textit{π}}} tonis. \edtext{Et hec}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}mv} | Et huiusmodi \textit{P\textsuperscript{y}} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}} | quidem \textit{αλmv}}} \edtext{amplius sunt in}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}mv} | amplius sunt exposita in \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{x}}}} ‘ \textit{ \edtext{conciliatoris mei}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}V\textsuperscript{b}mv} | conciliatoris nostri \textit{λ} | conciliatoris unde \textit{E\textsuperscript{a}} | mei \textit{P\textsuperscript{x}} | conciliatoris \textit{π}}} } \edtext{differentia .83a.}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | differentiis 93. \textit{P\textsuperscript{z}} | differentia sed \textit{P\textsuperscript{x}}}} \edtext{exposita.}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{}{\Afootnote[nosep]{Pietro d'Abano \textit{Concil.} diff. 83}}’ +\pend + +\pstart +\textbf{15} \edtext{Nosce}{\Cfootnote[nosep]{\textit{ακπ} | Notandum \textit{mv}}} \edtext{quoque}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} ‘ \edtext{ex \textit{musice} quinto}{\Cfootnote[nosep]{\textit{ακmv} | ex quinto musice \textit{π}}} quod \edtext{\hyperref[Pt]{ptholomeus}}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}mv} | thonus \textit{P\textsuperscript{x}}}} \edtext{sextam hiis addit}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}} | sextam hiis addidit \textit{P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}mv} | sexta hiis addidit \textit{E\textsuperscript{a}} | addidit sextam \textit{π}}} consonantiam \edtext{compositam}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | compositam et \textit{E\textsuperscript{a}}}} ex \edtext{dyatesseron et dyapason}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | dyatesseron dyapason \textit{G\textsuperscript{u}} | dyatesseron \textit{P\textsuperscript{y}}}}, que constat ex \edtext{multiplici}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | multiplici et \textit{V\textsuperscript{a}mv}}} \edtext{superpartiente}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | superpartienti \textit{P\textsuperscript{y}V\textsuperscript{a}} | superparticulare \textit{V\textsuperscript{b}} | superparticulari \textit{M\textsuperscript{a}mv} | superpartem \textit{P\textsuperscript{z}}}} \edtext{qua proportione}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}mv} | quam proportionem \textit{V\textsuperscript{m}V\textsuperscript{z}} | secundum quam proportionem \textit{M\textsuperscript{a}} | in qua proportione \textit{π} | de qua proportione \textit{P\textsuperscript{y}}}} \edtext{se habet}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | se habent \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | habet se \textit{P\textsuperscript{y}} | habet \textit{E\textsuperscript{a}V\textsuperscript{z}}}} octo ad .3.. Continet enim \edtext{octo}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} bis tria, \edtext{propter}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | per \textit{G\textsuperscript{u}}}} multiplicem proportionem ex qua \edtext{visum}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}} | visum est \textit{πE\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{a}mv}}} consurgere dyapason, et duas \edtext{eius partes}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{y}mv} | partes eius \textit{π} | eius partes eius \textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} quod est \edtext{tertia}{\Cfootnote[nosep]{\textit{ακmv} | 3. \textit{π}}} scilicet \edtext{duo}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | secundo \textit{E\textsuperscript{a}} | 32. \textit{P\textsuperscript{z}}}} propter \edtext{superpartientem}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | partientem \textit{M\textsuperscript{a}}}} \edtext{a}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | ex \textit{P\textsuperscript{p}V\textsuperscript{z}}}} qua nascitur dyatesseron.\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} V. 8–9}}’ \edtext{Communiter}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} \edtext{tamen}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{pictagorici}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{musice}{\Cfootnote[nosep]{\textit{γκπmv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}}}} \edtext{institutores}{\Cfootnote[nosep]{\textit{αP\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | instructores \textit{λ} | inpositores \textit{P\textsuperscript{p}}}} \edtext{posuerunt}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | proposuerunt \textit{P\textsuperscript{y}}}} omnes \edtext{proportiones}{\Cfootnote[nosep]{\textit{ακmv} | consonantias \textit{π}}} musicales consurgere ex multiplici et \edtext{superparticulari}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | supermusicales consurgere ex multiplici et superparticulari \textit{M\textsuperscript{a}}}}, \edtext{nullamque}{\Cfootnote[nosep]{\textit{ακmv} | nullam vero \textit{π}}} ex \edtext{superpartiente}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}P\textsuperscript{x}} | superpartienti \textit{αV\textsuperscript{m}V\textsuperscript{z}} | superparticulari \textit{mv}}}, \edtext{quod}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | et \textit{V\textsuperscript{m}}}} videtur \hyperref[Ar]{aristoteles} sentire \edtext{xli}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | xiº \textit{V\textsuperscript{m}} | 4° \textit{G\textsuperscript{u}V\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{16} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | AUT QUIA. \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}mv}}} } Soluit \edtext{dicens}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | dicentes \textit{E\textsuperscript{a}}}} causam esse \textit{ \edtext{quoniam in}{\Cfootnote[nosep]{\textit{ακmv} | quia in \textit{π}}} \edtext{ambobus scilicet \edtext{in}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}}}} graui et acuto}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | scilicet graui et acuto ambobus \textit{P\textsuperscript{p}}}} \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | cum \textit{P\textsuperscript{y}}}} melodia \edtext{utrorumque}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | utrorum \textit{P\textsuperscript{y}}}}, vnum enim \edtext{alteri}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | altero \textit{P\textsuperscript{y}} | alter \textit{P\textsuperscript{p}} | alterius \textit{V\textsuperscript{a}}}} \edtext{coniunctum}{\Cfootnote[nosep]{\textit{γπP\textsuperscript{y}mv} | constitum \textit{P\textsuperscript{x}} | consitum \textit{λ}}} \edtext{melodiam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | melodiam uel consonanciam \textit{G\textsuperscript{u}}}} \edtext{reddit, quia graue et acutum sunt \edtext{dissimilia}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | difficilima \textit{E\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fieri ex dissimilibus \textit{G\textsuperscript{u}}}}.} \edtext{ \edtext{Et}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{γmv}}} \edtext{\hyperref[Ty]{ \edtext{thimoteus}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} }}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | ethymous \textit{V\textsuperscript{m}} | thymolis \textit{P\textsuperscript{x}} | entimomus \textit{γmv} | \textit{recte: timaeus, methinks}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | qui \textit{P\textsuperscript{z}} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{extimauit}{\Cfootnote[nosep]{\textit{ακmv} | existimauit \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} musice primo melodiam uel consonantiam fieri ex dissimilibus, non autem ex \edtext{similibus}{\Cfootnote[nosep]{\textit{ακmv} | consimilibus \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}}. \textit{Si autem \edtext{proueniat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} utrorunque in utrisque \edtext{concordia}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | concordiam \textit{P\textsuperscript{p}P\textsuperscript{u}}}} non fit melodia, \edtext{cum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | si \textit{V\textsuperscript{a}}}} autem \edtext{sic fuerit}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | fuerit sic \textit{V\textsuperscript{a}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{γπP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}mv} | quod \surplus{quod} \textit{M\textsuperscript{a}} | quia \textit{E\textsuperscript{a}}}} graue \edtext{maius sit}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}mv} | sit maius \textit{πP\textsuperscript{y}} | maius fuerit \textit{V\textsuperscript{a}} | maius fit \textit{V\textsuperscript{m}}}} acuto et fortius,} tunc quod est acutum \edtext{ \edtext{assumit}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}mv}}} rationem grauis, ita quod acutum sentitur}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}mv} | sumit \textit{V\textsuperscript{a}}}} \edtext{graue}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | nisi \textit{M\textsuperscript{a}V\textsuperscript{m}} | enim \textit{P\textsuperscript{x}} | \textit{om}. \textit{P\textsuperscript{p}}}} cum due \edtext{nite}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{o}}}} \edtext{concurrunt}{\Cfootnote[nosep]{\textit{ακmv} | concordant \textit{π}}} in \edtext{ypatem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv}}}. Dicitur autem melodia \edtext{a melle}{\Cfootnote[nosep]{\textit{αλπmv} | a melos \textit{P\textsuperscript{x}}}}, \edtext{quoniam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | q\expan{uan}tum \textit{(orig. \textup{ȹ\textsuperscript{\textasciitilde }tum})} \textit{P\textsuperscript{z}}}} est consonantia \edtext{delectabilissima}{\Cfootnote[nosep]{\textit{ακπ}}} ualde ex acuto \edtext{et graui}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | grauique \textit{P\textsuperscript{y}} | et graui est \textit{M\textsuperscript{a}}}} \edtext{debite}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | indebite \textit{P\textsuperscript{z}}}} composita. \edtext{}{\Cfootnote{etcetera. \textit{V\textsuperscript{b}V\textsuperscript{z}} | sequitur 14m. problema 19e. particule. \textit{P\textsuperscript{x}}}} \gap{}\begin{longtable}{P{0.10350553505535055\textwidth}P{0.20387453874538744\textwidth}P{0.28856088560885607\textwidth}P{0.2540590405904059\textwidth}} +\Panel{G}{label}{1}{l}\tabcellsep 1296\tabcellsep ut\\ +\tabcellsep \tabcellsep \tabcellsep \\ +\Panel{a.}{label}{1}{l}\tabcellsep 1152.\tabcellsep re.\tabcellsep Dyatonus\\ +\Panel{b.}{label}{1}{l}\tabcellsep 1034.\tabcellsep mi.\tabcellsep \\ +\Panel{c.}{label}{1}{l}\tabcellsep 972.\tabcellsep fa ut.\tabcellsep Dyatesseron.\\ +\Panel{d.}{label}{1}{l}\tabcellsep 864.\tabcellsep solre.\tabcellsep \\ +\Panel{e.}{label}{1}{l}\tabcellsep 786.\tabcellsep la mi.\tabcellsep \\ +\Panel{f.}{label}{1}{l}\tabcellsep 739.\tabcellsep fa ut.\tabcellsep \\ +\Panel{g.}{label}{1}{l}\tabcellsep 646.\tabcellsep solreut.\tabcellsep dyapason.\\ +\Panel{a.}{label}{1}{l}\tabcellsep 576.\tabcellsep lamire.\tabcellsep \\ +\Panel{b.}{label}{1}{l}\tabcellsep 554.\tabcellsep mi\tabcellsep \\ +\Panel{b.}{label}{1}{l}\tabcellsep 512.\tabcellsep fa.\tabcellsep \\ +\Panel{c.}{label}{1}{l}\tabcellsep 486\tabcellsep solfaut.\tabcellsep dyatesseron dyapason.\\ +\Panel{d.}{label}{1}{l}\tabcellsep 432.\tabcellsep lasolre\tabcellsep dyapente dyapason.\\ +\Panel{e.}{label}{1}{l}\tabcellsep 384.\tabcellsep la mi.\tabcellsep \\ +\Panel{f.}{label}{1}{l}\tabcellsep 349.\tabcellsep faut.\tabcellsep \\ +\Panel{g.}{label}{1}{l}\tabcellsep 324.\tabcellsep solreut.\tabcellsep bis dyapason.\\ +\Panel{a.}{label}{1}{l}\tabcellsep \tabcellsep lamire\tabcellsep \\ +\tabcellsep \tabcellsep \tabcellsep \\ +\tabcellsep \tabcellsep \tabcellsep \\ +\tabcellsep \tabcellsep \tabcellsep \\ +\tabcellsep \tabcellsep \tabcellsep \\ +\tabcellsep \tabcellsep \tabcellsep \end{longtable} +\pend + +\pstart +\edtext{\subsubsection {Quartumdecimum problema}\label{edition-text book-19a part14}}{\lemma{Quartumdecimum + problema} \Cfootnote[nosep]{\textit{V\textsuperscript{a}mv} | 13m. problema. \textit{G\textsuperscript{u}} | «14m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{Quartumdecimum}Quartumdecimum. \textit{P\textsuperscript{y}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID LATET DYAPASON}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | PROPTER QUID DYAPASON \textit{V\textsuperscript{m}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID LATET DYAPASON ET UIDETUR UNIUS SONI ESSE, UT IN FINIKIO ET IN HOMINE? QUE ENIM IN ACUTIS EXISTUNT NON UNIUS SONI, SED PROPORTIONALITER AD INUICEM DYAPASON. \textsuperscript{2}AUT QUIA SICUT IPSE ESSE UIDETUR SONUS PROPTER ANALOGUM, EQUALITAS IN SONIS, EQUALE AUTEM UNIUS? HOC AUTEM IDEM IN FISTULIS DECIPIUNTUR \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Decimum quartum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} dyapason cum \edtext{sit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} proportio satis distans \edtext{quoniam dupla}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}mv} | quoniam duplo \textit{P\textsuperscript{y}} | quamdaperla \textit{P\textsuperscript{x}}}} latet \edtext{in tantum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{z}mv} | iterum \textit{M\textsuperscript{a}V\textsuperscript{m}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{απmv} | quare \textit{κ}}} videtur sonus ex ipsa \edtext{resultatus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}m} | resultatis \textit{V\textsuperscript{b}} | resultans \textit{πv}}} esse vnus et \edtext{quasi}{\Cfootnote[nosep]{\textit{αλπmv} | quare \textit{P\textsuperscript{x}}}} vnum tonum simpliciter habere?} Et \edtext{hoc}{\Cfootnote[nosep]{\textit{αλπmv} | hec \textit{P\textsuperscript{x}}}} declarat sicut apparet \edtext{etcetera}{\Cfootnote[nosep]{\textit{ακmv} | eidem \textit{V\textsuperscript{z}} | \textit{om}. \textit{π}}}. Communiter \edtext{quidem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quid \textit{P\textsuperscript{z}} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{inuenitur littera}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | littera inuenitur \textit{G\textsuperscript{u}} | inuenitur \textit{E\textsuperscript{a}}}} \edtext{in finitis}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | infinitatis \textit{mv} | in infinitis \textit{G\textsuperscript{u}}}}, \edtext{alia infantis}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | aliam infantis \textit{E\textsuperscript{a}} | alias infantis \textit{V\textsuperscript{z}} | alia infinitis \textit{P\textsuperscript{x}} | et alia infantis \textit{V\textsuperscript{m}} | \textit{om}. \textit{G\textsuperscript{u}}}} \textit{ \edtext{aliter finikio}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | aliter finibrio \textit{V\textsuperscript{z}} | alia finikio \textit{γP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}},} sed \edtext{forte}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} debet \edtext{dicere in fidibus}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}mv} | dici in fidibus \textit{P\textsuperscript{y}V\textsuperscript{z}} | habere in fidibus \textit{V\textsuperscript{m}} | esse in fidibus \textit{π} | infidibus \textit{V\textsuperscript{a}}}} seu cordis. \textit{Et in homine similiter} \edtext{declarat}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}} | declaratur \textit{αλmv}}} ita \edtext{quod}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ut \textit{V\textsuperscript{a}}}} \edtext{per hoc}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}mv} | hoc \textit{P\textsuperscript{y}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{tangat}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | tangit \textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}}}} duplicem melodiam \edtext{tactu}{\Cfootnote[nosep]{\textit{γλπP\textsuperscript{y}mv} | tacta \textit{P\textsuperscript{x}} | tactam \textit{E\textsuperscript{a}}}} uel pulsu factam et \edtext{uoce}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv} | note \textit{E\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{o}}}}. \textit{Soni \edtext{siquidem}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | quidem \textit{V\textsuperscript{m}}}} \edtext{existentes}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | existentis \textit{}}} \edtext{acuti}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} quia non concurrunt adeo in vnum, non sunt \edtext{unius}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | vinus \textit{v} | minus \textit{γm}}} soni ut graues aut \edtext{sic}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | sunt \textit{απmv} | \textit{om}. \textit{V\textsuperscript{z}}}} compositi ex grauibus \edtext{sed}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ut \textit{V\textsuperscript{a}}}} \edtext{in dyapason. Hoc accidit}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | dyapason \textit{V\textsuperscript{a}}}} quoniam toni se habent proportionaliter ad inuicem ex graui \edtext{et}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv} | ex \textit{E\textsuperscript{a}V\textsuperscript{m}}}} acuto,} \edtext{ \textit{est \edtext{enim}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | autem \textit{V\textsuperscript{z}}}} optima consonantiarum} \edtext{.35}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}mv} | .xxv° \textit{P\textsuperscript{y}} | tria quinto \textit{κG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}mv}}} } Soluit dicens \edtext{causam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | causa \textit{G\textsuperscript{u}}}} esse \textit{ \edtext{quare}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}mv} | quia \textit{P\textsuperscript{x}V\textsuperscript{z}} | quoniam \textit{M\textsuperscript{a}}}} sonus apparet \edtext{vnicus}{\Cfootnote[nosep]{\textit{αλπmv} | mutus \textit{P\textsuperscript{x}}}} esse propter \edtext{anologiam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}mv}}} et proportionem sonorum ad inuicem \edtext{in}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ut \textit{V\textsuperscript{a}}}} dyapason, ex qua resultat equalitas grandis in sonis.} Quod autem \edtext{equalitatem habet}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | habet equalitatem \textit{λ}}} \edtext{vnius}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{q}mv} | unus \textit{P\textsuperscript{y}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{soni existit}{\Cfootnote[nosep]{\textit{κ} | existit soni \textit{απmv}}}, et non solum \edtext{hoc accidit}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | accidit hoc \textit{M\textsuperscript{a}} | accidit \textit{π}}} in \edtext{sono voce facto}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | voce facto \textit{π} | sono uel voce \textit{V\textsuperscript{a}}}} \edtext{aut}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} pulsu, sed \edtext{etiam}{\Cfootnote[nosep]{\textit{γλπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{x}}}} \edtext{in sono}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{flatu}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | filata \textit{P\textsuperscript{z}}}} facto, \edtext{uel}{\Cfootnote[nosep]{\textit{κ} | ut \textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} in \edtext{fistulis}{\Cfootnote[nosep]{\textit{αλπmv}}}. In \edtext{illis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | hiis \textit{V\textsuperscript{a}}}} enim \edtext{decipiuntur}{\Cfootnote[nosep]{\textit{αλπmv} | recipiuntur \textit{P\textsuperscript{x}}}} etiam \edtext{ut in}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{uocis sono}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uoce sono \textit{P\textsuperscript{z}} | sonis \textit{G\textsuperscript{u}}}}, propter \edtext{debitam enim tonorum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | debitam enim sonorum \textit{P\textsuperscript{y}} | enim debitam tonorum \textit{π}}} \edtext{consonantiam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | dissonantiam \textit{P\textsuperscript{p}}}} accidit plures tonos non \edtext{discerni}{\Cfootnote[nosep]{\textit{αλπmv} | diuisi \textit{P\textsuperscript{x}}}} sed vnum apparere \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | et \textit{P\textsuperscript{z}}}} \edtext{diuersitates}{\Cfootnote[nosep]{\textit{αλπmv} | diuisi \textit{P\textsuperscript{x}}}} \edtext{illic non extent}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}V\textsuperscript{m}mv} | illic non extant \textit{P\textsuperscript{y}} | illic quod extent \textit{E\textsuperscript{a}} | illic non existant \textit{πP\textsuperscript{x}}}} \edtext{sensibiles}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | consimiles \textit{mv} | \textit{om}. \textit{P\textsuperscript{z}}}}, \edtext{ceu}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}}}} videmus \edtext{ex}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv} | in \textit{πE\textsuperscript{a}V\textsuperscript{z}}}} saporibus \edtext{composita ex}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}} | compositis ex \textit{π} | composita \textit{γλE\textsuperscript{a}mv} | conposita \textit{P\textsuperscript{y}}}} diuersis \edtext{in}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ex \textit{G\textsuperscript{u}}}} quibus \edtext{vnus}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | vnius \textit{V\textsuperscript{a}}}} consurgit \edtext{delectabilis}{\Cfootnote[nosep]{\textit{αλπmv}}} et nullius excessus, \edtext{ut}{\Cfootnote[nosep]{\textit{γκmv} | ut qui \textit{πE\textsuperscript{a}} | ut quod \textit{P\textsuperscript{y}}}} \edtext{conficitur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | conficitur ex \textit{V\textsuperscript{a}}}} \edtext{decoctione}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | de remotione \textit{P\textsuperscript{z}}}} \edtext{ex}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{cucurbitis}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{z}mv} | cucurbite \textit{π}}}, \edtext{cepis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}mv} | sepis \textit{P\textsuperscript{p}V\textsuperscript{o}}}}, uel \edtext{alleis}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}} | aliis \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{o}mv}}}, \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cum autem \textit{P\textsuperscript{z}}}} \edtext{tamen}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | tantum \textit{P\textsuperscript{z}}}} vnum \edtext{sit}{\Cfootnote[nosep]{\textit{αλπmv} | fit \textit{P\textsuperscript{x}}}} saporis insipidi et \edtext{alterum}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | alter \textit{G\textsuperscript{u}V\textsuperscript{z}}}} \edtext{acuti}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{z}V\textsuperscript{z}} | sequitur 15m. probleme 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Quintumdecimum problema}\label{edition-text book-19a part15}}{\lemma{Quintumdecimum + problema} \Cfootnote[nosep]{\textit{V\textsuperscript{a}mv} | «15m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | Quintumdecimum. \surplus{Quintumdecimum} \textit{P\textsuperscript{y}} | 14m. problema: \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID LEGES}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID LEGES QUIDEM NON IN CONUERSIONIBUS FACIEBANT, ALII UERO CANTUS CHORICI? \textsuperscript{2}AUT QUIA LEGES QUIDEM AGONIZANTIUM FUERUNT? QUIBUS UTIQUE MUTARI POTENTIBUS ET DISTENDI, CANTUS FIEBAT LONGUS ET MULTIFORMIS. QUEMADMODUM IGITUR ET UERBA, ET CANTUS MUTATIONEM SEQUEBANTUR, SEMPER ALTERA FACTA. \textsuperscript{3}MAGIS ENIM CANTU NECESSE IMITARI QUAM UERBIS. PROPTER QUOD ET DITIRAMBI, QUONIAM AUTEM IMITATIUI, FIEBANT. NON ADHUC HABENT CONUERSIUOS, PRIUS AUTEM HABEBANT. CAUSA AUTEM QUONIAM ANTIQUITUS LIBERI ROTABANT IPSI, MULTOS IGITUR AGONISTICE CANTARE DIFFICILE ERAT, QUARE IN ARMONIA CANTUM DELECTABILITER. MUTARE ENIM MULTIS MUTATIONIBUS UNO FACILE QUAM MULTIS ET AGONISTE ID EST CONSUETUDINEM SERUANT. PROPTER QUOD SIMPLICIORES FACIEBANT SIBI MELODIAS. CONUERSIUUS AUTEM SIMPLEX, NUMERUS ENIM EST ET UNO MENSURATUR. \textsuperscript{4}EADEM AUTEM EST CAUSA ET PROPTER QUOD QUE QUIDEM A SCENA NON CONUERSIUA, CHORI ENIM CONUERSIUA. QUI ENIM CANTAT IN SCENA AGONISTA ET MUTATOR, CHORUS AUTEM MINUS MUTATUR \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Decimum quintum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} antiquitus \edtext{cantatores}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv}}} \edtext{constituerunt}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | constituerint \textit{E\textsuperscript{a}}}} \edtext{quosdam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | quorundam «quosdam» (in mg.) \textit{V\textsuperscript{o}}}} cantus dictos leges non habentes \edtext{conuersiones}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | conuersionem \textit{P\textsuperscript{y}}}}, sed alii cantus \edtext{ \edtext{chorici}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | choris \textit{E\textsuperscript{a}} | conci «corici» (in mg.) \textit{V\textsuperscript{o}}}} \edtext{et conuersiui}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | conuersiui et \textit{P\textsuperscript{y}}}} \edtext{fuere}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | fuerunt \textit{P\textsuperscript{p}} | finem \textit{P\textsuperscript{y}} | fide \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}mv} | fuere chorici et conuersiui \textit{V\textsuperscript{a}}}}?} Nosce quod \edtext{per}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} leges non in conuersionibus factas \edtext{audio}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | aut dyo \textit{V\textsuperscript{b}}}} cantus \edtext{simplices}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{expansos}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | expansus \textit{P\textsuperscript{p}}}} in quibus \edtext{potius fit}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | fit potius \textit{P\textsuperscript{y}} | fit \textit{P\textsuperscript{z}}}} \edtext{commutatio}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | comitatio \textit{V\textsuperscript{z}} | connumeratio \textit{P\textsuperscript{z}}}} uerborum quam cantus, ita quod in eis non \edtext{constituantur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | constituuntur \textit{P\textsuperscript{y}}}} \edtext{circuli}{\Cfootnote[nosep]{\textit{ακπ} | circula \textit{mv}}} \edtext{conuersiui}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | conuersuum \textit{P\textsuperscript{p}}}}, \edtext{sicut}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | finis \textit{P\textsuperscript{y}}}} est cantus \edtext{alicuius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} insignis \edtext{gesti}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{a}mv} | egesti \textit{E\textsuperscript{a}} | testi \textit{V\textsuperscript{b}}}}. \edtext{ \edtext{Choricos}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}} | Per choricos \textit{mv}}} autem cantus \edtext{intelligo}{\Cfootnote[nosep]{\textit{γκmv} | ego intelligo \textit{P\textsuperscript{y}}}} \edtext{conuersiuos}{\Cfootnote[nosep]{\textit{λP\textsuperscript{y}V\textsuperscript{a}mv} | conuersiuos cantus \textit{V\textsuperscript{b}} | uersiuos \textit{P\textsuperscript{x}}}} primis \edtext{utcunque}{\Cfootnote[nosep]{\textit{γκmv} | utrisque \textit{P\textsuperscript{y}}}} \edtext{oppositos}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}} | oppositis \textit{γmv}}}, ut apparebit in \edtext{causa}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | tria \textit{V\textsuperscript{a}}}}. \edtext{Est autem chorus}{\Cfootnote[nosep]{\textit{γκmv} | Est autem \textit{P\textsuperscript{y}}}} \edtext{curator}{\Cfootnote[nosep]{\textit{γκmv} | curatio \textit{P\textsuperscript{y}}}} inoperabilis, \edtext{beniuolentia}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv} | beniuolentiam \textit{V\textsuperscript{z}}}} enim \edtext{solum prebet}{\Cfootnote[nosep]{\textit{λP\textsuperscript{y}V\textsuperscript{b}mv} | prebet solum \textit{P\textsuperscript{x}} | solus prebet \textit{V\textsuperscript{a}}}} quibus \edtext{adest}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}mv} | adest ut \textit{M\textsuperscript{a}}}} \edtext{.xlviii}{\Cfootnote[nosep]{\textit{γλP\textsuperscript{y}mv} | 4. scilicet \textit{P\textsuperscript{x}}}}.}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | AUT QUIA. \textit{P\textsuperscript{z}mv} | CHORICOS. \textit{E\textsuperscript{a}}}} } Soluit \edtext{et primo}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | primo et \textit{G\textsuperscript{u}}}} assignat causam quesiti. Secundo \edtext{ex hac}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} infert \edtext{causam}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | causam etiam \textit{πE\textsuperscript{a}}}} \edtext{cuiusdam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}}}} \edtext{alterius}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | altius alterius \textit{E\textsuperscript{a}} | alterius perfectis \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{cantus \edtext{secunda \textit{EADEM AUTEM}}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}} | ibi secunda \textit{EADEM AUTEM} \textit{V\textsuperscript{b}} | secunda in \textit{EADEM AUTEM} \textit{V\textsuperscript{a}m} | secunda eadem \textit{E\textsuperscript{a}} | EADEM \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}}. \edtext{Etiam}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}mv} | Et \textit{M\textsuperscript{a}V\textsuperscript{z}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} primo respondet ad \edtext{primam partem}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | partem prima \textit{P\textsuperscript{x}}}} dicens}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \textit{ \edtext{causam esse quoniam leges fuerunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} cantus constituti ab agonizantibus et \edtext{bellatoribus}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | bellatorum \textit{E\textsuperscript{a}}}}, \edtext{ceu}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} sunt cantus \edtext{gestorum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}} \edtext{insignium}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | insignum \textit{E\textsuperscript{a}P\textsuperscript{z}}}}. Quas \edtext{quidem}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | quam \textit{P\textsuperscript{x}V\textsuperscript{m}}}} leges ut possent consequi recitando \edtext{quod}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | quid \textit{V\textsuperscript{z}}}} in eis continebatur \edtext{distendebant}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}mv} | diffe distendebant \textit{P\textsuperscript{y}} | descendebant \textit{P\textsuperscript{x}} | discebant \textit{π}}} cantando, \edtext{nunquam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | inde quam \textit{P\textsuperscript{z}}}} \edtext{faciendo}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}mv} | patiendo \textit{V\textsuperscript{a}}}} conuersionem uel circulationem ad \edtext{id}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | idem \textit{G\textsuperscript{u}}}} \edtext{unde}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | unum \textit{E\textsuperscript{a}}}} \edtext{inceperant}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | inceperunt \textit{G\textsuperscript{u}} | ceperant \textit{λ}}} \edtext{reddeuntes}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}m} | redeuntes \textit{πM\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}v}}}. Propter quod \edtext{eorum}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} cantus \edtext{fiebat}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | fiebant \textit{P\textsuperscript{x}P\textsuperscript{z}}}} longus et multarum manerierum, secundum uerborum \edtext{prelatorum}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | prolatorum \textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | prolapsorum \textit{E\textsuperscript{a}}}} \edtext{diuersitatem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}}. Nam secundum quod uerba gestorum fiebant continue \edtext{ \edtext{altera}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}} | alta \textit{γP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | alto \textit{E\textsuperscript{a}}}} uel melius}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} altera et diuersa mutatione \edtext{similiter}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | simili \textit{G\textsuperscript{u}}}}.\edtext{Et}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} in \edtext{cantu}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | cantum \textit{V\textsuperscript{b}}}} similem obseruabant mutationem, \edtext{ut}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ut ad \textit{π} | et \textit{M\textsuperscript{a}}}} \edtext{commutationem}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | commutationi \textit{P\textsuperscript{y}}}} uerborum \edtext{cantus}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{comitaretur}{\Cfootnote[nosep]{\textit{γP\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}mv} | cum comitaretur \textit{E\textsuperscript{a}} | comodaceretur \textit{V\textsuperscript{z}} | commutaretur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}}}} \edtext{mutatio}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}mv} | imitatio \textit{P\textsuperscript{x}} | commutatio \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}}, \edtext{ad uerba enim}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | enim ad verba \textit{G\textsuperscript{u}}}} amplius quam ad cantum attendebant.} Propter quod \edtext{dicte sunt}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | dicta sunt \textit{G\textsuperscript{u}P\textsuperscript{q}}}} leges \edtext{cantus huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{a}mv} | cantus huiusmodi \textit{P\textsuperscript{y}V\textsuperscript{b}} | cantus \textit{π}}} \edtext{a}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}mv} | ad \textit{P\textsuperscript{x}}}} legendo, \edtext{uelut}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{m}} | ut \textit{mv} | ultra \textit{P\textsuperscript{x}} | illud \textit{V\textsuperscript{z}} | visum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | uideret[?] \textit{V\textsuperscript{o}}}} in lectionibus et \edtext{proprie}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | precipue \textit{P\textsuperscript{y}}}} \edtext{diuinis}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in diuinis \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, ut apparebit \edtext{.xlviii.}{\Cfootnote[nosep]{\textit{αλmv} | .44. \textit{π} | .42. \textit{P\textsuperscript{x}}}}, \edtext{vna}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ubi vna \textit{M\textsuperscript{a}}}} \edtext{dictio}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | dicto \textit{P\textsuperscript{x}V\textsuperscript{m}}}} post aliam profertur non \edtext{multum}{\Cfootnote[nosep]{\textit{αλπmv} | multam \textit{P\textsuperscript{x}}}} uocem \edtext{diuersificando}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | diuersimode \textit{P\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \edtext{\textit{MAGIS \edtext{ENIM}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | EST \textit{V\textsuperscript{a}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} .} \edtext{Tangit}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{z}mv} | Tangit enim \textit{M\textsuperscript{a}V\textsuperscript{m}} | Tanquam \textit{P\textsuperscript{y}}}} causam \edtext{alterius}{\Cfootnote[nosep]{\textit{κ} | plures alterius \textit{mv} | plus alterius \textit{πE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}}}} \edtext{partis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}mv} | partium \textit{P\textsuperscript{y}}}}, dicens quod in cantu \edtext{armonico}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}mv} | armonizato \textit{C\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{sufficienter}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | sufficientis \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}}}} non \edtext{debet}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}mv} | debent \textit{M\textsuperscript{a}}}} \edtext{per oppositum accidere}{\Cfootnote[nosep]{\textit{κV\textsuperscript{a}mv} | per appositum accidere \textit{E\textsuperscript{a}} | per oppositum \textit{P\textsuperscript{y}} | hoc accidere per oppositum \textit{π}}}, nam \edtext{in eo}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{a}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} quod \edtext{dictum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{est}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{a}} | \textit{om}. \textit{E\textsuperscript{a}mv}}}, \textit{ \edtext{in legibus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | legibus \textit{P\textsuperscript{z}} | in lectionibus \textit{V\textsuperscript{a}}}} amplius \edtext{oportet}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{a}mv} | \textit{om}. \textit{π}}} \edtext{imitari}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | immutari \textit{λE\textsuperscript{a}P\textsuperscript{z}}}} \edtext{cantum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}mv} | auiter \textit{V\textsuperscript{o}}}} reddendo ipsum \edtext{melodiosum}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | melodicum \textit{P\textsuperscript{x}}}} quam uerba,} cum cantus \edtext{sit magis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | magis sit \textit{P\textsuperscript{y}} | fit magis \textit{P\textsuperscript{u}V\textsuperscript{a}}}} finis \edtext{musici}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | amici \textit{P\textsuperscript{x}}}} actus uerbis, ampliorem \edtext{inducens}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | iudices \textit{P\textsuperscript{z}}}} delectationem, propter quod \edtext{dictum}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}} | dictum est \textit{λV\textsuperscript{a}mv}}} 10°. quod \textit{uox delectabilis \edtext{est cantantis}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}mv} | cantantis est \textit{π} | est cantus \textit{E\textsuperscript{a}V\textsuperscript{a}}}} sine \edtext{sermone}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | sermonem \textit{κ} | prouisione \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}}}} \edtext{etiam. Et}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{z}mv} | etcetera. Et \textit{M\textsuperscript{a}V\textsuperscript{m}} | etiam. Et etiam \textit{π}}} }}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} \textit{ \edtext{ \edtext{ideo}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | \textit{om}. \textit{π}}} quidam modi \edtext{cantandi dicti \edtext{ditirambi}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | dicti dichitambi cantando \textit{P\textsuperscript{y}} | cantandi dictirambi \textit{P\textsuperscript{p}V\textsuperscript{a}mv} | dicti Tytira ubi \textit{G\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} \edtext{fiunt}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fuerunt \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, cum quis \edtext{magis cantum imitatur}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}mv} | cantum ymitatur magis \textit{V\textsuperscript{a}} | magis imitatur cantu \textit{G\textsuperscript{u}P\textsuperscript{q}} | cantum magis imitatur \textit{V\textsuperscript{z}} | magis cantus ymitantur \textit{P\textsuperscript{z}} | magis cantum immutatur \textit{E\textsuperscript{a}} | magis cantum mutatur \textit{V\textsuperscript{b}}}} uerbis.} Est autem \edtext{ditirambus}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}V\textsuperscript{b}v} | dichitambis \textit{P\textsuperscript{y}} | ditrambis \textit{P\textsuperscript{z}} | dytiranbum \textit{G\textsuperscript{u}}}} cantus qui \edtext{concidit}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | accidit \textit{V\textsuperscript{z}}}} in \edtext{frigistum}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | fixgistum \textit{P\textsuperscript{y}}}}, \edtext{unde}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} ‘ \edtext{ \edtext{8° \textit{politicorum} }{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}V\textsuperscript{a}mv} | scilicet politicum \textit{P\textsuperscript{x}}}} }{\Cfootnote[nosep]{\textit{ακπmv} | \textit{polliticorum} .8. \textit{P\textsuperscript{y}}}} \edtext{\hyperref[Phil]{filoxenus}}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}mv} | philoseus \textit{P\textsuperscript{x}} | filoserius \textit{V\textsuperscript{a}} | phylosherius \textit{V\textsuperscript{b}} | phiis \textit{P\textsuperscript{z}}}} conatus in \edtext{dorista}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | corista \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | corialtera \textit{V\textsuperscript{o}}}} facere \edtext{ditirambum}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}mv} | dichitambis \textit{P\textsuperscript{y}} | distanbu \textit{V\textsuperscript{z}}}} \edtext{fabulas}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}} | fabulans \textit{γE\textsuperscript{a}mv}}} non fuit \edtext{potens}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}}, sed ab \edtext{ipsa}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | ipso \textit{π} | illa \textit{E\textsuperscript{a}}}} \edtext{natura}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} decidit in \edtext{frigistum.}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{}{\Afootnote[nosep]{Arist. \textit{Pol.} VIII, 1342b, l. 9}}’ Hec autem \edtext{.xlviii.}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | 28 \textit{P\textsuperscript{z}}}} \edtext{erunt}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | fiunt \textit{P\textsuperscript{y}} | \textit{om}. \textit{V\textsuperscript{a}}}} manifesta adhuc. Siquidem \edtext{rediens}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | rediens ad \textit{π}}} leges \edtext{inquit}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv} | in quid \textit{V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}}}} quia \edtext{cantus huius dicti}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}} | cantus huiusmodi dicti \textit{V\textsuperscript{b}mv} | \textit{om}. \textit{π}}} \edtext{leges fiebant ut dictum continue}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}} | ut dictum est leges fiebant continue \textit{π} | leges fiebant ut dictum est continue \textit{γλmv}}} faciendo \edtext{per mutationem}{\Cfootnote[nosep]{\textit{ακmv} | mutationem \textit{π}}}. \textit{Secundum uerba ideo non \edtext{sunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} amplius conuersiui, sed \edtext{tamen}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | cum \textit{P\textsuperscript{y}V\textsuperscript{a}}}} antiquitus \edtext{fuerunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | finitur \textit{P\textsuperscript{u}}}}. \edtext{Cuius quidem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | Huius \textit{V\textsuperscript{a}}}} \edtext{causa}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | causa est \textit{V\textsuperscript{a}mv}}} quoniam ab antiquo \edtext{ipsimet}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | corpore \textit{P\textsuperscript{z}}}} liberi \edtext{nobilesque}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | nobiles qui \textit{P\textsuperscript{z}} | nobiles \textit{P\textsuperscript{x}} | ignobilesque \textit{P\textsuperscript{y}}}} faciebant \edtext{cantus}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{rotationes}{\Cfootnote[nosep]{\textit{κ} | rotatos \textit{γmv} | rotatiuos \textit{πE\textsuperscript{a}} | recitatiuos \textit{P\textsuperscript{y}}}} uel \edtext{conuersiuos}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | conuersiones \textit{P\textsuperscript{y}}}} \edtext{quoniam}{\Cfootnote[nosep]{\textit{απmv} | quantum \textit{V\textsuperscript{m}} | quam \textit{P\textsuperscript{x}}}} plures \edtext{erant}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}}, et ideo difficile fiebat \edtext{eis}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | eos \textit{P\textsuperscript{x}}}} cantare agonistice uel \edtext{leges}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | legem \textit{G\textsuperscript{u}} | legere \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} facere.} \edtext{Choros}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}mv} | Coram \textit{V\textsuperscript{a}}}} autem faciebant siue cantus \edtext{conuersiuos}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | conuersionis \textit{P\textsuperscript{y}}}} qui fiunt in choris, \edtext{ubi}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | nisi \textit{E\textsuperscript{a}}}} sufficientes \edtext{et quieti}{\Cfootnote[nosep]{\textit{ακmv} | etiam qui \textit{π}}} amplius \edtext{imitari conantur}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{z}mv} | uolunt imitari \textit{π}}} melodiam quam \edtext{uerba}{\Cfootnote[nosep]{\textit{ακπ} | uerbo \textit{mv}}}. \textit{Propter \edtext{quod}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} delectabile \edtext{cantare secundum armoniam}{\Cfootnote[nosep]{\textit{απmv} | est cantare secundum armoniam \textit{λ} | est secundum armoniam cantare \textit{P\textsuperscript{x}}}} illam \edtext{commutatam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}} | commutatiuam \textit{P\textsuperscript{y}mv} | commutationem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | continentem \textit{P\textsuperscript{z}} | commitationem \textit{V\textsuperscript{a}} | connitatiuam \textit{V\textsuperscript{b}}}} ubi pauci conueniebant. Nam \edtext{hii de facili}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | de facili hii \textit{P\textsuperscript{p}V\textsuperscript{a}} | hii qui de facili \textit{G\textsuperscript{u}}}} possunt mutare cantum \edtext{pluribus}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | multis \textit{V\textsuperscript{a}}}} \edtext{mutationibus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | mutatoribus \textit{G\textsuperscript{u}P\textsuperscript{p}}}}, \edtext{et id est quod dicitur: quod vni mutare cantum pluribus mutationibus}{\Cfootnote[nosep]{\textit{κV\textsuperscript{a}mv} | \textit{om}. \textit{πE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}}}} \edtext{facilius}{\Cfootnote[nosep]{\textit{αλπmv}}} est quam \edtext{multis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | multus \textit{P\textsuperscript{z}} | paucis \textit{P\textsuperscript{p}}}}, quare \edtext{agoniste}{\Cfootnote[nosep]{\textit{ακmv} | agonistice \textit{π}}} cantantes uel leges consuetudinem \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | huiusmodi \textit{G\textsuperscript{u}V\textsuperscript{b}}}} ut tactum \edtext{est}{\Cfootnote[nosep]{\textit{γκπmv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}}}} \edtext{obseruant}{\Cfootnote[nosep]{\textit{ακmv} | obseruabant \textit{π}}}.} \edtext{Qui}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}V\textsuperscript{c}mv} | Quod \textit{P\textsuperscript{x}} | Que \textit{C\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | Sed \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}}}} \edtext{mutatione}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | mutationem \textit{λ} | imitatione \textit{G\textsuperscript{u}}}} uerborum \edtext{mutantur}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{m}} | imitantur \textit{M\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}mv} | immutantur \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}}}}, \textit{et \edtext{ideo}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | non \textit{G\textsuperscript{u}}}} melodias ualde simplices faciebant et \edtext{incompositas}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | compositas \textit{P\textsuperscript{q}P\textsuperscript{u}}}}, quoniam \edtext{conuersiuus}{\Cfootnote[nosep]{\textit{ακmv} | conuersus \textit{π}}} cantus quo utebantur est numerus \edtext{quidem}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}P\textsuperscript{y}} | quidam \textit{γλE\textsuperscript{a}mv}}} simplex, qui \edtext{vnitate}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | vnitatem \textit{P\textsuperscript{u}} | in unitate \textit{P\textsuperscript{y}} | musice \textit{P\textsuperscript{x}}}} tantum \edtext{mensurabatur}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}P\textsuperscript{y}mv} | mensurabitur \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{z}} | mensurabilis est \textit{M\textsuperscript{a}} | mensurabis \textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}},} ita quod conuersio si \edtext{aliqua}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}} | alia \textit{γE\textsuperscript{a}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} erat \edtext{ibi}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ubi \textit{M\textsuperscript{a}}}} potius \edtext{in}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} simplicem \edtext{quam \edtext{in}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{compositum}{\Cfootnote[nosep]{\textit{αλmv} | compositam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | compotum \textit{P\textsuperscript{x}}}}, \edtext{referebatur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}V\textsuperscript{o}mv}}}, ut in numeris \edtext{dicimus}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}V\textsuperscript{z}mv} | dicto \textit{P\textsuperscript{x}V\textsuperscript{m}} | diuinis \textit{E\textsuperscript{a}}}} illum numerum simplicem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} qui \edtext{continue}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{crescit}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}v}}} mensuratus \edtext{per vnitatem}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | permutatione \textit{P\textsuperscript{y}}}}. Similiter et cantus potest \edtext{simplex dici}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}V\textsuperscript{o}mv} | dici simplex \textit{P\textsuperscript{z}} | simpliciter dici \textit{E\textsuperscript{a}} | duplex dici \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{qui}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | que \textit{P\textsuperscript{x}P\textsuperscript{z}}}} \edtext{contineatur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{a}mv} | continetur \textit{V\textsuperscript{b}} | continuatur \textit{πP\textsuperscript{y}}}} \edtext{per additionem solam}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | solum per additionem \textit{π} | per additionem soli \textit{V\textsuperscript{z}}}} uerbi ad \edtext{ista}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | istam \textit{M\textsuperscript{a}M\textsuperscript{b}} | verba \textit{πE\textsuperscript{a}P\textsuperscript{y}}}}. +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{EADEM.}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | EANDEM. \textit{πE\textsuperscript{a}}}} } \edtext{Applicat}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | aplicat \surplus{aplicat} \textit{V\textsuperscript{a}}}} \edtext{istam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | illam \textit{P\textsuperscript{x}V\textsuperscript{z}}}} causam \edtext{ad quesitum adhuc}{\Cfootnote[nosep]{\textit{λ} | ad quesitum ad hoc \textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}} | ad quesitum aliud huic \textit{γπmv}}}, \edtext{simile}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | similem \textit{λ}}} dicens quod \textit{ \edtext{ista}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}mv} | illa \textit{V\textsuperscript{b}V\textsuperscript{m}} | ita \textit{P\textsuperscript{p}}}} eadem \edtext{causa est}{\Cfootnote[nosep]{\textit{κπ} | est causa \textit{γE\textsuperscript{a}mv} | causa \textit{P\textsuperscript{y}}}}, \edtext{quia}{\Cfootnote[nosep]{\textit{κ} | quare \textit{απmv}}} \edtext{illi}{\Cfootnote[nosep]{\textit{λ} | ille \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}} | isti \textit{γP\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | iste \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{cantus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cantus scilicet \textit{P\textsuperscript{z}}}} qui \edtext{a scena}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}mv} | scena \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | ascene \textit{G\textsuperscript{u}P\textsuperscript{q}}}} dicuntur non sunt conuersiui, chori \edtext{autem}{\Cfootnote[nosep]{\textit{ακπ} | aut \textit{mv}}} \edtext{conuertuntur}{\Cfootnote[nosep]{\textit{ακπ}}}, \edtext{quoniam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | quia \textit{V\textsuperscript{z}}}} \edtext{ille}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | illi \textit{V\textsuperscript{a}P\textsuperscript{z}}}} qui \edtext{cantat}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | cantant \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}}}} a scena est \edtext{sicut}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | sicut qui \textit{V\textsuperscript{a}}}} \edtext{agonistice}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | agonista \textit{M\textsuperscript{a}V\textsuperscript{z}} | agoniste \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}}}} \edtext{cantans}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | cantat \textit{V\textsuperscript{a}}}} \edtext{aut}{\Cfootnote[nosep]{\textit{αλπmv} | que \textit{P\textsuperscript{x}}}} \edtext{leges}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | legens \textit{πE\textsuperscript{a}}}},} \edtext{cantat}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | cantus \textit{P\textsuperscript{y}}}} enim \edtext{agonizantium}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv}}} \edtext{gesta}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}} \edtext{commutans}{\Cfootnote[nosep]{\textit{αλπmv}}} \edtext{cantum}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} secundum uerba \edtext{ut}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | aut \textit{V\textsuperscript{a}}}} \edtext{agoniste}{\Cfootnote[nosep]{\textit{γκπ} | agonistice \textit{E\textsuperscript{a}mv} | agonistici \textit{P\textsuperscript{y}}}} \edtext{ceu}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} \edtext{visum est}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{z}mv} | visum \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{p}}}}, una enim \edtext{dictio}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} indiget \edtext{aspiratione}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | inspiratione \textit{π} | expiratione \textit{E\textsuperscript{a}} | apparatione \textit{V\textsuperscript{a}}}}, \edtext{alia uero}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | altera uero \textit{P\textsuperscript{y}} | alia \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} lenitate et \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | huiusmodi \textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}}}} \edtext{consimili}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | consimiliter \textit{G\textsuperscript{u}}}} alteratione. +\pend + +\pstart +\textbf{5} \textit{Sed \edtext{choricus}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} cantus \edtext{minus}{\Cfootnote[nosep]{\textit{λP\textsuperscript{y}V\textsuperscript{b}mv} | vnus \textit{πE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}}}} \edtext{commutatur}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}mv} | commutatus \textit{π} | alteratur commutatur \textit{P\textsuperscript{y}} | commitatur \textit{P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}}}},} amplius \edtext{enim}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | eius \textit{M\textsuperscript{a}}}} vnum tenorem et circulum retinet \edtext{conseruatum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | reseruatum \textit{P\textsuperscript{p}P\textsuperscript{u}}}}. \edtext{Notandum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | Nota \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} quod \edtext{a scena}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | scena \textit{P\textsuperscript{z}}}} multas habet significationes, aliquando \edtext{namque}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}V\textsuperscript{o}} | enim \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv}}} \edtext{idem est}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | idem \textit{E\textsuperscript{a}} | eadem est \textit{P\textsuperscript{z}} | ratione est \textit{P\textsuperscript{y}}}} quod \edtext{umbra}{\Cfootnote[nosep]{\textit{ακmv} | nichilominus \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | inquimus \textit{P\textsuperscript{p}}}} uel locus umbratus \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uel \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{coopertus}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{z}mv}}} in \edtext{teatro}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | intratio \textit{P\textsuperscript{z}}}} \edtext{dicitur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | diuiditur \textit{γmv}}}, \edtext{interdum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | etiam interdum \textit{π} | in circulum \textit{γmv}}} \edtext{totum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{teatrum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{o}mv} | tractum \textit{P\textsuperscript{z}}}}, et \edtext{quandoque}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | quando \textit{V\textsuperscript{b}} | quoniam \textit{P\textsuperscript{z}}}} recitatio operationis. \edtext{Vnde olim \edtext{poete}{\Cfootnote[nosep]{\textit{γπP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}mv} | pote \textsuperscript{de} \textit{E\textsuperscript{a}}}} libros \edtext{suos}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} deferebant a scene ut \edtext{appropriarentur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | approbarentur \textit{πP\textsuperscript{y}} | apropinquiuarentur \textit{V\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}}. Dicitur \edtext{etiam}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}} | et \textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}mv} | enim \textit{G\textsuperscript{u}}}} tabernaculum \edtext{mercenariorum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | mercendariorum \textit{V\textsuperscript{a}}}} \edtext{coopertum}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{z}mv}}} \edtext{asseribus}{\Cfootnote[nosep]{\textit{ακE\textsuperscript{a}G\textsuperscript{u}mv} | aceribus \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}}. Hic autem \edtext{per}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | pro \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{ascena}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ascene \textit{P\textsuperscript{y}}}} potest intelligi: locus \edtext{ubi colliguntur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in quo congregantur \textit{G\textsuperscript{u}P\textsuperscript{q}}}} homines ut gesta \edtext{librorum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}V\textsuperscript{c}mv} | liberorum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{cantare audiant et \edtext{insignium}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}V\textsuperscript{o}mv}}} }{\Cfootnote[nosep]{\textit{γκP\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | et insignium cantare audiant \textit{G\textsuperscript{u}P\textsuperscript{q}} | cantare audiatur et insignium \textit{P\textsuperscript{p}} | cantare audiante insignum \textit{E\textsuperscript{a}}}}. \edtext{Et \edtext{id}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | ratione \textit{P\textsuperscript{y}}}} etiam \edtext{.xxix.}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | 30º \textit{M\textsuperscript{a}M\textsuperscript{b}}}} \edtext{et .xlviii.}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | et 38º \textit{V\textsuperscript{z}} | 28 \textit{V\textsuperscript{a}}}} \edtext{apparebit}{\Cfootnote[nosep]{\textit{ακ} | patet \textit{mv}}} }{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 16. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Sextumdecimum problema}\label{edition-text book-19a part16}}{\lemma{Sextumdecimum + problema} \Cfootnote[nosep]{\textit{V\textsuperscript{a}mv} | «16m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{xvim.}Sextumdecimum. \textit{P\textsuperscript{y}} | 15tum problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DELECTABILIUS}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID DELECTABILIUS ANTIFONUM CONSONO? \textsuperscript{2}AUT QUIA MAGIS MANIFESTUM FIT CONSONARE? \textsuperscript{3}AUT QUANDO AD CONSONANTIAM CANTANT, NECESSE ENIM ALTERAM CONSONARE? QUARE DUE AD UNAM UOCEM FACTE DESTRUUNT ALTERAM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Decimum sextum problema. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} cantus antiphonus in quo \edtext{ \edtext{quedam extat}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}mv} | extat quedam \textit{P\textsuperscript{y}}}} resonantia}{\Cfootnote[nosep]{\textit{απmv} | quedam restat consonantia \textit{κ}}} uel \edtext{contra}{\Cfootnote[nosep]{\textit{γN\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}mv} | circa \textit{M\textsuperscript{a}} | etiam \textit{π}}} \edtext{consonantiam}{\Cfootnote[nosep]{\textit{κπN\textsuperscript{u}V\textsuperscript{a}mv} | sonantia \textit{P\textsuperscript{y}V\textsuperscript{b}} | consonantia uel etiam consonantia \textit{E\textsuperscript{a}}}} \edtext{tonorum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | tenorum \textit{G\textsuperscript{u}P\textsuperscript{z}}}} super \edtext{tonos}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}V\textsuperscript{b}mv} | tonis \textit{E\textsuperscript{a}} | chanos \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | cantus \textit{V\textsuperscript{a}}}} est \edtext{delectabilior}{\Cfootnote[nosep]{\textit{ακmv} | delectabilis magis \textit{π}}} \edtext{auditu}{\Cfootnote[nosep]{\textit{ακmv} | auditui \textit{π}}} quam sonus \edtext{qui est consonus}{\Cfootnote[nosep]{\textit{βγλπmv} | qui est sonus \textit{P\textsuperscript{x}} | \textit{om}. \textit{E\textsuperscript{a}}}} et vniformis in quo non sentitur \edtext{contra}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | circa \textit{M\textsuperscript{a}} | aliqua \textit{π}}} \edtext{resonantia}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}mv} | resonantiam \textit{κ} | sonantia \textit{P\textsuperscript{y}}}}.} \edtext{Apparentur}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | Apparent \textit{E\textsuperscript{a}N\textsuperscript{u}} | Apparatur \textit{C\textsuperscript{a}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{uerbi gratia}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | ut gratia \textit{P\textsuperscript{x}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} sicut \edtext{si}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} duo \edtext{succinant}{\Cfootnote[nosep]{\textit{γP\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | subcinat \textit{V\textsuperscript{m}}}} equaliter et tertius \edtext{precinat}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | subcinant \textit{V\textsuperscript{z}}}} \edtext{hic}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv} | hoc \textit{E\textsuperscript{a}V\textsuperscript{z}}}} \edtext{precinens}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | tertius \textit{V\textsuperscript{a}}}} \edtext{contrasonat}{\Cfootnote[nosep]{\textit{βλP\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | consonat \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}mv}}} et \edtext{antiphonizat}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv}}} \edtext{super illos}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | si super illos \textit{mv} | super istos \textit{P\textsuperscript{p}P\textsuperscript{u}} | gratia istos \textit{P\textsuperscript{x}} | contra illos \textit{V\textsuperscript{m}}}} \edtext{duos}{\Cfootnote[nosep]{\textit{βγλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | duos etcetera \textit{G\textsuperscript{u}P\textsuperscript{x}} | \textit{om}. \textit{E\textsuperscript{a}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } \edtext{Soluit}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{assignans}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | assignando \textit{M\textsuperscript{a}} | et assignat \textit{πP\textsuperscript{y}}}} \edtext{duplicem causam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | duas + causas \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, dicens \textit{ \edtext{id}{\Cfootnote[nosep]{\textit{βκ} | illud \textit{γmv} | ideo \textit{πE\textsuperscript{a}}}} esse quoniam sonus \edtext{antiphonus}{\Cfootnote[nosep]{\textit{βγκN\textsuperscript{u}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{redditur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | redditur et \textit{β}}} manifestior et sensibilior \edtext{sono}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sonis \textit{G\textsuperscript{u}}}} consonante et vniformi.} \edtext{Quod}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Qui \textit{G\textsuperscript{u}}}} autem \edtext{sensibilius est sufficienter}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | scensibilius suficienter est \textit{V\textsuperscript{a}} | est sensibilius sufficienter \textit{π}}} magis \edtext{delectat}{\Cfootnote[nosep]{\textit{αλπmv}}}, \edtext{eo quod non}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} est tale sicut apparet in \edtext{tactu}{\Cfootnote[nosep]{\textit{αλπmv} | cantu \textit{P\textsuperscript{x}}}} relatione \edtext{aliorum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} sensuum. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT QUANDO.}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{b}mv} | AUT QUESITI. \textit{P\textsuperscript{x}V\textsuperscript{m}} | AUT QUIA. \textit{V\textsuperscript{a}} | AUT. \textit{V\textsuperscript{z}}}} } Assignat aliam causam, dicens quod \textit{ \edtext{quando}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{aliqui cantant}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}N\textsuperscript{u}mv} | cantantur aliqua \textit{P\textsuperscript{y}}}} \edtext{consonantiam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | consonantia \textit{P\textsuperscript{z}}}} facientes in \edtext{qua}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}N\textsuperscript{u}mv} | quo \textit{P\textsuperscript{y}}}} \edtext{acutum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | acentum \textit{P\textsuperscript{z}}}} non \edtext{excedat}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | excedit \textit{G\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{y}}}} graue \edtext{aut}{\Cfootnote[nosep]{\textit{ακmv} | uel \textit{π}}} econuerso,\edtext{necesse}{\Cfootnote[nosep]{\textit{βπP\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | tunc necesse \textit{V\textsuperscript{a}} | necessarium \textit{M\textsuperscript{a}}}} est quod uox \edtext{vnius}{\Cfootnote[nosep]{\textit{βκN\textsuperscript{u}mv} | unius uox \textit{P\textsuperscript{y}} | huius \textit{πE\textsuperscript{a}}}} \edtext{consonet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | consonat \textit{G\textsuperscript{u}}}} omnino uoci \edtext{alterius}{\Cfootnote[nosep]{\textit{βγκπmv} | alteri \textit{E\textsuperscript{a}}}},} \edtext{sed debet}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}} | si debet \textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{z}V\textsuperscript{o}mv} | sicut dicere \textit{P\textsuperscript{z}}}} fieri consonantia. Si autem tertia \edtext{adueniens}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | adueniet \textit{P\textsuperscript{y}}}} non \edtext{antiphonet}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | antiphonat \textit{P\textsuperscript{z}} | autem antiphonet \textit{P\textsuperscript{p}} | antiphanizet \textit{P\textsuperscript{x}}}}, \edtext{ymmo}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}} | sermo \textit{P\textsuperscript{y}}}} \edtext{consonizare}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | consonare \textit{P\textsuperscript{z}}}} uelit, \edtext{oportet}{\Cfootnote[nosep]{\textit{βγκπmv} | debet \textit{E\textsuperscript{a}}}} eam destrui, \textit{ \edtext{quoniam}{\Cfootnote[nosep]{\textit{ακmv} | quando \textit{π}}} due uoces \edtext{ \edtext{equalis uigoris}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | uigoris equalis \textit{V\textsuperscript{z}} | equales uigoris \textit{P\textsuperscript{z}V\textsuperscript{m}}}} ad tertiam \edtext{relate}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}mv} | relate et \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | ad tertiam relate equalis vigoris \textit{γ}}} \edtext{destruunt}{\Cfootnote[nosep]{\textit{βγπV\textsuperscript{m}V\textsuperscript{z}mv} | destruuntur \textit{M\textsuperscript{a}} | destruant \textit{E\textsuperscript{a}P\textsuperscript{x}}}} et \edtext{occultant}{\Cfootnote[nosep]{\textit{αλπmv}}} \edtext{aliam}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}E\textsuperscript{a}mv} | alteram \textit{π} | \textit{om}. \textit{P\textsuperscript{y}}}} penitus tertiam.} +\pend + +\pstart +\textbf{4} \edtext{ \edtext{Notandum}{\Cfootnote[nosep]{\textit{ακmv} | Notandum quod \textit{P\textsuperscript{z}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | Nota \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} secundum ‘boecium primo \textit{musice} \edtext{quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{consonantia}{\Cfootnote[nosep]{\textit{αλπmv} | consonantiam \textit{P\textsuperscript{x}}}} est acuti soni \edtext{grauisque}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | grauis quia \textit{P\textsuperscript{z}}}} \edtext{mixtura}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | mixtatio \textit{P\textsuperscript{x}}}} suauiter \edtext{vniformiterque}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | et uniformiterque \textit{M\textsuperscript{a}} | et uniformiter quod \textit{E\textsuperscript{a}} | et vniformiter \textit{π}}} auribus \edtext{accidens}{\Cfootnote[nosep]{\textit{ακmv} | accedens \textit{π}}}. Sed dissonantia est duorum sonorum sibimet \edtext{impermixtorum}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}v}}} ad \edtext{aurem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv} | aures \textit{P\textsuperscript{y}V\textsuperscript{b}}}} \edtext{ueniens}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | perueniens \textit{λ}}} aspera \edtext{atque}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{λ} | utcunque \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{iniocunda}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | iocunda \textit{V\textsuperscript{a}}}} \edtext{percussio}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}. Nam dum \edtext{sibimet}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | sibi \textit{M\textsuperscript{a}}}} \edtext{misceri}{\Cfootnote[nosep]{\textit{βγP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | miseri \textit{E\textsuperscript{a}} | permisceri \textit{M\textsuperscript{a}} | conmisceri \textit{π}}} \edtext{uolunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uoluit \textit{P\textsuperscript{z}}}} et quodammodo \edtext{integri}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | integer \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | integra \textit{P\textsuperscript{z}}}} \edtext{uterque nititur}{\Cfootnote[nosep]{\textit{βγκmv} | utraque nititur \textit{E\textsuperscript{a}} | nititur vterque \textit{π}}} peruenire, \edtext{cunque alter}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | cum alter \textit{G\textsuperscript{u}} | equaliter \textit{V\textsuperscript{a}}}} alteri \edtext{officit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | efficit \textit{G\textsuperscript{u}P\textsuperscript{u}}}} ad sensum insuauiter, \edtext{uterque}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | utrisque \textit{G\textsuperscript{u}}}} \edtext{transmittitur}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | transmicteri \textit{N\textsuperscript{u}}}}.\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} I .8 (Freidlein 195, ll. 6–13)}}’ Videtur siquidem quantum facit ad sermonem \hyperref[Ar]{ \edtext{aristoteles}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv}}} } quod antiphonus sit delectabilior ex contrariis ualde distantibus consurgens ut ex \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ypatem \textit{M\textsuperscript{a}}}} et \edtext{nete}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | nete uel nite \textit{π}}}, \edtext{consonans}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | consonant \textit{M\textsuperscript{a}} | consonatus \textit{P\textsuperscript{z}}}} \edtext{autem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aut \textit{G\textsuperscript{u}}}} \edtext{quando}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}V\textsuperscript{z}mv} | quoniam \textit{P\textsuperscript{x}} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{ex non adeo}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | non ex adeo \textit{P\textsuperscript{y}V\textsuperscript{a}} | non ex ita \textit{P\textsuperscript{x}} | non adeo \textit{π}}} \edtext{differentibus}{\Cfootnote[nosep]{\textit{ακmv} | distantibus siue differentibus \textit{π}}}, sicut ex cordis \edtext{mediis}{\Cfootnote[nosep]{\textit{ακπ} | melodiis \textit{mv}}}, ut apparebit consequenter. \edtext{}{\Cfootnote{etcetera. \textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 17; problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Decimumseptimum problema}\label{edition-text book-19a part17}}{\lemma{Decimumseptimum + problema} \Cfootnote[nosep]{\textit{γmv} | «17m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{decimum septimum}Decimumseptimum. \textit{P\textsuperscript{y}} | 16tum. Problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID QUINQUE}{\Cfootnote[nosep]{\textit{P\textsuperscript{u}V\textsuperscript{m}} | PROPTER QUID QUANDOQUE \textit{P\textsuperscript{p}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID QUINQUE NON CANTANT ANTIFONAM? \textsuperscript{2}AUT QUIA NON EADEM CONSONA CONSONANTIE, QUEMADMODUM IN DYAPASON? ILLA ENIM IN GRAUI PROPORTIONALE, SICUT ACUTA IN ACUTO, QUEMADMODUM IGITUR EADEM EST SIMUL ET ALIA. QUE AUTEM IN DYAPENTE ET DYATESSERON NON HABENT, ITA QUARE NON APPARET QUANDO ANTIFONE SONUS, NON ENIM EST IDEM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Decimum septimum problema. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} quinque cantantes, uel \edtext{etiam}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | et \textit{P\textsuperscript{p}} | \textit{om}. \textit{V\textsuperscript{b}}}} quatuor, \edtext{vnam non}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | vna non \textit{mv} | non unam \textit{M\textsuperscript{a}}}} cantant \edtext{antiphonam}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}} | antiphona \textit{E\textsuperscript{a}N\textsuperscript{u}mv} | anphpuam \textit{V\textsuperscript{a}}}},} tres \edtext{autem uel}{\Cfootnote[nosep]{\textit{ακπ} | aut \textit{mv}}} sex possunt cantare? +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } Soluit dicens causam esse \textit{quoniam \edtext{ipsa}{\Cfootnote[nosep]{\textit{κ} | ista \textit{απmv}}} proportio \edtext{que}{\Cfootnote[nosep]{\textit{κ} | quam \textit{απmv}}} \edtext{habet}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}M\textsuperscript{a}} | habent \textit{βγπV\textsuperscript{m}V\textsuperscript{z}mv}}} quinque ad inuicem non \edtext{est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | est debita \textit{P\textsuperscript{z}}}} \edtext{proportio}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | concordia \textit{G\textsuperscript{u}P\textsuperscript{q}}}} debita que \edtext{consonet}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | consonat \textit{G\textsuperscript{u}P\textsuperscript{q}} | conicet \textit{P\textsuperscript{y}}}} et \edtext{correspondeat}{\Cfootnote[nosep]{\textit{βγκπmv}}} tali consonantie in qua \edtext{sit}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} \edtext{antiphonizare, quemadmodum}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{antiphonizare contingit}{\Cfootnote[nosep]{\textit{βγκmv} | contingit \textit{πE\textsuperscript{a}}}} \edtext{in}{\Cfootnote[nosep]{\textit{αλπmv} | et \textit{P\textsuperscript{x}}}} dyapason, ubi \edtext{est}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{proportio}{\Cfootnote[nosep]{\textit{αλπmv} | proportio et \textit{P\textsuperscript{x}}}} dupla. Ipsa enim \edtext{habet proportionem}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}mv} | proportionem habet \textit{P\textsuperscript{y}} | habet proportiones \textit{E\textsuperscript{a}}}} \edtext{in graui}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | magnam \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, graue enim proportionatum est graui \edtext{in ipsa}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}, \edtext{sicut}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | enim \textit{V\textsuperscript{m}}}} acutum acuto \edtext{et graue cum acuto}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | et \textit{P\textsuperscript{y}} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{etiam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{πP\textsuperscript{y}}}}.} Hoc autem non est \edtext{in}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} aliis. \textit{ \edtext{Ymmo}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{sicut}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | in sicut \textit{P\textsuperscript{x}} | sicut in \textit{P\textsuperscript{y}}}} ipsa est eadem inter se et \edtext{proportionalis}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}} | proportionaliter \textit{V\textsuperscript{z}}}} vno \edtext{modo}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} ita, secundum alium modum \edtext{habet}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} \edtext{quandam alietatem et}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | alietatem et \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{G\textsuperscript{u}}}} diuersitatem inter se, eo quod in ipsa est excessus \edtext{manifestus}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}}, \edtext{etsi}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{G\textsuperscript{u}}}} sit ad \edtext{equalitatem}{\Cfootnote[nosep]{\textit{αλπmv} | inequalitatem \textit{P\textsuperscript{x}}}} reductus. Sed \edtext{consonantie}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | consonauere \textit{P\textsuperscript{z}}}} uel proportiones que sunt circa dyatesseron uel dyapente non sic \edtext{se habent}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{a}P\textsuperscript{x}mv} | habent \textit{E\textsuperscript{a}} | se habet \textit{V\textsuperscript{m}V\textsuperscript{z}}}}. \edtext{neque}{\Cfootnote[nosep]{\textit{ακmv}}} \edtext{enim}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{in hiis}{\Cfootnote[nosep]{\textit{βγκπ} | hiis \textit{E\textsuperscript{a}} | in eis \textit{mv}}} \edtext{tantus}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}} | cantus \textit{γE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} excessus, \edtext{neque}{\Cfootnote[nosep]{\textit{ακmv}}} ad equalitatem \edtext{sit}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | sic \textit{βM\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} reductus. Et \edtext{ideo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | non \textit{P\textsuperscript{z}}}} sonus licet fiat antiphonus, secundum \edtext{istas}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | illas \textit{γmv}}} \edtext{duas}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} proportiones non redditur manifestus. Non \edtext{enim}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{est in ipso}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | in ipso est \textit{P\textsuperscript{y}}}} \edtext{idemptitas}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}}}} cum quodam excessu sicut \edtext{dictum est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | dicunt \textit{P\textsuperscript{y}}}} in dyapason euenire.} Id \edtext{autem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} potest \edtext{declarari}{\Cfootnote[nosep]{\textit{αλπmv} | delectari \textit{P\textsuperscript{x}}}} \edtext{ex}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in \textit{P\textsuperscript{p}}}} naturis, quia \edtext{si}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | sicut \textit{M\textsuperscript{a}}}} debet cantari \edtext{antiphona}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv}}}, oportet debitam proportionem \edtext{interuenire}{\Cfootnote[nosep]{\textit{ακmv} | ante venire \textit{π}}} \edtext{ \edtext{superantium}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | superantium et \textit{P\textsuperscript{z}}}} ad superatos}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | sirantium ad frantos \textit{γmv}}} et econtra \edtext{secundum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sed \textit{G\textsuperscript{u}}}} \edtext{graue et acutum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | acutum et graue \textit{β}}}. \edtext{Sed}{\Cfootnote[nosep]{\textit{αλπmv} | Et \textit{P\textsuperscript{x}}}} id non \edtext{accidit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} in quinque uocibus, \edtext{nam \edtext{uel}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}V\textsuperscript{b}mv} | universaliter \textit{κ}}} quatuor \edtext{antiphonizabunt uno}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}V\textsuperscript{b}mv} | antiphonizabunt \textit{β}}} aut \edtext{tres}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | tribus uel \textit{G\textsuperscript{u}P\textsuperscript{p}}}} duobus}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}, \edtext{non quidem}{\Cfootnote[nosep]{\textit{απmv} | non quid \textit{M\textsuperscript{a}} | nunc quid \textit{V\textsuperscript{z}} | numquam \textit{P\textsuperscript{x}V\textsuperscript{m}}}} quatuor \edtext{contra}{\Cfootnote[nosep]{\textit{αλπmv} | 4a. \textit{P\textsuperscript{x}}}} vnum, quia uox eius oppositis \edtext{obtunderetur}{\Cfootnote[nosep]{\textit{βγλπmv} | obtundentur \textit{E\textsuperscript{a}} | obtundetur \textit{P\textsuperscript{x}}}} omnino, ita \edtext{ut}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | quod \textit{V\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{p}}}} \edtext{non}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{possit}{\Cfootnote[nosep]{\textit{ακmv} | possint \textit{π}}} sufficienter \edtext{percipi}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}}. Neque tres contra duos, \edtext{quoniam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} \edtext{propter}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{paruum}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | partium «paruum» (in mg.) \textit{V\textsuperscript{o}}}} excessum non poterit excedentia \edtext{manifestari vnius ad alterum, quare \edtext{non contraphonizare contingit}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{m}} | contingit non contraphonizare \textit{V\textsuperscript{a}} | non contraphonizare \textit{P\textsuperscript{y}} | non contrasonizare contingit \textit{mv} | non antiphonizare contingit \textit{G\textsuperscript{u}}}} \edtext{ \edtext{cum id}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | cum illud \textit{E\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{b}}}} requiratur omnifariam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | moueri \textit{P\textsuperscript{z}}}}. \edtext{Unde relinquitur}{\Cfootnote[nosep]{\textit{γκπmv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{quod antiphonizare, ut apparebit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}v} | ut apparebit quod antiphonizare \textit{π} | quod antiphonizare \textit{V\textsuperscript{a}} | ut apparebit \textit{P\textsuperscript{y}}}} \edtext{extet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | existet \textit{G\textsuperscript{u}P\textsuperscript{q}}}} secundum dyapason proprie. \edtext{}{\Cfootnote{et cetera \textit{V\textsuperscript{z}} | et cetera et cetera \textit{P\textsuperscript{z}} | sequitur 18; problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Decimumoctauum problema}\label{edition-text book-19a part18}}{\lemma{Decimumoctauum + problema} \Cfootnote[nosep]{\textit{γmv} | «18m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | Decimumoctauum. \surplus{decimum + octauum.} \textit{P\textsuperscript{y}} | 17m. Problema \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DYAPASON}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID DYAPASON CONSONANTIA CANTATUR SOLA? ORGANIZANT ENIM SECUNDUM HANC, ALIAM NULLAM. \textsuperscript{2}AUT QUIA SOLA EX ANTIPHONIS EST CORDIS, IN ANTIPHONIS AUTEM ET ALTERAM SI CANTAT, IDEM FACIT. UNA ENIM QUODAMMODO UTRORUNQUE HABET CORDAS, QUARE ET UNA CANTATA IN HAC CONSONANTIA CANTATUR SYMPHONIA ET AMBO CANTANTES. \textsuperscript{3}AUT HAC QUIDEM CANTATA. HAC UERO FISTULATA, QUEMADMODUM UNAM UTRANQUE CANTANT. PROPTER QUOD SOLA CANTATUR, QUIA UNAM HABENT CORDE UOCEM ANTIPHONAM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Decimum octauum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | Quare cum \textit{G\textsuperscript{u}} | Querit quare \textit{λ}}} dyapason sola consonantiarum \edtext{cantatur maxime}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | maxime cantatur \textit{G\textsuperscript{u}P\textsuperscript{q}} | cantanti maxime \textit{E\textsuperscript{a}} | maxime \textit{P\textsuperscript{p}}}} \edtext{consonans}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | sonans \textit{V\textsuperscript{m}} | consonantiarum \textit{P\textsuperscript{y}}}} inter ceteras? \edtext{Quod ostenditur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{quia}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv} | quoniam \textit{P\textsuperscript{y}V\textsuperscript{b}}}} secundum \edtext{ipsam}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | ipsas \textit{V\textsuperscript{a}P\textsuperscript{u}}}} cantantes \edtext{organizant}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}mv}}} \edtext{uoces}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}V\textsuperscript{o}mv} | uocem \textit{G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{m}}}} in \edtext{altum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | alterum \textit{P\textsuperscript{z}}}} \edtext{leuantes}{\Cfootnote[nosep]{\textit{κ} | eleuantes \textit{απmv}}}, \edtext{quod secundum}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quia secundum \textit{E\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{nullam}{\Cfootnote[nosep]{\textit{βγG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | nullam uero \textit{P\textsuperscript{z}} | nullum \textit{E\textsuperscript{a}} | ullam \textit{V\textsuperscript{m}}}} aliarum \edtext{ita}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | sic \textit{G\textsuperscript{u}P\textsuperscript{q}} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{manifeste}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | melodice \textit{P\textsuperscript{y}}}} agere \edtext{contingit}{\Cfootnote[nosep]{\textit{αλπmv}}}.} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | AUT QUIA \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv}}} }. \edtext{Soluit dicens}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | Dicit \textit{V\textsuperscript{a}}}} \edtext{causam esse primam}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | primam causam esse \textit{P\textsuperscript{p}} | causam esse \textit{V\textsuperscript{a}} | causam esse primo \textit{G\textsuperscript{u}} | causam esse propriam \textit{V\textsuperscript{z}}}} \textit{quoniam ipsa \edtext{sola}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} constituitur ex cordis antiphonis seu consonantibus \edtext{ut}{\Cfootnote[nosep]{\textit{βγκπmv} | in \textit{E\textsuperscript{a}}}} \edtext{graui}{\Cfootnote[nosep]{\textit{ακmv} | graui et \textit{π}}} acuto \edtext{per}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | propter \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{z}}}} proportionem duplam.\edtext{In antiphonis enim cordis ita se habet}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | \textit{om}. \textit{γmv}}} \edtext{quod si altera \edtext{cantetur}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}} | cantetur simul \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}} | \textit{om}. \textit{γmv}}} \edtext{siue \edtext{tangatur}{\Cfootnote[nosep]{\textit{βγG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | tangetur \textit{E\textsuperscript{a}} | tangitur \textit{M\textsuperscript{a}}}}, ut \edtext{media in quam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | medio in qua \textit{M\textsuperscript{a}V\textsuperscript{z}}}} ambe \edtext{declinant}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | declinent \textit{G\textsuperscript{u}} | determinant \textit{P\textsuperscript{x}}}} extreme ut apparebit, \edtext{idem fit}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | idem sit \textit{E\textsuperscript{a}G\textsuperscript{u}} | iterum ad idem \textit{V\textsuperscript{a}}}},}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} } \edtext{ \edtext{ac si}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | si \textit{κ}}} \edtext{ambe cantarentur}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | cantarentur ambe \textit{P\textsuperscript{u}} | ambe cantantur \textit{M\textsuperscript{a}} | ambe cantarent \textit{P\textsuperscript{x}} | ambo cantarentur \textit{G\textsuperscript{u}}}}, \edtext{eo}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | ita \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | et \textit{V\textsuperscript{z}}}} quod \edtext{illa}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | illam \textit{N\textsuperscript{u}} | ipsa \textit{V\textsuperscript{b}}}} \edtext{vna}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | non \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} habet \edtext{in se aliqualiter}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aliqualiter in se \textit{P\textsuperscript{y}} | in se aliquam \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{ut in virtute}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ut in unitate \textit{N\textsuperscript{u}} | ut virtute \textit{V\textsuperscript{a}} | virtute \textit{π}}} \edtext{cordas}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cordis \textit{G\textsuperscript{u}}}} vtrorumque sonorum puta grauis et \edtext{acuti}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | acute \textit{V\textsuperscript{m}}}}, quare accidit \edtext{in}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{z}mv} | et \textit{V\textsuperscript{m}} | ex \textit{M\textsuperscript{a}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}V\textsuperscript{b}mv}}} \edtext{consonantia}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} quod vna \edtext{cantata uel}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | cantilena \textit{P\textsuperscript{y}}}} \edtext{pulsata}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | pulsetur \textit{P\textsuperscript{y}}}} cantetur et altera, ac si ambe cantarentur, propter \edtext{conuenientiam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | inconuenientiam \textit{V\textsuperscript{z}}}} quam \edtext{habent}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | habet \textit{M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{z}}}} in \edtext{medio}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | media \textit{G\textsuperscript{u}}}}, \edtext{ceu ostendunt}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{z}mv} | ceu ostenduntur \textit{N\textsuperscript{u}} | seu ostendunt \textit{E\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | sicut ostendunt \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}}}} \edtext{pigmenta}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv}}} \edtext{ex diuersis}{\Cfootnote[nosep]{\textit{αλπmv} | ex diuersis \textit{(\textup{\sic{ex diuersis ex diuersis}} a.c.)} \textit{P\textsuperscript{x}}}} optime \edtext{constructa}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | constituta \textit{V\textsuperscript{m}}}} in saporem \edtext{consurgentia}{\Cfootnote[nosep]{\textit{ακmv} | concurrentia \textit{π}}} \edtext{delectamentum}{\Cfootnote[nosep]{\textit{κ} | delectatiuum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | delectantium \textit{P\textsuperscript{z}} | delectatium \textit{E\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | AUT QUIA \textit{mv} | QUOD \textit{V\textsuperscript{m}}}}.} \edtext{Assignat aliam causam dicens}{\Cfootnote[nosep]{\textit{αλπ} | assignat aliam causam dicens causam \textit{mv} | soluit dicens causam \textit{P\textsuperscript{x}}}} \edtext{ideo esse}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}} | esse ideo \textit{mv} | id esse \textit{P\textsuperscript{y}} | esse \textit{P\textsuperscript{x}}}} \textit{ \edtext{quia}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | quoniam \textit{P\textsuperscript{z}V\textsuperscript{b}}}} si vna \edtext{cordarum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | corda \textit{β}}} cantetur ut ypate et altera fistuletur ut \edtext{nete}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{y}mv} | nete tunc \textit{P\textsuperscript{z}} | vite \textit{P\textsuperscript{u}V\textsuperscript{c}}}} cantando et fistulando utrobique cantatur \edtext{vna quia media}{\Cfootnote[nosep]{\textit{ακmv} | quia media \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{z}}}}.\edtext{Et ideo sola \edtext{symphonia}{\Cfootnote[nosep]{\textit{βP\textsuperscript{x}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}}}} cantatur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}, \edtext{quoniam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | et propter hoc \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} corde \edtext{cantate}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | cantante \textit{V\textsuperscript{a}} | cantato \textit{G\textsuperscript{u}}}} seu \edtext{fistulate}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}} vnam habent uocem scilicet \edtext{antiphonam}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | amptiipheniam \textit{V\textsuperscript{a}}}},} de quo \edtext{planius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | plenius \textit{P\textsuperscript{y}V\textsuperscript{a}} | amplius \textit{π}}} apparebit .19. et \edtext{.20.}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | .2º. \textit{V\textsuperscript{z}}}} Omnia \edtext{enim hec}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | hec \textit{P\textsuperscript{z}} | enim hinc \textit{αmv}}} \edtext{problemata}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | problema \textit{G\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{ \edtext{concidunt}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | coincidunt \textit{P\textsuperscript{z}}}}, super eodem enim \edtext{fundantur}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | fundatur \textit{C\textsuperscript{a}V\textsuperscript{o}}}} medio}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | concidunt \textit{β}}}. Sic \edtext{ergo}{\Cfootnote[nosep]{\textit{βP\textsuperscript{x}} | igitur \textit{γλπE\textsuperscript{a}mv}}} \edtext{ille}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}} | iste \textit{απM\textsuperscript{a}V\textsuperscript{z}mv}}} due \edtext{solutiones}{\Cfootnote[nosep]{\textit{ακmv} | questiones \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \expan{communi}ones \textit{(orig. \textup{ⳋ\textsuperscript{o}nes})} \textit{P\textsuperscript{z}}}} \edtext{magis differunt}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | differunt magis \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} ratione modi quam \edtext{rei}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | s\expan{u}b\expan{iect}i \textit{(orig. \textup{sb'i})} \textit{M\textsuperscript{a}}}}, cum vna sit uocalis \edtext{et}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{altera uocalis et}{\Cfootnote[nosep]{\textit{βγκmv} | alia \textit{P\textsuperscript{p}P\textsuperscript{z}} | \textit{om}. \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}}}} instrumentalis. \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{z}V\textsuperscript{z}} | sequitur 19; problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Decimumnonum problema}\label{edition-text book-19a part19}}{\lemma{Decimumnonum problema} \Cfootnote[nosep]{\textit{γmv} | «19m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{decimum nonum.}Decimumnonum. \textit{P\textsuperscript{y}} | 18m problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID ANTIPHONIS}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID ANTIPHONIS HOC SOLIS INEST? \textsuperscript{2}AUT QUIA SOLE EQUALITER DISTANT MEDIO? MEDIETAS IGITUR SIMILITUDINEM QUANDAM FACIT SONORUM. ET UIDETUR AUDITUS DICERE QUOD IPSA ET QUOD UTREQUE ULTIME \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Decimum nonum problema etcetera. \edtext{Consequenter}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} querit \edtext{causam causae}{\Cfootnote[nosep]{\textit{αλmv} | causam \textit{πP\textsuperscript{x}}}} precedentis \edtext{problematis}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}, dicens \textit{quare in \edtext{antiphonis}{\Cfootnote[nosep]{\textit{αλπmv} | antiphonia \textit{P\textsuperscript{x}}}} cordis \edtext{inest}{\Cfootnote[nosep]{\textit{ακmv} | ita est \textit{π}}} quod vna cantata \edtext{cantetur et altera}{\Cfootnote[nosep]{\textit{ακmv} | cantatur altera \textit{π}}}, et quod idem \edtext{consonat}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}m} | consonet \textit{V\textsuperscript{a}v} | sonat \textit{P\textsuperscript{y}V\textsuperscript{m}} | esse sonat \textit{P\textsuperscript{z}}}} utrobique \edtext{sicut si \edtext{ambo}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | anbe \textit{V\textsuperscript{a}}}} \edtext{cantarent}{\Cfootnote[nosep]{\textit{κ} | cantarentur \textit{αmv}}} }{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}?} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{ακπ} | Deinde. \textit{mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}} | QUIA. \textit{M\textsuperscript{a}} | \textit{om}. \textit{V\textsuperscript{a}}}} } Soluit dicens causam esse \textit{ \edtext{quia}{\Cfootnote[nosep]{\textit{αλπmv} | quoniam \textit{P\textsuperscript{x}}}} sole \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}V\textsuperscript{b}}}} cordarum antiphone in quibus \edtext{existit}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | estit \textit{V\textsuperscript{a}} | consistit \textit{π}}} dyapason equaliter \edtext{distant a}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | distantia \textit{P\textsuperscript{u}}}} media \edtext{corda}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}},} ut dicatur a mese \edtext{que}{\Cfootnote[nosep]{\textit{βγκmv} | quod \textit{πE\textsuperscript{a}}}} est \edtext{uere}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | nete \textit{γmv}}} media \edtext{vii.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | enim \textit{G\textsuperscript{u}P\textsuperscript{u}}}} \edtext{cordarum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}mv} | corde \textit{G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}}}}, ut visum \edtext{est}{\Cfootnote[nosep]{\textit{γπP\textsuperscript{x}M\textsuperscript{a}V\textsuperscript{z}mv} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{m}}}}. \textit{Illud \edtext{autem}{\Cfootnote[nosep]{\textit{ακπ} | aut \textit{mv}}} quod \edtext{est}{\Cfootnote[nosep]{\textit{ακmv} | vere est \textit{π}}} medium \edtext{conficit quandam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | consistit in quadam \textit{P\textsuperscript{z}}}} \edtext{similitudinem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{y}mv} | similem \textit{N\textsuperscript{u}} | consonantiam \textit{π}}} et \edtext{conuenientiam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | conuenientia \textit{P\textsuperscript{z}}}} sonorum cum extremis,} reddit \edtext{enim}{\Cfootnote[nosep]{\textit{ακπ} | cum \textit{mv}}} \edtext{similitudinem fere sonum}{\Cfootnote[nosep]{\textit{κ} | similem fere sonum \textit{απmv}}} media tacta, ac si \edtext{tangerentur ambe ultime}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ambe vltimis tangerentur \textit{P\textsuperscript{p}}}}. Et hoc est quod \edtext{dicit}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}m} | \textit{om}. \textit{V\textsuperscript{a}}}}: \textit{auditus videtur \edtext{diiudicare}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv}}} quod \edtext{ipsa}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv} | ista \textit{V\textsuperscript{z}} | \textit{om}. \textit{V\textsuperscript{o}}}} media cordarum et \edtext{quod}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{b}V\textsuperscript{z}}}} \edtext{utreque}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{z}} | utrorunque \textit{V\textsuperscript{m}} | \textit{om}. \textit{π}}} extreme \edtext{constituant}{\Cfootnote[nosep]{\textit{αλmv} | constituunt \textit{π} | \textit{om}. \textit{P\textsuperscript{x}}}} vnum \edtext{sonum}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}}.} Et \edtext{ideo}{\Cfootnote[nosep]{\textit{αλπmv} | rem \textit{P\textsuperscript{x}}}} in antiphonis \edtext{solis}{\Cfootnote[nosep]{\textit{ακmv} | solum \textit{π}}} accidit quod vna \edtext{corda}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} tacta uel \edtext{cantata}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | canta \textit{V\textsuperscript{a}}}} \edtext{cantetur}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | cantentur \textit{γG\textsuperscript{u}mv} | cantetur et \textit{P\textsuperscript{z}}}} \edtext{reliqua}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}mv} | relique \textit{γ} | altera \textit{λ}}}, cum \edtext{in}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{medium}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | mediam \textit{P\textsuperscript{x}}}} \edtext{concurratur}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | concurrant \textit{M\textsuperscript{a}} | concurrat \textit{π}}}, quare dyapason \edtext{tantum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Sed \textit{P\textsuperscript{y}} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} inter alias \edtext{proportiones}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | concordias \textit{G\textsuperscript{u}P\textsuperscript{q}} | \textit{om}. \textit{P\textsuperscript{p}}}} \edtext{sola}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | solo \textit{G\textsuperscript{u}}}} ex \edtext{antiphonis est apparentius}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv} | apparentiis antiphonis est \textit{V\textsuperscript{b}} | antiphonis est apparentior \textit{P\textsuperscript{y}}}} tonis. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 20. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Uigesimum problema}\label{edition-text book-19a part20}}{\lemma{Uigesimum problema} \Cfootnote[nosep]{\textit{γmv} | «20m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{Uigesimum. problema}Uigesimum. \textit{P\textsuperscript{y}} | 19mum. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID SI QUIS}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}} | PROPTER QUOD SI QUIS NOSTRUM \textit{V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID SI QUIS NOSTRUM MEDIAM MOUET, CONCORDANS ALIAS CORDAS, UTITUR INSTRUMENTO, NON SOLUM QUANDO SECUNDUM MEDIE FIAT SONUM DEFICIT, ET UIDETUR NON CONCORDANS, SED ET SECUNDUM ALIAM MELODIAM? SI AUTEM LICHANUM AUT ALIQUEM ALIUM SONUM, TUNC UIDETUR DIFFERE SOLUM QUANDO ILLA QUIS UTITUR. \textsuperscript{2}AUT RATIONABILITER HOC ACCIDIT, OMNES ENIM UTILES CANTUS MULTOTIENS MEDIA UTUNTUR. \textsuperscript{3}ET OMNES BONI POETE FREQUENTER AD MEDIAM OBUIANT. QUAMUIS DISCEDANT, CITO REUERTUNTUR, AD ALIAM AUTEM ITA NEQUE UNAM. \textsuperscript{4}QUEMADMODUM EX ORATIONIBUS: QUIBUSDAM ABLATIS CONIUNCTIONIBUS, NON EST ORATIO GRECA, UT AUTEM ET UERO. ET QUIDAM AUTEM NON DEFICIUNT, PROPTER ID QUOD HIIS QUIDEM NECESSARIUM EST ESSE UTI MULTOTIENS, SI ERIT ORATIO, HIIS AUTEM NON. \textsuperscript{5}ITA AUTEM ET SONORUM MEDIA SICUT CONIUNCTIO EST ET MAXIME BONORUM, PROPTER ID QUOD MULTOTIENS INEST IPSIS SONIS \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Uigesimum problema. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} \edtext{si aliquis}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | siquis \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}} | aliquis \textit{V\textsuperscript{z}}}} \edtext{nostrum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | modorum \textit{P\textsuperscript{p}P\textsuperscript{u}}}} scientium \edtext{pulsare}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | pulsaret \textit{P\textsuperscript{x}V\textsuperscript{m}}}} \edtext{instrumentum}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}V\textsuperscript{a}}}} \edtext{tangat}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | tangit \textit{P\textsuperscript{x}P\textsuperscript{y}}}} \edtext{cordam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}} mediam ut mese, utitur instrumento tali \edtext{modo}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} ac si omnes \edtext{alias}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{πP\textsuperscript{y}}}} cordas extremas ad inuicem \edtext{concordantia}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | concordantes \textit{G\textsuperscript{u}V\textsuperscript{a}}}} reduceret, quod declarat? \edtext{Non}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Nam \textit{P\textsuperscript{p}}}} enim quando \edtext{media corda}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | corda media \textit{P\textsuperscript{p}V\textsuperscript{z}}}} tangitur sonus deficit \edtext{et videtur}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | uidetur \textit{E\textsuperscript{a}} | ut uidetur \textit{P\textsuperscript{z}} | et videtur \surplus{videtur} \textit{P\textsuperscript{p}}}} non fieri \edtext{concordantia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}mv} | concordia \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} in instrumento, \edtext{sed}{\Cfootnote[nosep]{\textit{βγκπmv} | serui \textit{E\textsuperscript{a}}}} quod plus \edtext{est}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}, \edtext{apparet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | videtur \textit{G\textsuperscript{u}P\textsuperscript{q}}}} quod \edtext{tactus}{\Cfootnote[nosep]{\textit{αλmv} | cantus \textit{πP\textsuperscript{x}}}} \edtext{istius corde}{\Cfootnote[nosep]{\textit{βγκπ} | istius \textit{E\textsuperscript{a}} | illius corde \textit{mv}}} \edtext{resonet}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | restent \textit{P\textsuperscript{y}} | insonet \textit{V\textsuperscript{a}}}} in \edtext{quandam melodiam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | quadam melodia \textit{P\textsuperscript{y}}}}. \edtext{Id}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | Illud \textit{V\textsuperscript{a}}}} autem \edtext{non}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} contingit in aliis cordis extremis, sicut \edtext{est}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | est in \textit{γG\textsuperscript{u}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} lychanos, que est tertia post ypatem. Si \edtext{quis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quos \textit{P\textsuperscript{z}}}} enim sonum \edtext{causaret}{\Cfootnote[nosep]{\textit{αλ} | causet \textit{G\textsuperscript{u}} | cantet \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | carent \textit{P\textsuperscript{x}}}} per \edtext{cordam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} hanc uel per aliam ut paramese \edtext{uel}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{G\textsuperscript{u}}}} paranete, \edtext{tunc}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | etcetera \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{solum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | sonum \textit{C\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} videtur \edtext{differentia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | differri \textit{P\textsuperscript{z}}}} in sono et \edtext{dissimphonia}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | dissymphoniam \textit{V\textsuperscript{b}} | disynphoniam \textit{V\textsuperscript{a}} | in disinphonia \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{causari}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | causare \textit{γmv}}} \edtext{quando}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | cum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} quis utitur tangendo illam cordam que \edtext{non}{\Cfootnote[nosep]{\textit{ακC\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | si \textit{P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{est}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} recte media.} Uel aliter quod \edtext{tunc}{\Cfootnote[nosep]{\textit{αλπmv} | esse \textit{P\textsuperscript{x}}}} \edtext{solum}{\Cfootnote[nosep]{\textit{ακmv} | non \textit{G\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}}}} est \edtext{differentia sonorum}{\Cfootnote[nosep]{\textit{ακmv} | sonorum differentia \textit{π}}} \edtext{ad inuicem}{\Cfootnote[nosep]{\textit{ακmv} | ad se inuicem \textit{π}}} \edtext{visa, qua}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | qua uissa \textit{V\textsuperscript{b}} | uisa, quo \textit{P\textsuperscript{z}} | In secunda qua \textit{P\textsuperscript{y}}}} \edtext{ \edtext{discernitur}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}mv} | discernit \textit{P\textsuperscript{x}}}} quod vnus est delectabilior \edtext{altero}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}V\textsuperscript{b}mv} | altera \textit{P\textsuperscript{x}} | alio \textit{π}}}, \edtext{quando}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | qua \textit{P\textsuperscript{y}}}} \edtext{quis}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | quamuis \textit{P\textsuperscript{z}}}} \edtext{utitur tali modo}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | utitur modo \textit{π}}} }{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | destruitur tali modo \textit{V\textsuperscript{a}}}} media corda \edtext{recte}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | recta \textit{V\textsuperscript{a}}}} taliter quod in \edtext{eam}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | ea \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}}}} \edtext{consonent}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | consonant \textit{P\textsuperscript{p}P\textsuperscript{u}}}} due ultime, quod est \edtext{difficile}{\Cfootnote[nosep]{\textit{αλπmv} | difficila \textit{P\textsuperscript{x}}}} \edtext{mihi}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | minis \textit{P\textsuperscript{y}}}}. +\pend + +\pstart +\textbf{2} \edtext{Notandum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Nota \textit{P\textsuperscript{p}P\textsuperscript{u}}}} quod \hyperref[Ar]{aristoteles} \edtext{multotiens dicit}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}mv} | dicit multotiens \textit{λπV\textsuperscript{a}} | multotiens dicere \textit{P\textsuperscript{y}}}} \textit{ \edtext{videtur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} } \edtext{eo quod}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | quod \textit{P\textsuperscript{y}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{b}}}} scientia \edtext{consistit in sensu}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | in sensu consistit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{et}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | ut \textit{γπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} auditu et ratione, \edtext{ceu}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}mv} | seu \textit{C\textsuperscript{a}V\textsuperscript{o}} | sicut \textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} \edtext{alie}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | alii \textit{P\textsuperscript{y}}}}. \hyperref[Pyth]{ \edtext{Pictagoras}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}}}} } tamen omne quod \edtext{ipsius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ipsi \textit{P\textsuperscript{p}}}} \edtext{nitebatur}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{b}mv} | utebatur \textit{V\textsuperscript{a}} | uidebatur \textit{πE\textsuperscript{a}}}} \edtext{rationi}{\Cfootnote[nosep]{\textit{αλV\textsuperscript{o}mv} | ratione \textit{P\textsuperscript{x}} | rationem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | et omni \textit{P\textsuperscript{z}}}} magis \edtext{inherere}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}mv} | inherere \hyperref[Ar]{aristotelem} \textit{V\textsuperscript{b}} | inheretur \textit{E\textsuperscript{a}} | adherere \textit{π}}}, \hyperref[Ax]{ \edtext{aristoxenus}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{z}mv} | ar\expan{istoteles} \textit{V\textsuperscript{a}}}} } vero \edtext{sensui}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | sensum \textit{P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}}}}, quos ambos \edtext{\hyperref[Pt]{ptholomeus} in eius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}mv} | pertheus in eius \textit{λ} | ptolomeus in sua \textit{π}}} \edtext{ \textit{armonica} }{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | \textit{armonico} \textit{P\textsuperscript{y}} | retorica \textit{π}}} detestatur medium \edtext{obseruans}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} cum declinatione \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | tamen \textit{P\textsuperscript{p}}}} rationem amplius. ‘\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} V .3}}’ +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AUT.} Soluit per simile in aliis repertum dicens \edtext{primo}{\Cfootnote[nosep]{\textit{αλπ} | pro \textit{P\textsuperscript{x}mv}}} \textit{ \edtext{rationabiliter id}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | id rationabiliter \textit{πM\textsuperscript{a}} | rationabiliter illud \textit{V\textsuperscript{a}} | illud rationabiliter \textit{V\textsuperscript{b}}}} fieri} quod in \edtext{quesito}{\Cfootnote[nosep]{\textit{ακmv} | quesito est \textit{G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | 5to est \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}V\textsuperscript{c}}}} \edtext{proposito}{\Cfootnote[nosep]{\textit{κ} | propositum \textit{βπE\textsuperscript{a}V\textsuperscript{b}mv} | propositum est \textit{V\textsuperscript{a}}}}. \textit{Nam omnes cantus utiles et \edtext{laudati}{\Cfootnote[nosep]{\textit{ακmv} | laudatiui \textit{π}}} \edtext{attingentes}{\Cfootnote[nosep]{\textit{αλπmv}}} \edtext{finem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | fine \textit{P\textsuperscript{z}}}} musice cuiuscunque \edtext{multotiens}{\Cfootnote[nosep]{\textit{ακmv} | melodie \textit{π}}} \edtext{utuntur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | utitur \textit{γmv}}} corda media} \edtext{reducendo}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | reducenda \textit{P\textsuperscript{y}}}} \edtext{ceteras et maxime supremas}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{b}mv} | et maxime super primas et ceteras \textit{V\textsuperscript{a}}}} \edtext{proportionaliter}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | proportionatas \textit{G\textsuperscript{u}} | proportionabiliter \textit{V\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{p}}}} ad \edtext{ipsam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv}}}. +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{ET OMNES.}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | OMNES. \textit{V\textsuperscript{a}}}} } Declarat \edtext{id}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | illud \textit{P\textsuperscript{p}P\textsuperscript{x}}}} secundo \edtext{et}{\Cfootnote[nosep]{\textit{βγP\textsuperscript{x}P\textsuperscript{z}mv} | \textit{om}. \textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} primo in metrica, que est \edtext{ \edtext{musica quedam}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quedam musica \textit{P\textsuperscript{p}}}} ut \edtext{apparuit}{\Cfootnote[nosep]{\textit{βκ} | apparebit \textit{γπmv}}}, \edtext{dicens}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} quod}{\Cfootnote[nosep]{\textit{βγκπmv} | musica \textit{E\textsuperscript{a}}}} \textit{ \edtext{omnes boni poete utentes hac parte musice metrica dicta, \edtext{quam}{\Cfootnote[nosep]{\textit{βπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | qua \textit{γmv} | \textit{om}. \textit{V\textsuperscript{m}}}} }{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} frequenter \edtext{conuertunt se}{\Cfootnote[nosep]{\textit{ακmv} | se conuertunt \textit{π}}} ad mediam cordam siue ad \edtext{id}{\Cfootnote[nosep]{\textit{αλπmv} | illud \textit{P\textsuperscript{x}}}} quod proportionatur illi, quod si \edtext{accidat}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | accidit \textit{P\textsuperscript{x}V\textsuperscript{z}}}} \edtext{recedere quandoque ab ea}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}} | quandoque recedere ab ea \textit{P\textsuperscript{y}V\textsuperscript{b}mv} | quandoque ab ipsa recedere \textit{π}}}, \edtext{cito}{\Cfootnote[nosep]{\textit{ακmv} | statim \textit{π}}} \edtext{ad ipsam reddeunt}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | redeunt ad ipsam \textit{π} | ad ipsam redit \textit{P\textsuperscript{y}}}} \edtext{tanquam}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv}}} ad perfectum, \edtext{sed}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | seu \textit{V\textsuperscript{m}}}} ad nullam \edtext{aliarum}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{a}mv} | aliorum \textit{V\textsuperscript{b}} | aliam \textit{π}}} \edtext{ita}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{πM\textsuperscript{a}}}} reuertuntur, \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{z}V\textsuperscript{o}}}} non ut \edtext{ \edtext{hic tactum}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}} | hic tactum est \textit{γπmv} | hic cantum \textit{λE\textsuperscript{a}N\textsuperscript{u}}}} \edtext{perficiat}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{z}mv} | proficiat \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{κπN\textsuperscript{u}V\textsuperscript{b}mv} | huiusmodi \textit{P\textsuperscript{y}}}}.} +\pend + +\pstart +\textbf{5} Nosce quod eximii poete \edtext{tunc}{\Cfootnote[nosep]{\textit{ακmv} | cum \textit{π}}} \edtext{obuiant}{\Cfootnote[nosep]{\textit{αλπmv}}} ad mediam cordam et ad sibi \edtext{proportionale}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | proportionalem \textit{P\textsuperscript{y}P\textsuperscript{z}} | proportionabilem \textit{P\textsuperscript{p}}}}, \edtext{quando}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | cum \textit{V\textsuperscript{a}}}} \edtext{apud}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{m}mv}}} nos \edtext{vsitate}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{construuntur}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}mv} | construunt \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | construant \textit{P\textsuperscript{z}V\textsuperscript{o}} | constituunt \textit{G\textsuperscript{u}N\textsuperscript{u}} | consciliunt \textit{V\textsuperscript{a}}}} carmina in quibus sunt tempora \edtext{sillabarum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}v}}} ad inuicem \edtext{conproportionata}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | aproporpationata \textit{V\textsuperscript{a}} | proportionata \textit{V\textsuperscript{z}} | composita \textit{π} | proportionata \textit{P\textsuperscript{y}V\textsuperscript{b}}}} ex breui et \edtext{longo}{\Cfootnote[nosep]{\textit{κπ} | longa \textit{αmv}}}. \edtext{Sillaba}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv}}} \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} breuis vnum \edtext{ \edtext{habet tempus}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | tempus habet \textit{P\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}, longa uero duo, \edtext{quale quod constructum}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}mv} | quale quod constructum est \textit{γπ}}} \edtext{ex}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} \edtext{dactilo}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv}}} \edtext{vicissim}{\Cfootnote[nosep]{\textit{βγG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | inessim \textit{P\textsuperscript{z}} | incisam \textit{E\textsuperscript{a}}}} et spondeo \edtext{et}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}}}} non ex \edtext{altero. Tantum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | altera \textit{G\textsuperscript{u}}}} \edtext{neque in \edtext{exametro}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{b}mv}}} trocheo, nisi in fine \edtext{dactilo}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}}, \edtext{quidem}{\Cfootnote[nosep]{\textit{αλmv} | quodam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | quod \textit{P\textsuperscript{z}}}} \edtext{nunquam}{\Cfootnote[nosep]{\textit{βγV\textsuperscript{m}V\textsuperscript{z}mv} | tantum \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} neque \edtext{spondeo in quinto pede}{\Cfootnote[nosep]{\textit{βγκmv} | ex spondeo in quinto \textit{πE\textsuperscript{a}}}} \edtext{aut}{\Cfootnote[nosep]{\textit{βγκπmv} | haud \textit{E\textsuperscript{a}}}} \edtext{iambo}{\Cfootnote[nosep]{\textit{βλπV\textsuperscript{a}} | in ambo \textit{E\textsuperscript{a}P\textsuperscript{x}m}}} \edtext{ei}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | sibi \textit{G\textsuperscript{u}P\textsuperscript{a}} | eius \textit{V\textsuperscript{a}}}} opposito. Constat \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} ex \edtext{prima breui}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | breui prima \textit{V\textsuperscript{a}}}} et \edtext{ultima}{\Cfootnote[nosep]{\textit{ακmv} | altera \textit{π}}} longa, \edtext{quo utimur}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}mv} | quo utuntur \textit{P\textsuperscript{z}V\textsuperscript{o}} | continitur \textit{V\textsuperscript{a}}}} licentia \edtext{quandoque}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{πV\textsuperscript{z}}}} poetica in principio \edtext{tertii pedis}{\Cfootnote[nosep]{\textit{βγλ} | .3ii. \textit{P\textsuperscript{x}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}}. Tunc \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} \edtext{fit aliter}{\Cfootnote[nosep]{\textit{κ} | aliter fit \textit{απmv}}} \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} cum \edtext{seceditur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | sedetur \textit{P\textsuperscript{y}} | seccetur \textit{V\textsuperscript{a}} | descendit \textit{G\textsuperscript{u}} | se redditur \textit{P\textsuperscript{z}}}} a media corda \edtext{uel ab eo}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | quod est \textit{P\textsuperscript{z}}}} sibi \edtext{consimile}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | simile \textit{πE\textsuperscript{a}V\textsuperscript{z}}}}. \edtext{Debent}{\Cfootnote[nosep]{\textit{αλπmv} | Debet \textit{P\textsuperscript{x}}}} \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} \edtext{carmina fore}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | fore carmina \textit{P\textsuperscript{z}}}} bene \edtext{cantatiua}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}mv} | cantantia \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}}}} ut \edtext{que}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | quia \textit{V\textsuperscript{a}}}} \edtext{\hyperref[Ov]{ouidii}}{\Cfootnote[nosep]{\textit{βγλmv} | ouii \textit{E\textsuperscript{a}} | toni \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | enim \textit{P\textsuperscript{z}} | eum \textit{V\textsuperscript{o}}}} \edtext{non}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | \textit{om}. \textit{λ}}} \edtext{autem que sunt}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}} | autem que \textit{V\textsuperscript{m}} | aut que sunt \textit{V\textsuperscript{z}} | autem sic que \textit{απmv}}} \hyperref[Hor]{ \edtext{oracii}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}v}}} } et ideo \edtext{aliqui}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{z}mv} | aliquos \textit{πM\textsuperscript{a}V\textsuperscript{m}}}} versus \edtext{construunt}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | ostendunt \textit{V\textsuperscript{m}}}} \edtext{dictos leoninos}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | leoninos dictos \textit{πP\textsuperscript{y}} | leoninos \textit{M\textsuperscript{a}V\textsuperscript{m}}}} quasi \edtext{rithimicam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | rithimos \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | rithimicis \textit{P\textsuperscript{z}} | rithimia \textit{P\textsuperscript{y}}}} \edtext{commiscentes}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | commiscente \textit{E\textsuperscript{a}} | commiscentis \textit{P\textsuperscript{z}} | consistentes \textit{N\textsuperscript{u}}}} metrice. +\pend + +\pstart +\textbf{6} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{QUEMADMODUM.} Declarat secundo in \edtext{coniunctione}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}mv} | coniectione \textit{P\textsuperscript{x}V\textsuperscript{z}} | iniunctione \textit{V\textsuperscript{o}}}} orationis \edtext{prosaice}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}m}}} \edtext{dicens}{\Cfootnote[nosep]{\textit{ακπ} | id \textit{mv}}} quod \textit{sicut in aliquibus orationibus \edtext{in quibus}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} \edtext{videlicet}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | scilicet \textit{mv} | uidet \textit{E\textsuperscript{a}} | \textit{om}. \textit{V\textsuperscript{z}}}} multa \edtext{coadunantur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | coadunata \textit{P\textsuperscript{y}}}}, non \edtext{constituitur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | constituuntur \textit{V\textsuperscript{o}}}} \edtext{oratio}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | omnino \textit{P\textsuperscript{z}}}} \edtext{greca}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}E\textsuperscript{a}} | gramatica \textit{γmv}}}, que est \edtext{orationum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | questionum \textit{P\textsuperscript{z}}}} \edtext{congruissima}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cum grauissima \textit{P\textsuperscript{x}P\textsuperscript{z}}}} et perfectissima, \edtext{remotis}{\Cfootnote[nosep]{\textit{βγκπmv} | motis \textit{E\textsuperscript{a}}}} quibusdam \edtext{coniunctionibus}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | coniectionibus \textit{P\textsuperscript{x}V\textsuperscript{z}}}} \edtext{tanquam vinculis conuenientibus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}}, \edtext{puta}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} ut \edtext{autem}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | aurem \textit{P\textsuperscript{x}V\textsuperscript{m}}}} uero \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}V\textsuperscript{o}mv} | quedam \textit{P\textsuperscript{z}} | quod \textit{P\textsuperscript{p}} | quid \textit{P\textsuperscript{u}}}} et \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | huiusmodi \textit{βG\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{b}}}}. Unde et \edtext{quidam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv}}} \edtext{construere uolentes}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | uolentes construere \textit{π}}} \edtext{orationem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | orationem orationi \textit{V\textsuperscript{o}}}} \edtext{grecam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | gramaticam \textit{γmv}}} \edtext{congruissimam et perfectam}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{o}} | perfectam et congruissimam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | congruissimam et perfectissimam \textit{mv} | congruisima et perfectam \textit{} | congrauissimam et perfectam \textit{P\textsuperscript{z}}}} bene sonantem, \edtext{et}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} ne sequatur vocalis \edtext{ad}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | post \textit{P\textsuperscript{p}} | \textit{om}. \textit{P\textsuperscript{y}}}} uocalem, \edtext{quod}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | que \textit{P\textsuperscript{z}} | quidam \textit{λ}}} \edtext{grecus}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | gramaticus \textit{γmv} | creus \textit{P\textsuperscript{z}}}} \edtext{horret}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | abhoret \textit{} | oret \textit{κ} | honoret \textit{P\textsuperscript{z}}}} etiam in scriptura, \edtext{non}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in \textit{G\textsuperscript{u}}}} \edtext{deficiunt}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | proficiunt \textit{V\textsuperscript{z}}}} \edtext{in}{\Cfootnote[nosep]{\textit{αλπmv} | et \textit{P\textsuperscript{x}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{b}mv}}} \edtext{coniunctionalibus}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | coniunctionibus \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}}}} partium ligaturis, cum \edtext{oporteat}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv}}} \edtext{eis}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | eos \textit{G\textsuperscript{u}} | ac eis \textit{P\textsuperscript{p}}}} multotiens vti si \edtext{debet}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{m}} | debeat \textit{πP\textsuperscript{x}V\textsuperscript{z}mv}}} oratio \edtext{perfici}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} conuenienter; in hiis autem \edtext{deficiunt}{\Cfootnote[nosep]{\textit{κ} | deficiunt, quandoque \textit{απmv}}} } \edtext{ceu}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | sceu \textit{G\textsuperscript{u}}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | etiam \textit{P\textsuperscript{z}}}} cantus, interdum \edtext{recedunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | reddunt \textit{P\textsuperscript{z}}}} a media \edtext{corda}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}}. Quia \edtext{quandoque}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quinque \textit{P\textsuperscript{z}}}} non \edtext{sit}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | fit \textit{P\textsuperscript{y}V\textsuperscript{m}}}} necessarium \edtext{sepe uti}{\Cfootnote[nosep]{\textit{βγλP\textsuperscript{z}V\textsuperscript{o}m} | uti sepe \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | sepe \textit{E\textsuperscript{a}}}}, sicut \edtext{in}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} orationibus \edtext{minus}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | unus \textit{P\textsuperscript{z}} | viris \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{grecis}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | gramaticis \textit{γmv}}} \edtext{aut}{\Cfootnote[nosep]{\textit{αλπmv} | cum \textit{P\textsuperscript{x}}}} alio modo, \edtext{uelut}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ualde \textit{β} | uniuersaliter \textit{M\textsuperscript{a}} | ultra \textit{V\textsuperscript{z}}}} sunt alie partes orationis preter est uerbum \edtext{substantiuum}{\Cfootnote[nosep]{\textit{βγλG\textsuperscript{u}P\textsuperscript{z}mv} | substantium \textit{E\textsuperscript{a}P\textsuperscript{u}} | subactium \textit{P\textsuperscript{x}} | \textit{om}. \textit{P\textsuperscript{p}}}} expressum \edtext{aut}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | uel \textit{G\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{a}}}} \edtext{intellectum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | subintellectum \textit{G\textsuperscript{u}P\textsuperscript{q}}}} in \edtext{omnibus}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | orationibus \textit{πV\textsuperscript{z}}}}. Uel aliter, quia \edtext{coniunctiones}{\Cfootnote[nosep]{\textit{αλπmv} | coniectiones \textit{P\textsuperscript{x}}}} sunt duplices, \edtext{quedam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quia quedam \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{namque}{\Cfootnote[nosep]{\textit{ακ} | enim sunt \textit{πmv}}} \edtext{maxime}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{b}mv} | et maxime \textit{E\textsuperscript{a}} | ualde \textit{V\textsuperscript{a}}}} necessarie in \edtext{oratione}{\Cfootnote[nosep]{\textit{ακmv} | orationibus \textit{π}}}, cum \edtext{protenditur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}V\textsuperscript{o}mv} | protendentur \textit{P\textsuperscript{p}P\textsuperscript{u}} | protenduntur \textit{P\textsuperscript{z}}}} puta \edtext{et proprie si}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | et si proprie \textit{V\textsuperscript{a}} | et proprie .enim.[?] \textit{P\textsuperscript{y}} | si \textit{π}}} \edtext{quia}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | que \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{aut}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}} | autem \textit{αG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} et \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}mv} | huiusmodi \textit{γN\textsuperscript{u}} | similia \textit{π}}}. Alie \edtext{uero}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | nec \textit{M\textsuperscript{a}} | uero nec \textit{V\textsuperscript{z}}}} \edtext{quasi}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | que \textit{G\textsuperscript{u}}}} minime, ut \edtext{quidem siquidem nempe quippe}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | siquidem quidem nempe quippe \textit{V\textsuperscript{b}} | quidem siquidem nempe apparet \textit{E\textsuperscript{a}} | quippe nempe siquidem \textit{G\textsuperscript{u}P\textsuperscript{q}}}} et \edtext{huius}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | huiusmodi \textit{γE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{q}}}}. Modo \edtext{oratio}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | oro \textit{P\textsuperscript{y}}}} \edtext{perfecte}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | perfecta \textit{P\textsuperscript{y}V\textsuperscript{a}P\textsuperscript{z}}}} \edtext{greca}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | gramatica \textit{γmv}}} constituitur, \edtext{quando utitur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{hoc}{\Cfootnote[nosep]{\textit{βλπmv} | hac \textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}}}} modo coniunctionis \edtext{duplici}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | 2a. \textit{P\textsuperscript{x}} | \textit{om}. \textit{G\textsuperscript{u}}}}, puta \edtext{priori}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | prioris \textit{V\textsuperscript{a}}}} \edtext{significatiua}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | significatio \textit{P\textsuperscript{x}V\textsuperscript{m}}}} \edtext{et non significatiua}{\Cfootnote[nosep]{\textit{βγG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}mv} | et non significatam \textit{V\textsuperscript{m}} | et non significam \textit{P\textsuperscript{x}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{z}}}}. Dico autem \edtext{perfecte}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | perfecta \textit{V\textsuperscript{a}}}} \edtext{greca}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}E\textsuperscript{a}} | gramatica \textit{γmv}}} quia \edtext{greci}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | gramatici \textit{γmv}}} et potissime \edtext{\hyperref[Ga]{galienus}}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{q}} | Gal\expan{ienus} \textit{(orig. \textup{Gal'})} \textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}} | gallici \textit{γV\textsuperscript{z}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{maxime}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}mv} | et maxime \textit{P\textsuperscript{y}} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{utitur}{\Cfootnote[nosep]{\textit{βP\textsuperscript{x}} | utitur ista \textit{E\textsuperscript{a}} | utuntur \textit{γλπmv}}} \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{b}mv}}} \edtext{ligamentis}{\Cfootnote[nosep]{\textit{κπ} | ligamentalibus \textit{βE\textsuperscript{a}V\textsuperscript{b}mv} | ligamentationibus \textit{V\textsuperscript{a}}}} \edtext{sinchathegorematis}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}} | \textit{The word in question in συγκατηγόρημα: "a word in logick that imports somewhat with another, as {\itshape all, none, certain,} etc. which signify little of themselves, but add to the force of other words (N. Bailey, {\itshape An Universal Eytmological English Dictionary}, 17th ed. (London: T. Osborne et al., 1759)).}}} \edtext{etiam}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | et \textit{πV\textsuperscript{m}}}} secundis, \edtext{ut et}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | et et \textit{V\textsuperscript{z}} | et \textit{P\textsuperscript{z}} | ut \textit{V\textsuperscript{a}}}} \edtext{plura}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | plura \surplus{plura} \textit{M\textsuperscript{a}}}} \edtext{quandoque adiungat}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | quandoque adiungantur \textit{V\textsuperscript{a}} | quando adiungat \textit{P\textsuperscript{y}} | coniungat quandoque \textit{P\textsuperscript{p}}}} vna \edtext{puta}{\Cfootnote[nosep]{\textit{βγκπmv} | pauca \textit{E\textsuperscript{a}}}}: \edtext{ac et}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | a. et \textit{N\textsuperscript{u}} | Et ac \textit{G\textsuperscript{u}} | ac etiam et \textit{V\textsuperscript{a}}}}, \edtext{nimirum}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}mv} | in nimirum \textit{P\textsuperscript{x}} | numerum \textit{V\textsuperscript{b}} | minimum \textit{P\textsuperscript{z}}}}, quidem, \edtext{demum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | deinde \textit{G\textsuperscript{u}P\textsuperscript{z}}}}. \edtext{Tales}{\Cfootnote[nosep]{\textit{βγκπmv} | Deles \textit{E\textsuperscript{a}}}} \edtext{autem}{\Cfootnote[nosep]{\textit{βγκmv} | aut \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}} coniunctiones \edtext{apud}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{grecos}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | gramaticos \textit{γmv}}} dicuntur \edtext{parapliromatice}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}} | \textit{The word in question is παραπληρωματικός, i.e. expletive. Cf. \xref{http://www.perseus.tufts.edu/hopper/text?doc=Perseus\%3Atext\%3A1999.04.0057\%3Aentry\%3Dparaplhrwmatiko\%2Fs}{[www.perseus.tufts.edu]}}}}, \edtext{id est}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | et \textit{V\textsuperscript{m}} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{completiue}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | complete \textit{P\textsuperscript{x}} | copulatiue \textit{P\textsuperscript{y}}}} sermonis, \edtext{utpote}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | ut puta \textit{P\textsuperscript{p}P\textsuperscript{u}} | ut poete \textit{P\textsuperscript{z}V\textsuperscript{z}}}} \edtext{di. ta. ra. ni. ge.}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}} | di.ru. ru. ru. ge. \textit{P\textsuperscript{y}} | di ta ra ge \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | di. ca. na. ge. \textit{G\textsuperscript{u}P\textsuperscript{z}}}} etcetera. +\pend + +\pstart +\textbf{7} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ITA AUTEM.} \edtext{Applicat}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} ad propositum \edtext{tertio}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | 3 \textit{C\textsuperscript{a}V\textsuperscript{o}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, dicens quod \textit{simili modo se habet \edtext{cordarum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | corda \textit{G\textsuperscript{u}P\textsuperscript{q}}}} media uel \edtext{ei}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | enim \textit{P\textsuperscript{y}} | sibi \textit{P\textsuperscript{p}}}} proportionale \edtext{in}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}mv} | et \textit{βV\textsuperscript{m}V\textsuperscript{z}}}} sonis, \edtext{ceu}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{coniunctio}{\Cfootnote[nosep]{\textit{αλπmv} | coniectio \textit{P\textsuperscript{x}}}} in orationibus \edtext{gramaticis}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}} | gramaticalibus \textit{V\textsuperscript{z}} | gramatice \textit{M\textsuperscript{a}V\textsuperscript{a}mv} | gramatico \textit{V\textsuperscript{b}}}} et proprie \edtext{bonis seu grecis}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{z}} | grecis seu bonis \textit{P\textsuperscript{x}} | seu grecis \textit{P\textsuperscript{y}} | bonis ceu grecis \textit{M\textsuperscript{a}} | bonis ceu gramaticis \textit{γmv}}}.} Nam \edtext{cordarum}{\Cfootnote[nosep]{\textit{ακmv} | corda \textit{π}}} \edtext{media}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{b}mv} | medio \textit{V\textsuperscript{a}} | melodia \textit{E\textsuperscript{a}}}} est \edtext{proprie}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | propria \textit{G\textsuperscript{u}V\textsuperscript{a}}}} de numero bonarum \edtext{reddentium}{\Cfootnote[nosep]{\textit{ακmv} | cordarum reddentium \textit{π}}} mellifluum \edtext{sonum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{consonum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | sonum \textit{P\textsuperscript{y}}}} extremis. \textit{Et quia \edtext{hiis}{\Cfootnote[nosep]{\textit{γκ} | is \textit{βmv} | \sout{hi}is \textit{E\textsuperscript{a}} | id \textit{π}}} multotiens \edtext{debet}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | debent \textit{M\textsuperscript{a}}}} \edtext{in esse sonis}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{a}} | esse in sonis \textit{π} | in esse sonus \textit{V\textsuperscript{b}} | inesse sonis \textit{mv}}} } ideo \edtext{ut}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{propositum est}{\Cfootnote[nosep]{\textit{κ} | propositum \textit{απmv}}} multotiens, \edtext{cum possunt}{\Cfootnote[nosep]{\textit{βγκ} | cum post \textit{mv} | compositum \textit{πE\textsuperscript{a}}}} vtuntur \edtext{corda}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | verba uel vera \textit{V\textsuperscript{a}}}} media secundum quod \edtext{ei}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ea \textit{P\textsuperscript{z}} | et \textit{G\textsuperscript{u}} | est \textit{P\textsuperscript{y}}}} \edtext{consonant}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | consona \textit{P\textsuperscript{y}}}} extreme, et de hoc \edtext{itidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{.36°. apparebit consequenter}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | .36. apparebit. \textit{P\textsuperscript{y}} | apparebit consequenter .36°. \textit{π}}} \edtext{problemate.}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \sout{p}\gap{} \textit{P\textsuperscript{y}}}} \edtext{}{\Cfootnote{etcetera. \textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | et cetera. sequitur 21; problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Uigesimumprimum problema}\label{edition-text book-19a part21}}{\lemma{Uigesimumprimum + problema} \Cfootnote[nosep]{\textit{γmv} | «21m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{uigesimum. primum.}Uigesimumprimum \textit{P\textsuperscript{y}} | Uigesimum problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID CANTANTIUM}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID CANTANTIUM GRAUIUS CANTANTES ACUTE CANTANTIBUS, SI DISSONANT, MAGIS MANIFESTI FIUNT? SIMILITER AUTEM ET RITHIMO: QUI IN GRAUIORI PECCANTES MANIFESTI MAGIS. \textsuperscript{2}UTRUM QUOD PLUS TEMPUS GRAUI, HIC AUTEM MAGIS SENSIBILIS? \textsuperscript{3}AUT QUIA IN PLURI TEMPORE MULTUM EXHIBET, UELOX AUTEM ET ACUTUM LATET PROPTER UELOCITATEM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}?} Uigesimum primum problema. \textit{ \edtext{Quare cantantes}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | Querit quare cantantes \textit{λ} | \textit{om}. \textit{P\textsuperscript{p}}}} de numero \edtext{grauius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | grauium \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{cantantium}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cantantes \textit{P\textsuperscript{p}}}}, si dissonent \edtext{et}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{errent}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}} | errarent \textit{γ} | erteant \textit{P\textsuperscript{x}} | haberent \textit{mv}}} in cantu suo \edtext{ab}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | ab \surplus{ab} \textit{V\textsuperscript{a}}}} ordine debito, \edtext{magis redduntur}{\Cfootnote[nosep]{\textit{απV\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}} \edtext{manifesti}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | manifesto \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | manifeste \textit{P\textsuperscript{u}}}} in suo errore quam illi \edtext{qui}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{o}}}} cantant \edtext{acutius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | acutus \textit{G\textsuperscript{u}}}}?} Et addit \edtext{quod}{\Cfootnote[nosep]{\textit{ακmv} | quoniam \textit{π}}} \textit{ \edtext{non solum accidit hoc}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | hoc non sollum accidit \textit{V\textsuperscript{a}} | non solum hoc accidit \textit{π}}} in musica \edtext{armonica}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | armonia \textit{P\textsuperscript{z}} | \textit{om}. \textit{E\textsuperscript{a}}}}, que ex \edtext{uocibus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | motibus \textit{P\textsuperscript{z}}}} constat, sed etiam \edtext{in}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ex \textit{G\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{rithimica}{\Cfootnote[nosep]{\textit{γκπmv} | mathematica \textit{P\textsuperscript{y}}}} }, que coherentiam et \edtext{consonantiam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{uerborum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vocum \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{contemplatur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | contemplantur \textit{V\textsuperscript{b}}}}: utrum \edtext{bene}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}mv} | bene bene \textit{V\textsuperscript{o}}}} uel male \edtext{consonet}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | consonent \textit{V\textsuperscript{a}} | constent \textit{N\textsuperscript{u}}}}. \textit{ \edtext{Qui}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{z}V\textsuperscript{o}mv} | Que \textit{P\textsuperscript{x}} | Quando \textit{G\textsuperscript{u}} | Quoniam \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{enim}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | est \textit{V\textsuperscript{m}}}} \edtext{peccant}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | potest causat \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{in}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}mv} | secundam \textit{V\textsuperscript{b}}}} ipsa \edtext{secundum}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} grauius \edtext{magis manifestantur}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | magis manifestatur \textit{πV\textsuperscript{z}}}} quam si \edtext{peccarent}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | peccaret \textit{P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}}}} secundum acutius.} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{UTRUM.} Soluit \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | et \surplus{et} \textit{V\textsuperscript{m}}}} \edtext{assignat}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}} \edtext{duplicem causam quasi}{\Cfootnote[nosep]{\textit{ακmv} | quasi duplicem causam \textit{π}}} \edtext{consimilem}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}, dicens causam esse \textit{quoniam graue \edtext{plus habet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | habet plus \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{temporis quam acutum. \edtext{Ubi}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | Illi \textit{P\textsuperscript{z}}}} \edtext{autem}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | aut \textit{mv}}} plus est}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{temporis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}} | temporis et \textit{βγmv}}}, amplius potest peccari, \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | ut \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{peccatum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | punctum \textit{V\textsuperscript{m}}}} \edtext{similiter}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | \textit{om}. \textit{N\textsuperscript{u}}}} \edtext{magis percipi}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | percipi magis \textit{M\textsuperscript{a}}}}.} +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AUT QUIA.} \edtext{ \edtext{Assignat}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{y}}}} causam dicens}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}} | Soluit dicens \textit{V\textsuperscript{z}} | Dicens \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | Assignat aliam causam dicens \textit{γπmv}}} \edtext{id}{\Cfootnote[nosep]{\textit{βλP\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | illud \textit{E\textsuperscript{a}P\textsuperscript{x}} | hoc \textit{V\textsuperscript{a}mv} | ideo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} esse \textit{ \edtext{quia}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quare \textit{P\textsuperscript{z}} | quod \textit{P\textsuperscript{x}}}} \edtext{in}{\Cfootnote[nosep]{\textit{βγκmv} | et \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}} tempore \edtext{maiori}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{exhibet}{\Cfootnote[nosep]{\textit{βP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}mv}}} \edtext{graue}{\Cfootnote[nosep]{\textit{ακπ} | grauem \textit{mv}}} tardum et multum sonum}, \edtext{quare \edtext{fit}{\Cfootnote[nosep]{\textit{βγκmv} | sit \textit{E\textsuperscript{a}}}} esse ipsius manifestum propter sui tarditatem. Sed uelox et acutum, quia in minori tempore dat uelocem \edtext{sonum}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | suum \textit{V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}, \edtext{ideo}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | acutum autem \textit{G\textsuperscript{u}P\textsuperscript{q}}}} latet propter eius uelocitatem, ita quod peccatum non perpenditur \edtext{etiam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} inexistens notabiliter. \edtext{}{\Cfootnote{et cetera \textit{V\textsuperscript{z}} | sequitur 22m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Uigesimumsecundum problema}\label{edition-text book-19a part22}}{\lemma{Uigesimumsecundum + problema} \Cfootnote[nosep]{\textit{γmv} | «22m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{vigesimum secundum.}Uigesimum secundum. \textit{P\textsuperscript{y}} | 21mum. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{q}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID MULTI}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}P\textsuperscript{q}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID MULTI MAGIS CANTANTES RITHIMUM SALUANT QUAM PAUCI? \textsuperscript{2}AUT QUIA MAGIS APUD UNUM ET RECTOREM INTENDUNT ET GRAUIUS INCIPIUNT, QUARE FACILE IDEM ATTINGUNT? IN UELOCITATE ENIM PECCATUM EST PLUS \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Uigesimum + secundum problema. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} multi cantantes melius \edtext{conseruant}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}N\textsuperscript{u}mv} | consonant \textit{P\textsuperscript{y}} | seruant \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{rithimum}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}mv} | rithimum conseruando \textit{P\textsuperscript{y}}}} et vniuersaliter omnem \edtext{armoniam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{z}mv} | armonicam \textit{M\textsuperscript{a}V\textsuperscript{m}}}} \edtext{quam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | que \textit{V\textsuperscript{b}}}} acceperunt cantare quam pauci?} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AUT.} \edtext{Soluit dicens}{\Cfootnote[nosep]{\textit{πγM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}mv} | dicit \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{z}} | Dicit id \textit{V\textsuperscript{m}}}} \edtext{causam esse}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | esse causam \textit{V\textsuperscript{m}}}} \textit{quoniam ipsi amplius \edtext{intendunt}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | attendunt \textit{P\textsuperscript{y}}}} et \edtext{ordinantur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | ordinant \textit{π} | coadunantur \textit{P\textsuperscript{y}}}} \edtext{ad vnum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}}, \edtext{tanquam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv}}} ad \edtext{rectorem}{\Cfootnote[nosep]{\textit{βγκmv} | Rethorem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | regulam \textit{P\textsuperscript{z}} | terrorem \textit{E\textsuperscript{a}}}} \edtext{ouium}{\Cfootnote[nosep]{\textit{κ} | omnium \textit{βπE\textsuperscript{a}V\textsuperscript{b}mv} | opposittum \textit{V\textsuperscript{a}}}}, et grauius possunt incipere cum \edtext{fuerint}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fuerunt \textit{G\textsuperscript{u}P\textsuperscript{p}}}} multi \edtext{quoniam}{\Cfootnote[nosep]{\textit{βγκπmv} | quantum \textit{E\textsuperscript{a}}}} \edtext{uox vnius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | unus \textit{P\textsuperscript{z}}}} \edtext{fortificat}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | confortat \textit{P\textsuperscript{y}}}} et \edtext{substentat}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}m}}} uocem alterius. Propter quod de facili \edtext{possunt in vnum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in vnum possunt \textit{P\textsuperscript{p}}}} \edtext{deuenire}{\Cfootnote[nosep]{\textit{αλπmv} | peruenire \textit{P\textsuperscript{x}}}} } \edtext{ \edtext{illudque}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | et illud \textit{P\textsuperscript{y}}}} illesum conseruare in uelocitate. \edtext{Autem}{\Cfootnote[nosep]{\textit{ακ} | Aut \textit{mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{non contingit hoc}{\Cfootnote[nosep]{\textit{κ} | hoc non contingit \textit{γE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | non contingit \textit{P\textsuperscript{y}} | hoc non conuenit \textit{P\textsuperscript{p}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} cum difficilius sit seruare acutum \edtext{quam graue}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | quam grauius \textit{P\textsuperscript{p}} | graue \textit{P\textsuperscript{z}}}}, ut dicetur \edtext{.26°.}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{a}} | .36. \textit{πmv} | 36º 26a. \textit{V\textsuperscript{b}}}}, quare \textit{in uelocitate \edtext{magis contingit}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | contingit magis \textit{γmv} | magis conuenit \textit{P\textsuperscript{p}}}} peccare,} etsi \edtext{peccatum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | peccant \textit{β}}} \edtext{plerumque sit}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | sit plerumque \textit{P\textsuperscript{p}V\textsuperscript{b}} | plerumque fit \textit{V\textsuperscript{m}V\textsuperscript{z}} | plurimumque sit \textit{E\textsuperscript{a}P\textsuperscript{y}}}} magis latens ut \edtext{etiam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | et \textit{β}}} \edtext{alii}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | alii magis \textit{P\textsuperscript{z}}}} ostendunt \edtext{actus}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}. Et \edtext{id}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | idem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | ad \textit{P\textsuperscript{z}}}} quidem \edtext{.45°.}{\Cfootnote[nosep]{\textit{ακmv} | 35. \textit{π}}} \edtext{repetitur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | reputetur \textit{V\textsuperscript{a}}}}. \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{z}V\textsuperscript{z}} | sequitur 23. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Uigesimumtertium problema}\label{edition-text book-19a part23}}{\lemma{Uigesimumtertium + problema} \Cfootnote[nosep]{\textit{γmv} | «23m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{vigesimum tertium.}Vigesimum.tertium. \textit{P\textsuperscript{y}} | 22m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DUPLEX}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}} | PROPTER QUID DUPLEX UITE \textit{V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID DUPLEX NITE YPATE? \textsuperscript{2}AUT PRIMUM QUIDEM QUIA EX MEDIO CORDA CANTATA ET TOTA CONSONANT DYAPASON? \textsuperscript{3}SIMILITER AUTEM SE HABET IN FISTULIS, QUE ENIM PER MEDIUM FORAMEN FISTULE CONSONANT PER TOTAM FISTULAM DYAPASON. ADHUC ET IN ALIIS IN DUPLICI DISTANTIA ACCIPITUR DYAPASON, ET ILLI QUI PERFORANT FISTULAS ITA ACCIPIUNT. SIMILITER ET CUM DYAPENTE EMIOLIUM, QUIA QUI FISTULAS CONCORDANT IN YPATEM CERAM PONUNT, NITEM AUTEM USQUE AD MEDIUM REPLENT. SIMILITER AUTEM ET PER DYAPENTE EMIOLIO, ET PER QUATUOR EPITRICA DISTANTIA ACCIPIUNT. \textsuperscript{4}AMPLIUS IN TRIANGULIS PSALTERIIS EQUALI DISTENSIONE FACTA CONSONANT DYAPASON. HEC QUIDEM DUPLEX EXISTENS, ALIA UERO MEDIA LONGITUDINE \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Uigesimum + tertium problema. \edtext{Quare}{\Cfootnote[nosep]{\textit{βγP\textsuperscript{x}P\textsuperscript{z}mv} | Quia \textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{p}}}} in \edtext{12.}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}mv} | 13º \textit{M\textsuperscript{a}} | 21. \textit{V\textsuperscript{z}} | 2°. \textit{π}}} \edtext{dixerat}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | dixit \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \textit{duplicem \edtext{nitem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}} | uicem \textit{π} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{constituere}{\Cfootnote[nosep]{\textit{αλπmv} | constituit \textit{P\textsuperscript{x}}}} \edtext{ypatem}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv}}} }? Ideo causam \edtext{huius}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | huiusmodi \textit{mv} | eius \textit{V\textsuperscript{a}}}} querit, dicens: \textit{quare \edtext{duplex}{\Cfootnote[nosep]{\textit{βγκπmv} | dupliciter \textit{E\textsuperscript{a}}}} \edtext{nite}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}} | vite \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} constituit \edtext{ypatem}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv}}}?} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | AUT PRIMUM. \textit{γE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}mv}}} } \edtext{Soluit}{\Cfootnote[nosep]{\textit{αλπmv} | Soluit dicens \textit{P\textsuperscript{x}}}} et primo ostendit \edtext{quomodo}{\Cfootnote[nosep]{\textit{αλπmv} | quod \textit{P\textsuperscript{x}}}} ex duplici \edtext{nite}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}} | nitem \textit{N\textsuperscript{u}} | vite \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} causetur \edtext{ypate}{\Cfootnote[nosep]{\textit{αE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | ypatem \textit{G\textsuperscript{u}M\textsuperscript{a}}}} \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} cantu, secundo \edtext{in instrumentis}{\Cfootnote[nosep]{\textit{ακmv} | instrumentis in \textit{π}}} \edtext{flatu}{\Cfootnote[nosep]{\textit{αλπmv}}}, tertio \edtext{ductu}{\Cfootnote[nosep]{\textit{απmv} | in ductu \textit{κ}}}, \edtext{2a}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | 2a ibi \textit{G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}mv} | ibi 2a \textit{V\textsuperscript{b}}}} \textit{SIMILITER}, \edtext{3a}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | 3a ibi \textit{γG\textsuperscript{u}P\textsuperscript{z}mv}}} \textit{AMPLIUS}, \edtext{dicens}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | dicit \textit{E\textsuperscript{a}V\textsuperscript{z}} | dicens primo \textit{π} | dicit primo \textit{V\textsuperscript{a}}}} causam \edtext{esse}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | \textit{om}. \textit{N\textsuperscript{u}}}} \edtext{ex hoc primitus \edtext{sumendam}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} }{\Cfootnote[nosep]{\textit{ακmv} | sumendam ex hoc \textit{π}}}, \textit{quoniam \edtext{quando}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ante \textit{M\textsuperscript{a}}}} media cordarum \edtext{cuiuslibet}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | cuilibet \textit{P\textsuperscript{y}}}} \edtext{instrumenti}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{cantatur}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | incantatur \textit{P\textsuperscript{x}P\textsuperscript{y}}}}, tunc et \edtext{omnes alie}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | alie omnes \textit{P\textsuperscript{y}} | omnes aut \textit{M\textsuperscript{a}V\textsuperscript{z}}}} \edtext{coordinantur}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}mv} | coadunantur \textit{V\textsuperscript{a}}}} ad \edtext{ipsam}{\Cfootnote[nosep]{\textit{κ} | illam \textit{απmv}}} mediam et \edtext{consonant}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | consonat \textit{P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{per eam, cum ex ea}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | per illam, cum ex ea \textit{E\textsuperscript{a}} | cum per eam \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{constituatur}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}V\textsuperscript{b}mv} | constituitur \textit{κV\textsuperscript{a}}}} dyapason}, ut \edtext{apparuit}{\Cfootnote[nosep]{\textit{βγκmv} | apparebit \textit{πE\textsuperscript{a}}}} \edtext{.20}{\Cfootnote[nosep]{\textit{αV\textsuperscript{m}V\textsuperscript{z}mv} | 2° \textit{M\textsuperscript{a}P\textsuperscript{x}} | 3° \textit{π}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{SIMILITER.} \edtext{Ostendit 2° similiter fore}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | Ostendit 2°. fore similiter \textit{P\textsuperscript{p}} | Ostendit 2º similiter \textit{λ} | Ostendit 2º fore \textit{V\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{x}}}} in instrumentis \edtext{et}{\Cfootnote[nosep]{\textit{κ} | in \textit{απmv}}} \edtext{flatis}{\Cfootnote[nosep]{\textit{κ} | sufflatis \textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | fistulatis \textit{P\textsuperscript{z}}}}, dicens \textit{ \edtext{simili modo}{\Cfootnote[nosep]{\textit{ακmv} | similiter \textit{π}}} se habere in fistulis,} in quibus sunt \edtext{quedam}{\Cfootnote[nosep]{\textit{βγκπmv}}} \edtext{foramina}{\Cfootnote[nosep]{\textit{αλπmv} | formalia \textit{P\textsuperscript{x}}}} habentia similitudinem cum cordis, in eis enim \edtext{est}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | \textit{om}. \textit{P\textsuperscript{y}V\textsuperscript{a}}}} \edtext{magnum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | magno \textit{V\textsuperscript{m}}}} foramen, cuius sonus \edtext{grauis}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}}, \edtext{proportionatum}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | proportionatus \textit{P\textsuperscript{x}} | proportionatur \textit{πV\textsuperscript{z}} | est proportionatus \textit{mv}}} \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | ypati \textit{V\textsuperscript{z}} | ypatem \textit{M\textsuperscript{a}}}} \edtext{et}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | ut \textit{P\textsuperscript{y}}}} \edtext{secundum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}mv} | secundus \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} medium, \edtext{assimilatum}{\Cfootnote[nosep]{\textit{ακmv} | assimilatur \textit{π}}} mese et \edtext{plura}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | plura et \textit{P\textsuperscript{y}}}} \edtext{parua}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}}. \edtext{Super}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | Sunt \textit{V\textsuperscript{m}}}} que \edtext{fistulantur}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}mv} | fistulentur \textit{M\textsuperscript{a}} | fistulatur \textit{βG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} attributa \edtext{nete}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}mv} | vite \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}}}}, \textit{in quibus siquidem soni qui \edtext{fiunt}{\Cfootnote[nosep]{\textit{βγκπmv} | sunt \textit{E\textsuperscript{a}}}} per medium \edtext{foramen}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | foramen dicit \textit{N\textsuperscript{u}} | foramen dicte \textit{P\textsuperscript{y}}}} \edtext{fistule}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | fistule \surplus{fistule} \textit{N\textsuperscript{u}}}} consonant et \edtext{inducunt}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ducunt \textit{V\textsuperscript{z}}}} per totam fistulam secundum \edtext{aliqua eius}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | eius aliqua \textit{V\textsuperscript{a}} | aliqua enim \textit{P\textsuperscript{z}}}} foramina omnia dyapason, \edtext{cum}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} in ipsum, \edtext{ceu}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}} | sicut \textit{V\textsuperscript{a}}}} \edtext{in}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} medium, \edtext{reducantur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}} | reducuntur \textit{P\textsuperscript{y}mv}}} reliqua. Similiter \edtext{et}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}V\textsuperscript{z}}}} in aliis \edtext{id accidit}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv} | accidit id \textit{P\textsuperscript{y}} | illud accidit \textit{P\textsuperscript{x}V\textsuperscript{b}} | accidit \textit{π}}} instrumentis, in quibus predicta \edtext{potest}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | possunt \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{aptari}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | adaptari \textit{απV\textsuperscript{z}mv}}} foraminum similitudo, \edtext{nam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | uero \textit{P\textsuperscript{x}V\textsuperscript{m}} | non \textit{V\textsuperscript{z}}}} in eis \edtext{etiam}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{a}mv} | in \textit{E\textsuperscript{a}} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{dyapason constituitur}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{z}V\textsuperscript{o}mv} | constituitur dyapason \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | dyapason constituunt \textit{P\textsuperscript{x}}}} \edtext{in esse}{\Cfootnote[nosep]{\textit{ακmv} | inest \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{G\textsuperscript{u}}}} secundum duplicem \edtext{distantiam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | substantiam \textit{G\textsuperscript{u}}}}:} puta \edtext{vnius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | unus \textit{P\textsuperscript{z}}}} extremi ad medium vna, et alterius ad ipsum reliqua, uel quia ex numero consurgit duplari. Quod ostenditur quia \textit{illi qui perforant fistulas tali modo \edtext{suscipiunt}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv}}} \edtext{distantiam}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}} | distantia \textit{βP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv}}} ut \edtext{inde}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in \textit{P\textsuperscript{p}}}} \edtext{consurgat}{\Cfootnote[nosep]{\textit{βγκπmv} | consurgit \textit{E\textsuperscript{a}}}} dyapason cum reliquis proportionibus. \edtext{Nam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Quam \textit{V\textsuperscript{a}} | \textit{om}. \textit{mv}}} \edtext{taliter}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | aliter \textit{V\textsuperscript{a}}}} \edtext{operantur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | opponatur \textit{γmv}}}: perforando et \edtext{coaptando}{\Cfootnote[nosep]{\textit{αλπmv} | coadaptando \textit{P\textsuperscript{x}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | et \textit{P\textsuperscript{y}}}} secundum proportionem sexquialteram \edtext{reddatur}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | addatur \textit{P\textsuperscript{z}} | \textit{om}. \textit{κ}}} dyapente, \edtext{quod}{\Cfootnote[nosep]{\textit{βγκπmv} | et \textit{E\textsuperscript{a}}}} declarat. Nam \edtext{qui}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | si qui \textit{P\textsuperscript{u}} | si \textit{V\textsuperscript{m}}}} \edtext{fistulas taliter}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | taliter fistulas \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{consonas}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | consonans \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}} | consonantes \textit{P\textsuperscript{y}}}} faciunt ut consurgat dyapason apponunt \edtext{ceram}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | seram \textit{C\textsuperscript{a}P\textsuperscript{a}V\textsuperscript{c}V\textsuperscript{o}}}} uel \edtext{aliquod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aliquod huiusmodi \textit{P\textsuperscript{p}}}} \edtext{viscosum glutinosum}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{z}mv} | glutinosum uiscosum \textit{β} | viscosum siue glutinosum \textit{πE\textsuperscript{a}}}} \edtext{in}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ut \textit{G\textsuperscript{u}}}} foramine \edtext{maiori}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | maiore \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{proportionato}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}mv} | proportionate \textit{P\textsuperscript{z}V\textsuperscript{o}}}} ypate, ut sonus eius \edtext{subgrauetur, et foramina per \edtext{nitem}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{representata}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | representatam \textit{V\textsuperscript{m}}}} replent \edtext{cera}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}V\textsuperscript{b}mv} | ceram \textit{P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | cera et \textit{P\textsuperscript{p}} | cera ut \textit{P\textsuperscript{u}}}} usque ad medium}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}},} \edtext{ \edtext{ut}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | in \textit{P\textsuperscript{y}}}} eis \edtext{angustatis}{\Cfootnote[nosep]{\textit{αV\textsuperscript{o}mv} | coangustatis \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} sonus \edtext{reddatur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{q}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} acutior, \edtext{ita}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{γ}}} ut \edtext{possit duplex}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | possint duplices \textit{V\textsuperscript{b}}}} \edtext{nite}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}} | vite \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} in \edtext{ypatem}{\Cfootnote[nosep]{\textit{κmv} | ypate \textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{consurgere uel crescere}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{z}} | concurrere \textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}}, \edtext{cum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ut \textit{P\textsuperscript{y}}}} vna \edtext{exacuatur}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | exacuat \textit{M\textsuperscript{a}}}} et \edtext{reliqua}{\Cfootnote[nosep]{\textit{ακmv} | altera \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} subgrauetur \edtext{sibi}{\Cfootnote[nosep]{\textit{ακmv} | sibique \textit{π}}} \edtext{appropinquantes}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | appropinquent \textit{π}}} \edtext{utcunque}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}mv} | ubicunque \textit{V\textsuperscript{z}} | utrunque \textit{M\textsuperscript{a}V\textsuperscript{o}} | uterque \textit{P\textsuperscript{z}} | utrisque \textit{P\textsuperscript{y}}}} eodem modo \edtext{secundum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{debitam distantiam foraminum}{\Cfootnote[nosep]{\textit{πP\textsuperscript{y}V\textsuperscript{b}mv} | debita distantia foraminum \textit{E\textsuperscript{a}N\textsuperscript{u}} | debitam distantia foraminum \textit{V\textsuperscript{a}} | debita foramina \textit{κ}}} \edtext{cum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | ut \textit{V\textsuperscript{a}}}} \edtext{cere}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | cera \textit{P\textsuperscript{y}}}} uel alterius \edtext{appositione}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}} | appone \textit{E\textsuperscript{a}} | oppositione \textit{mv} | propositione \textit{P\textsuperscript{y}}}}, ita quod \edtext{etiam}{\Cfootnote[nosep]{\textit{βγκπmv} | in \textit{E\textsuperscript{a}}}} \edtext{lignum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | ligamen \textit{γmv}}} \edtext{submittunt}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | submittitur \textit{P\textsuperscript{a}P\textsuperscript{z}} | subimmictunt \textit{N\textsuperscript{u}V\textsuperscript{b}} | subimmittunt \textit{P\textsuperscript{y}}}} \edtext{subtile}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | utile \textit{M\textsuperscript{a}} | fistule \textit{γmv}}} in \edtext{foramen}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | foramine \textit{P\textsuperscript{z}}}} medium secundum \textit{sexquialteram proportionem, \edtext{seu}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | ceu \textit{P\textsuperscript{x}V\textsuperscript{z}}}} emiolam faciunt dyapente. Similiter per epitricam \edtext{distantiam}{\Cfootnote[nosep]{\textit{πγM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv} | distantia \textit{E\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}}}} que est cum numerus continet \edtext{alium totum}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | totum alium \textit{E\textsuperscript{a}V\textsuperscript{z}} | alterum totum \textit{π}}} ut visum \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | \textit{om}. \textit{N\textsuperscript{u}}}} \edtext{et eius}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | in eius \textit{P\textsuperscript{z}} | \textsubscript{7[?]} etiam \textit{V\textsuperscript{a}}}} tertiam partem, \edtext{ut}{\Cfootnote[nosep]{\textit{βγκπmv} | et \textit{E\textsuperscript{a}}}} .4. ad \edtext{.3.}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | 3a et \textit{V\textsuperscript{a}}}} \edtext{se \edtext{habet}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | habent \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}V\textsuperscript{a}}}}. Accipiunt per .4. \edtext{id est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | enim \textit{P\textsuperscript{p}}}} dyatesseron \edtext{grece}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | graue \textit{G\textsuperscript{u}P\textsuperscript{q}}}} }. +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AMPLIUS.} Declarat \edtext{3°. in instrumento tactibili}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}} | tertio instrumento tactibili \textit{λE\textsuperscript{a}V\textsuperscript{a}mv} | 3°. in instrumento tangibili \textit{πP\textsuperscript{y}}}}, dicens quod \edtext{insuper etiam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | etiam insuper \textit{P\textsuperscript{z}V\textsuperscript{z}}}} \textit{simili modo in psalteriis, que habent \edtext{figuram}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | triam \textit{V\textsuperscript{a}}}} triangularem, \edtext{et}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} in canonibus \edtext{facta}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | factam \textit{P\textsuperscript{z}V\textsuperscript{o}}}} proportionali \edtext{distensione}{\Cfootnote[nosep]{\textit{ακmv} | distantia \textit{π}}} cordarum \edtext{ipsarum}{\Cfootnote[nosep]{\textit{κP\textsuperscript{q}P\textsuperscript{y}P\textsuperscript{z}mv} | ipsorum \textit{γE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} ex acuto et graui \edtext{consonant et adducunt}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}v} | adducunt et consonant \textit{P\textsuperscript{p}} | consonant et addunt \textit{P\textsuperscript{y}} | consonat ut adducunt \textit{P\textsuperscript{z}}}} dyapason. In ipsa enim duplex corda, ut \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} et \edtext{nite}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}} | vite \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}}, \edtext{et alia}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | et aliam \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}} | taliter \textit{P\textsuperscript{z}}}} in \edtext{quam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | qua \textit{G\textsuperscript{u}}}} \edtext{concidunt}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}} | concidat \textit{E\textsuperscript{a}V\textsuperscript{b}mv} | conferat \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | constat \textit{G\textsuperscript{u}} | cum superat \textit{P\textsuperscript{z}}}} que \edtext{est}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | est in \textit{V\textsuperscript{a}}}} \edtext{media}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | mediam \textit{V\textsuperscript{b}}}} \edtext{distantia}{\Cfootnote[nosep]{\textit{ακmv} | distante \textit{π}}} \edtext{uere}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uero \textit{P\textsuperscript{z}} | \textit{om}. \textit{G\textsuperscript{u}}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | et \textit{P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | a \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} mese.} Vel aliter duplex \edtext{nete}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}} concurrit in \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}}: et \edtext{constituitur}{\Cfootnote[nosep]{\textit{αλπmv} | construitur \textit{P\textsuperscript{x}}}} tunc sonus \edtext{corde medie}{\Cfootnote[nosep]{\textit{βκmv} | medie corde \textit{P\textsuperscript{p}} | cordis medie \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | totidem medie \textit{γ}}} secundum distantiam ut \edtext{apparebit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | apparebat \textit{P\textsuperscript{u}V\textsuperscript{c}} | apparuit \textit{βγ}}} \edtext{vigesimo}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}mv} | vigesimo problemate \textit{V\textsuperscript{b}} | 22° \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{G\textsuperscript{u}V\textsuperscript{z}}}}. \edtext{}{\Cfootnote{et cetera \textit{V\textsuperscript{z}} | sequitur 24. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Uigesimumquartum problema}\label{edition-text book-19a part24}}{\lemma{Uigesimumquartum + problema} \Cfootnote[nosep]{\textit{γmv} | «24m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{vigesimum quartvm.}Vigesimumquartum. \textit{P\textsuperscript{y}} | 23m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID IN TENUIBUS}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID IN TENUIBUS MENTEM APPONERE, YPATE SOLA UIDETUR CONTRASONARE? \textsuperscript{2}AUT QUIA CONNATURALIS MAXIME FIT SONO SONUS QUI EST AB IPSA PROPTER ID QUOD CONSONANS EST? SIMUL AUGERI AUTEM SIMILI UIDETUR SOLUS. ALII UERO PROPTER PARUITATEM INMANIFESTI \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Uigesimum + quartum problema. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} \edtext{cum}{\Cfootnote[nosep]{\textit{κ} | cum in \textit{βγG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | in \textit{E\textsuperscript{a}P\textsuperscript{z}}}} subtilibus cordis, \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uti \textit{P\textsuperscript{z}}}} nete et \edtext{paranete}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}mv} | paranetum \textit{V\textsuperscript{b}}}}, \edtext{sonum}{\Cfootnote[nosep]{\textit{αλπmv}}} acutum \edtext{et paruum}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{reddentibus}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}v}}} \edtext{quis}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | siquis \textit{β}}} mentem id est rationem et sensum seu \edtext{auditum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | aditum \textit{β}}} \edtext{apponit}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | apponet \textit{V\textsuperscript{a}} | apponitum \textit{P\textsuperscript{y}}}}?} Hec enim scientia, ut \edtext{pretactum est}{\Cfootnote[nosep]{\textit{κP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | pretactum est \surplus{constat est} \textit{P\textsuperscript{p}} | pretactum \textit{α} | tactum est \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, constat \edtext{in}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}} ratione et sensu. Tunc sola ypate \edtext{sine}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | fine \textit{V\textsuperscript{m}}}} aliis \edtext{videtur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | ut \textit{β}}} \edtext{antisonare}{\Cfootnote[nosep]{\textit{βγκmv} | antiphonizare \textit{π}}} \edtext{ \edtext{sonitu reliquas}{\Cfootnote[nosep]{\textit{αλmv} | sonitu reliqua \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | soni cum reliquas \textit{P\textsuperscript{x}}}} \edtext{superando}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | superando esse \textit{P\textsuperscript{z}}}}, quod \edtext{prius dictum est}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | prius dictum est \surplus{est} \textit{P\textsuperscript{p}} | dictum est prius \textit{V\textsuperscript{a}}}} \edtext{antiphonare}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}N\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}} | inantiphonare \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{q}}}} } \edtext{Soluit dicens}{\Cfootnote[nosep]{\textit{βγκπmv} | dicit \textit{E\textsuperscript{a}}}} causam esse \textit{ \edtext{quia}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quoniam \textit{G\textsuperscript{u}}}} sonus qui ab ipsa causatur principalissime efficitur connaturalis et proportionalis \edtext{alii}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | alteri \textit{P\textsuperscript{p}P\textsuperscript{x}}}} \edtext{sono}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sono \surplus{alterius corde inferiorum sub medio existentis} \textit{G\textsuperscript{u}}}}, propter hoc \edtext{quod cum sua}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quod quando \textit{G\textsuperscript{u}}}} \edtext{consonantia}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | contrasonantia \textit{βγV\textsuperscript{z}mv}}} est \edtext{etiam simul}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}mv} | simul etiam \textit{P\textsuperscript{y}} | et simul \textit{M\textsuperscript{a}} | etiam similis \textit{P\textsuperscript{x}V\textsuperscript{z}}}} \edtext{consonans}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | contrasonans \textit{P\textsuperscript{y}}}} }. \edtext{Quando}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Quoniam \textit{P\textsuperscript{p}} | Contra \textit{P\textsuperscript{y}}}} \edtext{enim}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | est \textit{P\textsuperscript{x}V\textsuperscript{z}}}} sonus \edtext{ipsius}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | hominis \textit{V\textsuperscript{a}}}} cum sono alterius corde \edtext{inferiori}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{m}mv} | inferioris \textit{αP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}}}} sub \edtext{medio}{\Cfootnote[nosep]{\textit{αλπmv} | media \textit{P\textsuperscript{x}}}} \edtext{existentis}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}P\textsuperscript{y}mv} | existentibus \textit{N\textsuperscript{u}} | existente \textit{P\textsuperscript{x}}}} \edtext{construitur}{\Cfootnote[nosep]{\textit{κ} | constituitur \textit{βγπmv} | constitutus \textit{E\textsuperscript{a}}}}, \edtext{consonantia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | consonantia \surplus{est etiam simul sonsonans quando enim sonus ipsius cum sono alterius corde inferioris sub medio existentis constituitur consonantia} \textit{C\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{c}V\textsuperscript{o}}}} ut iam patuit dyapason. \textit{Et similiter \edtext{solus sonus huius corde}{\Cfootnote[nosep]{\textit{κN\textsuperscript{u}V\textsuperscript{a}} | solum sonus huius corde \textit{P\textsuperscript{y}} | solus sonus huius cordis \textit{E\textsuperscript{a}} | solus sonus huiusmodi corde \textit{V\textsuperscript{b}mv} | sonus huius corde solus \textit{π}}} inter alios sonos \edtext{videtur}{\Cfootnote[nosep]{\textit{αλπmv} | uideretur \textit{P\textsuperscript{x}}}} \edtext{augeri}{\Cfootnote[nosep]{\textit{αλπmv} | augere \textit{P\textsuperscript{x}}}} et \edtext{crementum}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | incrementum \textit{P\textsuperscript{y}V\textsuperscript{z}}}} in tonando accipere}, quia ipsa reddit sonum sola grauiorem \edtext{aliis, alie uero \edtext{acutum}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | acutum aliis \textit{V\textsuperscript{b}}}} \edtext{aut}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | et \textit{λ} | autem \textit{P\textsuperscript{y}} | ut \textit{E\textsuperscript{a}}}} minus grauem.}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{Sonus autem \edtext{grauis}{\Cfootnote[nosep]{\textit{κ} | grauis sonum \textit{βπE\textsuperscript{a}V\textsuperscript{b}mv}}} \edtext{ebetat}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}mv}}} \edtext{acute}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | acuto \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}, \textit{ \edtext{ \edtext{sed}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | et \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{soni}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sonus \textit{G\textsuperscript{u}P\textsuperscript{q}}}} aliarum cordarum \edtext{subtilium}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{b}mv} | subtillius \textit{V\textsuperscript{a}}}} }, quia sunt \edtext{parui}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}} | parue \textit{G\textsuperscript{u}P\textsuperscript{q}} | praui \textit{P\textsuperscript{u}V\textsuperscript{o}mv} | graui \textit{P\textsuperscript{z}}}}, non \edtext{percipiuntur}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | percipitur \textit{G\textsuperscript{u}P\textsuperscript{q}} | perciuntur \textit{V\textsuperscript{a}}}} manifeste, \edtext{propter}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | propterea \textit{V\textsuperscript{z}}}} quod \edtext{non apparent}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | non apparet \textit{P\textsuperscript{y}V\textsuperscript{m}} | non apparebit \textit{V\textsuperscript{a}} | apparent non \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{consonare}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}mv} | contrasonare \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}}}}. \edtext{Stat}{\Cfootnote[nosep]{\textit{αλπmv} | Et stat \textit{P\textsuperscript{x}}}} \edtext{igitur}{\Cfootnote[nosep]{\textit{βγλmv} | ergo \textit{P\textsuperscript{x}} | enim \textit{πE\textsuperscript{a}}}} in hoc, \edtext{quia}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | quod \textit{P\textsuperscript{y}V\textsuperscript{m}}}} sonus \edtext{ypate}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | ypatem \textit{M\textsuperscript{a}} | parypate \textit{P\textsuperscript{z}V\textsuperscript{c}}}} fortis \edtext{est}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | et \textit{V\textsuperscript{m}}}}, aliarum uero debilis. \edtext{Qui autem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Qui \textit{P\textsuperscript{z}} | Quia \textit{P\textsuperscript{a}V\textsuperscript{c}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}} | huiusmodi \textit{γG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{q}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{consonat}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}mv} | consonant \textit{P\textsuperscript{z}} | contrasonat \textit{γλE\textsuperscript{a}N\textsuperscript{u}} | contra consonat \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{debili}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | debiliter \textit{P\textsuperscript{y}}}} cum eo \edtext{quod}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv}}} recipit, \edtext{magnus}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | maior \textit{πP\textsuperscript{y}}}} \edtext{enim}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | est \textit{V\textsuperscript{a}}}} motus minorem \edtext{debilitat et obtundit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | obtundit et debilitat \textit{G\textsuperscript{u}}}}. \edtext{Huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | Huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{b}mv}}} autem sonus \edtext{cordis}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}} | corde \textit{βγG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{z}mv}}} licet \edtext{sit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} fortior \edtext{ceteris}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | aliis \textit{P\textsuperscript{y}}}}, quia tamen grauior et \edtext{dimensionatior}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{z}mv} | indimensionatior \textit{P\textsuperscript{y}} | dimensionationem \textit{V\textsuperscript{m}} | diuisionatorem \textit{P\textsuperscript{x}}}} sonum aliorum de facili \edtext{recipit}{\Cfootnote[nosep]{\textit{κ} | suscipit \textit{απmv}}} et exaltat, \edtext{ita}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} ut dyapason \edtext{inducat}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | inducit \textit{P\textsuperscript{u}} | inducta \textit{P\textsuperscript{y}} | indicat \textit{V\textsuperscript{a}}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 25. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Uigesimumquintum problema}\label{edition-text book-19a part25}}{\lemma{Uigesimumquintum + problema} \Cfootnote[nosep]{\textit{γmv} | «25m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{vigesimum. quintum.}Vigesimum quintum. \textit{P\textsuperscript{y}} | 24m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID MEDIA}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}} | PROPTER QUID MEDIA VOCATUR \textit{V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID MEDIA UOCATUR IN ARMONIIS, OCTO UERO NON EST MEDIUM? \textsuperscript{2}AUT QUIA SEPTEM CORDARUM ERANT ARMONIE ANTIQUITUS? SEPTEM AUTEM HABENT MEDIUM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Uigesimum + quintum problema. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} in armoniis \edtext{quedam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | quandam \textit{V\textsuperscript{a}}}} cordarum ut \edtext{mese}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | nete \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{appellatur}{\Cfootnote[nosep]{\textit{αλπmv} | appellantur \textit{V\textsuperscript{a}}}} media \edtext{recte}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | ratione \textit{P\textsuperscript{y}V\textsuperscript{a}}}} \edtext{.7.}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | .a. 7[?] \textit{V\textsuperscript{b}}}} cordarum?} Equaliter enim distat ab \edtext{eis}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | hiis \textit{G\textsuperscript{u}} | aliis \textit{P\textsuperscript{y}}}}, \textit{sed octo cordarum non est medium} \edtext{directe}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | recte \textit{P\textsuperscript{z}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{arismetricum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv}}}, \edtext{sed}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} potius geometricum. Et ideo octo cordarum non uocatur \edtext{aliqua media}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aliquod medium \textit{P\textsuperscript{p}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AUT.} Soluit \edtext{dicens}{\Cfootnote[nosep]{\textit{βγκπmv} | dicit \textit{E\textsuperscript{a}}}} causam esse \textit{quoniam antiquitus, ut \edtext{visum est}{\Cfootnote[nosep]{\textit{γκπmv} | visum \textit{βE\textsuperscript{a}}}}, non \edtext{fuerunt}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | fecerunt \textit{P\textsuperscript{y}}}} nisi septem corde \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} instrumentis armonicis.Septem autem \edtext{medium habet}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | habet medium \textit{βG\textsuperscript{u}M\textsuperscript{a}} | medium habent \textit{mv}}} \edtext{equidistans}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}m} | equidistant \textit{V\textsuperscript{m}} | que distans \textit{P\textsuperscript{z}}}} ab extremis,} \edtext{puta}{\Cfootnote[nosep]{\textit{αλπmv}}} .4., \edtext{ut}{\Cfootnote[nosep]{\textit{αλπmv} | ait \textit{P\textsuperscript{x}}}} \edtext{mese}{\Cfootnote[nosep]{\textit{αλπmv} | \surplus{n} mese \textit{P\textsuperscript{x}}}}. Id autem \edtext{factum}{\Cfootnote[nosep]{\textit{ακmv} | factum est \textit{π}}} \edtext{quia}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} dyapason, \edtext{que}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | qui \textit{P\textsuperscript{z}}}} est \edtext{optima}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | comparatio \textit{P\textsuperscript{y}}}} consonantiarum, ordinatur amplius \edtext{cum}{\Cfootnote[nosep]{\textit{αλπmv} | causa \textit{P\textsuperscript{x}}}} \edtext{fuerit}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | fuit \textit{V\textsuperscript{z}}}} medium \edtext{uerum}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} in cordis inuenire. Et ideo ‘ \edtext{ \textit{musice} primo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | primo \textit{musice} \textit{P\textsuperscript{z}}}} cum \edtext{\hyperref[Co]{estiacus colophonius}}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}mv} | ostiatus \hyperref[Co]{colophonius} \textit{N\textsuperscript{u}} | estimatus \hyperref[Co]{colophimus} \textit{P\textsuperscript{x}} | estimatus \hyperref[Co]{colofonius} \textit{E\textsuperscript{a}} | existimatus \hyperref[Co]{colofonius} \textit{π} | estyrginatus \hyperref[Co]{colophonius} \textit{V\textsuperscript{a}} | stiatiis elephinus \textit{V\textsuperscript{z}}}} \edtext{decimam}{\Cfootnote[nosep]{\textit{αmv} | quartam \textit{κπ} | 4am. 10am. \textit{V\textsuperscript{b}}}} cordam \edtext{.9.}{\Cfootnote[nosep]{\textit{ακmv} | cum \textit{π}}} preexistentibus \edtext{addidisset}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}mv} | \textit{om}. \textit{M\textsuperscript{a}}}}, \hyperref[Ty]{ \edtext{thimoteus}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}mv}}} } \edtext{superveniens}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{q}P\textsuperscript{u}mv} | superveniens et \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}}}} \hyperref[Ty]{ \edtext{milexius}{\Cfootnote[nosep]{\textit{κ}}} } \edtext{xiam.}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}P\textsuperscript{u}} | aliam \textit{P\textsuperscript{p}} | nullam \textit{G\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{q}} | unam \textit{P\textsuperscript{z}}}} \edtext{adiunxit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | adiunxerunt \textit{P\textsuperscript{z}}}},\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} I .20 (ed. Friedlein, pp. 208–209)}}’ ita ut \edtext{signato}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | significando \textit{P\textsuperscript{z}}}} \edtext{uero}{\Cfootnote[nosep]{\textit{απmv} | ut \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | sit \textit{V\textsuperscript{z}}}} medio in hiis puta sexta \edtext{consonet}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | consonat \textit{P\textsuperscript{y}}}} dyapason. +\pend + +\pstart +\textbf{3} \edtext{Nosce}{\Cfootnote[nosep]{\textit{ακπ} | Notandum \textit{mv}}}, ut \edtext{indicatum}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}mv} | iudicatum \textit{V\textsuperscript{a}} | dictum \textit{π}}} \edtext{est}{\Cfootnote[nosep]{\textit{λP\textsuperscript{z}V\textsuperscript{a}mv} | \textit{om}. \textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{o}}}} \edtext{superius}{\Cfootnote[nosep]{\textit{αλπmv} | finis \textit{P\textsuperscript{x}}}}, \textit{.7. \edtext{antiquitus fuisse cordas}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | fuisse cordas antiquitus \textit{π} | fuisse cordas \textit{P\textsuperscript{y}}}} } ‘septem planetarum, \edtext{secundum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{o}}}} boecium, \edtext{imitatione}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}m} | imitationem \textit{V\textsuperscript{a}} | immutatione \textit{V\textsuperscript{b}v} | mutatione \textit{P\textsuperscript{x}}}}, \edtext{ita}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ea \textit{P\textsuperscript{z}}}} ut \edtext{suprema}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | supra \textit{P\textsuperscript{y}}}} earum \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ypatem \textit{M\textsuperscript{a}}}} reddatur saturno propter tarditatem motus\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} I .20 (Friedlein 206, ll. 10–1, 15–6)}}’ utrobique. Infima lune \edtext{ceu}{\Cfootnote[nosep]{\textit{βλP\textsuperscript{z}V\textsuperscript{b}} | seu \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | sicut \textit{P\textsuperscript{x}V\textsuperscript{a}mv}}} nete ob eius \edtext{uelocitatem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | velocitatem motus \textit{P\textsuperscript{p}}}}. Que autem \edtext{intermedio}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{z}} | intermedie \textit{P\textsuperscript{x}} | in medio \textit{P\textsuperscript{y}} | in intermedio \textit{N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv}}} ordine planetarum \edtext{attribuantur}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}} | atribuatur \textit{V\textsuperscript{m}V\textsuperscript{z}} | attribuentur \textit{mv} | attribuebantur \textit{πP\textsuperscript{y}}}} \edtext{mediis}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | aliis mediis \textit{P\textsuperscript{y}} | medicinis \textit{V\textsuperscript{z}}}} iuxta \edtext{eorum}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{z}V\textsuperscript{o}mv} | earum \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{mediocrem}{\Cfootnote[nosep]{\textit{βγπP\textsuperscript{x}mv} | mediocrum \textit{E\textsuperscript{a}} | mediocritatem \textit{V\textsuperscript{m}}}} cursum. Et id quidem .32°. apparebit \edtext{ \edtext{et magis}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | magis et \textit{P\textsuperscript{z}} | et maxime \textit{V\textsuperscript{z}}}} \edtext{.44°}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | .44° problematum \textit{P\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{u}V\textsuperscript{z}} | sequitur 26. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Uigesimumsextum problema}\label{edition-text book-19a part26}}{\lemma{Uigesimumsextum + problema} \Cfootnote[nosep]{\textit{γmv} | «26m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | Vigesimumsextum. \surplus{vigesimum + sextum.} \textit{P\textsuperscript{y}} | 25m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID IN ACUTO}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID IN ACUTO DISCORDANT PLURIMI? \textsuperscript{2}UTRUM QUIA FACILIUS ACUTUM DIMITTERE QUAM GRAUE? \textsuperscript{3}AUT QUIA PEIUS GRAUI? PECCATUM PEIORIS OPERATIO \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Uigesimum sextum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} \edtext{plurimi}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | plurimum \textit{P\textsuperscript{z}}}} cantantes \edtext{vna discordant amplius}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | amplius discordant una \textit{P\textsuperscript{z}} | una discordant \textit{V\textsuperscript{a}}}} in acuto quam \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} graui?} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{UTRUM.}{\Cfootnote[nosep]{\textit{αλπmv} | AUT. \textit{P\textsuperscript{x}}}} } \edtext{Soluit}{\Cfootnote[nosep]{\textit{ακ} | Soluit et \textit{πmv}}} \edtext{assignans}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}m} | assignando \textit{M\textsuperscript{a}} | assignat \textit{πv}}} duplicem causam probabilem prius, dicens \edtext{id}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | illud \textit{P\textsuperscript{x}V\textsuperscript{b}mv} | ideo \textit{P\textsuperscript{p}P\textsuperscript{u}}}} esse \textit{ \edtext{quoniam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quia \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{leuius est}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | leuius \textit{E\textsuperscript{a}} | facilius et leuius est \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{dimittere}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv}}} \edtext{acutum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}}?} Et recessus ab eo sepius \edtext{contingit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | conuenit \textit{P\textsuperscript{p}}}} quam a graui propter breuitatem temporis \edtext{existentie}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}mv} | existentis \textit{V\textsuperscript{m}} | ex natura \textit{P\textsuperscript{y}V\textsuperscript{a}}}} ipsius, propter quod \edtext{dictum est}{\Cfootnote[nosep]{\textit{γκπ} | dictum \textit{βE\textsuperscript{a}mv}}} \edtext{22°.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | 21°. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}: quod \textit{in uelocitate \edtext{peccatum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | rectatum \textit{P\textsuperscript{u}}}} \edtext{plus}{\Cfootnote[nosep]{\textit{ακmv} | magis \textit{π}}} existit.} Non tamen ut \edtext{expositum adeo est}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | expositum adeo \textit{V\textsuperscript{a}} | expositum est adeo \textit{π}}} \edtext{manifestum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | magnum \textit{P\textsuperscript{z}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}V\textsuperscript{c}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{peccatum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | pretactum \textit{M\textsuperscript{a}}}} \edtext{in}{\Cfootnote[nosep]{\textit{αλπmv} | et \textit{P\textsuperscript{x}}}} graui, propter quod \edtext{apparet hoc}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | apparet hic \textit{M\textsuperscript{a}} | hoc quod apparet \textit{P\textsuperscript{y}}}} in nullo illi \edtext{aduersari}{\Cfootnote[nosep]{\textit{ακπ}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακπ} | AUT QUIA. \textit{mv}}} } \edtext{Soluit assignans}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{z}} | Soluit assignando \textit{M\textsuperscript{a}V\textsuperscript{m}} | Assignat \textit{απmv}}} aliam causam \edtext{necessariam magis}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | magis necessariam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}}}}, \edtext{dicens}{\Cfootnote[nosep]{\textit{βγκπmv} | dicit \textit{E\textsuperscript{a}}}} \edtext{id}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | illud \textit{P\textsuperscript{x}} | hoc \textit{γmv} | ideo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} esse \textit{ \edtext{quoniam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | quia \textit{λ}}} \edtext{peccatum}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | pretactum \textit{V\textsuperscript{z}} | predictum \textit{V\textsuperscript{a}}}} quod \edtext{committitur}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{o}V\textsuperscript{z}mv} | conuertitur \textit{P\textsuperscript{z}}}} in acutum \edtext{cantando}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | cantum cantando \textit{P\textsuperscript{y}}}} \edtext{deterius \edtext{est}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{seu}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | et \textit{P\textsuperscript{y}}}} \edtext{difficilius}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | difficilius est \textit{V\textsuperscript{z}}}} quam peccatum quod \edtext{committitur}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}mv}}} in \edtext{graue}{\Cfootnote[nosep]{\textit{γN\textsuperscript{u}P\textsuperscript{x}mv} | grauem \textit{λ} | grauius \textit{P\textsuperscript{y}}}} cantando}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} }. Cum \edtext{molestius}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}} | molestius sit \textit{απM\textsuperscript{a}V\textsuperscript{z}mv}}} cantare acuta quam \edtext{grauia}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | grauia u\expan{tru}m \textit{(orig. \textup{u})} \textit{M\textsuperscript{a}}}} \edtext{.37.}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}. \textit{ \edtext{Peioris autem}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Peioris \textit{P\textsuperscript{p}} | Autem peioris autem \textit{P\textsuperscript{x}}}} \edtext{seu}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{difficilioris}{\Cfootnote[nosep]{\textit{αλπmv} | difficiliorum \textit{P\textsuperscript{x}}}} actus peccatum \edtext{maius}{\Cfootnote[nosep]{\textit{βγκmv} | maius est \textit{π} | \textit{om}. \textit{E\textsuperscript{a}}}}.} Et \edtext{ideo}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | \textit{om}. \textit{γmv}}} \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} ipso amplius accidit \edtext{discordari}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | discordare \textit{P\textsuperscript{y}}}}. Quod enim \edtext{difficilius}{\Cfootnote[nosep]{\textit{ακmv} | difficilius est \textit{π}}} agere magis \edtext{contingit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | conuenit \textit{G\textsuperscript{u}P\textsuperscript{q}}}} peccato \edtext{corrumpere}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | corpore \textit{P\textsuperscript{p}}}}, ut aurum arte construere. \edtext{Et id etiam .46. \edtext{rescribetur}{\Cfootnote[nosep]{\textit{ακ} | rescribetur capitulo \textit{mv}}} }{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}. \edtext{}{\Cfootnote{et cetera \textit{V\textsuperscript{z}} | sequitur 27. problema. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Uigesimumseptimum problema}\label{edition-text book-19a part27}}{\lemma{Uigesimumseptimum + problema} \Cfootnote[nosep]{\textit{γmv} | «27m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{vigesimum septimum.} Vigesimumseptimum \textit{P\textsuperscript{y}} | 26m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID AUDIBILE}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID AUDIBILE SOLUM HABET SENSIBILIUM? ET ENIM, IN QUANTUM ABSQUE RATIONE, CANTUS TAMEN HABET CONSUETUDINEM, SED NON COLOR, NEQUE ODOR, NEQUE HUMOR HABET. \textsuperscript{2}AUT QUIA MOTUM HABET SOLUM UNIFORMEM, QUO SONUS NOS MOUET? HUIUS ENIM ET ALIIS INEST, MOUET ENIM ET COLOR UISUM, SED CONSEQUENTEM HUIUS SONO SENTIMUS MOTUM. HEC ENIM HABET SIMILLIMA IN RITHIMIS ET IN SONORUM ORDINATIONE ACUTORUM ET GRAUIUM, NON IN MIXTIONE. SED CONSONANTIA NON HABET CONSUETUDINEM, IN ALIIS AUTEM SENSIBILIBUS HOC NON EST. \textsuperscript{3}MOTUS AUTEM IPSI OPERATIUI SUNT, OPERATIONES ENIM CONSUETUDINIS SIGNIFICATIO EST \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Uigesimum + septimum problema etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} audibili \edtext{tantummodo de numero sensibilium hoc inest}{\Cfootnote[nosep]{\textit{κN\textsuperscript{u}V\textsuperscript{b}mv} | tantummodo hoc inest de numero sensibilium \textit{π} | tantummodo sensibilium hoc inest \textit{E\textsuperscript{a}P\textsuperscript{y}} | tantum de numero seu suum hoc inest \textit{V\textsuperscript{a}}}}? \edtext{ \edtext{Quia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}mv} | Qui \textit{V\textsuperscript{o}} | Quod \textit{P\textsuperscript{z}}}} etiam in quantum est cantus sine}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} ratione \edtext{solo}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}V\textsuperscript{b}mv} | solummodo \textit{V\textsuperscript{a}} | sono \textit{κ}}}, \edtext{tamen}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{y}mv} | cum \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | tantum \textit{V\textsuperscript{b}}}} auditus \edtext{sensibili}{\Cfootnote[nosep]{\textit{κ} | sensu \textit{απmv}}} }, quia hec scientia, ut visum \edtext{est}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{z}}}}, \edtext{perficitur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | percipitur \textit{G\textsuperscript{u}}}} ratione \edtext{et}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | ut \textit{P\textsuperscript{y}}}} sensu. Quis \edtext{eum}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cum \textit{P\textsuperscript{z}} | enim \textit{κG\textsuperscript{u}}}} \edtext{reddit sibi}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | sibi reddit \textit{P\textsuperscript{y}} | reddit \textit{π}}} consuetum, \edtext{non}{\Cfootnote[nosep]{\textit{βγκπmv} | et ideo \textit{E\textsuperscript{a}}}} autem \edtext{color odori aut sapori}{\Cfootnote[nosep]{\textit{κN\textsuperscript{u}V\textsuperscript{b}mv} | colori audiri aut sapori \textit{P\textsuperscript{y}} | color odori et sapori \textit{V\textsuperscript{a}} | colorem aut odorem aut saporem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | coloris odoris aut saporis \textit{P\textsuperscript{z}}}} id adest quod ea fiant consueta \edtext{in}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} tantum ut \edtext{que}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{audibilia}{\Cfootnote[nosep]{\textit{ακπ} | audibili \textit{mv}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AUT.} Soluit et \edtext{primo tangit}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}mv} | tangit primo \textit{V\textsuperscript{a}} | primo assignat \textit{P\textsuperscript{x}}}} partem \edtext{cause}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{ratione}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{audibilium}{\Cfootnote[nosep]{\textit{ακmv} | audibilis \textit{π}}}, \edtext{.2°}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | secundum \textit{N\textsuperscript{u}}}} ex \edtext{parte}{\Cfootnote[nosep]{\textit{αλπmv} | parte et \textit{P\textsuperscript{x}}}} \edtext{eorum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | eorum ex \textit{V\textsuperscript{b}}}} quibus \edtext{acquiritur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | adequatur \textit{β}}} \edtext{consuetudo}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}} | consuetudo ibi \textit{P\textsuperscript{p}} | consuetudo .2a \textit{M\textsuperscript{a}V\textsuperscript{m}} | consuetudo .2a ibi: \textit{γP\textsuperscript{z}V\textsuperscript{z}mv}}} \textit{MOTUS \edtext{AUTEM}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | ERGO \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{a}P\textsuperscript{p}}}} }. Dicit \edtext{igitur}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ergo \textit{P\textsuperscript{p}P\textsuperscript{x}}}} primo \edtext{id}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | idem \textit{V\textsuperscript{a}}}} esse \textit{quoniam audibile solum habet motum vniformem, propter \edtext{quod}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}V\textsuperscript{m}} | quem \textit{βγM\textsuperscript{a}V\textsuperscript{z}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} sonus habet nos \edtext{mouere}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | amouere \textit{V\textsuperscript{a}}}}.} ‘ \edtext{Mouet enim potentiam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | Potentiam enim mouet \textit{V\textsuperscript{a}}}} audiendi, cum sit \edtext{virtus}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | virtus motiua \textit{P\textsuperscript{y}}}} passiua, et eam deducit in \edtext{actum}{\Cfootnote[nosep]{\textit{βγλP\textsuperscript{z}V\textsuperscript{o}} | actu \textit{E\textsuperscript{a}} | acutum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}mv}}}, \edtext{ut apparet}{\Cfootnote[nosep]{\textit{ακmv} | ut patet in \textit{π}}} \edtext{2°}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | 3º \textit{M\textsuperscript{a}}}} \textit{de anima.} \edtext{}{\Afootnote[nosep]{Arist. \textit{De an.} II .12 , 424a l. 19 (Cf. 416b l. 33 and 419b l. 5)}}’ \textit{Sed hic \edtext{modus}{\Cfootnote[nosep]{\textit{αλπmv} | motus \textit{P\textsuperscript{x}}}} mouendi \edtext{aliis etiam inest}{\Cfootnote[nosep]{\textit{ακmv} | aliis inest etiam \textit{π}}} obiectis \edtext{sensuum}{\Cfootnote[nosep]{\textit{βγκπmv} | sensibili \textit{E\textsuperscript{a}}}}, nam color mouet \edtext{sensum}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}} | visum \textit{απmv} | sensum uisus \textit{M\textsuperscript{a}}}} } et in \edtext{actum}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | acutum \textit{βγG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}mv}}} deducit; \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | et \surplus{et} \textit{V\textsuperscript{m}}}} similiter odor et sapor. \textit{ \edtext{Sed}{\Cfootnote[nosep]{\textit{ακmv} | Hoc \textit{π}}} in \edtext{auditu}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | auditu 8 \textit{P\textsuperscript{p}}}} \edtext{ultra hoc}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | ultra \textit{P\textsuperscript{z}} | universaliter \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} existit \edtext{quod}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | quia \textit{πV\textsuperscript{m}}}} \edtext{percipiendo}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | percipiendo et \textit{M\textsuperscript{a}}}} sonum \edtext{sentimus etiam motum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | etiam motum sentimus \textit{P\textsuperscript{z}} | percipimus etiam motum \textit{G\textsuperscript{u}P\textsuperscript{q}} | sentimus et motum \textit{E\textsuperscript{a}}}} quo mediante defertur ad aures \edtext{quod}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | quam \textit{N\textsuperscript{u}}}} \edtext{etiam non solum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | non solum etiam \textit{V\textsuperscript{a}} | etiam non \textit{P\textsuperscript{y}}}} accidit in \edtext{sono}{\Cfootnote[nosep]{\textit{κV\textsuperscript{a}} | sono in \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{o}mv} | sono uel \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | sompno est \textit{P\textsuperscript{z}}}} \edtext{communi}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}}, uerum \edtext{etiam}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{similiter}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | communiter \textit{V\textsuperscript{z}}}} \edtext{se}{\Cfootnote[nosep]{\textit{ακπ} | si \textit{mv}}} habet in rithimis et in \edtext{coordinatione}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}mv} | eo ordine \textit{V\textsuperscript{a}}}} seu \edtext{coniunctione}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | coniectione \textit{P\textsuperscript{x}V\textsuperscript{z}}}} grauium sonorum et acutorum ad inuicem \edtext{vnius}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | vnus \textit{G\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{b}} | humimus \textit{V\textsuperscript{a}}}} quasi iuxta alium, ut non reddatur \edtext{vna}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}mv} | ulla \textit{P\textsuperscript{x}} | uera \textit{λ} | recta \textit{π} | \textit{om}. \textit{P\textsuperscript{y}}}} commixtio.} \edtext{Quia}{\Cfootnote[nosep]{\textit{αλπmv} | Quoniam \textit{P\textsuperscript{x}}}} in ea \edtext{non id accidit}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | id non accidit \textit{V\textsuperscript{m}} | non accidit id \textit{π}}}, \edtext{cum sonus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | consonus \textit{V\textsuperscript{o}}}} adeo \edtext{vniformiter}{\Cfootnote[nosep]{\textit{αλπmv} | uniforma \textit{P\textsuperscript{x}}}} \edtext{aerem et suauiter}{\Cfootnote[nosep]{\textit{ακmv} | et suauiter aerem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | aera et suauiter \textit{V\textsuperscript{a}} | aerem \textit{V\textsuperscript{o}}}} \edtext{concitet}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | excitet \textit{G\textsuperscript{u}P\textsuperscript{p}} | continet \textit{β} | concurrit \textit{V\textsuperscript{b}mv} | ycurit \textit{V\textsuperscript{a}}}} ut aures \edtext{universaliter}{\Cfootnote[nosep]{\textit{κ} | uel \textit{γE\textsuperscript{a}mv} | nichil \textit{βπ}}} percipiant \edtext{sensibile}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} ex \edtext{aeris}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | aere \textit{V\textsuperscript{o}}}} motu. Et \edtext{ideo}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} videmus infirmos \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}mv} | huiusmodi \textit{γN\textsuperscript{u}} | \textit{om}. \textit{π}}} adeo \edtext{melodioso}{\Cfootnote[nosep]{\textit{βγG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}mv} | melodiose \textit{P\textsuperscript{z}}}} \edtext{delectari}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}} | delectari sono \textit{γπE\textsuperscript{a}N\textsuperscript{u}mv}}}, non autem \edtext{priori}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | priori scilicet difficiliori \textit{P\textsuperscript{p}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{eum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | cum \textit{V\textsuperscript{a}}}} \edtext{fugientes}{\Cfootnote[nosep]{\textit{βγκπmv} | fugiente \textit{E\textsuperscript{a}}}} et maxime \edtext{galleatam}{\Cfootnote[nosep]{\textit{βP\textsuperscript{x}mv} | galeanterra \textit{P\textsuperscript{z}}}} habentes passionem seu \edtext{ouum}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | animam \textit{P\textsuperscript{x}}}}. \textit{Et ideo consonantia \edtext{sic}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | sit \textit{mv} | ac \textit{G\textsuperscript{u}}}} armonica non recipit consuetudinem,} quemadmodum \edtext{neque}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} alii pretacti \edtext{sensuum}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{a}} | sensum \textit{V\textsuperscript{b}mv} | sensu \textit{P\textsuperscript{x}}}}, \edtext{cum nichil}{\Cfootnote[nosep]{\textit{α} | cum nichil aliud \textit{π} | uel naturaliter \textit{κ}}} sensibilius preter perceptionem speciei \edtext{sonabilis}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | sensibilis \textit{π} | subtilis \textit{P\textsuperscript{y}}}} percipiatur ad auditum \edtext{peruenire}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | perueniente \textit{λ}}}, quod \edtext{et}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{πV\textsuperscript{a}}}} in reliquis dictum est \edtext{sensibus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sensibilibus \textit{G\textsuperscript{u}}}} accidere. \textit{ \edtext{Sed}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Seu \textit{G\textsuperscript{u}}}} in aliis \edtext{sensibus}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | sensibus pariter \textit{P\textsuperscript{z}} | sensibilibus \textit{αG\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{V\textsuperscript{m}}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{ \edtext{color odor et sapor}{\Cfootnote[nosep]{\textit{κ} | color sapor et odor \textit{G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}} | sapor color et odor \textit{P\textsuperscript{p}}}} }{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | colore odore et sapore \textit{mv} | colori odori et sapori \textit{γP\textsuperscript{z}} | coloribus odoribus et saporibus \textit{β} | coloris odoris saporis \textit{E\textsuperscript{a}}}}, non inest,} ut \edtext{eorum sumantur}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | sumantur eorum \textit{P\textsuperscript{y}} | eorum seruatur \textit{π}}} species cum aeris \edtext{motus}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | motu \textit{V\textsuperscript{m}}}} perceptione. +\pend + +\pstart +\textbf{3} \edtext{Nota}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | Notandum \textit{M\textsuperscript{a}mv}}} quod sicut duplex \edtext{est mixtio}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | est vni uisio \textit{P\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{y}}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | vna \textit{π} | \textit{om}. \textit{P\textsuperscript{y}}}} ad sensum \edtext{quedam}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{et alia}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{x}V\textsuperscript{m}mv} | alia \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{V\textsuperscript{z}}}} ad intellectum, id est uera et non uera, ita \edtext{et duplex grauis et acuti}{\Cfootnote[nosep]{\textit{κV\textsuperscript{b}m} | duplex acuti et grauis \textit{βV\textsuperscript{a}} | ut duplex grauis et acuti \textit{E\textsuperscript{a}v} | et duplex est grauis et acuti \textit{π}}} \edtext{permixtio, taliter}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | permixtionaliter \textit{P\textsuperscript{y}}}} ut ex \edtext{vna reddatur}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | una reddatur \surplus{vna reddatur} \textit{P\textsuperscript{y}} | vna tendatur \textit{P\textsuperscript{x}}}} \edtext{uera}{\Cfootnote[nosep]{\textit{γκπmv} | vna \textit{β}}} consonantia, ex \edtext{altera uero}{\Cfootnote[nosep]{\textit{ακmv} | alia vero \textit{π}}} apparens magis. +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{MOTUS.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | MOTUS AUTEM. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv}}} } Τangit causam sumptam \edtext{ex secunda parte}{\Cfootnote[nosep]{\textit{ακmv} | ex alia parte \textit{π}}} dicens \edtext{cum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | Est \textit{P\textsuperscript{y}}}} \edtext{igitur}{\Cfootnote[nosep]{\textit{αλπmv} | ergo \textit{P\textsuperscript{x}}}} \edtext{visibilia}{\Cfootnote[nosep]{\textit{ακmv} | audibilia \textit{π}}} \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} ad multum \edtext{recurrant}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | retractant \textit{P\textsuperscript{z}}}} \edtext{ad}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} organum cum \edtext{motu}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | motus \textit{G\textsuperscript{u}P\textsuperscript{x}}}} aeris \edtext{sensibili}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}V\textsuperscript{m}} | sensibilis \textit{M\textsuperscript{a}V\textsuperscript{z}} | sensibiliter \textit{γP\textsuperscript{x}mv}}}, \textit{et \edtext{ \edtext{motus}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | motus aeris \textit{V\textsuperscript{b}}}} \edtext{sint}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | sicut \textit{βE\textsuperscript{a}V\textsuperscript{z}} | sic \textit{P\textsuperscript{u}}}} \edtext{operatiui}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sensicun \textit{P\textsuperscript{x}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} }. \edtext{Operationes enim fiunt per \edtext{eos}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | eas \textit{P\textsuperscript{x}} | omnes \textit{P\textsuperscript{y}}}} \edtext{ \edtext{actiones}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{c}mv} | aptiones uel aptiones \textit{V\textsuperscript{a}}}} proprie dicte, \edtext{cum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{c}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} ‘ \edtext{proprium actionis}{\Cfootnote[nosep]{\textit{αV\textsuperscript{c}mv} | proprius actionis \textit{β} | proprium \textit{κ}}} \edtext{sit}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{c}mv} | sic \textit{P\textsuperscript{y}}}} esse in \edtext{motu}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{c}V\textsuperscript{m}V\textsuperscript{z}mv} | motu ut \textit{M\textsuperscript{a}}}}, \edtext{auctor}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{c}V\textsuperscript{z}mv} | auctorum \textit{V\textsuperscript{m}}}} \textit{ \edtext{.6.}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{c}mv} | \textit{om}. \textit{N\textsuperscript{u}}}} principiorum.} \edtext{}{\Afootnote[nosep]{Ps.-Herm. Tris. \textit{De sex re. princ.} II .1}}’}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{c}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} Et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} \textit{signum \edtext{consuetudinis}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \surplus{et signum} consuetudinis \textit{P\textsuperscript{y}}}} \edtext{acquirende}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}} | acquirendo \textit{V\textsuperscript{b}mv}}} uel \edtext{acquisite}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}} sit operatio,} nam ‘consuetudo \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | est in \textit{β}}} multotiens \edtext{aliquid}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}P\textsuperscript{y}mv} | aliud \textit{P\textsuperscript{x}} | id \textit{N\textsuperscript{u}}}} facere. \edtext{13° .21a.}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | ut 13° .21a. \textit{M\textsuperscript{a}} | 13 .21a. \textit{πmv} | 13°. 23e. \textit{P\textsuperscript{y}}}} \edtext{}{\Afootnote[nosep]{Ps.-Arist. \textit{Prob.} XXI .14 , 928b ll. 25–26}}’ \textit{Consuetudo \edtext{siquidem}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{πV\textsuperscript{z}}}} \edtext{adipiscetur magis}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | magis adipiscetur \textit{πV\textsuperscript{z}}}} in \edtext{audibilibus quam in ceteris}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | audibilibus quod in ceteris \textit{N\textsuperscript{u}} | audibilibus quam ceteris \textit{P\textsuperscript{z}} | ceteris audibilibus audibilibus quam in ceteris \textit{P\textsuperscript{y}}}} \edtext{sensibilibus}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}mv} | sensibus \textit{P\textsuperscript{x}V\textsuperscript{b}P\textsuperscript{z}V\textsuperscript{o}}}} }, \edtext{et id tangetur etiam 29}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}V\textsuperscript{b}mv} | et id tangetur et 29º \textit{V\textsuperscript{a}} | et id tangetur etiam 20° \textit{P\textsuperscript{x}} | \textit{om}. \textit{π}}}, \edtext{nosce}{\Cfootnote[nosep]{\textit{ακπ} | notandum \textit{mv}}} quod causa \edtext{fundatur \hyperref[Ar]{aristoteles}}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \hyperref[Ar]{aristoteles} fundatur \textit{βπV\textsuperscript{z}}}} \edtext{super}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | supra \textit{G\textsuperscript{u}P\textsuperscript{q}}}} hoc: \edtext{quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} \edtext{generatio}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | genera \textit{E\textsuperscript{a}} | genero \textit{P\textsuperscript{x}}}} \edtext{soni et uocis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | uocis et soni \textit{P\textsuperscript{y}V\textsuperscript{a}}}} consistit in quodam \edtext{fieri et}{\Cfootnote[nosep]{\textit{απmv} | motu et \textit{λ} | \textit{om}. \textit{P\textsuperscript{x}}}} transmutari. Sunt \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} de genere successiuorum entium, cum \edtext{sunt}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | sint \textit{βπ}}} in motu, et \edtext{fiunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | fuit \textit{P\textsuperscript{z}}}} \edtext{tantum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | in tantum \textit{P\textsuperscript{y}}}} \edtext{color}{\Cfootnote[nosep]{\textit{ακmv} | color vero \textit{π}}} odor \edtext{et}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} sapor de \edtext{manerie}{\Cfootnote[nosep]{\textit{ακmv} | numero \textit{π}}} permanentium, que post factum \edtext{habent esse}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}N\textsuperscript{u}mv} | esse habent \textit{P\textsuperscript{y}} | habet esse \textit{P\textsuperscript{x}} | esse remanent \textit{π}}} et non \edtext{prius}{\Cfootnote[nosep]{\textit{βγκπmv} | plus \textit{E\textsuperscript{a}}}}. Quod \edtext{indicat}{\Cfootnote[nosep]{\textit{ακ} | inducat \textit{mv} | denotat \textit{π}}} ‘aristoteles , \edtext{quia singulariter \textit{de anima} 2°}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | quia singulariter 2° \textit{de anima} \textit{V\textsuperscript{z}} | quia 2°. de anima \textit{π} | quia similiter de alia sermo \textit{V\textsuperscript{a}}}} \edtext{determinauit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | determinant \textit{P\textsuperscript{z}}}} de \edtext{modo generationis}{\Cfootnote[nosep]{\textit{ακmv} | generatione \textit{π}}} \edtext{soni et uocis}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vocis et soni \textit{G\textsuperscript{u}P\textsuperscript{q}} | et uocis \textit{P\textsuperscript{x}}}},\edtext{}{\Afootnote[nosep]{Arist. \textit{De an.} II .8 , 419b l. 9}}’ \edtext{et}{\Cfootnote[nosep]{\textit{ακmv} | Et modo inmutandi et \textit{π}}} non \edtext{aliorum}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}, \edtext{sed inde sensu et sensato}{\Cfootnote[nosep]{\textit{ακmv} | sic de aliis \textit{π}}}. Cum \edtext{igitur modus}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | modus igitur \textit{V\textsuperscript{a}} | igitur motus \textit{V\textsuperscript{z}} | ergo modo \textit{P\textsuperscript{x}}}} generationis \edtext{soni et}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | soni \textit{P\textsuperscript{z}} | et \textit{V\textsuperscript{a}}}} \edtext{perceptionis}{\Cfootnote[nosep]{\textit{ακπ} | preceptionis \textit{mv}}} \edtext{ut ad}{\Cfootnote[nosep]{\textit{ακmv} | ad \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}} multum \edtext{conueniat}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | conueniant \textit{P\textsuperscript{y}} | contingit \textit{P\textsuperscript{p}}}} cum operatione \edtext{siue}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}mv} | seu \textit{P\textsuperscript{u}V\textsuperscript{o}}}} actione, que \edtext{fit}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sit \textit{G\textsuperscript{u}} | sit in \textit{E\textsuperscript{a}}}} mediante motu \edtext{qua}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quam \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | que \textit{P\textsuperscript{y}} | quia \textit{G\textsuperscript{u}P\textsuperscript{z}}}} consuetudo ut \edtext{dictum}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | dictum est \textit{γπE\textsuperscript{a}V\textsuperscript{z}mv}}} \edtext{acquiritur}{\Cfootnote[nosep]{\textit{γκπmv} | adquiratur ad \textit{N\textsuperscript{u}} | adquantur \textit{P\textsuperscript{y}}}} \edtext{visibilia}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | visibilis \textit{V\textsuperscript{a}} | audibilia \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}} | sensibilia \textit{N\textsuperscript{u}} | \textit{om}. \textit{V\textsuperscript{o}}}} pre aliis \edtext{sensibilibus}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{m}mv} | sensibus \textit{πM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | sensibus uel sensibilibus \textit{V\textsuperscript{b}}}} \edtext{reddentur}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | redduntur \textit{P\textsuperscript{z}V\textsuperscript{o}} | reddetur \textit{E\textsuperscript{a}P\textsuperscript{y}}}} consueta, ut \edtext{ostendunt}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{a}mv} | ostendit \textit{P\textsuperscript{x}V\textsuperscript{b}}}} \edtext{eris}{\Cfootnote[nosep]{\textit{βγλπmv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{x}}}} et \edtext{nauium}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | manifestum \textit{P\textsuperscript{x}}}} \edtext{malleatores}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}}}} non audiendo, \edtext{quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | quia \textit{P\textsuperscript{u}}}} \edtext{in}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} illis \edtext{non}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}} | non ut \textit{β}}} \edtext{acquiratur}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | acquiratur etiam \textit{αmv} | acquiratur \surplus{audibilia pre aliis sensibus redduntur consueta ut ostendunt quod in illis non acquiritur} \textit{P\textsuperscript{z}}}} consuetudo \edtext{utcunque}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | uterque \textit{P\textsuperscript{z}} | utrumque \textit{λP\textsuperscript{y}}}}. \edtext{}{\Cfootnote{et cetera \textit{V\textsuperscript{z}} | sequitur 28. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Uigesimumoctauum problema}\label{edition-text book-19a part28}}{\lemma{Uigesimumoctauum + problema} \Cfootnote[nosep]{\textit{γmv} | «28m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{vigesimum octauum.} Vigesimum octauum. \textit{P\textsuperscript{y}} | 27m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID LEGES}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}} | PROPTER QUID SECUNDUM LEGES \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID LEGES APPELLANTUR QUAS CANTANT? \textsuperscript{2}AUT QUIA PRIUSQUAM SCIANT LITTERAS, UIDERUNT LEGES NON LATEANT, QUEMADMODUM IN AGATHUSIS AMPLIUS CONSUEUERUNT? ET POSTERIORIBUS IGITUR CANTIBUS PRIMOS IDEM APPELLAUERUNT QUIDAM PRIMAS \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Uigesimum + octauum problema. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} \edtext{illi}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aliqui illi \textit{G\textsuperscript{u}P\textsuperscript{q}}}} cantus quos primitus \edtext{aliqui cantant}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | cantant aliqui \textit{γmv} | obliqui cantant \textit{P\textsuperscript{z}}}} leges \edtext{appellantur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | appellant \textit{N\textsuperscript{u}}}}.} \edtext{Nosce}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | Nota \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{per}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} leges hic audio cantus in quibus \edtext{mox aliqui}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{u}} | aliqui mox \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | statim aliqui \textit{γmv}}} \edtext{edocentur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | docentur \textit{P\textsuperscript{y}}}} cum incipiunt cognitionem habere, sicut illi \edtext{qui ordinati}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \surplus{ordinati} qui ordinati \textit{P\textsuperscript{y}}}} sunt a lege ut \edtext{cantentur}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | cantetur \textit{mv} | cantent \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}}}} legaliter. \edtext{Tamen}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | Cum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, \edtext{ut visum \edtext{est}{\Cfootnote[nosep]{\textit{γκmv} | \textit{om}. \textit{βE\textsuperscript{a}}}} .15.}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}, in laudem dei \edtext{ \edtext{ceu}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{m}}}} in lege nostra}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{docentur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | docent \textit{P\textsuperscript{p}}}} \edtext{pueruli}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}m}}} \edtext{salutationem}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | salutatio neque \textit{V\textsuperscript{a}}}} virginis \edtext{uel}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}mv} | aut \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{b}V\textsuperscript{z}mv}}} cantare. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv}}} } \edtext{Soluit dicens}{\Cfootnote[nosep]{\textit{βγπP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | Soluit dicit \textit{E\textsuperscript{a}} | Dicit \textit{M\textsuperscript{a}}}} causam esse \textit{quia cantantes leges \edtext{ceu}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}} | seu \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}mv}}} \edtext{puerili}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}m} | pueri \textit{π}}} antequam aliquid sciuissent de litteris et cantibus choricis, iam \edtext{uiderant}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}V\textsuperscript{o}mv} | uiderunt \textit{P\textsuperscript{z}} | uideant \textit{P\textsuperscript{p}P\textsuperscript{u}}}} leges \edtext{seu}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ceu \textit{V\textsuperscript{z}}}} \edtext{audiuerant}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{scientes etiam}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | etiam scientes \textit{G\textsuperscript{u}P\textsuperscript{q}} | scientes \textit{P\textsuperscript{z}} | scientes et \textit{E\textsuperscript{a}V\textsuperscript{a}}}} \edtext{ipsas}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | ipsos \textit{V\textsuperscript{a}mv}}} cantare ad hoc ut \edtext{non}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} lateant}. \edtext{Sed}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Sed ut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | Seu \textit{P\textsuperscript{y}}}} \edtext{reddantur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv} | redduntur \textit{V\textsuperscript{b}} | declaratum \textit{P\textsuperscript{y}}}} manifeste \edtext{note}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uoce \textit{κ} | nete \textit{P\textsuperscript{z}}}}, \edtext{uelut}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | ultra \textit{P\textsuperscript{x}} | illud \textit{P\textsuperscript{y}} | uel \textit{V\textsuperscript{a}} | uolox \textit{V\textsuperscript{z}} | uol\expan{ui}t \textit{(orig. \textup{uolt'})} \textit{V\textsuperscript{m}}}} ‘principia \edtext{in}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | et \textit{P\textsuperscript{y}}}} scientia \edtext{et}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uel \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{locus}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | uelud \textit{V\textsuperscript{a}} | \textit{om}. \textit{V\textsuperscript{z}}}} ianue in domo\edtext{}{\Afootnote[nosep]{Arist. \textit{Met.} II .1 , 993b ll. 4–5}} \edtext{ut ostensum \edtext{est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | \textit{om}. \textit{β}}} \edtext{.18}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | 18ua. «problemate 8uo» (in mg.) \textit{M\textsuperscript{a}} | supra \textit{P\textsuperscript{y}} | \textit{om}. \textit{V\textsuperscript{z}}}} . As cited in d'Abano's commentary on Book XVIII, Problem 8, where the paraphrased quotation begins with "nota"}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} ’ Nam quod primitus \edtext{discitur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | dicitur \textit{P\textsuperscript{z}V\textsuperscript{c}}}} optime \edtext{imprimitur}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv}}} cum anima sit tunc \edtext{ceu}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{z}} | seu \textit{E\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | sicut \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}mv} | tamquam \textit{G\textsuperscript{u}P\textsuperscript{y}}}} tabula rasa, et \edtext{perfecte}{\Cfootnote[nosep]{\textit{ακmv} | bene \textit{π}}} \edtext{retinetur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | retinere \textit{V\textsuperscript{m}}}}, et \edtext{huius}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}m} | huiusmodi \textit{γG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{a}v} | vnius \textit{E\textsuperscript{a}}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quedam \textit{P\textsuperscript{p}}}} consuetudo \edtext{potissime fuit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | fuit potissime \textit{N\textsuperscript{u}} | fuit \textit{P\textsuperscript{y}}}} \textit{apud \edtext{quosdam nominatos}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | nominatos quosdam \textit{G\textsuperscript{u}}}} \edtext{agathyrsos}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{z}}}}.} Quod autem \edtext{primum quis}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | primus quis \textit{mv} | primum \textit{κ} | primitus \textit{G\textsuperscript{u}P\textsuperscript{q}}}} adipiscitur prius \edtext{nomen}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}V\textsuperscript{o}mv} | notum \textit{P\textsuperscript{p}P\textsuperscript{u}} | non \textit{P\textsuperscript{z}}}} \edtext{suscipit}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{z}mv} | suscepit \textit{V\textsuperscript{m}}}}, \edtext{tanquam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv}}} \edtext{notum}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | motum \textit{P\textsuperscript{y}V\textsuperscript{z}} | natum \textit{E\textsuperscript{a}}}} cum anima nomen \edtext{imponatur}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | imponat \textit{M\textsuperscript{a}} | imponat ut \textit{απmv}}} \edtext{cognoscit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cognoscat \textit{G\textsuperscript{u}P\textsuperscript{q}} | cognoscet \textit{P\textsuperscript{z}}}}. \textit{Itaque cum \edtext{alii}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}} | aliis \textit{P\textsuperscript{z}V\textsuperscript{b}mv}}}, cantus \edtext{ut}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{chorici}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | theorici \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} siue conuersiui et vniuersaliter \edtext{tragici}{\Cfootnote[nosep]{\textit{βγκπmv} | turgici \textit{E\textsuperscript{a}}}}, \edtext{sint}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}} | sunt \textit{V\textsuperscript{z}} | sit \textit{P\textsuperscript{z}} | sicut \textit{γP\textsuperscript{y}V\textsuperscript{m}mv}}} posterius cantibus legalibus \edtext{cantati}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | cantari \textit{P\textsuperscript{y}}}}, puta cum \edtext{sciuerint}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{b}P\textsuperscript{u}P\textsuperscript{z}mv} | sciuerunt \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{a}V\textsuperscript{o}}}} litteras et \edtext{fuerint}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | fuerunt \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}} | fuerit \textit{E\textsuperscript{a}V\textsuperscript{a}}}} adulti leges, \edtext{primos cantus}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | cantus primos \textit{V\textsuperscript{b}}}} seu primas melodias quod idem \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | etiam \textit{P\textsuperscript{y}}}} \edtext{appellarunt}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{m}mv} | appellauerunt \textit{P\textsuperscript{u}P\textsuperscript{z}M\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}}}},} sicut \edtext{scientie}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | scire \textit{P\textsuperscript{z}}}} de sermone cum prius \edtext{instruantur in hiis pueri}{\Cfootnote[nosep]{\textit{λ} | instruantur in hiis puer \textit{P\textsuperscript{x}} | instruantur in eis pueri \textit{απmv}}} dicuntur primitiue. \edtext{}{\Cfootnote{etcetera. \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | sequitur 29. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Uigesimumnonum problema}\label{edition-text book-19a part29}}{\lemma{Uigesimumnonum + problema} \Cfootnote[nosep]{\textit{γmv} | «29m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{vigesimum nonum.} Vigesimumnonum. \textit{P\textsuperscript{y}} | 28m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID RITHIMI}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID RITHIMI ET CANTUS, UOX EXISTENS, CONSUETUDINIBUS ASSIMILANTUR, SAPORES AUTEM NON, SED NEQUE COLORES ET ODORES? \textsuperscript{2}AUT QUIA MOTUS SUNT QUEMADMODUM ET OPERATIONES? IAM UTIQUE ACTIO QUIDEM MORALE ET FACIT CONSUETUDINEM, SAPORES AUTEM ET COLORES NON FACIUNT SIMILITER \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Uigesimum nonum problema etcetera. Repetit \edtext{27m problema dicens}{\Cfootnote[nosep]{\textit{λ} | .27. partem dicens \textit{P\textsuperscript{x}} | .27m. dicens \textit{β} | .27m. particulariter dicens \textit{γE\textsuperscript{a}mv} | problema \textit{π}}} \textit{ \edtext{quare rithimi}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}}, quantum ad speciem musice \edtext{rithimicam}{\Cfootnote[nosep]{\textit{γκπmv} | nebincam \textit{P\textsuperscript{y}}}}, et cantus et uox \edtext{pronunciatiua}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | pronunciatam \textit{P\textsuperscript{x}V\textsuperscript{z}}}} quantum ad armonicam \edtext{similitudinem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | similem \textit{β} | \textit{om}. \textit{π}}} \edtext{acquirunt}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | adquirit \textit{P\textsuperscript{z}}}} \edtext{consuetudinis}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | consuetudines \textit{V\textsuperscript{z}} | consuetudinem \textit{π} | similitudinem consuetudinis \textit{P\textsuperscript{y}}}}? Redduntur enim consueti, sed sapores \edtext{aut}{\Cfootnote[nosep]{\textit{ακE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uel \textit{G\textsuperscript{u}}}} \edtext{color uel odores}{\Cfootnote[nosep]{\textit{κ} | colores uel odores \textit{βE\textsuperscript{a}V\textsuperscript{b}mv} | odores vel colores \textit{πV\textsuperscript{a}}}} non proportionantur consuetudini.} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } Soluit dicens causam esse \textit{ \edtext{quia}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | quoniam \textit{V\textsuperscript{a}}}} motus \edtext{qui}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quia \textit{P\textsuperscript{p}}}} sunt circa sensibilia \edtext{auditus}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{P\textsuperscript{y}V\textsuperscript{m}}}} \edtext{tanquam}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv}}} operationes \edtext{existunt}{\Cfootnote[nosep]{\textit{αλπmv} | existant \textit{P\textsuperscript{x}}}} }. Quod \edtext{declarat}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | declaratur \textit{G\textsuperscript{u}}}} quia sicut \edtext{videmus}{\Cfootnote[nosep]{\textit{ακmv} | nos videmus \textit{π}}} \textit{in actione morali quod actus eius \edtext{inducit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | inducunt \textit{P\textsuperscript{y}}}} consuetudinem et \edtext{inclinationem}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | delectationem uel inclinationem \textit{V\textsuperscript{a}}}} ad \edtext{istud}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{a}} | i\expan{llu}d \textit{(orig. \textup{i\textsuperscript{d}})} \textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | illud \textit{G\textsuperscript{u}P\textsuperscript{z}mv} | id \textit{V\textsuperscript{b}}}} uel \edtext{ad}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{illud}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{a}mv} | id \textit{V\textsuperscript{b}} | aliquid \textit{P\textsuperscript{x}}}} agendum,} ita \edtext{similiter}{\Cfootnote[nosep]{\textit{ακπ}}} est in \edtext{sensibus}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | sensibilibus \textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}mv}}} auditus. Ex multotiens \edtext{enim audire}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{q}mv} | audire enim \textit{E\textsuperscript{a}} | quidem audire \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{vnum}{\Cfootnote[nosep]{\textit{απmv} | in vnum \textit{P\textsuperscript{x}V\textsuperscript{m}} | nimium \textit{M\textsuperscript{a}V\textsuperscript{z}}}} cantum inducitur consuetudo, \edtext{qua}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}mv} | que \textit{γλN\textsuperscript{u}} | etiam \textit{P\textsuperscript{y}} | in \textit{E\textsuperscript{a}}}} habituata cantus \edtext{ille}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}mv} | iste \textit{C\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{reputatur}{\Cfootnote[nosep]{\textit{ακmv} | redditur \textit{π}}} delectabilis, \edtext{etiam}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | et \textit{M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}}}} si non sit secundum ueritatem, non autem circa sensibilia aliorum sensuum, \edtext{ut declaratum, accidit}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}} | ut declaratum est, accidit \textit{γπmv}}}. Et hoc \edtext{est}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv} | etiam \textit{V\textsuperscript{m}}}} quod subditur \edtext{sapores}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | saporem \textit{V\textsuperscript{z}} | sapor \textit{V\textsuperscript{m}}}} \edtext{qui}{\Cfootnote[nosep]{\textit{αλπmv} | que \textit{P\textsuperscript{x}}}} sunt sensibilia; \textit{gustus et odores qui \edtext{olfatus}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{u}V\textsuperscript{o}m} | olfaciunt \textit{E\textsuperscript{a}}}} non id \edtext{operantur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | operatur \textit{P\textsuperscript{z}}}},} quod ex ipsis consuetudo \edtext{consimilibus}{\Cfootnote[nosep]{\textit{κ} | similiter \textit{βP\textsuperscript{z}} | consimiliter \textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{audibilibus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | audibilis \textit{G\textsuperscript{u}} | adeoibilibus \textit{V\textsuperscript{a}} | audientibus \textit{P\textsuperscript{q}P\textsuperscript{y}}}} \edtext{acquiratur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 30. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Trigesimum problema}\label{edition-text book-19a part30}}{\lemma{Trigesimum problema} \Cfootnote[nosep]{\textit{γmv} | «30m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | Trigesimum. \surplus{trigesimum problema.} \textit{P\textsuperscript{y}} | 29m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID NEQUE YPODORISTIUM}{\Cfootnote[nosep]{\textit{V\textsuperscript{o}} | PROPTER QUID NEQUE \textit{P\textsuperscript{p}P\textsuperscript{u}} | PROPTER QUID YPODORISTIUM \textit{V\textsuperscript{m}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID NEQUE YPODORISTIUM NEQUE YPOFRIGISTIUM NON EST IN TRAGEDIA ROTATIUUM? \textsuperscript{2}AUT NON HABET CONUERSIUUM? SED A SCENA, IMMUTATIUA ENIM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema .30m. etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} \edtext{ypodoristium}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv}}} \edtext{et}{\Cfootnote[nosep]{\textit{αλπmv} | 7. \textit{P\textsuperscript{x}}}} \edtext{ypophirgium}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}}}} cantare \edtext{non}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ut \textit{V\textsuperscript{z}}}} \edtext{est}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | \textit{om}. \textit{γmv}}} \edtext{rotatiuum}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | rotatum \textit{N\textsuperscript{u}} | rota tantum \textit{P\textsuperscript{y}}}} et \edtext{conuersiuum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}} in \edtext{tragedia}{\Cfootnote[nosep]{\textit{αλπmv}}} }, \edtext{ubi}{\Cfootnote[nosep]{\textit{αλπmv} | nisi \textit{P\textsuperscript{x}}}} \edtext{obseruentur}{\Cfootnote[nosep]{\textit{ακmv} | obseruantur \textit{π}}} diuersitates sonorum secundum \edtext{graue}{\Cfootnote[nosep]{\textit{αλπmv} | grauem \textit{P\textsuperscript{x}}}} et acutum \edtext{ascensione}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{et}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | ac \textit{γN\textsuperscript{u}mv}}} descensione per circulos \edtext{casuum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}} | QUANDO. \textit{P\textsuperscript{x}}}} } Soluit dicens causam esse \textit{ \edtext{quia}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | quia ut \textit{P\textsuperscript{y}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}m} | huiusmodi \textit{γG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{q}v}}} cantare non \edtext{habent}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | habet \textit{πV\textsuperscript{m}}}}, ut expositum \edtext{est}{\Cfootnote[nosep]{\textit{κV\textsuperscript{a}} | \textit{om}. \textit{βπE\textsuperscript{a}V\textsuperscript{b}mv}}}, \edtext{conuersiuum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | masiuum \textit{P\textsuperscript{y}} | conuersionum \textit{P\textsuperscript{z}}}} } in quo magis \edtext{attenditur}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv}}} ad \edtext{cantus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cantum \textit{G\textsuperscript{u}}}} quam ad uerba. \textit{Sed potius \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}m} | huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{b}v}}} cantus est \edtext{immutatiuus}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{z}mv} | immitatiuus \textit{V\textsuperscript{m}} | imitatiuus \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | imutatiuus \textit{P\textsuperscript{z}}}}, \edtext{qui}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}} | quod \textit{π} | quam \textit{γP\textsuperscript{x}mv}}} dicitur \edtext{ascena}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{x}V\textsuperscript{b}mv}}} } contentus sub legibus et comedia, ut visum \edtext{est}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{z}mv} | est in \textit{V\textsuperscript{m}} | \textit{om}. \textit{βP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}}}} .15., in \edtext{quo}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} amplius \edtext{attenditur}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} ad verba quam ad \edtext{cantum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | cantus \textit{M\textsuperscript{a}V\textsuperscript{z}}}}, et \edtext{id}{\Cfootnote[nosep]{\textit{ακπ} | illud \textit{mv}}} amplius \edtext{apparebit}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{48°}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | 4º 8º \textit{P\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{3} \edtext{Nosce}{\Cfootnote[nosep]{\textit{ακπ} | Notandum \textit{mv}}} ut apparet ‘ \edtext{.8. \textit{ \edtext{politicorum}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{z}}}} } aristotelem}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}} | .8. \textit{polliticorum} aristotelem \textit{E\textsuperscript{a}} | .8. \textit{polliticorum} quod \textit{P\textsuperscript{y}} | .8. \textit{phisicorum} aristotelem \textit{mv}}} \edtext{}{\Afootnote[nosep]{Arist. \textit{Pol.} VIII , 1324b ll. 12–18}}’tangere tres \edtext{cantus modos}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}} | modos cantus \textit{λπ} | cantus mentis \textit{γmv}}}: precipue \edtext{phrigistium}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}} | philigistium \textit{γmv}}}, \edtext{doricum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}} | doricum uel doristicum \textit{π} | choricum \textit{P\textsuperscript{y}}}}, et \edtext{lidium}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}}}}. \edtext{Phrigistius}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | Frigisticus uel phigistius \textit{π}}} est \edtext{troianus}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv}}}, \edtext{qui}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | que \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}} est \edtext{cantus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{agrestis}{\Cfootnote[nosep]{\textit{αλπmv} | terrestris \textit{P\textsuperscript{x}}}} \edtext{incitatiuus}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{o}} | et incitatiuus \textit{γP\textsuperscript{z}mv} | imitatiuus \textit{P\textsuperscript{p}P\textsuperscript{u}} | mutans \textit{G\textsuperscript{u}}}} \edtext{in}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ad \textit{P\textsuperscript{y}P\textsuperscript{z}}}} \edtext{iram}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} et passionem, \edtext{ceu}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | seu \textit{πE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{m}}}} \edtext{qui}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | que \textit{G\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{y}}}} fistule \edtext{in quam}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | in quem \textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}mv} | in quo \textit{P\textsuperscript{x}} | in qua \textit{P\textsuperscript{u}} | in quod \textit{V\textsuperscript{m}} | inquit \textit{V\textsuperscript{z}} | nunquam \textit{G\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{concidit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | occidit \textit{P\textsuperscript{z}}}} decenter \edtext{ditirantibus}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}} | quid dithitambis \textit{P\textsuperscript{y}} | qui dithirambus \textit{N\textsuperscript{u}} | ex tyranbus \textit{πE\textsuperscript{a}}}}. \edtext{Dorista}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | Doristas \textit{γmv}}} siquidem \edtext{maluaficiacus}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | maluafiati cuius \textit{P\textsuperscript{y}}}} cantus laudabilis ‘ \edtext{ \edtext{tanquam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}} | tam \textit{P\textsuperscript{z}}}} \edtext{stabilis}{\Cfootnote[nosep]{\textit{βγκ} | stabilis et \textit{πE\textsuperscript{a}}}} \edtext{virilis}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | uiribus \textit{P\textsuperscript{z}} | \textit{om}. \textit{M\textsuperscript{a}V\textsuperscript{b}}}},}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} \edtext{}{\Afootnote[nosep]{Arist. \textit{Pol.} VIII , 1324b l. 12}}’‘ \edtext{ \edtext{ \edtext{unde .48.}{\Cfootnote{unde .40. \textit{βV\textsuperscript{a}} | unde 41. \textit{π} | \textit{om}. \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} ``magnificus \edtext{stabilis}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | stabilis et \textit{P\textsuperscript{x}} | stabilisimus \textit{V\textsuperscript{a}}}} ''}{\Cfootnote[nosep]{\textit{βπP\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | \textit{om}. \textit{M\textsuperscript{a}V\textsuperscript{b}}}} `` \edtext{cytharicissimus}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | cithantissimus \textit{P\textsuperscript{x}π}}} omnium''}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} \edtext{}{\Afootnote[nosep]{Ps.-Arist. \textit{Prob.} XIX .48 , 922b l. 15}}’‘ \edtext{et}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{ceu}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | seu \textit{G\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{m}V\textsuperscript{o}}}} omnium \edtext{superhabundantiarum}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}}}} \edtext{mediis}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | medius \textit{βM\textsuperscript{a}}}} laudatus in quo \edtext{pueruli}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{a}}}} sunt \edtext{edocendi}{\Cfootnote[nosep]{\textit{ακπ}}}.\edtext{}{\Afootnote[nosep]{Arist. \textit{Pol.} VIII , 1324b ll. 12–18}}’ \edtext{Lidius}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{z}m}}} \edtext{quidem dicitur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | dicitur quidem \textit{V\textsuperscript{b}} | siquidem dicitur \textit{mv} | dicitur \textit{V\textsuperscript{a}}}} a \hyperref[Tor]{ \edtext{chorebo}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}V\textsuperscript{o}}}} } \edtext{lidorum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}m}}} rege. Qui omnibus laudabilior \edtext{est}{\Cfootnote[nosep]{\textit{κ} | \textit{om}. \textit{απmv}}}. ‘ \edtext{Cum}{\Cfootnote[nosep]{\textit{κ} | Cum enim \textit{απmv}}} \edtext{sit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | sint \textit{P\textsuperscript{z}}}} \edtext{aliorum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | alium \textit{P\textsuperscript{y}}}} \edtext{medius}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}} | mediis \textit{P\textsuperscript{z}V\textsuperscript{b}mv}}}, tria in se \edtext{continet}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | continens \textit{P\textsuperscript{y}}}} quod medium \edtext{rationem habens}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | habens rationem \textit{P\textsuperscript{y}} | commune habens \textit{πE\textsuperscript{a}}}} uirtutis \edtext{quod}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | et \textit{P\textsuperscript{y}}}} decens \edtext{et}{\Cfootnote[nosep]{\textit{κ} | et quod \textit{απmv}}} \edtext{possibile}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | possibile et \textit{P\textsuperscript{y}}}},\edtext{}{\Afootnote[nosep]{Arist. \textit{Pol.} VIII , 1324b ll. 32–34}}’ \edtext{que}{\Cfootnote[nosep]{\textit{βγκπmv} | quod \textit{E\textsuperscript{a}}}} in cantu et maxime puerorum sunt obseruanda. Unde ‘ \edtext{boecius \textit{musice} .4.}{\Cfootnote[nosep]{\textit{ακmv} | boecius .4. \textit{musice} \textit{π}}} si quis totas constitutiones \edtext{faciat}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | faciet \textit{mv} | facit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} acutiores uel \edtext{graues}{\Cfootnote[nosep]{\textit{ακ} | grauiores \textit{πmv}}} totas \edtext{remittat}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | remittit \textit{P\textsuperscript{p}P\textsuperscript{z}}}} dyapason consonantie species, \edtext{efficiet}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | efficiat \textit{G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{a}} | \textit{om}. \textit{V\textsuperscript{m}}}} modos septem \edtext{ceu}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} sunt \edtext{ypodorius}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{ypofrigius}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}m}}} \edtext{ypolidius}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}P\textsuperscript{y}m} | ypodolius \textit{v}}} \edtext{dorius}{\Cfootnote[nosep]{\textit{αλmv} | chorius \textit{π} | polius \textit{V\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{frigius}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{lidius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}m}}} \edtext{mixolidius}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} IV .15 (Friedlein p. 342, ll. 10–14)}}’ \edtext{ypermixolidius}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}} | \textit{om}. \textit{π}}}. Duplat \edtext{igitur}{\Cfootnote[nosep]{\textit{βγλG\textsuperscript{u}mv} | ergo \textit{P\textsuperscript{x}} | enim \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | 7 \textit{P\textsuperscript{z}}}} uel triplat \edtext{quod \hyperref[Ar]{aristoteles} \hyperref[Bo]{boecius}}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | quod \hyperref[Ar]{aristoteles} et \hyperref[Bo]{boecius} \textit{V\textsuperscript{b}} | quod \hyperref[Ar]{aristoteles} \hyperref[Bo]{boecius} .31 \textit{mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}}. \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{z}V\textsuperscript{z}} | sequitur 3.1; problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Trigesimumprimum problema}\label{edition-text book-19a part31}}{\lemma{Trigesimumprimum + problema} \Cfootnote[nosep]{\textit{γmv} | «31m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{trigesimum.primum} Trigesimum primum. \textit{P\textsuperscript{y}} | Trigesimum problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID CIRCA FRINICHUM}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID CIRCA \textit{P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID CIRCA PHRINICUM FUERUNT MAGIS DULCE MELODIA? \textsuperscript{2}AUT PROPTER ID QUOD MULTIPLICES SUNT TUNC CANTUS IN TRAGEDIIS METRORUM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}?} Pricesimum primum problema \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} est quod \edtext{apud phrinicum}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{y}} | apud plinitum \textit{V\textsuperscript{a}} | apud finitum \textit{V\textsuperscript{b}mv} | circa frinichum \textit{G\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}} | apphimitum \textit{P\textsuperscript{x}} | id est caput frontum \textit{P\textsuperscript{z}}}}, \edtext{qui}{\Cfootnote[nosep]{\textit{αλmv} | quod \textit{πP\textsuperscript{x}}}} est modus \edtext{cantantium}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | cantatiuum \textit{P\textsuperscript{z}} | cantantium uel cantuum \textit{V\textsuperscript{o}}}} quorundam, \edtext{melodie}{\Cfootnote[nosep]{\textit{ακπ} | melodia \textit{mv}}} \edtext{fuerunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fiunt \textit{P\textsuperscript{p}V\textsuperscript{c}} | finitur \textit{P\textsuperscript{u}}}} magis suaues quam \edtext{apud}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | amplius \textit{P\textsuperscript{x}}}} \edtext{alios}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | alias \textit{C\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}}?} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | APUD. \textit{V\textsuperscript{a}}}} } \edtext{Soluit dicens}{\Cfootnote[nosep]{\textit{βγκπmv} | Soluit dicit \textit{E\textsuperscript{a}}}} causam esse \textit{ \edtext{quoniam}{\Cfootnote[nosep]{\textit{αλπ} | quia \textit{P\textsuperscript{x}mv}}} cantus \edtext{apud}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{m}mv}}} \edtext{eum}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cum \textit{P\textsuperscript{x}} | enim \textit{G\textsuperscript{u}}}} fuerunt \edtext{multiplices et \edtext{differenter}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | differentes \textit{P\textsuperscript{z}}}} \edtext{compositi}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{z}V\textsuperscript{o}mv} | appositi \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} propter \edtext{quod}{\Cfootnote[nosep]{\textit{βγλπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{secundum plurimum fuerunt}{\Cfootnote[nosep]{\textit{αλπmv} | fuerunt secundum plurimum \textit{V\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} in \edtext{tragediis}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}} \edtext{metrorum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | metris \textit{G\textsuperscript{u}P\textsuperscript{q}}}}.} Tales autem sunt suaues maxime, cum eorum \edtext{sit}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sunt \textit{E\textsuperscript{a}}}} principaliter \edtext{finis}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} iocunditatem inducere. \edtext{}{\Cfootnote{et cetera \textit{V\textsuperscript{z}} | sequitur 32. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Trigesimumsecundum problema}\label{edition-text book-19a part32}}{\lemma{Trigesimumsecundum + problema} \Cfootnote[nosep]{\textit{γmv} | «32m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | Trigesimumsecundum. \surplus{trigesimum + secundum} \textit{P\textsuperscript{y}} | 31m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DYAPASON}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID DYAPASON APPELLATUR, SED NON SECUNDUM NUMERUM DYAOCTO, QUEMADMODUM ET DYATESSERON ET DYAPENTE? \textsuperscript{2}AUT QUIA SEPTEM FUERUNT CORDE ANTIQUITUS? POSTEA EXTRAHENS TERTIAM, \hyperref[Ter]{TERPANDERUS} NITEM APPOSUIT. ET IN HOC APPELLATA EST. DYAPASON, SED NON DYAOCTO, DYASEPTEM ENIM ERAT \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema 32m. etcetera. \textit{ \edtext{Quare consonantia}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}mv} | Querit quare consonantia \textit{λ} | \textit{om}. \textit{C\textsuperscript{a}V\textsuperscript{o}}}} dupla \edtext{dyapason}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} siue per totum appellatur, \edtext{et non dicitur}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | non dicitur \textit{V\textsuperscript{m}} | \textit{om}. \textit{P\textsuperscript{p}} | et omnino dicitur \textit{P\textsuperscript{u}}}} \edtext{dyocto}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}m}}} propter numerum \edtext{octonarium}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}m} | octogenarium \textit{πE\textsuperscript{a}}}},} in \edtext{quem}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | quam \textit{P\textsuperscript{x}} | quod \textit{V\textsuperscript{m}}}} videtur \edtext{terminari}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | terminatur \textit{G\textsuperscript{u}}}} \edtext{in}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{parigraphia}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{proportionum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | portionum \textit{N\textsuperscript{u}}}}? \edtext{Terminatur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv}}} \edtext{enim}{\Cfootnote[nosep]{\textit{ακπ} | eius \textit{mv}}} super \edtext{octo}{\Cfootnote[nosep]{\textit{αλπmv} | scilicet \textit{P\textsuperscript{x}}}}. Et \edtext{subdit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | tangit \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}m} | huiusmodi \textit{γv} | hic \textit{G\textsuperscript{u}} | eius \textit{P\textsuperscript{y}}}} \edtext{motiuum}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv}}} dicens \textit{ \edtext{quemadmodum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | quod deinde \textit{P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{dicitur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | dicitur in \textit{V\textsuperscript{z}}}} dyatesseron,} quia \edtext{finitur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | terminatur \textit{V\textsuperscript{z}}}} in \edtext{4°}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | 8uo \textit{M\textsuperscript{a}}}} loco in predicta descriptione, aut quia \edtext{fit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | finitur \textit{P\textsuperscript{y}}}} in \edtext{quatuor}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | 8 \textit{M\textsuperscript{a}}}} cordis musice. 5°. \textit{et similiter dyapente} \edtext{siue per 5°.}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{terminatur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | finitur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} in 5° \edtext{loco}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{uel in 5. \edtext{constat}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | stat \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{cordis}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | locis \textit{V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } Soluit dicens causam esse \edtext{cur}{\Cfootnote[nosep]{\textit{αλπmv} | cum \textit{P\textsuperscript{x}}}} dyapason dicitur et non \edtext{dyaocto}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}v} | dyoto \textit{V\textsuperscript{b}}}} \textit{ \edtext{quia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | qui \textit{P\textsuperscript{z}}}} corde \edtext{instrumentorum antiquitus \edtext{.7. tantum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | tantum septem \textit{V\textsuperscript{z}}}} fuere}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | antiquitus instrumentorum 7º. tantum fuere \textit{V\textsuperscript{a}} | instrumentorum antiquitus tantum .5. .7. fuere \textit{P\textsuperscript{y}} | instrumentorum antiquitus 7 fuere \textit{π}}}. Postmodum superuenit \hyperref[Ter]{ \edtext{tripandius}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv}}} }, \edtext{qui}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{a}mv} | que \textit{P\textsuperscript{x}} | quia \textit{V\textsuperscript{b}}}} \edtext{tertiam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | illam \textit{V\textsuperscript{z}}}} subtraxit \edtext{cordam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | cordas \textit{P\textsuperscript{y}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | \textit{om}. \textit{V\textsuperscript{a}mv}}} paramese \edtext{cuius}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | eius \textit{P\textsuperscript{y}}}} quidem loco \edtext{nitem}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{apponit}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | apposuit \textit{απM\textsuperscript{a}mv}}} }, ita ut \edtext{non}{\Cfootnote[nosep]{\textit{απE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} videatur \edtext{mutasse}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | immutasse \textit{G\textsuperscript{u}P\textsuperscript{q}}}} numerum, \edtext{sed}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | secundum \textit{V\textsuperscript{b}}}} proportionem \edtext{potius}{\Cfootnote[nosep]{\textit{βγκπmv} | passio \textit{E\textsuperscript{a}}}}, \textit{et propter hoc appellata est dyapason,} \edtext{quoniam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}} | quia \textit{λmv}}} ex tali mutatione \edtext{optima}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | opposita \textit{P\textsuperscript{y}}}} \edtext{adinuenta est}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}mv} | est adinuenta \textit{λ} | inuenta est \textit{π} | adiuncta est \textit{V\textsuperscript{b}}}} consonantia. \textit{Non itaque \edtext{dicitur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | dicta est \textit{V\textsuperscript{a}}}} \edtext{dyaocto}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}}, \edtext{cum corde}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} non \edtext{sunt}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}} | sint \textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv}}} nisi \edtext{.7.}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | octo \textit{V\textsuperscript{a}}}} } Potius enim \edtext{dicendum esset}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | debent esse \textit{V\textsuperscript{m}} | deberet esse \textit{V\textsuperscript{b}} | deberet dici \textit{V\textsuperscript{a}mv}}} dyaseptem, cum \edtext{tantum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | tanto \textit{P\textsuperscript{z}}}} isto \edtext{numero}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | modo \textit{V\textsuperscript{b}}}} \edtext{ \edtext{imitando}{\Cfootnote[nosep]{\textit{λN\textsuperscript{u}P\textsuperscript{y}} | immutando \textit{γE\textsuperscript{a}mv} | mutando \textit{P\textsuperscript{x}}}} qui \edtext{planetarum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | plerum \textit{V\textsuperscript{a}}}} \edtext{numerum ut uisum est}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}mv} | ut uisum est numero \textit{λ} | numerum ut uisum \textit{N\textsuperscript{u}} | numero ut uisum \textit{P\textsuperscript{y}}}} \edtext{contineantur}{\Cfootnote[nosep]{\textit{ακ} | contineant \textit{mv}}} }{\Cfootnote[nosep]{\textit{ακmv} | contineantur imitando numerum planetarum vt uisum est \textit{π}}}. \edtext{Quia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Quare \textit{P\textsuperscript{z}}}} \edtext{tamen}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}P\textsuperscript{z}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}} | tam \textit{E\textsuperscript{a}} | cum \textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{z}mv}}} \edtext{corde prius .7.}{\Cfootnote[nosep]{\textit{κN\textsuperscript{u}V\textsuperscript{b}mv} | prius corde .7. \textit{πE\textsuperscript{a}} | corde .7. prius \textit{V\textsuperscript{a}} | corde prius \textit{P\textsuperscript{y}}}} \edtext{fuerunt}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | fuere \textit{V\textsuperscript{a}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | non \textit{P\textsuperscript{y}}}} \edtext{apparuit}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | apparebit \textit{πE\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{y}}}}, \edtext{pauciores}{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}v} | paucitores \textit{N\textsuperscript{u}}}} pluresque \edtext{demum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{u}mv} | deinde \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{adinuente}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | adinuenientem \textit{M\textsuperscript{a}} | adinueniendo \textit{V\textsuperscript{z}} | adueniente \textit{V\textsuperscript{m}}}}, \edtext{tamquam}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{z}}}} nomen stabilius, \edtext{elegerunt}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}v} | elegerant \textit{C\textsuperscript{a}V\textsuperscript{o}}}} potius dyapason \edtext{dicere}{\Cfootnote[nosep]{\textit{βγκπmv}}} seu per totum et perfectum quam dyaseptem, \edtext{tanquam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}} nomen magis \edtext{denotatiuum}{\Cfootnote[nosep]{\textit{βγm} | denotatur \textit{E\textsuperscript{a}} | denominatiuum \textit{P\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | determinatum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | deuotatiuum \textit{P\textsuperscript{x}v}}} essentie ipsius. \edtext{ \edtext{Et}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | Et hoc \textit{V\textsuperscript{z}} | Ut \textit{V\textsuperscript{b}}}} \edtext{tactum quidem}{\Cfootnote[nosep]{\textit{βπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | tactu quidem \textit{E\textsuperscript{a}} | quidem tactum est \textit{V\textsuperscript{z}}}} \edtext{.25. problema}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | 25° problemate \textit{P\textsuperscript{y}V\textsuperscript{b}mv} | est hoc 25º problemate \textit{M\textsuperscript{a}} | est hoc prius \textit{π}}} }{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}. \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{z}V\textsuperscript{z}} | sequitur 33m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Trigesimumtertium problema}\label{edition-text book-19a part33}}{\lemma{Trigesimumtertium + problema} \Cfootnote[nosep]{\textit{γmv} | «33m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{trigesimum tertium.} Trigesimum quartum tertium. \textit{P\textsuperscript{y}} | 32m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID CONSONANTIUS}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID CONSONANTIUS EST IN GRAUE QUAM A GRAUI IN ACUTUM? \textsuperscript{2}UTRUM QUIA A PRINCIPIO FIT INCIPERE? \textsuperscript{3}MEDIA ENIM ET PRINCIPALIS ACUTISSIMA PARACORDE. HOC AUTEM NON A PRINCIPIO, SED A FINE. \textsuperscript{4}AUT QUIA GRAUE AB ACUTO FORTIUS ET MAGIS UOCALE \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}?} Problema 33m. etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} in cantu \edtext{maior extat}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | extat maior \textit{G\textsuperscript{u}P\textsuperscript{y}} | maior existit \textit{V\textsuperscript{z}}}} consonantia \edtext{si}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sed \textit{G\textsuperscript{u}}}} incipiatur ab acuto et \edtext{terminetur}{\Cfootnote[nosep]{\textit{αλmv} | terminatur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}} | preterminetur \textit{P\textsuperscript{z}}}} in \edtext{grauem}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | grauim \textit{G\textsuperscript{u}} | graue \textit{αmv}}}, quam si a graui \edtext{preincipiens}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}mv} | incipiens \textit{M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}}}} terminetur in acutum?} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{UTRUM.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | UTRUM QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } Soluit \edtext{et assignat}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | assignando \textit{G\textsuperscript{u}P\textsuperscript{u}}}} duplicem causam dicens primo \edtext{id}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | illud \textit{S\textsuperscript{c}V\textsuperscript{c}mv}}} esse \textit{quia \edtext{contingit}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}mv} | conuenit \textit{G\textsuperscript{u}P\textsuperscript{q}}}} incipere \edtext{a}{\Cfootnote[nosep]{\textit{βγκmv} | in \textit{πE\textsuperscript{a}}}} principio rei in qualibet re}, modo \edtext{ipsum acutum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | acutum ipsum \textit{G\textsuperscript{u}}}} \edtext{tenet}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | retinet \textit{γmv}}} \edtext{locum principii}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}V\textsuperscript{o}mv} | principium locum \textit{P\textsuperscript{u}} | locum principaliter \textit{M\textsuperscript{a}} | principium \textit{G\textsuperscript{u}P\textsuperscript{p}}}} in \edtext{instrumento}{\Cfootnote[nosep]{\textit{αλπmv} | ipso instrumento \textit{P\textsuperscript{x}}}}. Nam prime corde minores sunt ille \edtext{que}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | qui \textit{E\textsuperscript{a}} | qua \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{sonum reddunt}{\Cfootnote[nosep]{\textit{βγπmv} | reddunt sonum \textit{P\textsuperscript{x}} | sonum reddunt sonum \textit{E\textsuperscript{a}} | reddunt \textit{λ}}} acutum, \edtext{a}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | in \textit{P\textsuperscript{y}}}} quibus \edtext{oportet}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} incipere, ut ordo seruetur naturalis in arte. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{MEDIA}. \edtext{Remouet \edtext{dubitationem}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | dubium \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, quia \edtext{crederet}{\Cfootnote[nosep]{\textit{βγκπ} | diceret \textit{mv}}} aliquis \edtext{quod}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{z}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} ab omni corda acuta \edtext{esset}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}mv} | esse \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} incipiendum. \edtext{Unde}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{π}}} \edtext{id}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | illud \textit{P\textsuperscript{p}}}} \edtext{remouens}{\Cfootnote[nosep]{\textit{κN\textsuperscript{u}} | remouet \textit{γπP\textsuperscript{y}mv}}} \edtext{dicens}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | dicit \textit{V\textsuperscript{z}}}} quod}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \textit{ \edtext{corda media et principalis est}{\Cfootnote[nosep]{\textit{γN\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | corda media principalis est \textit{λ} | corda principalis et media est \textit{P\textsuperscript{y}} | corda media est principalis et \textit{G\textsuperscript{u}} | et principalis est \textit{E\textsuperscript{a}}}} acutissima \edtext{seu}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | sive \textit{G\textsuperscript{u}P\textsuperscript{q}}}} fortissima \edtext{peracorde}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}V\textsuperscript{m}} | peracordis \textit{πE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | per .7. cordas \textit{γmv}}}, id est \edtext{cordis}{\Cfootnote[nosep]{\textit{κπ} | corde \textit{αmv}}}, iuxta ipsam \edtext{existentis}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | existentes \textit{V\textsuperscript{b}} | existentibus \textit{πM\textsuperscript{a}}}}. Unde \edtext{hec}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | hoc \textit{E\textsuperscript{a}P\textsuperscript{z}}}} non \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{tangenda in principio}{\Cfootnote[nosep]{\textit{ακmv} | in principio tangenda \textit{π}}}, sed potius in fine,} propter eius excessum, \edtext{ista}{\Cfootnote[nosep]{\textit{βγλmv} | ita \textit{E\textsuperscript{a}P\textsuperscript{x}} | ita quod \textit{π}}} siquidem aut est media \edtext{positione}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | pone \textit{P\textsuperscript{y}}}} recte \edtext{ceu}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} mese, \edtext{aut}{\Cfootnote[nosep]{\textit{αλπmv} | autem \textit{P\textsuperscript{x}}}} virtute \edtext{puta}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | pauca \textit{P\textsuperscript{y}} | sicut \textit{P\textsuperscript{p}}}} \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}}, cum in \edtext{mediam}{\Cfootnote[nosep]{\textit{βγκπmv} | media \textit{E\textsuperscript{a}}}} \edtext{condescendit}{\Cfootnote[nosep]{\textit{βγκmv} | condescendat \textit{π}}} cum \edtext{nete}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}}, ut \edtext{uisum est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | uisum \textit{β}}} 20°. +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακπ} | AUT ET. \textit{mv}}} } \edtext{Assignat}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | Soluit assignans \textit{V\textsuperscript{m}}}} \edtext{aliam causam}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | causam aliam \textit{P\textsuperscript{x}} | aliam \textit{P\textsuperscript{y}}}} dicens \edtext{id etiam}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | id \textit{γP\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | ideo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{esse}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} \textit{quoniam graue \edtext{incipiens ab acuto}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | ab acuto incipiens \textit{P\textsuperscript{y}} | descendens ab acuto \textit{π}}} \edtext{fortius}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} est. Diutius enim \edtext{permanet}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv}}} et \edtext{magis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} uocale existit quam econuerso.} Hoc autem facere \edtext{magis est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | est \textit{P\textsuperscript{p}}}} \edtext{connaturale}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | contra naturale \textit{βV\textsuperscript{z}} | contra naturalem \textit{E\textsuperscript{a}} | cum naturale \textit{P\textsuperscript{z}}}} \edtext{ac}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | hoc \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} etiam \edtext{morale}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | mortale \textit{P\textsuperscript{y}V\textsuperscript{z}}}} \edtext{quam}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | quod \textit{V\textsuperscript{m}} | quidem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} suum contrarium. ‘Videmus enim in operibus nature quod ipsa in principio a leuibus et debilibus incipit, non enim tunc est, operosa sed in fine, \edtext{ut \edtext{dictum est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | dictum \textit{N\textsuperscript{u}} | dicatur \textit{P\textsuperscript{y}}}} \edtext{10a.}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | 20. \textit{V\textsuperscript{b}}}} }{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} X .45 , 895b l. 27 to 896a l. }}’Et ideo \edtext{est videre}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | videndum que \textit{V\textsuperscript{a}}}} optimos cantatores naturam \edtext{imitantes}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | mutantes \textit{P\textsuperscript{x}V\textsuperscript{m}}}} \edtext{ \edtext{hoc}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | hec \textit{G\textsuperscript{u}}}} \edtext{seruare}{\Cfootnote[nosep]{\textit{κ} | obseruare \textit{βπE\textsuperscript{a}V\textsuperscript{b}mv}}} }{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}, \edtext{quod}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cum \textit{G\textsuperscript{u}}}} in acuto leuiter incipientes \edtext{in}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}P\textsuperscript{z}}}} \edtext{grauem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}} | graue \textit{βπV\textsuperscript{a}mv}}} postea conterminant, et non econtra concordant. \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{z}V\textsuperscript{z}} | sequitur 34. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Trigesimumquartum problema}\label{edition-text book-19a part34}}{\lemma{Trigesimumquartum + problema} \Cfootnote[nosep]{\textit{γmv} | «34m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{trigesimum quartum.} Trigesimumquartum. \textit{P\textsuperscript{y}} | 33m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID BIS QUIDEM}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID BIS \textit{P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID BIS QUIDEM PER ACUTOS. ET BIS DYATESSERON NON CONSONAT, BIS DYAPASON AUTEM? \textsuperscript{2}AUT QUIA BIS PER ACUTOS NEQUE BIS DYATESSERON EST, QUOD AUTEM PER QUATUOR AUT PER QUINQUE \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}?} Problema 34m. etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} \edtext{bis paracutos seu bis paracuta}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | bis paracuta seu bis paracutos \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | bisperacuta \textit{G\textsuperscript{u}} | bis paraclitos seu bis paracuta \textit{V\textsuperscript{z}}}} id est bis dyapente \edtext{et}{\Cfootnote[nosep]{\textit{αλπmv} | seu \textit{P\textsuperscript{x}}}} bis dyatesseron \edtext{siue bis per quatuor \edtext{id est}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | in \textit{E\textsuperscript{a}}}} dyatesseron}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{z}}}} non \edtext{consonant}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | consonat \textit{V\textsuperscript{z}}}} \edtext{et}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | id est \textit{G\textsuperscript{u}P\textsuperscript{y}}}} \edtext{simphoniam}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv}}} constituunt, dyapason uero concordat?} Dicitur autem bis paracutos \edtext{ \edtext{dyapente}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}, quia constat ex duobusduabus \edtext{acutis}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv} | in \textit{V\textsuperscript{m}}}} \edtext{vno}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vna \textit{P\textsuperscript{p}} | non \textit{P\textsuperscript{y}}}} graui \edtext{seu}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}mv} | siue \textit{V\textsuperscript{a}} | ceu \textit{P\textsuperscript{x}}}} breuibus \edtext{et}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | aut \textit{P\textsuperscript{y}}}} \edtext{longo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | longa \textit{P\textsuperscript{p}}}}, more \edtext{dactili}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}mv}}} }{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \edtext{\textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } Soluit dicens causam esse \textit{quoniam \edtext{bis paracutos}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} }}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \textit{uel bis dyapente \edtext{uel}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}P\textsuperscript{y}} | et \textit{γλE\textsuperscript{a}N\textsuperscript{u}mv}}} \edtext{bis dyatesseron}{\Cfootnote[nosep]{\textit{αλmv} | dyatesseron \textit{πP\textsuperscript{x}}}} non est dare, quod constituant \edtext{aliquam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | aliqualiter \textit{P\textsuperscript{x}} | \textit{om}. \textit{V\textsuperscript{z}}}} consonantiam, \edtext{quoniam \edtext{illud}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | id \textit{G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{a}}}} quod per quatuor se habet aut per quinque licet \edtext{proportionem}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | proportione \textit{P\textsuperscript{y}}}} \edtext{constituant}{\Cfootnote[nosep]{\textit{γλG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | constituat \textit{P\textsuperscript{x}} | constituant aliquam consonantiam \textit{P\textsuperscript{y}}}} et per consequens consonantiam, ut per quatuor}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quoniam illud quod per 4 \textit{E\textsuperscript{a}} | ut per quatuor \textit{P\textsuperscript{p}}}} dyatesseron \edtext{uel}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{u}V\textsuperscript{o}mv} | uel per \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}}}} quinque dyapente.} \edtext{Quando enim}{\Cfootnote[nosep]{\textit{βγκmv} | Quando \textit{P\textsuperscript{z}V\textsuperscript{o}} | epsa enim \textit{E\textsuperscript{a}} | Quoniam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{minus extremum prime, et}{\Cfootnote[nosep]{\textit{γλN\textsuperscript{u}mv} | minus extremum prime ad \textit{P\textsuperscript{x}} | extremum prime minus \textit{πE\textsuperscript{a}} | minus \textit{P\textsuperscript{y}}}} \edtext{extremum magis}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | extremum maius \textit{απM\textsuperscript{a}mv}}} 2e comparantur ad inuicem nulla consonantiarum resultat inde, ut videbitur \edtext{.41°.}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | .11°. \textit{P\textsuperscript{y}}}}, ubi \edtext{repetitur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | reperitur \textit{V\textsuperscript{z}}}} \edtext{idem}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | id \textit{V\textsuperscript{b}mv} | inde \textit{V\textsuperscript{a}}}} amplioris expositionis gratia.\edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | sequitur 35. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Trigesimumquintum problema}\label{edition-text book-19a part35}}{\lemma{Trigesimumquintum + problema} \Cfootnote[nosep]{\textit{γmv} | «35m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{trigesimum quintum.} Trigesimum quintum. \textit{P\textsuperscript{y}} | 34m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DYAPASON}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID DYAPASON OPTIMA CONSONANTIA EST? \textsuperscript{2}AUT QUIA IN OMNIBUS TERMINIS RATIONES SUNT, ALIORUM AUTEM NON IN OMNIBUS? QUONIAM AUTEM DUPLEX NITE YPATES. QUOT NITE DUE YPATEM UNUM, ET QUALIS YPATE DUO NITE QUATUOR, ET SEMPER ITA. \textsuperscript{3}MEDIE AUTEM EMIOLIA. QUOD ENIM PER QUINQUE EMIOLIUM NON IN OMNIBUS NUMERIS EST. NON ENIM UNUM MINUS, MAIUS TANTUM AUTEM ET ADHUC MEDIUM. QUARE NON TOTA AD TOTA COMPARANTUR, SED INSUNT PARTES. \textsuperscript{4}SIMILITER ET IN EO QUOD EST PER QUATUOR SE HABET, EPITRICON ENIM EST QUANTUM INCIDERE QUOD ET ADHUC IN QUATUOR EPITRICON EST. \textsuperscript{5}AUT PERFECTISSIMA QUE EST EX UTRISQUE, ET QUIA MENSURA MELODIE? PER TOTUM ID QUOD FERTUR QUE EST SECUNDUM MEDIUM MOTUS FORTISSIMUS, INCIPIENTE AUTEM ET FINIENTE MOLLIOR. QUANDO AUTEM FORTISSIMUS MOTUS, ET UOX ACUTIOR EIUS QUΟD FERTUR, PROPTER QUOD ET CORDE TENSE ACUTIUS SONANT, UELOCIOR ENIM MOTUS FIT. \textsuperscript{6}SONUS AUTEM AUT AERIS AUT ALIUS CUIUSDAM MOTUS, CAUSA QUE EST PER MEDIUM PORUM ACUTISSIMUM OPORTET FIERI. QUARE SI HOC NON ACCIDIT, NON ERIT MOTUS ALICUIUS \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema 35m. etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} dyapason est optima \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} dulcissima consonantiarum?} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \edtext{\textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } Soluit \edtext{et assignat}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{z}V\textsuperscript{o}mv} | assignando \textit{G\textsuperscript{u}P\textsuperscript{u}} | dicit et assignat \textit{E\textsuperscript{a}} | dicens \textit{P\textsuperscript{p}}}} \edtext{duplicem causam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | causam esse duplicem \textit{P\textsuperscript{p}}}}, \edtext{ \edtext{secunda}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}} | .2a. ibi \textit{γV\textsuperscript{z}mv}}} \textit{AUT.} \edtext{Adhuc}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}} | Ad hoc \textit{N\textsuperscript{u}P\textsuperscript{x}} | Item \textit{mv}}} \edtext{primo}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | post \textit{E\textsuperscript{a}}}} dat causam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{π}}} \edtext{quare}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}} | quare est \textit{γP\textsuperscript{p}P\textsuperscript{z}mv}}} optima consonantiarum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}, \edtext{dicens}{\Cfootnote[nosep]{\textit{βγκπmv} | dicit \textit{E\textsuperscript{a}}}} \edtext{illud}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}mv} | id \textit{βλE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | ideo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} esse \textit{quoniam proportiones \edtext{secundum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | per \textit{V\textsuperscript{a}mv}}} quas \edtext{constituitur huius consonantia}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | constituitur huiusmodi consonantia \textit{γN\textsuperscript{u}mv} | huius consonantia constituitur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{sumuntur}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | sumitur \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{z}}}} ex omnibus terminis summis numerorum.} \edtext{Multi enim sunt}{\Cfootnote[nosep]{\textit{βκπV\textsuperscript{b}mv} | Multi sunt enim \textit{V\textsuperscript{a}} | Et multi enim sunt \textit{E\textsuperscript{a}}}} modi \edtext{quibus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | qui vim \textit{P\textsuperscript{p}}}} \edtext{corde}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv}}} \edtext{ad inuicem comparate}{\Cfootnote[nosep]{\textit{ακmv} | comparate ad inuicem \textit{π}}} \edtext{hanc efficiunt}{\Cfootnote[nosep]{\textit{αλπmv} | efficiunt hanc \textit{V\textsuperscript{a}} | hac efficiunt \textit{P\textsuperscript{x}}}} \edtext{consonantiam}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | consonantia \textit{P\textsuperscript{x}}}}. Quod declarat \edtext{tam ratione substantie quam}{\Cfootnote[nosep]{\textit{βγκπmv} | causa ratione substantie tam \textit{E\textsuperscript{a}}}} \edtext{ex parte}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}}}} \edtext{ \edtext{quantitatis et qualitatis}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}} | qualitatis et quantitatis \textit{V\textsuperscript{a}V\textsuperscript{z}mv} | quantitatis qualitatis \textit{V\textsuperscript{o}} | quantitatis et qualiter \textit{P\textsuperscript{p}P\textsuperscript{x}} | quantitatis \textit{G\textsuperscript{u}M\textsuperscript{a}}}}, dicens \edtext{primo}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{o}mv} | primo esse \textit{V\textsuperscript{a}} | sermo \textit{P\textsuperscript{z}}}} quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} \textit{ \edtext{duplex \edtext{nite}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}} | nitem \textit{N\textsuperscript{u}}}}, cum accepta fuerit, \edtext{assumit rationem}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | rationem assumit \textit{P\textsuperscript{z}} | affruat nomen et rationem \textit{P\textsuperscript{p}}}} et substantiam \edtext{ypates}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | ypatos \textit{P\textsuperscript{y}} | compates \textit{P\textsuperscript{x}}}}. Et \edtext{similiter}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | sit \textit{G\textsuperscript{u}} | dicitur \textit{P\textsuperscript{p}}}} \edtext{ratione}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | rationem \textit{β}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} } \edtext{quantitatis}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | quantitatum \textit{β}}}, ut \edtext{querenti}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | querente \textit{β} | conuenienti \textit{π}}} \edtext{quot}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{a}V\textsuperscript{o}mv} | quod \textit{P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}}}} \edtext{nite}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{constituunt}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | constituerunt \textit{G\textsuperscript{u}P\textsuperscript{u}}}} ypatem \edtext{vnam}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | unum \textit{P\textsuperscript{z}} | ueram \textit{P\textsuperscript{y}} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{dicendum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | dicendum est \textit{V\textsuperscript{a}}}}, \edtext{quoniam}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | quod \textit{πM\textsuperscript{a}V\textsuperscript{a}}}} due, et secundum \textit{ \edtext{quale etiam}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | etiam quale \textit{V\textsuperscript{b}} | qualem etiam \textit{P\textsuperscript{p}P\textsuperscript{u}} | quale scensiam \textit{V\textsuperscript{a}}}} due \edtext{nite}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}} | netes \textit{V\textsuperscript{a}mv} | uite nete \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{z}}}} sunt, \edtext{qualis}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{m}mv} | quales \textit{P\textsuperscript{x}V\textsuperscript{a}} | qualis \surplus{qualis} \textit{V\textsuperscript{z}}}} est \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ypaten \textit{M\textsuperscript{a}}}} \edtext{vna}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | nam \textit{P\textsuperscript{y}}}}, et quatuor \edtext{nete}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} eodem modo \edtext{sunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | sunt et \textit{P\textsuperscript{z}}}} \edtext{due ypate}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{o}} | ypate due \textit{P\textsuperscript{z}} | due ypates \textit{γM\textsuperscript{a}V\textsuperscript{z}mv} | due ipates \textit{V\textsuperscript{m}} | duo ypate \textit{V\textsuperscript{a}}}},} \edtext{et sex tres}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | et 6. et 3. \textit{G\textsuperscript{u}} | 26. 3. \textit{mv} | 2. 63. \textit{P\textsuperscript{z}}}}. \edtext{Et}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}}}} \edtext{ratione substantie ac}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | ratione substantie et \textit{P\textsuperscript{y}} | ratione substantie \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | ratione substantie Et ratione substantie \textit{G\textsuperscript{u}P\textsuperscript{u}}}} accidentis \edtext{considerando}{\Cfootnote[nosep]{\textit{ακmv} | consideratio \textit{π}}} \textit{et ita \edtext{semper}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | et semper \textit{V\textsuperscript{a}}}} } \edtext{procedendo}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | protendendo \textit{N\textsuperscript{u}}}} due \edtext{nite}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}} | netes \textit{mv}}} vnam constituunt ypatem. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{MEDIE.} Ostendit quod dyapente et dyatesseron non est optima \edtext{consonantia}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}} | consonantiarum \textit{βγπmv}}}, primo dicens \edtext{quod}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} \textit{proportio \edtext{medietatis}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | equalitatis \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{P\textsuperscript{p}}}} \edtext{emiola}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}mv} | ennola \textit{P\textsuperscript{p}}}}. Et exponit, \edtext{dicens quod illud quod}{\Cfootnote[nosep]{\textit{αmv} | dicens quod id quod \textit{λ} | dicens quod illud \textit{πE\textsuperscript{a}P\textsuperscript{x}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | et \textit{V\textsuperscript{o}}}} \edtext{per}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | pro \textit{P\textsuperscript{p}} | quod \textit{G\textsuperscript{u}}}} \edtext{quinque}{\Cfootnote[nosep]{\textit{αλπmv} | que \textit{P\textsuperscript{x}}}} est \edtext{emiolum}{\Cfootnote[nosep]{\textit{β} | emidelium \textit{πE\textsuperscript{a}}}}, et tale non reperitur in omnibus numeris;} \edtext{ymmo}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}}}} \edtext{in nullis ita}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | nullis ita \textit{V\textsuperscript{m}} | in nulla \textit{P\textsuperscript{y}}}} ut \edtext{dicatur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | dicitur \textit{P\textsuperscript{z}}}} omnis et perfecta, \edtext{ut dyapason dicitur perfecta}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}}, consonantia. \textit{Non \edtext{enim}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{perfecte totum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | totum perfecte \textit{V\textsuperscript{z}} | perfecte \textit{M\textsuperscript{a}V\textsuperscript{m}}}} \edtext{comprehendit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}} | comprehendunt \textit{V\textsuperscript{b}mv} | apprehendit \textit{P\textsuperscript{y}P\textsuperscript{z}}}} numerus maior minorem;} \edtext{ymmo}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}}}} duorum \edtext{numerorum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | minorum \textit{P\textsuperscript{y}V\textsuperscript{a}}}} vnus \edtext{est sicut quid}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}} | est sicut qui \textit{λV\textsuperscript{b}mv} | est sicut quem \textit{P\textsuperscript{x}} | quidem est sicut \textit{P\textsuperscript{y}}}} maius \edtext{et aliud}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | et alius \textit{π} | alius \textit{V\textsuperscript{z}} | et aliud sicut \textit{P\textsuperscript{y}}}} minus, eo \edtext{quod}{\Cfootnote[nosep]{\textit{αλπmv} | etiam \textit{P\textsuperscript{x}}}} talis consonantia consistit in proportione sexquialtera, in \edtext{qua}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quo \textit{G\textsuperscript{u}}}} \edtext{vnum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vnus \textit{P\textsuperscript{p}}}} continet \edtext{alium totum}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | aliud totum \textit{V\textsuperscript{z}} | ad totum \textit{N\textsuperscript{u}} | totum aliud \textit{P\textsuperscript{y}}}} \edtext{semel}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | simul \textit{P\textsuperscript{z}}}} \textit{ \edtext{tantum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} et eius medietatem. Propter quod in \edtext{hac}{\Cfootnote[nosep]{\textit{βγκπmv} | eius \textit{E\textsuperscript{a}}}} consonantia non \edtext{fit}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | sit \textit{E\textsuperscript{a}G\textsuperscript{u}V\textsuperscript{o}}}} \edtext{comparatio}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | operatio \textit{V\textsuperscript{z}}}} \edtext{totius ad totum,}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{p}}}} } \edtext{ \edtext{ut}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cum \textit{G\textsuperscript{u}}}} \edtext{vnus numerus}{\Cfootnote[nosep]{\textit{λγG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | vnius numeri \textit{β} | minus numerus \textit{P\textsuperscript{x}P\textsuperscript{z}}}} \edtext{bis quod}{\Cfootnote[nosep]{\textit{αλmv} | bisque \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | uel quod \textit{P\textsuperscript{x}}}} \edtext{totum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | totus \textit{G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}}}} mensuret \edtext{alterius}{\Cfootnote[nosep]{\textit{ακmv} | alterum \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}},}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{p}}}} \textit{ \edtext{sed \edtext{fit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sit \textit{G\textsuperscript{u}}}} comparatio}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{p}}}} totius ad partes,} quare non \edtext{erit}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}P\textsuperscript{y}mv} | est \textit{N\textsuperscript{u}} | erunt \textit{P\textsuperscript{x}}}} optima consonantiarum \edtext{dyapente}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}}. +\pend + +\pstart +\textbf{4} \edtext{ \edtext{}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{SIMILITER.} Ostendit \edtext{consequenter}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{y}}}} quod \edtext{dyatesseron}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | dyapason «tesseron» \textit{V\textsuperscript{o}}}} non est optima \edtext{consonantiarum}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}}, \edtext{dicens}{\Cfootnote[nosep]{\textit{βγκπmv} | dicentes \textit{E\textsuperscript{a}}}} \textit{ \edtext{quod in}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}} | quando \textit{V\textsuperscript{a}}}} \edtext{illa}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | nulla \textit{P\textsuperscript{z}}}} \edtext{consonantia}{\Cfootnote[nosep]{\textit{βγλπmv} | consonantiarum \textit{P\textsuperscript{x}}}} que est per quatuor ut dyatesseron eodem modo se habet.} Non \edtext{enim est}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{z}mv} | tamen est \textit{P\textsuperscript{y}} | enim \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}}}} optima consonantiarum, cum \edtext{non fiat}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | non sit \textit{G\textsuperscript{u}} | enim non \textit{V\textsuperscript{a}}}} \edtext{comparatio}{\Cfootnote[nosep]{\textit{ακπ} | compositio \textit{mv}}} totius ad totum, quoniam \textit{ \edtext{epitricam}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv}}} \edtext{proportionem esse}{\Cfootnote[nosep]{\textit{βγπP\textsuperscript{x}mv} | proportionem \textit{E\textsuperscript{a}} | proportio esse \textit{λ}}} \edtext{quoddam}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | quoddam enim \textit{V\textsuperscript{z}} | quod \textit{π}}} est, \edtext{quantum interuenire}{\Cfootnote[nosep]{\textit{ακmv} | cantum inuenire \textit{π}}}, ut cum maior numerus continet \edtext{minorem}{\Cfootnote[nosep]{\textit{αλπmv} | maiorem \textit{P\textsuperscript{x}}}} totum et amplius cum hoc epitritioepitricusepitricon est \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | enim \textit{P\textsuperscript{p}}}} quatuor,} \edtext{id est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | et \textit{P\textsuperscript{y}}}} continet super hoc \edtext{eius tertiam partem}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | tertiam partem eius \textit{V\textsuperscript{a}}}}, ex quo \edtext{consonantia}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | consona \textit{V\textsuperscript{m}} | resonantia \textit{P\textsuperscript{y}}}} \edtext{resultat}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}} \edtext{quaterna}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quaternam \textit{P\textsuperscript{z}}}}. Et sic non fit comparatio totius ad totum, sed totius ad partem, ut dictum \edtext{est}{\Cfootnote[nosep]{\textit{κP\textsuperscript{z}} | est in \textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | in \textit{β}}} dyapente. +\pend + +\pstart +\textbf{5} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}} | AUTEM. \textit{P\textsuperscript{x}}}} } \edtext{Assignat}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Soluit et assignat \textit{λ}}} aliam causam, uel \edtext{quod}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | per \textit{V\textsuperscript{z}} | \textit{om}. \textit{πE\textsuperscript{a}P\textsuperscript{y}}}} \edtext{dictum}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | dictam \textit{P\textsuperscript{z}} | dictum est \textit{γM\textsuperscript{a}mv}}} confirmat per amplius, dicens \edtext{primo quod}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}} | primo \textit{V\textsuperscript{b}mv} | prima \textit{V\textsuperscript{a}}}} \textit{consonantia ex \edtext{hiis}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} utrisque composita, \edtext{puta}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} ex dyatesseron et \edtext{dyapente}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | dyapasson \textit{β}}}, est perfectissima.} Ipsa enim ut \edtext{dictum est}{\Cfootnote[nosep]{\textit{γκπmv} | dictum \textit{βE\textsuperscript{a}}}} \edtext{.13.}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | 14º. \textit{V\textsuperscript{z}}}} ex \edtext{hiis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} duabus \edtext{constat}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | consistit \textit{P\textsuperscript{y}}}} proportionibus, cum dyapason \edtext{sit}{\Cfootnote[nosep]{\textit{αλπmv} | fit \textit{P\textsuperscript{x}}}} fere \edtext{sex}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | sexto \textit{P\textsuperscript{x}} | >sexta \textit{V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{tonorum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | sonorum \textit{P\textsuperscript{z}}}} \edtext{simphonia}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}v}}}. \edtext{Et}{\Cfootnote[nosep]{\textit{αλπmv} | ex \textit{P\textsuperscript{x}}}} \edtext{dyatesseron}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} ex duobus tonis et \edtext{semitonio}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{o}mv} | semitonis \textit{P\textsuperscript{z}}}} \edtext{constet}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | constat \textit{πV\textsuperscript{a}}}}, \edtext{ac}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | ad \textit{P\textsuperscript{y}} | et \textit{P\textsuperscript{x}}}} dyapente ex \edtext{tribus}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | tribus tonis \textit{P\textsuperscript{p}} | duobus \textit{P\textsuperscript{y}}}} \edtext{et semitonio}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | semitonis \textit{P\textsuperscript{z}}}}, \edtext{que}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | constat que \textit{G\textsuperscript{u}}}} \edtext{coniuncta}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | coniecta \textit{P\textsuperscript{x}V\textsuperscript{z}}}} .6. \edtext{tonos}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | tonis \textit{P\textsuperscript{z}}}} fere constituunt. Dico autem \textit{ \edtext{fere}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} } \edtext{eo quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quia \textit{P\textsuperscript{z}}}} \edtext{semitonium}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{uel limes aut}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | aut limes uel \textit{P\textsuperscript{y}} | uel limes ac \textit{P\textsuperscript{p}V\textsuperscript{m}}}} \edtext{dyesis}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}v}}} \edtext{minor est}{\Cfootnote[nosep]{\textit{αλπmv} | minorem \textit{P\textsuperscript{x}}}} \edtext{tono}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | toto \textit{P\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{6} Quod autem sit perfectissima \edtext{ostenditur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ostendit \textit{P\textsuperscript{z}}}}, quoniam \textit{mensura extat et ratio omnium melodiarum est.} ‘ \edtext{Namque}{\Cfootnote[nosep]{\textit{ακπ} | Enim \textit{mv}}} simplicissima, ut ratio mensure \edtext{perquirit}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | requirit \textit{π} | per quare \textit{P\textsuperscript{y}}}}, \edtext{xº apparens}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{m}} | ut apparet in .10. \textit{π} | .10e. \textit{mv} | .4°. apparens \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{z}} | 4°. \surplus{mensure perquirit .4°.} apparens \textit{P\textsuperscript{x}}}} \edtext{ \textit{methaphysice} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{mathematice} \textit{P\textsuperscript{x}}}}.\edtext{}{\Afootnote[nosep]{Arist. \textit{Met.} X , 1052b ll. 34–37}}’Unde ‘2° \edtext{ \textit{musice} }{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{mathematice} \textit{P\textsuperscript{p}} | \textit{musice} dixit \textit{V\textsuperscript{a}}}} boecius: \edtext{dyapason}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}} | dyapente \textit{βγmv}}} est \edtext{maxima}{\Cfootnote[nosep]{\textit{απm} | maxime \textit{P\textsuperscript{x}v} | max\expan{ime} \textit{(orig. \textup{max})} \textit{λ}}} consonantiarum \edtext{et simplicitate}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | simplicitate \textit{E\textsuperscript{a}} | et simplicitati \textit{G\textsuperscript{u}}}} notissima.\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} II .18 (Freidlein 250, ll. 6–8)}}’ \edtext{Quod}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}} | Quid \textit{V\textsuperscript{b}mv}}} autem \edtext{sit}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv} | sint \textit{P\textsuperscript{y}}}} mensura apparet quia \textit{motus illius consonantie \edtext{que}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | qui \textit{P\textsuperscript{y}}}} secundum \edtext{medium}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | motum \textit{P\textsuperscript{y}}}} \edtext{existit}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | consistit \textit{λ}}} fortissimus est per totum \edtext{id per}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | id \textit{β} | per \textit{π}}} quod \edtext{fertur}{\Cfootnote[nosep]{\textit{βγκπmv}}} siue sit in principio siue in \edtext{fine}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | fine siue \textit{V\textsuperscript{a}}}}.} In medio \edtext{namque}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | nam \textit{V\textsuperscript{z}} | enim \textit{mv}}} \edtext{constat uirtus}{\Cfootnote[nosep]{\textit{β} | consistit virtus \textit{P\textsuperscript{x}} | virtus constat \textit{γλπE\textsuperscript{a}mv}}} totius, dyapason enim \edtext{ex}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{cordis}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}mv} | corde \textit{V\textsuperscript{a}V\textsuperscript{m}}}} \edtext{conficitur}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | efficitur \textit{P\textsuperscript{p}} | perficitur \textit{E\textsuperscript{a}}}} extremis et ad inuicem \edtext{confractis}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | constructis \textit{G\textsuperscript{u}P\textsuperscript{q}}}} et mediis, non autem \edtext{alie}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | ille \textit{V\textsuperscript{a}}}} consonantie. Et \edtext{quamquam}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} ut \edtext{dictum est}{\Cfootnote[nosep]{\textit{γκmv} | predictum est \textit{π} | dictum \textit{E\textsuperscript{a}N\textsuperscript{u}} | dicunt quidem \textit{P\textsuperscript{y}}}} \edtext{predicta consonantia}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | consonantia predicta \textit{V\textsuperscript{b}}}} \edtext{sit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fit \textit{G\textsuperscript{u}}}} perfectissima. \textit{Tamen \edtext{quando}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | quia \textit{P\textsuperscript{y}} | que \textit{P\textsuperscript{z}}}} motus \edtext{quo causatur}{\Cfootnote[nosep]{\textit{ακmv} | cantus \textit{π}}} \edtext{fuerit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | fiunt \textit{P\textsuperscript{y}}}} fortissimus et uelocissimus, efficietur hec \edtext{dulcior}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}} | delectatior \textit{γmv}}} consonantia \edtext{quam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | quod \textit{V\textsuperscript{a}}}} quando fuerit \edtext{minus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | minis \textit{G\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{u}}}} fortis \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | et minus \textit{P\textsuperscript{z}}}} uelox, eo quod tunc uox eius \edtext{quod}{\Cfootnote[nosep]{\textit{απmv} | que \textit{κ}}} mouetur \edtext{erit}{\Cfootnote[nosep]{\textit{απmv} | est \textit{κ}}} acutior \edtext{sonus, autem}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | sonus \textit{M\textsuperscript{a}} | et sonus autem \textit{π}}} \edtext{is}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | hiis \textit{E\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{c}V\textsuperscript{z}} | alius \textit{G\textsuperscript{u}} | aeris \textit{P\textsuperscript{p}} | similiter \gap{} \textit{P\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{y}}}} dulcior \edtext{obtuso}{\Cfootnote[nosep]{\textit{βγλπmv} | obtusus \textit{E\textsuperscript{a}} | aperenso \textit{P\textsuperscript{x}}}}, propter quod corde tense uelociter \edtext{sonant}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | consonant \textit{P\textsuperscript{z}}}}, eo quod motus \edtext{earum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aeris \textit{G\textsuperscript{u}}}} est uelox cito \edtext{pertransiens}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}}.} Cum enim corda \edtext{fuerit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | fuerit quia \textit{G\textsuperscript{u}} | fiunt qua \textit{mv}}} \edtext{tensa}{\Cfootnote[nosep]{\textit{ακπ} | tense \textit{mv}}}, \edtext{non}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}} | ut \textit{P\textsuperscript{x}} | \textit{om}. \textit{γmv}}} potest \edtext{in tantum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | iterum \textit{λ}}} \edtext{moueri et uagari}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | uagari et moueri \textit{V\textsuperscript{a}}}} a medio \edtext{sicut}{\Cfootnote[nosep]{\textit{αλπmv} | ac \textit{P\textsuperscript{x}}}} si fuerit \edtext{relaxata}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{a}} | laxata \textit{π}}}. +\pend + +\pstart +\textbf{7} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{SONUS.} \edtext{Et}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{πV\textsuperscript{a}}}} quia fecerat \edtext{mentionem}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}} de sono ultimo, \edtext{vnde causatur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | causatur vnde causatur \textit{G\textsuperscript{u}}}} ostendit, dicens \textit{sonum esse aut motum aeris \edtext{in se}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} aut \edtext{causa}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | causam \textit{P\textsuperscript{p}V\textsuperscript{z}}}} \edtext{cuiusdam}{\Cfootnote[nosep]{\textit{ακmv} | eiusdem \textit{π}}} alterius quod \edtext{in aere}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} mouetur. \edtext{Cuius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | Cum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} autem fuerit causa motus \edtext{qui}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | «qui» \textit{M\textsuperscript{a}} | \textit{om}. \textit{M\textsuperscript{b}}}} \edtext{per}{\Cfootnote[nosep]{\textit{αλπmv} | propter \textit{P\textsuperscript{x}}}} medietatem \edtext{pori}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ponitur \textit{V\textsuperscript{z}}}} uel meatus existit tunc et acutissimum oportet \edtext{sonum fieri}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | fieri sonum \textit{β}}} in poro.} ‘ \edtext{Sic enim aer}{\Cfootnote[nosep]{\textit{γN\textsuperscript{u}V\textsuperscript{o}mv} | Aer enim sic \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | Sicut enim aer \textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}}}} constringitur \edtext{et fortissimo motu \edtext{velocissime}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | velocissime \textit{P\textsuperscript{u}} | uelocissimo \textit{G\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | et velocissimo motu fortissimo \textit{P\textsuperscript{p}} | et fortissimo motu \textit{λ} | et fortissime \textit{V\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{cogitur moueri}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | moueri cogitur \textit{P\textsuperscript{p}V\textsuperscript{a}} | moueri \textit{P\textsuperscript{x}}}}, \edtext{ut declaratum \edtext{est}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{βV\textsuperscript{a}}}} \edtext{xia}{\Cfootnote[nosep]{\textit{ακm} | iia \textit{v}}},}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{}{\Afootnote[nosep]{Arist. \textit{Prob.} XI .15 , 900b ll. 10–12}}’et sonum tunc reddit acutum. Et ideo instrumenta perforantur, \edtext{que foramina}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}mv} | quod foramina \textit{P\textsuperscript{x}} | etiam \textit{V\textsuperscript{a}}}} \edtext{si}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{claudantur}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | clauduntur \textit{P\textsuperscript{x}P\textsuperscript{z}}}} minime \edtext{sonant}{\Cfootnote[nosep]{\textit{αλπmv}}}. \textit{Quare \edtext{contingit}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | concludit \textit{βγmv} | conuenit \textit{P\textsuperscript{p}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} quando non \edtext{est}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}} | erit \textit{βγmv}}} \edtext{porus}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | potest \textit{P\textsuperscript{y}}}} per medium, ut \edtext{dictum}{\Cfootnote[nosep]{\textit{βκπ} | dictum est \textit{γE\textsuperscript{a}mv}}}, existens, non causabitur \edtext{maneries}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{alicuius soni}{\Cfootnote[nosep]{\textit{ακmv} | aliqua soni uel alicuius \textit{π}}}.} +\pend + +\pstart +\textbf{8} Sciendum ‘ \edtext{ptolomeum}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{b}} | per tholomeum \textit{E\textsuperscript{a}P\textsuperscript{z}} | per th\expan{olomeu}m \textit{(orig. \textup{th\textsuperscript{m}})} \textit{V\textsuperscript{z}} | per thimotheum \textit{M\textsuperscript{a}} | perchium \textit{P\textsuperscript{x}}}} in \edtext{ \textit{armonica} }{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | \textit{armonicam} \textit{V\textsuperscript{a}} | \textit{armonica} sua \textit{V\textsuperscript{z}}}} \edtext{taliter declarare}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | alter declarare \textit{V\textsuperscript{m}}}} \label{quote-35.1}dyapason esse optimam et perfectissimam \edtext{consonantiarum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | consonantiam \textit{πP\textsuperscript{y}}}}, fere siquidem \edtext{vna}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{πP\textsuperscript{y}}}} existit \edtext{uocula}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | notula \textit{πP\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{z}}}}, vnum quodammodo sonum componens, puta \edtext{ceu}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{ \edtext{si denario}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | si denarius \textit{M\textsuperscript{a}V\textsuperscript{m}} | denarius \textit{V\textsuperscript{z}}}} aliquis numerorum \edtext{addatur}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{z}mv} | ad \gap{} \textit{V\textsuperscript{m}} | addarum \textit{E\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{y}}}}, ut duo, semper \edtext{remanet}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{z}V\textsuperscript{o}mv} | remanebit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{denarius}{\Cfootnote[nosep]{\textit{βγκmv} | binarius \textit{πE\textsuperscript{a}}}} \edtext{integer}{\Cfootnote[nosep]{\textit{αλπmv} | integri \textit{P\textsuperscript{x}}}} illesus,\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} V .10 (Freidlein 360, ll. 6–10)}}\edtext{}{\Bfootnote[nosep]{Ptol. \textit{Harm.} .. }}’ ‘ \edtext{non}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | nam \textit{V\textsuperscript{m}}}} enim ultra ipsum \edtext{numerus}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} quis \edtext{eleuatur}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}}, \edtext{ut uisum est}{\Cfootnote[nosep]{\textit{κπV\textsuperscript{b}mv} | ut uisum \textit{βV\textsuperscript{a}} | ut insum \textit{E\textsuperscript{a}}}} \edtext{.15}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | in 5º \textit{P\textsuperscript{z}}}}.\edtext{}{\Afootnote[nosep]{Arist. \textit{Prob.} XV .3 , 910b ll. 23–30}}’Quod \edtext{tamen non}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | non tamen \textit{G\textsuperscript{u}P\textsuperscript{q}} | tamen \textit{P\textsuperscript{y}}}} contingit in ceteris proportionibus, nam si tribus duo \edtext{coniungantur}{\Cfootnote[nosep]{\textit{αλπmv}}} statim \edtext{fiunt}{\Cfootnote[nosep]{\textit{αλπmv}}} .5. et \edtext{mutatur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}mv} | mutantur \textit{V\textsuperscript{z}} | mutant \textit{P\textsuperscript{x}}}} species numeri. \edtext{Sed si}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}mv} | Sed si tu \textit{V\textsuperscript{b}} | Sed \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | Si \textit{P\textsuperscript{p}}}} \edtext{duo addas}{\Cfootnote[nosep]{\textit{βλV\textsuperscript{a}mv} | addas duo \textit{V\textsuperscript{b}} | duo addat \textit{E\textsuperscript{a}} | duo addis \textit{P\textsuperscript{p}} | duo addit \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | duo additur \textit{G\textsuperscript{u}}}} \edtext{denario}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{z}mv} | denar\expan{ium} \textit{(orig. \textup{denar.})} \textit{V\textsuperscript{m}} | denarium \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} .12. \edtext{faciens}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}mv} | facies \textit{M\textsuperscript{a}P\textsuperscript{y}} | etiam faciens \textit{E\textsuperscript{a}}}}, \edtext{et}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | \textit{om}. \textit{γmv}}} \edtext{utrique}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv} | uterque \textit{M\textsuperscript{a}V\textsuperscript{z}} | utrumque \textit{N\textsuperscript{u}}}} \edtext{numerus}{\Cfootnote[nosep]{\textit{βγκmv} | videtur \textit{πE\textsuperscript{a}}}} \edtext{integer}{\Cfootnote[nosep]{\textit{αλπmv} | integri \textit{P\textsuperscript{x}}}} \edtext{conseruabitur}{\Cfootnote[nosep]{\textit{βγκmv} | conseruari \textit{πE\textsuperscript{a}}}}, \edtext{et similiter}{\Cfootnote[nosep]{\textit{βγκπmv} | et similiter \surplus{et similiter} \textit{E\textsuperscript{a}}}} \edtext{si addas}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{ternarium}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | ternarius \textit{M\textsuperscript{a}} | ternarios \textit{P\textsuperscript{y}} | denario \textit{V\textsuperscript{z}}}} et ceteros eodem modo. \edtext{Similiterque}{\Cfootnote[nosep]{\textit{αV\textsuperscript{m}V\textsuperscript{z}V\textsuperscript{o}mv} | Similiter quia \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}} | Similiter quoque \textit{P\textsuperscript{z}} | Similiter \textit{M\textsuperscript{a}}}} dyapason \edtext{simphonia}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | symphoniam \textit{G\textsuperscript{u}P\textsuperscript{q}} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{quancunque}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | quantumcunque \textit{γmv}}} \edtext{consonantiam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | consonantia \textit{M\textsuperscript{a}}}} aliam \edtext{sumat}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | suma \textit{P\textsuperscript{y}} | seruant \textit{M\textsuperscript{a}}}}, \edtext{seruat}{\Cfootnote[nosep]{\textit{αλπmv} | conseruat \textit{P\textsuperscript{x}}}} suam \edtext{consonantiam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | consonantiam ut \textit{P\textsuperscript{z}}}} \edtext{neque}{\Cfootnote[nosep]{\textit{ακmv}}} \edtext{immutat}{\Cfootnote[nosep]{\textit{ακmv} | inmutatur \textit{G\textsuperscript{u}P\textsuperscript{p}} | imitatur \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}}, ut ex \edtext{consona}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | consonantia \textit{γmv}}} reddat \edtext{se}{\Cfootnote[nosep]{\textit{ακπ} | sed \textit{mv}}} dissonam, \edtext{quod}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | quam \textit{V\textsuperscript{m}}}} in aliis non accidit \edtext{simphoniis}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}}.\edtext{}{\Cfootnote{etcetera. \textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 36. problema. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Trigesimumsextum problema}\label{edition-text book-19a part36}}{\lemma{Trigesimumsextum + problema} \Cfootnote[nosep]{\textit{γmv} | «36m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{trigesimum sextum.} Trigesimumsextum. \textit{P\textsuperscript{y}} | 35m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID SI QUIDEM}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}} | PROPTER QUID SI QUIDEM MEDIA \textit{V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID SI QUIDEM MEDIA MOUEBITUR ET ALIE CORDE SONANT, SI AUTEM ITERUM HEC QUIDEM MANET ALIARUM AUTEM QUEDAM MOUEATUR MOTA SOLA SONAT? \textsuperscript{1}AUT QUIA CONCORDARE EST OMNIBUS HABERE SE AUTEM QUODAMMODO AD MEDIAM OMNIBUS, ET ORDINATIO QUE EST UNIUSCUIUSQUE UTIQUE PER ILLAM EST? ELEUATA IGITUR CAUSA CONCORDANDI ET CONTINENTIS, NON ADHUC SIMILITER APPARERE EXISTERE. UNA AUTEM DISCORDANTE EXISTENTE MEDIA AUTEM MANENTE, RATIONABILITER QUOD EST SECUNDUM IPSAM DEFICIENS, ALIIS ENIM EXISTIT CONCORDARE \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema 36m. etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{βγπP\textsuperscript{x}mv} | Querit quare \textit{λ} | \textit{om}. \textit{E\textsuperscript{a}}}} si media \edtext{cordarum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | corda \textit{β}}} moueatur alie corde consonant illi, sed si postea fiat quod media \edtext{immobilis permaneat}{\Cfootnote[nosep]{\textit{βκP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | immobilis permaneat immobilis \textit{V\textsuperscript{a}}}} \edtext{et}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | est \textit{P\textsuperscript{y}}}} quedam \edtext{de}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} numero \edtext{aliarum a media}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | armoniarum aliarum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | aliarum \textit{V\textsuperscript{a}V\textsuperscript{o}}}} \edtext{moueatur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | moueantur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} solum \edtext{illa que}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | itaque \textit{V\textsuperscript{m}}}} \edtext{fuerit}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv} | fuit \textit{V\textsuperscript{z}} | sint \textit{V\textsuperscript{m}}}} mota sonat,} \edtext{ \edtext{ita quod}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | itaque \textit{P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{neque}{\Cfootnote[nosep]{\textit{βπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | in \textit{V\textsuperscript{a}}}} alia sonat}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} propter motum ipsius, neque \edtext{etiam}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in \textit{E\textsuperscript{a}} | \textit{om}. \textit{G\textsuperscript{u}}}} media. +\pend + +\pstart +\textbf{2} \edtext{Nosce quod \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | huiusmodi \textit{N\textsuperscript{u}} | de huiusmodi \textit{V\textsuperscript{b}mv} | de huius \textit{V\textsuperscript{a}}}} \edtext{problemate}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv} | problematis \textit{M\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{z}}}} \edtext{iam}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} sermo aliqualiter \edtext{precessit}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | processit \textit{V\textsuperscript{m}}}} in \edtext{20a.}{\Cfootnote[nosep]{\textit{ακ} | secundo \textit{mv}}} \edtext{problemate}{\Cfootnote[nosep]{\textit{ακ} | capitulo \textit{mv}}} }{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AUT.} Soluit dicens causam esse quoniam media cordarum concordat et consonat cum omnibus \edtext{cordis}{\Cfootnote[nosep]{\textit{ακπ} | cordis aliis \textit{mv}}}. \edtext{Quod}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | Ut \textit{V\textsuperscript{m}}}} ostenditur \textit{ \edtext{quoniam}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | quia \textit{V\textsuperscript{a}}}} concordare cum \edtext{omnibus}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | aliis \textit{V\textsuperscript{a}}}} \edtext{nichil}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}} | non \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{aliud}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}mv} | ad \textit{V\textsuperscript{a}} | \textit{om}. \textit{V\textsuperscript{o}}}} est quam se \edtext{habere aliqualiter}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | aliqualiter habere \textit{V\textsuperscript{z}}}} \edtext{ad mediam}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | ad medium \textit{G\textsuperscript{u}P\textsuperscript{p}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{omnis}{\Cfootnote[nosep]{\textit{βπV\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | omnes \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}}}}, \edtext{ordinatio enim}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}m} | enim ordinatio \textit{G\textsuperscript{u}P\textsuperscript{y}v}}} \edtext{vniuscuiusque}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | uniustus quia \textit{P\textsuperscript{z}}}} aliarum cordarum per illam existit. Quod probatur quoniam \edtext{ipsa}{\Cfootnote[nosep]{\textit{ακmv} | ista \textit{P\textsuperscript{p}P\textsuperscript{u}} | illa \textit{G\textsuperscript{u}P\textsuperscript{a}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{z}}}} media remota ex \edtext{instrumento}{\Cfootnote[nosep]{\textit{αλπmv} | instrumentorum \textit{P\textsuperscript{x}}}}, non amplius erit sentire \edtext{cordam}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{aliquam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ad quam \textit{P\textsuperscript{z}}}} que \edtext{existat}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | existit \textit{P\textsuperscript{u}V\textsuperscript{z}} | extat \textit{G\textsuperscript{u}}}} ratio concordandi alias \edtext{concorditerque}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | concorditerque alias \textit{P\textsuperscript{p}}}} retinendi. \edtext{Sed}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Sed si \textit{G\textsuperscript{u}}}} vna aliarum \edtext{remota}{\Cfootnote[nosep]{\textit{ακmv} | remoueatur \textit{π}}} ita quod causa existat discordandi \edtext{dummodo}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | dum \textit{P\textsuperscript{y}}}} media cordarum \edtext{recte maneat}{\Cfootnote[nosep]{\textit{ακmv} | remaneat \textit{π}}}, sicut \edtext{debet}{\Cfootnote[nosep]{\textit{αλπmv} | debeat \textit{P\textsuperscript{x}}}}, illud quod \edtext{erat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | erit \textit{P\textsuperscript{z}}}} \edtext{deficiens}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | indeficiens \textit{P\textsuperscript{y}}}}, ut corda ablata, \edtext{suppletur}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}v}}} per \edtext{mediam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | medium \textit{V\textsuperscript{o}}}}, ita \edtext{quod}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | ut \textit{V\textsuperscript{m}}}} \edtext{illa}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ista \textit{P\textsuperscript{p}P\textsuperscript{u}}}} remota \edtext{adhuc}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{aliis cordis inerit}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | inerit aliis cordis \textit{P\textsuperscript{p}} | cordis non erit \textit{V\textsuperscript{z}}}} concordare et consonantiam reddere per virtutem \edtext{medie}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | medicine \textit{V\textsuperscript{z}}}}.} Media enim est \edtext{ut}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{magistra}{\Cfootnote[nosep]{\textit{αλπmv} | magistram \textit{P\textsuperscript{x}}}} \edtext{et regula}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | et 2a \textit{V\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{aliarum omnium}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}mv} | omnium aliarum \textit{λG\textsuperscript{u}} | aliorum omnium \textit{V\textsuperscript{a}} | omnium ceterarum \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}}.\edtext{}{\Cfootnote{etcetera. \textit{V\textsuperscript{b}V\textsuperscript{z}} | sequitur 37. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Trigesimumseptimum problema}\label{edition-text book-19a part37}}{\lemma{Trigesimumseptimum + problema} \Cfootnote[nosep]{\textit{γmv} | «37m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{trigesimumseptimum} Trigesimumseptimum. \textit{P\textsuperscript{y}} | 36m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID QUOD EST IN UOCE}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID QUOD \textit{P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID QUOD EST IN UOCE ACUTO EXISTENTE MODICUM, GRAUI AUTEM SECUNDUM MULTUM GRAUE? QUIDEM ENIM PROPTER MULTITUDINEM GRAUE, ACUTUM AUTEM PROPTER PAUCITATEM UELOX EST. \textsuperscript{2}MOLESTUM MAGIS CANTARE ACUTA QUAM GRAUIA, ET PAUCI ASCENDENTIA POSSUNT CANTARE, ET LEGES DIRIGUNT, ET ACUTI DIFFICILES DIMITTERE PROPTER ID QUOD TENSI SUNT. \textsuperscript{3}MINUS OPUS MODICUM MOUERE QUAM MULTUM, QUARE ET AEREM. \textsuperscript{4}AUT IDEM ACUTE SONANS ESSE NATURA ET ACUTE CANERE, SED NATURA QUIDEM ACUTE UOCIS OMNIA PROPTER IMBECILLITATEM PRO EO QUOD NON POTEST MOUERE MULTUM AEREM, SED MODICUM. MODICUS AUTEM UELOCITER FERTUR. IN CANTANDO AUTEM ACUTUM POTENTIE SIGNUM, QUOD QUIDEM ENIM UELOCITER FERTUR, PROPTER QUOD ET ACUTUM POTENTIE SIGNUM. PROPTER QUOD ET QUI SUNT BONI HABITUS ACUTE UOCIS, ET MOLESTUM QUE ELEUANTUR CANTARE, GRAUIA AUTEM DEORSUM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema .37m. etcetera. \edtext{Querit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}mv} | Quare \textit{G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{c}} | Contingit \textit{V\textsuperscript{o}}}} quesitum \edtext{cuius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quarum \textit{G\textsuperscript{u}}}} \edtext{terminorum primitus}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | cuiustorum primitus \textit{N\textsuperscript{u}} | corpus primo \textit{P\textsuperscript{y}}}} tangit expositionem, dicens quod \textit{cum in uoce \edtext{acutum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | acuta \textit{V\textsuperscript{a}}}} \edtext{existat}{\Cfootnote[nosep]{\textit{αλπmv} | extat \textit{P\textsuperscript{x}}}} secundum modicum temporis, graue \edtext{autem secundum \edtext{multum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | uictum «multum» (in mg.) \textit{V\textsuperscript{o}}}}. \edtext{Nam}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | Namque \textit{V\textsuperscript{a}}}} graue}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} causatur \edtext{propter}{\Cfootnote[nosep]{\textit{βγκπmv} | secundum \textit{E\textsuperscript{a}}}} multitudinem aeris \edtext{moti}{\Cfootnote[nosep]{\textit{αλπmv} | motu \textit{P\textsuperscript{x}}}} qui tarde mouetur, acutum uero propter \edtext{paucitatem ipsius}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | tarditatem ipsius paucitatem \textit{P\textsuperscript{y}}}}, ex \edtext{qua}{\Cfootnote[nosep]{\textit{γκmv} | quo \textit{βπE\textsuperscript{a}}}} uelocitas causatur,} ‘sicut ex multitudine tarditas, \edtext{ut visum est .xia}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}mv} | ut visum .xia \textit{β} | ut visum est 11a particula. \textit{γ} | \textit{om}. \textit{π}}} \edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XI .16 , 900b ll. 24–28}}’ +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{MOLESTUM.}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | MOLESTAM. \textit{V\textsuperscript{z}}}} } \edtext{Secundo}{\Cfootnote[nosep]{\textit{ακE\textsuperscript{a}mv} | \textit{om}. \textit{π}}} \edtext{format}{\Cfootnote[nosep]{\textit{αλπmv} | fertur \textit{P\textsuperscript{x}}}} quesitum, dicens \textit{quare magis \edtext{difficile}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}} | difficile est \textit{λπmv}}} cantare \edtext{illa}{\Cfootnote[nosep]{\textit{αλmv} | ea \textit{πP\textsuperscript{x}}}} que sunt acuta quam \edtext{ea}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | illa \textit{P\textsuperscript{y}V\textsuperscript{a}}}} que sunt \edtext{grauia}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}}. Quod ostenditur \edtext{quoniam}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}mv} | quia \textit{λV\textsuperscript{a}}}} pauci sunt \edtext{qui possunt cantus}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}} | qui possint cantus \textit{N\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{ascendentes}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}} \edtext{cantare}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cantare et \textit{P\textsuperscript{p}}}} maxime, cum \edtext{sint}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | sunt \textit{P\textsuperscript{y}}}} acutissimi. Et ideo \edtext{huius non}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | huiusmodi non \textit{βV\textsuperscript{b}V\textsuperscript{z}mv} | tales non \textit{G\textsuperscript{u}P\textsuperscript{q}}}} cantant, sed potius \edtext{dirigunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | digerunt \textit{P\textsuperscript{z}}}} leges}, legales enim cantus constituunt. \textit{Sunt enim \edtext{tanquam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv}}} graues remissi faciles ad cantandum,} vt \edtext{visum est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | uisum \textit{β}}} \edtext{.15}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | in 15 \textit{P\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}}. Et non solum difficile \edtext{est in acutum tendere \edtext{et}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}mv} | id est \textit{V\textsuperscript{a}}}} \edtext{seruare}{\Cfootnote[nosep]{\textit{βγπP\textsuperscript{x}V\textsuperscript{z}mv} | seruant \textit{E\textsuperscript{a}} | reseruare \textit{M\textsuperscript{a}}}} \edtext{cantus}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv} | cantum \textit{V\textsuperscript{z}}}}, sed etiam \edtext{difficile}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | difficile est \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} mox cessare a cantibus acutis, eo quod \edtext{tensi}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | remissi \textit{γmv}}} sunt ualde \edtext{ceu}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{equum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}} \edtext{extensum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | excessum \textit{V\textsuperscript{b}}}} et uelocissime \edtext{currentem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | currente \textit{P\textsuperscript{u}}}} \edtext{molestum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | mosteli \textit{V\textsuperscript{b}}}} \edtext{est}{\Cfootnote[nosep]{\textit{κP\textsuperscript{z}} | \textit{om}. \textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} confestim \edtext{sistere}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | consistere \textit{P\textsuperscript{z}}}}, atque \edtext{similiter nauem uelocissime}{\Cfootnote[nosep]{\textit{αP\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | nauem similiter uelocissime \textit{V\textsuperscript{m}} | nauem uelocissime similiter \textit{M\textsuperscript{a}} | similiter manere uelocissime \textit{P\textsuperscript{x}} | nauem uelocissime \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{inpulsam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{MINUS.} Tertio \edtext{arguit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | argummentat \textit{N\textsuperscript{u}}}} in contrarium, \edtext{quasi}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quare \textit{P\textsuperscript{z}}}} dicat \edtext{quod}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | quia \textit{βγM\textsuperscript{a}V\textsuperscript{z}mv}}} \textit{ \edtext{minus}{\Cfootnote[nosep]{\textit{βγκπmv} | unus \textit{E\textsuperscript{a}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | sit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} opus et sic \edtext{maior}{\Cfootnote[nosep]{\textit{βγλP\textsuperscript{z}mv} | maior opus \textit{P\textsuperscript{x}} | minor \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} virtus \edtext{requiritur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | requiratur \textit{P\textsuperscript{y}}}} ad mouendum illud quod est modicum \edtext{quam quod}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | quod quam \textit{P\textsuperscript{u}} | quam quod est \textit{β} | quare illud quod est \textit{P\textsuperscript{x}} | quam ad \textit{G\textsuperscript{u}}}} multum}, non videtur \edtext{quod acutum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} mouere \edtext{cantando}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}mv} | euitando \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{sit}{\Cfootnote[nosep]{\textit{βγλπmv} | fit \textit{E\textsuperscript{a}P\textsuperscript{x}}}} difficile, cum sit modicum, et graue facile, quia multum \edtext{ymmo}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}}}} econuerso, quare sicut est. Universaliter in aliis ita \edtext{etiam videtur esse}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}V\textsuperscript{b}mv} | videtur esse \textit{πP\textsuperscript{x}} | videtur etiam \textit{V\textsuperscript{a}}}} in aere \edtext{qui}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | que \textit{P\textsuperscript{u}P\textsuperscript{x}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | videtur esse \textit{P\textsuperscript{p}}}} subiectum sonorum, eius enim medium \edtext{proprium}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}} | proprie \textit{P\textsuperscript{z}} | propositum \textit{V\textsuperscript{m}mv}}} est ipse in quo \edtext{causatur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | cantatur \textit{P\textsuperscript{y}}}} et recipitur primitus. +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv}}} } Soluit dicens causam esse \edtext{sumendam}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv}}} \edtext{ex hoc}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}, \textit{ \edtext{quia}{\Cfootnote[nosep]{\textit{αλπmv} | quod \textit{P\textsuperscript{x}}}} \edtext{idem}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} videtur esse naturaliter acute sonare et \edtext{acute cantare}{\Cfootnote[nosep]{\textit{ακ} | acuto cantare \textit{mv} | sonare \textit{π}}}, \edtext{et non}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | non \textit{κV\textsuperscript{o}}}} \edtext{differt}{\Cfootnote[nosep]{\textit{βγπP\textsuperscript{x}V\textsuperscript{z}mv} | differunt \textit{M\textsuperscript{a}} | dicent \textit{E\textsuperscript{a}}}} nisi \edtext{secundum quod}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | quod \textit{V\textsuperscript{a}} | sicut \textit{π}}} \edtext{superius differt}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}mv} | differt superius \textit{λ} | superius \textit{π}}} ab inferiori.} \edtext{Hoc}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | Huius \textit{M\textsuperscript{a}}}} autem \edtext{assumit}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv}}} \edtext{ut}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | et \textit{V\textsuperscript{b}}}} \edtext{declaret}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | declararet \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}mv}}} \edtext{per}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | quod \textit{M\textsuperscript{a}}}} \edtext{id}{\Cfootnote[nosep]{\textit{βγλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | illud \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{x}}}} quod \edtext{est}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} in uoce \edtext{vniversaliter}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | similiter \textit{V\textsuperscript{a}} | videtur \textit{π}}} \edtext{sic esse}{\Cfootnote[nosep]{\textit{απmv} | est \textit{κ}}} in sono. Unde \edtext{subdens}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}} \edtext{ait}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | autem \textit{mv} | aut \textit{V\textsuperscript{a}}}} ‘ \edtext{omnia}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | omnis \textit{G\textsuperscript{u}P\textsuperscript{q}}}} naturaliter acute \edtext{uocis}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | uocem \textit{γM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | vox \textit{P\textsuperscript{u}}}} \edtext{fieri}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} propter debilitatem \edtext{suam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}, eo quod non \edtext{possunt}{\Cfootnote[nosep]{\textit{βπP\textsuperscript{x}V\textsuperscript{a}} | possint \textit{λE\textsuperscript{a}V\textsuperscript{b}mv}}} multum aerem \edtext{mouere, qui}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | remouere, quod \textit{P\textsuperscript{z}}}} \edtext{grauis uocis est causa}{\Cfootnote[nosep]{\textit{βM\textsuperscript{a}V\textsuperscript{z}mv} | est causa grauis uocis \textit{γ} | grauis uocum est causa \textit{V\textsuperscript{m}} | grauis netis est causa \textit{P\textsuperscript{x}} | grauis est causa \textit{πE\textsuperscript{a}}}}. Sed modicum possunt, \edtext{modicus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | motus \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{autem aer motus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aut aer \textit{P\textsuperscript{p}}}} uelociter \edtext{fertur}{\Cfootnote[nosep]{\textit{βγκπmv}}}, \edtext{ut \edtext{visum est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | visum \textit{β}}} .xi°.}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XI .13 , 900a ll. 21–27 ; 21 , 901a ll. 31–32}}’ \edtext{Sepe atque}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{a}} | Sepe at quia \textit{E\textsuperscript{a}N\textsuperscript{u}} | Sepe ac \textit{V\textsuperscript{b}mv} | Aut quia \textit{π}}} acutum \edtext{sic uelociter mouetur}{\Cfootnote[nosep]{\textit{ακmv} | velociter mouetur sic \textit{π}}} si quis cantauerit secundum acutum. Signum \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | quid \textit{V\textsuperscript{o}}}} ex hoc \edtext{suscipitur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | accipitur \textit{P\textsuperscript{y}} | sumitur \textit{G\textsuperscript{u}P\textsuperscript{q}} | concipitur \textit{P\textsuperscript{z}}}} \edtext{cuiusdam}{\Cfootnote[nosep]{\textit{ακmv} | eiusdem \textit{π}}} vigoris \edtext{in}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | \textit{om}. \textit{γmv}}} eo quod mouet aliquid uelociter, quod non \edtext{fieret}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | fieretur \textit{V\textsuperscript{o}}}} nisi vigor adesset. Et \edtext{ideo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | non \textit{P\textsuperscript{z}}}} ex \edtext{hoc}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | hac \textit{P\textsuperscript{p}V\textsuperscript{a}mv}}} \edtext{confirmatione}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | confirmatiue \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}}}} concluditur \edtext{quod}{\Cfootnote[nosep]{\textit{απmv} | quod si \textit{κ}}} illi qui sunt bone complexionis quorum pulmones non \edtext{redundant}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{z}} | redundat \textit{P\textsuperscript{x}} | exundant \textit{V\textsuperscript{b}}}} \edtext{humiditatibus}{\Cfootnote[nosep]{\textit{αλπmv} | hominibus \textit{P\textsuperscript{x}}}} superfluis \edtext{existere}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | existunt \textit{V\textsuperscript{z}} | esse \textit{P\textsuperscript{y}}}} uocis acute eo quod organum est \edtext{exsiccatum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}} | excitatum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{solidum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | solum \textit{V\textsuperscript{a}}}}. Et quia difficile est \edtext{cantare}{\Cfootnote[nosep]{\textit{ακmv} | cantare ea \textit{π}}} que \edtext{eleuantur}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}}, cum acuta \edtext{extollantur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | excellenter \textit{P\textsuperscript{z}}}}, ipsa \edtext{fiet}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | fiat \textit{P\textsuperscript{y}V\textsuperscript{a}}}} cantare difficile, nam ‘ \edtext{eleuare}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | elleuare est \textit{M\textsuperscript{a}} | eleuantur \textit{π}}} contra \edtext{naturam,}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | naturam est, \textit{V\textsuperscript{z}}}} \edtext{ut \edtext{visum est}{\Cfootnote[nosep]{\textit{γκmv} | visum \textit{βE\textsuperscript{a}}}} particula \edtext{secunda}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | 11a \textit{V\textsuperscript{a}}}} .}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} II .38 , 870a l. 34}}’Et quia grauia \edtext{naturaliter tendunt}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | tendunt naturaliter \textit{G\textsuperscript{u}P\textsuperscript{q}} | naturaliter \textit{P\textsuperscript{p}}}} deorsum, quod \edtext{nobis magis}{\Cfootnote[nosep]{\textit{αλπmv} | magis nobis \textit{P\textsuperscript{x}}}} \edtext{naturale}{\Cfootnote[nosep]{\textit{ακmv} | naturale est \textit{π}}}, \edtext{ideo facile fit}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | facile fit ideo \textit{β} | ideo facile sit \textit{V\textsuperscript{m}} | facile igitur fit \textit{πE\textsuperscript{a}}}} \edtext{ipsa}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | ipsam \textit{V\textsuperscript{a}}}} cantare. Sic \edtext{igitur}{\Cfootnote[nosep]{\textit{αλπmv} | ergo \textit{P\textsuperscript{x}}}} \edtext{soluitur}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | soluit \textit{V\textsuperscript{m}} | sol\expan{ummod}o \textit{(orig. \textup{sol\textsuperscript{o}})} \textit{N\textsuperscript{u}} | solum \textit{P\textsuperscript{y}}}} adquesitum, \edtext{neque}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{ambiguitas}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{relinquitur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | relinquatur \textit{P\textsuperscript{y}}}} aliqua \edtext{que}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | quia \textit{P\textsuperscript{z}} | \textit{om}. \textit{M\textsuperscript{a}}}} in ‘ \edtext{.xia. particula}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | particula .11a. \textit{V\textsuperscript{b}} | 5a particula \textit{P\textsuperscript{p}P\textsuperscript{u}} | ille particula \textit{G\textsuperscript{u}}}} \edtext{intelligenti dicta,}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | intelligentis dicta, \textit{P\textsuperscript{z}} | intellecto dicta, \textit{G\textsuperscript{u}} | multa dicta, \textit{V\textsuperscript{a}}}} \edtext{quoniam}{\Cfootnote[nosep]{\textit{βγκπmv} | quando \textit{E\textsuperscript{a}}}} \edtext{in acute cantare siue sonare}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | in acutis cantare siue sonare \textit{P\textsuperscript{z}} | acute cantare siue sonare \textit{V\textsuperscript{a}} | in acuto cantare siue sonare \textit{P\textsuperscript{x}}}} \edtext{duo fit}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | duo sit \textit{V\textsuperscript{m}} | est duo \textit{π}}} \edtext{considerare: puta}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | consingulare: puta \textit{V\textsuperscript{a}}}} \edtext{modicum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{aerem}{\Cfootnote[nosep]{\textit{βγκπmv} | aerem \surplus{aerem} \textit{E\textsuperscript{a}}}} motum et quantum ad hoc videtur quod \edtext{acutum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | acute \textit{G\textsuperscript{u}P\textsuperscript{q}}}} mouere \edtext{sit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fit \textit{G\textsuperscript{u}}}} facile,\edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XI .14 , 900a ll. 34–36}}’cum \edtext{id}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}mv} | illud \textit{P\textsuperscript{x}} | \textit{om}. \textit{V\textsuperscript{a}}}} debiles agant et \edtext{impotentes}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}v}}}. \edtext{Est et}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}mv} | Et est \textit{π} | Est \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Est etiam \textit{V\textsuperscript{z}}}} considerare quod \edtext{illud}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | id \textit{V\textsuperscript{b}}}} \edtext{modicum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | motum \textit{P\textsuperscript{y}}}} aeris velociter mouetur, \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{quia quod}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | quod \textit{M\textsuperscript{a}} | quia \textit{P\textsuperscript{y}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | huiusmodi \textit{βγG\textsuperscript{u}mv}}} non \edtext{fit}{\Cfootnote[nosep]{\textit{βκπ} | sit \textit{γE\textsuperscript{a}mv}}} nisi a \edtext{constanti}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | constante \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} virtute. \edtext{Ideo}{\Cfootnote[nosep]{\textit{ακmv} | Item \textit{P\textsuperscript{z}V\textsuperscript{o}} | Ergo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{acutum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | acute \textit{G\textsuperscript{u}P\textsuperscript{q}}}} mouere denotat \edtext{constantiam}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{virtutis}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv}}}, et difficultatem per consequens, quare \edtext{apparuit}{\Cfootnote[nosep]{\textit{βγκπmv} | apparente \textit{E\textsuperscript{a}}}} ‘ \edtext{.xiiii°.}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | 24º \textit{N\textsuperscript{u}} | .34°. \textit{P\textsuperscript{y}}}} \edtext{xi°.}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{pueros}{\Cfootnote[nosep]{\textit{αλπmv} | paruos \textit{P\textsuperscript{x}}}} \edtext{uoces acutiores}{\Cfootnote[nosep]{\textit{γκN\textsuperscript{u}mv} | acutiores uoces \textit{πP\textsuperscript{y}} | acutiores \textit{E\textsuperscript{a}}}} habere \edtext{senioribus}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}mv} | senibus \textit{P\textsuperscript{x}P\textsuperscript{y}}}}, propter \edtext{consistentiam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | constantiam \textit{G\textsuperscript{u}P\textsuperscript{z}}}} \edtext{calidi}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | calidi eorum \textit{V\textsuperscript{b}}}} \edtext{virtuosi}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | unctuosi \textit{γmv}}}.\edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XI .14 , 900a l. 33 to 900b l. 8}}’ \edtext{}{\Cfootnote{etcetera. \textit{V\textsuperscript{b}V\textsuperscript{z}} | etcetera etcetera. \textit{P\textsuperscript{z}} | sequitur 38. problema. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Trigesimumoctauum problema}\label{edition-text book-19a part38}}{\lemma{Trigesimumoctauum + problema} \Cfootnote[nosep]{\textit{γmv} | «38m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{trigesimum octauum.} Trigesimumoctauum. \textit{P\textsuperscript{y}} | 37m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID ET RITHIMO}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}} | PROPTER QUID IN RITHIMO \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID ET RITHIMO ET CANTU ET OMNINO CONSONANTIIS GAUDENT OMNES? \textsuperscript{2}AUT QUIA MOTIBUS QUI SUNT SECUNDUM NATURAM GAUDEMUS SECUNDUM NATURAM? \textsuperscript{3}SIGNUM AUTEM PUEROS CONFESTIM NATOS GAUDERE IPSIS. PROPTER CONSUETUDINEM AUTEM MODIS CANTUUM GAUDEMUS. \textsuperscript{4}RITHIMO AUTEM GAUDEMUS PROPTER MOTUM ET ORDINATUM NUMERUM HABERE ET MOUERE NOS ORDINATE MAGIS. MAGIS PRIUS ENIM EST ORDINATUS MOTUS NATURA INORDINATO, QUARE ET SECUNDUM NATURAM MAGIS. \textsuperscript{5}SIGNUM AUTEM LABORANTES ENIM ET BIBENTES ET COMEDENTES ORDINATE SALUAMUS ET AUGEMUS NATURAM ET UIRTUTEM, INORDINATE AUTEM CORRUMPIMUS ET STUPEFACIMUS IPSAM. EGRITUDINES ENIM ORDINATIONIS CORPORIS NON SECUNDUM NATURAM MOTUS SUNT. \textsuperscript{6}CONSONANTIA GAUDEMUS QUONIAM COMPLEXIO EST CONTRARIORUM HABENTIUM PROPORTIONEM AD INUICEM. PROPORTIO AUTEM ORDINATIO, QUOD ERAT NATURA DELECTABILE. COMPLEXIONATUM AUTEM INCOMPLEXIONATO OMNE DELECTABILIUS ALITER. \textsuperscript{7}QUAMUIS SENSIBILE SIT UTRISQUE EXTREMIS EX EQUALI POTENTIAM HABET IN CONSONANTIA PROPORTIO \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema 38m. etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} omnia, ‘ita \edtext{quod}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | ut \textit{V\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{z}}}} etiam \edtext{bruta}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | bruta itaque \textit{P\textsuperscript{z}}}} \edtext{utcunque}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | utrunque \textit{P\textsuperscript{y}P\textsuperscript{z}}}} \edtext{ \edtext{sicut videbitur}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{m}mv} | sint videbitur \textit{P\textsuperscript{x}} | \textit{om}. \textit{V\textsuperscript{z}}}} .vii°. \edtext{xxixe.}{\Cfootnote[nosep]{\textit{βκmv} | 29e particule \textit{γ} | et 9e. \textit{E\textsuperscript{a}}}},}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XXVIII .7 , 949b l. 37 to 950a l. 16}}’ \edtext{exultantur}{\Cfootnote[nosep]{\textit{γλN\textsuperscript{u}mv} | exultant \textit{πE\textsuperscript{a}P\textsuperscript{y}}}} \edtext{rithimo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | rithimi \textit{P\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{et}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} cantu \edtext{ac}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}mv} | ac etiam \textit{λ} | et \textit{π}}} \edtext{vniuersaliter}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uidetur \textit{P\textsuperscript{z}}}} \edtext{consonantiarum}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | consonantiam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | consonantia \textit{P\textsuperscript{z}}}} auditu in \edtext{hiis}{\Cfootnote[nosep]{\textit{αλπmv} | huius \textit{P\textsuperscript{x}}}} }, \edtext{siquidem}{\Cfootnote[nosep]{\textit{βγκπmv} | quidem \textit{E\textsuperscript{a}}}} \edtext{verbis}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | \textit{om}. \textit{γmv}}} \edtext{triplex pretacta indicatur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | triplex pretacta inducatur \textit{P\textsuperscript{y}} | pretacta indicatur triplex \textit{V\textsuperscript{a}} | triplex iudicatur pretacta \textit{π}}} musica? +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | QUONIAM. \textit{M\textsuperscript{a}}}} } Soluit \edtext{primo dans causam vniversaliter dicens}{\Cfootnote[nosep]{\textit{ακmv} | primo vniversaliter dicens \textit{G\textsuperscript{u}} | dicens primo \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} causam \edtext{fore}{\Cfootnote[nosep]{\textit{ακmv} | esse \textit{π}}} communem, \textit{ \edtext{quoniam}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}mv} | quia \textit{V\textsuperscript{a}} | quare \textit{P\textsuperscript{x}}}} \edtext{gaudemus naturaliter}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}V\textsuperscript{m}mv} | naturaliter gaudemus \textit{V\textsuperscript{z}} | gaudere naturaliter \textit{P\textsuperscript{x}P\textsuperscript{y}} | gaudemus vniuersaliter \textit{E\textsuperscript{a}} | giludomus naturaliter \textit{V\textsuperscript{a}}}} motibus \edtext{naturalibus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | naturaliter \textit{P\textsuperscript{z}}}}, \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | que \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{in temperamento}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | temperamento \textit{P\textsuperscript{y}} | in temperato \textit{P\textsuperscript{u}}}} quodam consistant}. Sicut enim ‘excellentie sensibilium \edtext{corrumpunt}{\Cfootnote[nosep]{\textit{αλπmv} | corrumpuntur \textit{P\textsuperscript{x}}}} \edtext{sensus}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | sensum \textit{G\textsuperscript{u}V\textsuperscript{a}P\textsuperscript{z}}}}, \edtext{ut apparet \textit{de anima} 3°.,}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}} | ut apparet 3º \textit{de anima} , \textit{V\textsuperscript{a}V\textsuperscript{z}} | ut patet 3° \textit{de anima} , \textit{πmv}}} \edtext{}{\Afootnote[nosep]{Arist. \textit{De an.} III .13 , 435b l. 15 (Cf. 426a, l. 30)}}’ \edtext{ita et}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}V\textsuperscript{m}mv} | ita etiam \textit{V\textsuperscript{z}} | ita ut \textit{P\textsuperscript{x}} | et \textit{π} | itaque \textit{E\textsuperscript{a}}}} ‘ \edtext{ipsorum}{\Cfootnote[nosep]{\textit{ακmv} | ipsarum \textit{π}}} \edtext{conmensurationes}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} eos custodiunt, \edtext{ut}{\Cfootnote[nosep]{\textit{κ} | sicut \textit{απmv}}} \edtext{etiam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | et \textit{M\textsuperscript{a}} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{tactum est}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}} | tactum \textit{βV\textsuperscript{a}} | tactus est \textit{mv}}} in principio \edtext{huius}{\Cfootnote[nosep]{\textit{ακπ} | huiusmodi \textit{mv}}} \edtext{particule}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}}.\edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XΙΧ .2 , 917b ll. 22–29}}’ +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{SIGNUM.} \edtext{Declarat}{\Cfootnote[nosep]{\textit{αλπmv} | Ostendit \textit{P\textsuperscript{x}}}} secundo \edtext{quomodo}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quo \textit{G\textsuperscript{u}}}} in \edtext{vnoquoque}{\Cfootnote[nosep]{\textit{αλπmv} | unaquoque \textit{P\textsuperscript{x}}}} \edtext{trium}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | cum \textit{G\textsuperscript{u}V\textsuperscript{a}}}} \edtext{predictorum}{\Cfootnote[nosep]{\textit{απ} | predictorum sicut \textit{κmv}}} motus secundum naturam \edtext{existat}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}} | existit \textit{P\textsuperscript{x}mv} | existant \textit{V\textsuperscript{a}}}} et per consequens gaudere \edtext{fiat}{\Cfootnote[nosep]{\textit{ακmv} | faciat \textit{π}}} \edtext{ex eo}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}mv} | et eo \textit{V\textsuperscript{b}} | \textit{om}. \textit{π}}}. \edtext{Primoque}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}mv} | Primo quid \textit{V\textsuperscript{m}} | Primo quod \textit{P\textsuperscript{y}} | Primo \textit{πV\textsuperscript{z}}}} manifestans in \edtext{tactu}{\Cfootnote[nosep]{\textit{κ} | cantu \textit{αmv} | sensu \textit{π}}} \edtext{dicens}{\Cfootnote[nosep]{\textit{αλπ} | dicit \textit{P\textsuperscript{x}mv}}} \textit{ \edtext{huius}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{a}} | huiusmodi \textit{V\textsuperscript{b}mv} | hoc \textit{P\textsuperscript{y}}}} signum esse \edtext{quoniam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quia \textit{G\textsuperscript{u}}}} pueri \edtext{mox cum}{\Cfootnote[nosep]{\textit{ακmv} | cum mox \textit{π}}} fuerint nati accidit \edtext{ipsis}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | eis \textit{V\textsuperscript{z}}}} gaudere \edtext{cantu tum}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}} | cantu cum \textit{V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | cantu tamen \textit{P\textsuperscript{x}mv} | tamen \textit{M\textsuperscript{a}} | cantatum \textit{P\textsuperscript{z}}}} \edtext{propter}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | per \textit{G\textsuperscript{u}P\textsuperscript{q}}}} musicam \edtext{naturaliter}{\Cfootnote[nosep]{\textit{αλπmv} | universaliter \textit{P\textsuperscript{x}}}} \edtext{ipsis}{\Cfootnote[nosep]{\textit{ακmv} | sibi \textit{π}}} \edtext{inditam}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | indicatiua \textit{V\textsuperscript{b}mv}}}.} \edtext{Anima}{\Cfootnote[nosep]{\textit{βγκπmv} | Nam \textit{E\textsuperscript{a}}}} enim ‘ \edtext{maxime nostra}{\Cfootnote[nosep]{\textit{βκV\textsuperscript{a}} | nostra maxime \textit{V\textsuperscript{a}mv} | maxime \textit{E\textsuperscript{a}} | magis uel maxime \textit{π}}} ad similitudinem \edtext{numeri consoni}{\Cfootnote[nosep]{\textit{βγλπmv} | numerum consoni \textit{P\textsuperscript{x}} | numerius soni \textit{E\textsuperscript{a}}}} \edtext{constricta}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | constructa \textit{αM\textsuperscript{a}P\textsuperscript{z}} | constituta \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{existit}{\Cfootnote[nosep]{\textit{αλmv} | existat \textit{P\textsuperscript{x}} | est \textit{π}}}, \edtext{ut apparet per}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}} | ut patet per \textit{mv} | ut \textit{β} | per \textit{V\textsuperscript{a}}}} \edtext{damascenus}{\Cfootnote[nosep]{\textit{β} | damascenum \textit{γG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | dictum \textit{M\textsuperscript{a}V\textsuperscript{m}}}} in \textit{ \edtext{afforismis}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{o}mv} | amphorismis suis \textit{P\textsuperscript{z}}}} }.\edtext{}{\Afootnote[nosep]{Yuḥannā ibn Māsawaiyh \textit{Aph.} (See Vat. Lat. 2460, f. 39v, ll.10–11.)}}’ \edtext{Quare}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Et \textit{G\textsuperscript{u}}}} ‘primo \textit{de \edtext{regimine sanitatis}{\Cfootnote[nosep]{\textit{απV\textsuperscript{z}} | re\expan{gimine} sa\expan{nitatis} \textit{(orig. \textup{re. sa.})} \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}} } \edtext{pueri}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{familiariter}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | simili aliter \textit{V\textsuperscript{b}}}} dispositi sunt ad musicam.\edtext{}{\Afootnote[nosep]{Gal. \textit{De san. tu.} I .7}}’ \textit{ \edtext{Tum}{\Cfootnote[nosep]{\textit{βγπM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | Cum \textit{V\textsuperscript{z}} | Tamen \textit{E\textsuperscript{a}}}} etiam propter consuetudinem quam \edtext{adipiscimur}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | adispiscitur \textit{P\textsuperscript{z}} | adypiscimus \textit{E\textsuperscript{a}} | adipiscuntur \textit{V\textsuperscript{a}}}} deinceps \edtext{ \edtext{ex}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{maneriebus}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv}}} \edtext{cantuum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | cantantuum \textit{V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} gaudere accidit,} quidam \edtext{enim}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vero \textit{P\textsuperscript{p}}}} gaudent \edtext{vno}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} cantu, alii \edtext{uero}{\Cfootnote[nosep]{\textit{κ} | autem \textit{βπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} alio \edtext{secundum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | si \textit{M\textsuperscript{a}}}} quod consueti \edtext{fuerunt}{\Cfootnote[nosep]{\textit{βV\textsuperscript{a}V\textsuperscript{m}} | fuerint \textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}mv}}} audire a \edtext{natiuitate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | natiuitate audiant \textit{λ}}}. Quod autem infantes \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | huiusmodi \textit{γG\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{a}mv}}} cantibus \edtext{delectentur}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{z}mv} | delectantur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}}, id sciunt nutrices industriose que modis cantuum et \edtext{motuum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | motum \textit{V\textsuperscript{m}} | motibus \textit{mv}}} \edtext{quibusdam}{\Cfootnote[nosep]{\textit{ακmv} | quidam \textit{P\textsuperscript{z}V\textsuperscript{o}} | communium \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, cum \edtext{hii}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ii \textit{M\textsuperscript{a}}}} \edtext{tristentur}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | tristantur \textit{πV\textsuperscript{z}}}} et \edtext{plorant}{\Cfootnote[nosep]{\textit{αλπmv} | plorent \textit{P\textsuperscript{x}}}}, \edtext{ipsorum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ipsarum \textit{P\textsuperscript{z}}}} animos \edtext{demulciunt}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | demulcent \textit{π}}}, quiescere facientes et gaudere, cum ostensum sit \edtext{hanc}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ac \textit{P\textsuperscript{z}}}} esse \edtext{potentiam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | potentie \textit{P\textsuperscript{z}}}} musice. Unde ‘ \edtext{eodem}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}mv} | eodem modo \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} primo: nutrices \edtext{tribus modis consolantur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | consolantur tribus modis \textit{V\textsuperscript{a}}}} et ad \edtext{sompnum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}m} | \surplus{ad} sompnum \textit{V\textsuperscript{z}}}} prouocant pueros: ut appositione \edtext{mamillarum}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}m}}} ad os, melodia uocis, et motu.\edtext{}{\Afootnote[nosep]{Gal. \textit{De san. tu.} I .7}}’ +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \edtext{\textit{RITHIMO.} Secundo dat causam}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}} | \textit{RITHIMO.} Dat causam \textit{M\textsuperscript{a}} | \textit{RITHIMUS.} Secundo dat causam \textit{V\textsuperscript{m}} | \textit{RITHIMO.} Declarat secundo \textit{V\textsuperscript{a}} | \textit{RITHIMO.} Secundo declarat causam \textit{V\textsuperscript{b}mv} | AC HUIC. Dat causam 2° \textit{π}}} \edtext{rithimo quare}{\Cfootnote[nosep]{\textit{βG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{a}mv} | quare rithimo \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{z}} | rithimo \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}}}} \edtext{fit}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{y}mv} | sit \textit{πN\textsuperscript{u}}}} \edtext{gaudere quod}{\Cfootnote[nosep]{\textit{βγκπmv} | gaude quo \textit{E\textsuperscript{a}}}} secundo \edtext{signo manifestat}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}mv} | manifestat signo ibi \textit{π} | signo manifestat secunda ibi \textit{V\textsuperscript{a}} | signo inanimat \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}} \textit{ \edtext{SIGNUM AUTEM}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | SIGNO AUTEM \textit{G\textsuperscript{u}} | DIGNUM AUTEM \textit{γ} | \textit{om}. \textit{V\textsuperscript{z}}}} }, \edtext{dicens causam esse}{\Cfootnote[nosep]{\textit{βπP\textsuperscript{x}mv} | dicit causam esse \textit{γM\textsuperscript{a}V\textsuperscript{z}} | dicens causam \surplus{dicens causam} esse \textit{E\textsuperscript{a}} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{quare}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{z}} | quia \textit{V\textsuperscript{m}mv} | quoniam \textit{V\textsuperscript{a}}}} \textit{ \edtext{gaudemus}{\Cfootnote[nosep]{\textit{αλπmv} | gaudere \textit{P\textsuperscript{x}}}} rithimo. \edtext{Est}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{πV\textsuperscript{a}}}} \edtext{propter}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | propter quod \textit{V\textsuperscript{a}}}} \edtext{motum suauem et numerum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | numerum suauem et numerum \textit{V\textsuperscript{a}}}} ordinatum \edtext{eius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | 4º \textit{P\textsuperscript{z}}}} et proportionatum clausularum \edtext{vnius}{\Cfootnote[nosep]{\textit{ακmv} | vniuscuiusque \textit{π}}} \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} altera concordantium \edtext{quos}{\Cfootnote[nosep]{\textit{αλ} | quas \textit{πP\textsuperscript{x}mv}}} \edtext{habet}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}mv} | habet est \textit{V\textsuperscript{a}} | hoc \textit{P\textsuperscript{x}}}}. Que \edtext{autem huius}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}} | autem huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{a}V\textsuperscript{b}mv} | aut huius \textit{C\textsuperscript{a}V\textsuperscript{o}} | ab huius \textit{P\textsuperscript{x}}}} nos habent mouere \edtext{amplius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} paulatiue et ordinate, \edtext{nam}{\Cfootnote[nosep]{\textit{βγκπmv} | non \textit{E\textsuperscript{a}}}} motus \edtext{ordinatus et vniformis}{\Cfootnote[nosep]{\textit{αλπmv} | paulatiuus et ordinatus \textit{P\textsuperscript{x}}}} prior est \edtext{natura}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | nature \textit{G\textsuperscript{u}mv}}} \edtext{opposito}{\Cfootnote[nosep]{\textit{βγλπmv} | apposito \textit{E\textsuperscript{a}} | apposita \textit{P\textsuperscript{x}}}},} \edtext{ \edtext{ceu}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{m}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} habitus \edtext{priuatione}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}mv} | priuationem \textit{M\textsuperscript{a}} | priuationis \textit{P\textsuperscript{p}P\textsuperscript{u}}}}. \edtext{Ordinatum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | Ordinatus \textit{mv} | Ordinatam \textit{G\textsuperscript{u}P\textsuperscript{q}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{o}}}} enim habet \edtext{rationem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | ratione \textit{V\textsuperscript{a}}}} equalitatis, \edtext{inordinatum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | inordinatam \textit{G\textsuperscript{u}P\textsuperscript{q}} | id est ordinatus \textit{mv}}} uero \edtext{inequalitatis}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}V\textsuperscript{a}mv} | rationem inequalitatis \textit{π} | i\expan{n} car\expan{dinalita}tis \textit{(orig. \textup{ī car\textsuperscript{tis}})} \textit{V\textsuperscript{b}}}}. Omne \edtext{autem}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | enim \textit{G\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{z}}}} \edtext{inequale}{\Cfootnote[nosep]{\textit{αλπmv}}} \edtext{reducitur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | redditur \textit{V\textsuperscript{a}}}} ad equale, \edtext{ut}{\Cfootnote[nosep]{\textit{κ} | sicut \textit{απmv}}} \edtext{ad}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} primum et perfectum, \edtext{ut}{\Cfootnote[nosep]{\textit{ακπ} | et \textit{mv}}} \edtext{probatum est}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | probant \textit{απM\textsuperscript{a}mv}}} arismetrici et musici. Et ideo concluditur quod \textit{naturaliter magis \edtext{debeamus gaudere}{\Cfootnote[nosep]{\textit{ακmv} | debemus gaudere \textit{π}}} rithimo et \edtext{iocundari}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | iocundiori \textit{P\textsuperscript{z}} | iocunditati \textit{P\textsuperscript{x}V\textsuperscript{z}}}}, \edtext{tanquam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv}}} ordinato.} +\pend + +\pstart +\textbf{5} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{SIGNUM AUTEM.} Declarat \edtext{id}{\Cfootnote[nosep]{\textit{βE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}mv} | illud \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{signo}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}} | 2° \textit{V\textsuperscript{a}mv} | 2º signo \textit{M\textsuperscript{a}}}} dicens quod \textit{ \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{a}V\textsuperscript{b}mv}}} signum \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} \edtext{regimine}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | rithimo \textit{G\textsuperscript{u}}}} \edtext{vite}{\Cfootnote[nosep]{\textit{βγκmv} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{sumitur}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} tale, quia \edtext{nos}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | non \textit{V\textsuperscript{a}}}} \edtext{exercitantes}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | \gap{}.\gap{} \textit{G\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} \edtext{laborantes bibentesque}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | laborantesque bibentes \textit{P\textsuperscript{p}} | elaborantes bibentesque \textit{P\textsuperscript{z}} | laborantes et bibentes \textit{V\textsuperscript{z}}}} \edtext{et}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}} | ac \textit{βE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | atque \textit{V\textsuperscript{b}}}} \edtext{comedentes}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv}}} \edtext{conmensurate}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}mv} | mensurate \textit{V\textsuperscript{o}P\textsuperscript{u}}}} \edtext{et}{\Cfootnote[nosep]{\textit{βγκG\textsuperscript{u}mv} | ac \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} ordinate,} ‘ \edtext{ut precipit }{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | precipit \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} \textit{regimen} \edtext{galeni}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}mv} | caloris \textit{κ}}} \textit{ \edtext{sanatium}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}} | sanitatem \textit{π}}} },\edtext{}{\Afootnote[nosep]{Gal. \textit{De san. tu.} V .2}}’ \textit{saluamus et augmentamus \edtext{nostram naturam siue complexionem}{\Cfootnote[nosep]{\textit{γN\textsuperscript{u}mv} | naturam nostram siue complexionem \textit{λπ} | naturamque nostram siue complexionem \textit{E\textsuperscript{a}} | nostram siue coniunctionem \textit{P\textsuperscript{x}} | nostram complexionem siue naturam \textit{P\textsuperscript{y}}}}, \edtext{quantum}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} ad corpus magis \edtext{et virtutem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}N\textsuperscript{u}V\textsuperscript{b}mv} | ad virtutem \textit{P\textsuperscript{y}} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{quo ad animam plus. Per oppositum uero \edtext{cum}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | causa \textit{P\textsuperscript{z}}}} indebite \edtext{ac}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{G\textsuperscript{u}}}} inordinate vtimur}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{regimine sanitatis}{\Cfootnote[nosep]{\textit{ακmv} | regimine \textit{π}}} corrumpimus \edtext{ac}{\Cfootnote[nosep]{\textit{ακmv} | et \textit{π}}} stupefacimus \edtext{naturam nostram}{\Cfootnote[nosep]{\textit{βκmv} | nostram naturam \textit{γ} | naturam \textit{πE\textsuperscript{a}}}} \edtext{et}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}mv} | ac \textit{γ}}} virtutem.} \edtext{Quod}{\Cfootnote[nosep]{\textit{βγκπmv} | Quia \textit{E\textsuperscript{a}}}} \edtext{ostenditur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | ostendit \textit{V\textsuperscript{a}}}} \edtext{quia}{\Cfootnote[nosep]{\textit{αλπmv} | quam \textit{P\textsuperscript{x}}}} \textit{ \edtext{egritudines}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | egritudinales \textit{P\textsuperscript{y}}}} \edtext{sunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | serui \textit{V\textsuperscript{o}}}} motus cuiusdam \edtext{ordinationis}{\Cfootnote[nosep]{\textit{ακmv} | inordinationis \textit{π}}} et \edtext{concursus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | utrisque \textit{P\textsuperscript{z}}}} corporis \edtext{nostri}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} non secundum naturam} \edtext{uerum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | sed \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv}}} preter \edtext{naturam existentis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | naturam existentes \textit{V\textsuperscript{b}} | naturam existentem \textit{P\textsuperscript{z}} | naturas \textit{P\textsuperscript{y}}}}. \edtext{Quomodo}{\Cfootnote[nosep]{\textit{κV\textsuperscript{a}} | Quomodo autem \textit{βπE\textsuperscript{a}V\textsuperscript{b}} | Quomodo autem quod \textit{mv}}} ‘egritudo sit motus \edtext{ostensum differentia 7a}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | ostensum est differentia 7 \textit{E\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{a}mv} | ostensum differentia 7a alia \textit{βV\textsuperscript{b}} | uisum est prima \textit{π}}} \edtext{problemate quarto.}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quarto problemate. \textit{P\textsuperscript{p}}}} \edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} VII .4 , 886b ll. 5–6}}’ +\pend + +\pstart +\textbf{6} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{CONSONANTIA.}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | CONSONANTIAM. \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}}}} } Assignat tertio3am. causam \edtext{delectationis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | de delectatione \textit{P\textsuperscript{p}}}} consonantie, dicens \edtext{causam huius}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | huius causam \textit{V\textsuperscript{z}} | causam huiusmodi \textit{γG\textsuperscript{u}P\textsuperscript{q}mv} | causam \textit{P\textsuperscript{a}V\textsuperscript{c}}}} esse, \edtext{quare}{\Cfootnote[nosep]{\textit{αλπmv} | quia \textit{P\textsuperscript{x}}}} \textit{ \edtext{gaudeamus}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | gaudemus \textit{G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}}}} consonantia, quia ipsa \edtext{causatur}{\Cfootnote[nosep]{\textit{ακπ} | cantatur \textit{mv}}} ex \edtext{coniunctione}{\Cfootnote[nosep]{\textit{αλπmv} | coniectione \textit{P\textsuperscript{x}}}} \edtext{contrariorum}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | conexorum \textit{V\textsuperscript{a}}}} habentium proportionem ad inuicem secundum \edtext{acuitatem et grauitatem}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | grauitatem et acuitatem \textit{V\textsuperscript{a}}}} }. \edtext{Confranguntur}{\Cfootnote[nosep]{\textit{βλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Confrangantur \textit{P\textsuperscript{x}V\textsuperscript{a}} | Confrangitur \textit{P\textsuperscript{z}} | Cum frangantur \textit{V\textsuperscript{b}}}} \edtext{enim}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | enim ad inuicem \textit{V\textsuperscript{z}}}} oppositorum excellentie \edtext{ita}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} ut ex eis resultet vnum medium \edtext{contemperatum}{\Cfootnote[nosep]{\textit{κπN\textsuperscript{u}} | contemperamentum \textit{V\textsuperscript{b}mv} | contemperatiuum \textit{P\textsuperscript{y}} | temperatum \textit{V\textsuperscript{a}}}} \edtext{ac}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} proportionatum extremis, \edtext{ceu}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{o}} | seu \surplus{seu} \textit{V\textsuperscript{m}} | Sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} opposita \edtext{ostendunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ostendit \textit{P\textsuperscript{z}}}} contrariorum excellentium in \edtext{copulatione}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} ad inuicem \edtext{qualitatum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | qualitatis \textit{G\textsuperscript{u}P\textsuperscript{q}}}}. \textit{In \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{a}V\textsuperscript{b}mv} | hac \textit{P\textsuperscript{p}}}} autem proportione \edtext{copulationis}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv} | complexionis \textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}}}} \edtext{saluatur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | seruatur \textit{P\textsuperscript{p}}}} \edtext{ordinatio}{\Cfootnote[nosep]{\textit{αλπmv} | inordinatio \textit{P\textsuperscript{x}}}}, que naturaliter \edtext{ \edtext{delectabilis existit}{\Cfootnote[nosep]{\textit{βγλmv} | est delectabilis \textit{π} | delectabilis \textit{E\textsuperscript{a}}}}.}{\Cfootnote[nosep]{\textit{απmv} | delectabilis \textit{P\textsuperscript{x}}}} } \edtext{Quod autem hoc sit delectabile}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{P\textsuperscript{x}}}} ostenditur quoniam \edtext{habens}{\Cfootnote[nosep]{\textit{αλπmv} | hiis \textit{P\textsuperscript{x}}}} consonantiam est \edtext{complexionatum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv}}} \edtext{ \edtext{seu}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ceu \textit{P\textsuperscript{z}} | siue \textit{V\textsuperscript{b}}}} mixtum,}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \textit{ \edtext{omne autem \edtext{complexionatum}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{b}mv} | complexionatum et mixtum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{est \edtext{delectabilius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | delectabilis \textit{mv}}} quam \edtext{incomplexionatum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | in conmixtum \textit{G\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{uel}{\Cfootnote[nosep]{\textit{βγP\textsuperscript{x}mv} | seu \textit{λE\textsuperscript{a}} | et \textit{π}}} simplex, aliter tamen et aliter,} quoniam multo magis est delectabile \edtext{cum in simplicibus}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cum simplicibus \textit{P\textsuperscript{y}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{G\textsuperscript{u}} | id est \textit{P\textsuperscript{x}} | \textit{om}. \textit{P\textsuperscript{u}}}} in elementis primis remaneant \edtext{excellentie}{\Cfootnote[nosep]{\textit{βγκπmv} | \textit{om}. \textit{E\textsuperscript{a}}}}, in \edtext{complexionatis}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | conmixtis \textit{G\textsuperscript{u}}}} \edtext{autem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aut \textit{P\textsuperscript{q}P\textsuperscript{u}} | vero \textit{P\textsuperscript{p}}}} \edtext{consurgunt}{\Cfootnote[nosep]{\textit{γκmv} | confringantur \textit{βE\textsuperscript{a}} | refranguntur \textit{π}}} et ad medium \edtext{reducte sunt}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}m} | sunt reducte \textit{β} | deducte sunt \textit{V\textsuperscript{a}} | ducte sunt \textit{P\textsuperscript{u}}}}. +\pend + +\pstart +\textbf{7} \edtext{}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{QUAMUIS.} Remouet \edtext{2° dubitationem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | dubium \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, quia crederet aliquis \edtext{eo quod}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | quod \textit{M\textsuperscript{a}} | quia \textit{V\textsuperscript{a}}}} complexionatum compositum est ex \edtext{vtrisque}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | utique \textit{V\textsuperscript{a}}}} \edtext{ \edtext{extremorum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | postrimorum \textit{P\textsuperscript{p}}}} \edtext{non}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{posse}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}V\textsuperscript{a}mv} | posset \textit{V\textsuperscript{b}}}} delectabile fore. \edtext{Quod}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}N\textsuperscript{u}mv} | Et \textit{P\textsuperscript{y}}}} remouet, dicens}{\Cfootnote[nosep]{\textit{απV\textsuperscript{b}mv} | \textit{om}. \textit{κ}}} \textit{ \edtext{ \edtext{quodlibet}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | quod \textit{G\textsuperscript{u}} | quia licet \textit{P\textsuperscript{u}}}} \edtext{sit complexionatum}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | si complexionatum \textit{G\textsuperscript{u}} | complexionatum \textit{N\textsuperscript{u}} | complexionatum sit compositum \textit{P\textsuperscript{y}}}} ex utrisque}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} \edtext{extremorum excellentiis}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | excellentiis extremorum \textit{V\textsuperscript{z}} | extremorum excellentibus \textit{P\textsuperscript{p}P\textsuperscript{u}} | extremorum \surplus{non posse delectabile fore} excellentiis \textit{P\textsuperscript{y}}}} \edtext{constitutum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | constitutis \textit{P\textsuperscript{z}}}}.} \edtext{Nichilominus}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} tamen est \edtext{delectabile}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | delectabiliter \textit{P\textsuperscript{z}}}}, quoniam ipsum \edtext{constituitur}{\Cfootnote[nosep]{\textit{βγκπmv} | constitutum \textit{E\textsuperscript{a}}}} ex \edtext{contrariis et inequalibus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | inequalibus et contrariis \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, et non ex \edtext{omnino}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}} | non \textit{V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} similibus et equalibus, \edtext{sic}{\Cfootnote[nosep]{\textit{αλπmv} | sicut \textit{P\textsuperscript{x}}}} enim non \edtext{posset}{\Cfootnote[nosep]{\textit{αλ} | possunt \textit{P\textsuperscript{x}} | potest \textit{πmv}}} adeo \edtext{mouere}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | moue \textit{P\textsuperscript{z}}}}. \edtext{Et}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} ideo \edtext{thimoteus}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}mv}}} \edtext{consonantiam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | ponuit consonantiam \textit{P\textsuperscript{y}}}} fieri \edtext{ait ex dissimilibus}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}mv} | ex dissimilibus ait ayt \textit{G\textsuperscript{u}P\textsuperscript{q}} | aut ex dissimilibus \textit{E\textsuperscript{a}P\textsuperscript{z}} | ut ex similibus \textit{V\textsuperscript{m}} | ex dissimilibus \textit{P\textsuperscript{x}}}} in vnam et \edtext{eandem}{\Cfootnote[nosep]{\textit{αλπmv} | eadem \textit{P\textsuperscript{x}}}} uocem \edtext{uenientibus}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | euenientibus \textit{V\textsuperscript{b}}}}, \edtext{nam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}N\textsuperscript{u}mv} | non \textit{P\textsuperscript{y}}}} in uocibus que nulla equalitate discordant \edtext{nulla}{\Cfootnote[nosep]{\textit{βγκπmv} | in id \textit{E\textsuperscript{a}}}} \edtext{omnino}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{b}mv} | enim \textit{V\textsuperscript{a}}}} \edtext{extat}{\Cfootnote[nosep]{\textit{βγM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | existit \textit{G\textsuperscript{u}P\textsuperscript{q}}}} consonantia, \edtext{cum ea \edtext{sit}{\Cfootnote[nosep]{\textit{βλπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} ut tactum \edtext{est}{\Cfootnote[nosep]{\textit{λγπmv} | \textit{om}. \textit{βE\textsuperscript{a}}}} dissimilium inter se uocum}{\Cfootnote[nosep]{\textit{αλπmv} | sed dissimilitudo. neque similiter si acutum iungatur \textit{P\textsuperscript{x}}}} \edtext{in vnum}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{redacta}{\Cfootnote[nosep]{\textit{αλπmv} | reducta \textit{P\textsuperscript{x}}}} concordia. Si enim grauis graui misceatur, nulla \edtext{fit}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{z}V\textsuperscript{o}mv} | sit \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} consonantia sed dissimilitudo, \edtext{neque similiter si}{\Cfootnote[nosep]{\textit{ακmv} | similiter nec si \textit{G\textsuperscript{u}} | si autem similiter \textit{P\textsuperscript{p}} | ne similiter si \textit{P\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{o}}}} acutum \edtext{iungatur}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | coniungatur \textit{V\textsuperscript{b}}}} \edtext{acuto}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | acuta \textit{P\textsuperscript{p}}}}. Plato \edtext{siquidem}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{uoluit taliter consonantiam}{\Cfootnote[nosep]{\textit{N\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}mv} | uoluit talem consonantiam \textit{λ} | uoluit taliter consonantia \textit{E\textsuperscript{a}V\textsuperscript{a}} | uoluit dicere taliter consonantiam \textit{P\textsuperscript{y}} | uoluit tradere taliter consonantiam \textit{π}}} in \edtext{aure}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aere \textit{G\textsuperscript{u}} | autem \textit{P\textsuperscript{x}}}} \edtext{causari}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | causare \textit{P\textsuperscript{p}V\textsuperscript{a}}}}, \edtext{necesse}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | necessario \textit{P\textsuperscript{z}} | uocem \textit{P\textsuperscript{y}}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quidam \textit{P\textsuperscript{p}}}} \edtext{ait}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} sonum \edtext{uelociorem}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}N\textsuperscript{u}v} | uelocem tunc \textit{P\textsuperscript{x}}}} \edtext{esse}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | esse et \textit{λ}}} acutiorem, qui cum precesserit \edtext{grauem}{\Cfootnote[nosep]{\textit{ακπ} | graue \textit{mv}}} ingreditur \edtext{celeriter}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}mv}}} \edtext{in aurem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | aurem \textit{V\textsuperscript{m}} | maiorem \textit{P\textsuperscript{z}}}} ipsius \edtext{ledens}{\Cfootnote[nosep]{\textit{αλπmv}}} extremitatem \edtext{intrinsecam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}. Et ideo \edtext{quasi}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quia \textit{G\textsuperscript{u}}}} pulsus \edtext{cum tanto}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}N\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | cum canto \textit{P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | a tanto \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{motu}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | modi \textit{P\textsuperscript{p}}}} \edtext{retro reuertitur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | reuertitur \textit{P\textsuperscript{p}} | retrouertitur \textit{βγM\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{z}}}}, et quia \edtext{iam}{\Cfootnote[nosep]{\textit{βγκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ipse \textit{G\textsuperscript{u}P\textsuperscript{q}} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{pigrescit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} exire, obuiat graui \edtext{subintranti}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | superintranti \textit{V\textsuperscript{o}}}} et sibi \edtext{commiscetur}{\Cfootnote[nosep]{\textit{αλπmv} | commiscere \textit{P\textsuperscript{x}}}} \edtext{consonantiam}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | consonantias \textit{P\textsuperscript{z}} | consonantia \textit{V\textsuperscript{b}}}} \edtext{constituens}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}P\textsuperscript{y}mv} | consti\textit{deest} \textit{N\textsuperscript{u}}}} \edtext{musicalem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | musicales \textit{P\textsuperscript{z}}}}. \edtext{Id}{\Cfootnote[nosep]{\textit{αλπmv} | Illud \textit{P\textsuperscript{x}}}} tamen \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} \edtext{visum est}{\Cfootnote[nosep]{\textit{βκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uisum et \textit{E\textsuperscript{a}} | visum \textit{G\textsuperscript{u}P\textsuperscript{y}} | dictum est \textit{P\textsuperscript{p}}}} dictis non \edtext{conuenit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | continet \textit{P\textsuperscript{z}}}} \edtext{thimotei}{\Cfootnote[nosep]{\textit{mv}}} . \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 39m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Trigesimumnonum problema}\label{edition-text book-19a part39}}{\lemma{Trigesimumnonum + problema} \Cfootnote[nosep]{\textit{γmv} | «39m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{trigesimum nonum:} Trigesimumnonum. \textit{P\textsuperscript{y}} | 38m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DELECTABILIUS}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID DELECTABILIUS EST SECUNDUM CONSONANTIAM EO QUOD EST UNIUS UOCIS? \textsuperscript{2}AUT ET ANTIFONUM QUIDEM CONSONUM EST DYAPASON? EX PUERIS ENIM IUUENIBUS, ET NUMERUS FIT ANTIFONUM, QUI DISTANT COMMUNIS SICUT NITE AD YPATEM. CONSONANTIA AUTEM OMNIS DELECTABILIUS SIMPLICI SONO, PER QUE AUTEM DICTUM EST, ET HORUM DYAPASON DELECTABILISSIMA QUIDEM QUAM UNIUS SONI EST SIMPLICEM HABET SONUM. ORGANIZANT AUTEM IN DYAPASON CONSONANTIA. \textsuperscript{3}QUIA QUEMADMODUM IN METRIS PEDES HABENT AD SE IPSOS RATIONEM EQUALEM AD EQUALEM, AUT DUO AD UNUM, AUT ALIQUEM ALIUM, \textsuperscript{4}ET ITA IN CONSONANTIA SONI PROPORTIONEM HABENT MOTUS AD SE IPSOS. \textsuperscript{5}ALIARUM AUTEM CONSONANTIARUM IMPERFECTE, QUE ALTERIUS REUERSIUE SUNT IN MEDIUM FINIUNT, PROPTER QUOD POTENTIA NON EQUALES SUNT. EXISTENTES AUTEM INEQUALES PER CORRUPTIONEM SENSUI. QUEMADMODUM IN ROTIS IN DISSOLUENDO MAIUS SALTANS SONANTIBUS EST. \textsuperscript{6}AMPLIUS YPATE ACCIDIT EUNDEM FINEM PERIODORUM, QUI SUNT IN SONIS, HABERE; SECUNDA AUTEM NEATIS ICTUS AERIS YPATE EST. FINIENS AUTEM IN IDEM, NON IDEM FACIENTIBUS UNUM ET COMMUNE OPUS ACCIDIT FIERI, QUEMADMODUM SONANTIBUS SUB CANTU. ETENIM HII ALIA NON PARITER FISTULANTUR, SI IN IDEM CONUERTANT DELECTANT MAGIS FINE QUAM CONTRISTANT DIFFERENTIIS QUE SUNT AD FINEM, IN EO QUOD FIT EX DIFFERENTIBUS COMMUNE DELECTABILISSIMUM EX DYAPASON. ORGANIZANT AUTEM EX CONTRARIIS UOCIBUS; PROPTER HOC IN DYAPASON ORGANIZANT \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema .39m. etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} cantus et vniuersaliter sonus, existens secundum consonantiam, que est \edtext{copulatio}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}mv} | compositio \textit{P\textsuperscript{y}}}} quedam \edtext{suauem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | suaue \textit{V\textsuperscript{a}} | consuauem \textit{G\textsuperscript{u}}}} et mixtum reddens sonum, \edtext{delectabilior}{\Cfootnote[nosep]{\textit{αλπmv}}} est quam cantus et \edtext{omnino sonus qui}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | sonus qui omnino \textit{V\textsuperscript{a}} | vniversaliter sonus qui \textit{P\textsuperscript{p}} | non sonus qui \textit{P\textsuperscript{y}}}} fuerit vnius uocis et percussionis}, et uniuersaliter dyapason ad \edtext{alias}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | illas \textit{P\textsuperscript{z}}}} consonantias? +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}}}} } Soluit et primo assignat \edtext{causam vnam}{\Cfootnote[nosep]{\textit{ακmv} | vnam causam \textit{π}}}, secundo \edtext{alteram}{\Cfootnote[nosep]{\textit{ακmv} | aliam \textit{π}}} uel \edtext{priorem}{\Cfootnote[nosep]{\textit{ακmv} | primam \textit{π}}} confirmat. \edtext{secunda}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | ibi \textit{πV\textsuperscript{a}} | ibi secunda \textit{V\textsuperscript{b}} | secunda ibi \textit{mv}}} \textit{AMPLIUS}. Adhuc \edtext{prius dat causam}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | primo dat causam \textit{πV\textsuperscript{z}} | dat causam \textit{V\textsuperscript{a}}}} prime partis, \edtext{dicens}{\Cfootnote[nosep]{\textit{κP\textsuperscript{z}} | dicens primo \textit{αP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | primo dicens \textit{G\textsuperscript{u}}}} \edtext{id}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{z}mv} | illud \textit{P\textsuperscript{x}} | ideo \textit{P\textsuperscript{z}V\textsuperscript{m}} | hoc \textit{γ} | id ideo \textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}}}} esse quoniam \textit{dyapason est \edtext{antiphonum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | archifonum \textit{V\textsuperscript{b}} | archisonum \textit{V\textsuperscript{a}mv}}} \edtext{quoddam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | quiddam \textit{P\textsuperscript{y}}}} \edtext{consonum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv} | sonum \textit{V\textsuperscript{m}} | cum sonum \textit{P\textsuperscript{u}} | cum sonu \textit{V\textsuperscript{o}}}}.} \edtext{Secundum enim ipsam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | Secundum ipsam enim \textit{G\textsuperscript{u}} | Enim secundum ipsam \textit{V\textsuperscript{a}}}} \edtext{solam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | solum \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{fit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | sit \textit{G\textsuperscript{u}mv}}} \edtext{antiphonizare}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}}, ut \edtext{apparuit}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | apparebit \textit{πE\textsuperscript{a}}}}, et \edtext{organizare}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | organizare \surplus{ut apparuit et organizare} \textit{V\textsuperscript{m}} | agonizare \textit{P\textsuperscript{z}}}} cum sit ex \edtext{pluribus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{sonis uel uocibus consonantibus}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | vocibus et consonantibus sonis \textit{G\textsuperscript{u}} | sonis uel uocibus contrasonantibus \textit{P\textsuperscript{y}P\textsuperscript{z}}}} \edtext{coaptata}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | adaptata \textit{λ}}}. Ipsa \edtext{enim}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{q}mv} | enim est \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} ut dictum \edtext{est}{\Cfootnote[nosep]{\textit{ακmv} | fuit \textit{π}}} \edtext{optima}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | optima est \textit{λ}}} consonantiarum, \edtext{ac}{\Cfootnote[nosep]{\textit{ακmv} | et \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | quia \textit{P\textsuperscript{z}}}} \textit{suauissima ex uocibus \edtext{acutis puerorum}{\Cfootnote[nosep]{\textit{ακmv} | puerorum acutis \textit{π}}} et grauibus iuuenum consurgit. Fit enim \edtext{numerus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | unus \textit{P\textsuperscript{z}}}} \edtext{quidam}{\Cfootnote[nosep]{\textit{ακmv} | quidem \textit{π}}} et proportio \edtext{consonum}{\Cfootnote[nosep]{\textit{αλπmv} | sonum \textit{P\textsuperscript{x}}}} reddens \edtext{antiphonum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}}. \edtext{Alias}{\Cfootnote[nosep]{\textit{V\textsuperscript{b}} | Alii \textit{P\textsuperscript{p}} | Aliquando \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | Aliter \textit{P\textsuperscript{x}} | Uel \textit{V\textsuperscript{a}}}} \edtext{et}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | et cetera \textit{V\textsuperscript{z}} | etiam \textit{π}}} \edtext{viris fit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | fit uiris \textit{π} | iuris fit \textit{V\textsuperscript{a}} | uiris \textit{P\textsuperscript{y}}}} et \edtext{tunc}{\Cfootnote[nosep]{\textit{αλπmv} | cum \textit{P\textsuperscript{x}}}} iuuenibus \edtext{ueniat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ueniet \textit{P\textsuperscript{z}}}} \edtext{indeterminatio}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}} | in determinationem \textit{απM\textsuperscript{a}V\textsuperscript{z}mv}}} \edtext{de li}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | de lii \textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}mv} | de\expan{lectabi}li \textit{(orig. \textup{de\textsuperscript{li}})} \textit{P\textsuperscript{x}} | ly \textit{P\textsuperscript{u}}}} pueris, \edtext{prior}{\Cfootnote[nosep]{\textit{βγκπmv} | prius prior \textit{E\textsuperscript{a}}}} tamen \edtext{scriptura}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | scriptura tamen \textit{P\textsuperscript{z}}}} melior. Qui \edtext{siquidem}{\Cfootnote[nosep]{\textit{ακmv} | sic quidem sit \textit{π}}} \edtext{differunt}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | differenter \textit{P\textsuperscript{z}}}} \edtext{ab}{\Cfootnote[nosep]{\textit{κγE\textsuperscript{a}G\textsuperscript{u}m} | ad \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}v}}} inuicem ratione \edtext{acuitatis et grauitatis}{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}mv} | grauitatis et acuitatis \textit{P\textsuperscript{x}P\textsuperscript{y}}}} \edtext{uocis}{\Cfootnote[nosep]{\textit{βπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}mv} | u[?]as \textit{V\textsuperscript{b}} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{acquisite}{\Cfootnote[nosep]{\textit{αλπmv} | acquisita \textit{P\textsuperscript{x}}}} \edtext{secundum}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | sed \textit{πE\textsuperscript{a}}}} tempus, quanta est differentia \edtext{communis uel vniversalis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | universalis uel communis \textit{V\textsuperscript{a}} | communis et vniversalis \textit{π}}} et ultime \edtext{ad ypatem communem}{\Cfootnote[nosep]{\textit{απmv} | dyapente communem \textit{λ} | dyapente causam \textit{P\textsuperscript{x}}}} \edtext{supremam}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}mv} | supremamque \textit{M\textsuperscript{a}} | extremam \textit{P\textsuperscript{y}}}}.} Que quidem \edtext{due}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}} | secunde \textit{V\textsuperscript{b}mv}}} corde tacte reddunt consonantiam delectabilem, cum sonus \edtext{earum}{\Cfootnote[nosep]{\textit{αλπmv} | eorum \textit{P\textsuperscript{x}}}} sit compositus. \textit{Omnis autem consonantia \edtext{delectabilior}{\Cfootnote[nosep]{\textit{ακmv} | delectabilis \textit{π}}} \edtext{est}{\Cfootnote[nosep]{\textit{αλmv} | est magis \textit{π} | \textit{om}. \textit{P\textsuperscript{x}}}} quam \edtext{sonus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} \edtext{simplex}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}}. Et ideo dictum \edtext{est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}}}} prius quod dyapason de numero \edtext{sonorum}{\Cfootnote[nosep]{\textit{ακmv} | consonantiarum \textit{π}}} est delectabilissima \edtext{per respectum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | per respectu \textit{V\textsuperscript{m}} | et per respectum \textit{P\textsuperscript{z}} | in respectu \textit{P\textsuperscript{p}}}} ad \edtext{sonos}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} simplices \edtext{et}{\Cfootnote[nosep]{\textit{βκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{o}} | ut \textit{V\textsuperscript{b}}}} \edtext{vnum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vnam \textit{G\textsuperscript{u}}}} tantum. \edtext{Unde}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} secundum \edtext{eam}{\Cfootnote[nosep]{\textit{βγκπmv} | enim \textit{E\textsuperscript{a}}}} \edtext{solum}{\Cfootnote[nosep]{\textit{αλπ} | sonum \textit{mv}}} \edtext{ut prescriptum est}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}} | prescriptum est \textit{P\textsuperscript{x}} | prescriptum \textit{P\textsuperscript{y}} | ut scriptum est \textit{γmv}}} \edtext{organizare}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{z}mv}}} accidit} \edtext{.xviii.}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | 18° \textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | hiis \textit{G\textsuperscript{u}} | igitur \textit{P\textsuperscript{z}}}}, quod \edtext{in alia}{\Cfootnote[nosep]{\textit{γκπN\textsuperscript{u}mv} | nulla \textit{E\textsuperscript{a}}}} consonantiarum \edtext{non}{\Cfootnote[nosep]{\textit{βκπE\textsuperscript{a}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} contingit. Dicit autem \textit{ \edtext{communis}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | numerus \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}} } \edtext{quia}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | quod \textit{E\textsuperscript{a}P\textsuperscript{u}}}} \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ypatem \textit{M\textsuperscript{a}}}} et nete \edtext{sicut}{\Cfootnote[nosep]{\textit{αλπmv} | sint \textit{P\textsuperscript{x}}}} \edtext{et}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | est \textit{V\textsuperscript{z}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{aliarum}{\Cfootnote[nosep]{\textit{ακmv} | aliorum \textit{π}}} quedam \edtext{preponuntur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | proponuntur \textit{P\textsuperscript{z}}}} et alie supponuntur, \edtext{repetuntur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | repetunt \textit{P\textsuperscript{z}}}} enim \edtext{cum}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} determinatione \edtext{cum}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} plures \edtext{septem}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}mv} | enim \textit{P\textsuperscript{x}} | id est \textit{P\textsuperscript{y}}}} ponuntur corde ut \edtext{policorda}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}} | policorde \textit{P\textsuperscript{z}}}} \edtext{edocent}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv} | edocet \textit{V\textsuperscript{z}} | edocentur \textit{V\textsuperscript{o}}}} \edtext{\hyperref[Bo]{boecii}}{\Cfootnote[nosep]{\textit{γV\textsuperscript{z}mv} | boni \textit{M\textsuperscript{a}V\textsuperscript{m}} | uero \textit{P\textsuperscript{x}} | .10 \textit{P\textsuperscript{y}} | \textit{om}. \textit{πE\textsuperscript{a}}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{QUIA QUEMADMODUM.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}} | QUEMADMODUM. \textit{mv} | QUARE QUODDAM. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} } Declarat \edtext{deinde id}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{m}mv} | id deinde \textit{G\textsuperscript{u}} | illud deinde \textit{P\textsuperscript{p}P\textsuperscript{u}} | demum id \textit{P\textsuperscript{x}} | id demum \textit{P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | dictum id \textit{V\textsuperscript{b}} | deinde \textit{P\textsuperscript{y}}}}, dicens hoc esse \textit{quia \edtext{sicut}{\Cfootnote[nosep]{\textit{αλπmv} | sint \textit{P\textsuperscript{x}}}} in carminibus pedes \edtext{obtinent}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{z}mv} | optinet \textit{P\textsuperscript{x}} | oportunt \textit{V\textsuperscript{o}}}} \edtext{debitam}{\Cfootnote[nosep]{\textit{αλπmv} | determinatam \textit{P\textsuperscript{x}}}} proportionem ad inuicem, ut sit proportio aut equalis ad \edtext{equale}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{z}mv} | equalem \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}} | equalia \textit{G\textsuperscript{u}}}} }, ut \edtext{dicatur}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | dicitur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} in \edtext{dactilo}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv}}} \edtext{constante ex tribus sillabis equalium}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | ex tribus sillabis equalium constante \textit{P\textsuperscript{p}} | constantem ex tribus sillabis equalium \textit{P\textsuperscript{x}} | constare ex tribus sillabis equalium \textit{γmv}}} \edtext{}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | non \textit{V\textsuperscript{a}} | ut \textit{P\textsuperscript{p}P\textsuperscript{u}} | et \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{tandem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | tamen \textit{V\textsuperscript{a}} | tantumdem \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} temporum, \edtext{quia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | qui \textit{P\textsuperscript{p}}}} ex prima longa, que \edtext{est}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} duorum temporum, et duabusduobus breuibus, quarum \edtext{alter uterque}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}mv} | alter utram \textit{λ} | alterum utraque \textit{V\textsuperscript{a}} | altera utraque \textit{G\textsuperscript{u}} | ad alter utraque \textit{V\textsuperscript{o}}}} \edtext{vnius}{\Cfootnote[nosep]{\textit{αλπmv} | minus \textit{P\textsuperscript{x}}}}, \edtext{ubi}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | ut \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | et \textit{G\textsuperscript{u}} | nisi \textit{P\textsuperscript{y}}}} \edtext{duodue ad vnumunam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}mv} | unum ad duo \textit{V\textsuperscript{m}} | duo \textit{P\textsuperscript{z}}}} \edtext{comparantur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}} | comparatur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | operantur \textit{V\textsuperscript{b}mv}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | ubi \textit{P\textsuperscript{y}}}} dueduo breues ad \edtext{vnam}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | vnam ut duo breues ad vaiam \textit{V\textsuperscript{a}}}} \edtext{longam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | longam ad alteram breuem \textit{V\textsuperscript{z}}}}, \edtext{uel}{\Cfootnote[nosep]{\textit{αλπmv} | seu \textit{P\textsuperscript{x}}}} econtra, \edtext{ \edtext{ceu}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{y}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{m}} | sicut \textit{P\textsuperscript{x}}}} in \edtext{anapesto}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{m}mv} | apeston uel anapasco \textit{V\textsuperscript{a}}}} huic opposito, uel secundum alium \edtext{quendam}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}mv} | quamdam \textit{V\textsuperscript{m}} | quidem \textit{P\textsuperscript{x}}}} modum sicut \edtext{vna}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{m}mv} | nam \textit{P\textsuperscript{x}}}} \edtext{sillaba}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}mv}}} duorum temporum ad aliam consimilem, \edtext{ceu}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv} | seu \textit{E\textsuperscript{a}}}} \edtext{in}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} spondeo. \textit{ \edtext{Aut}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{m}mv} | An \textit{P\textsuperscript{x}}}} vnam longam \edtext{ad}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}mv} | et \textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}}}} alteram breuem \edtext{uel}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{m}mv} | aut \textit{P\textsuperscript{x}}}} econtra}}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{πV\textsuperscript{z}}}}, \edtext{uelut}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}mv} | ut \textit{λP\textsuperscript{y}} | uel \textit{V\textsuperscript{a}}}} in \edtext{trocheo}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}} \edtext{et}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | uel \textit{V\textsuperscript{m}}}} \edtext{iambo}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | iambico \textit{V\textsuperscript{m}}}}, \edtext{spondeus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | spondeo \textit{G\textsuperscript{u}}}} siquidem \edtext{sono proportionatur}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | proportionatur sono \textit{P\textsuperscript{z}} | sonus proportionatur \textit{P\textsuperscript{x}}}} graui et iuuenum uoci. \edtext{Tribrachus}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{z}} | Tribati \textit{V\textsuperscript{b}} | Tribitus \textit{P\textsuperscript{x}} | Attributus \textit{V\textsuperscript{m}}}} \edtext{uero}{\Cfootnote[nosep]{\textit{αλmv} | quidem \textit{P\textsuperscript{x}} | est \textit{P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{constans ex tribus breuibus}{\Cfootnote[nosep]{\textit{ακmv} | ex tribus breuibus constans \textit{π}}} \edtext{acute}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | acutis \textit{V\textsuperscript{a}}}}, sed \edtext{dactilus}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{anapestus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{trocheus et iambus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | iambus et trocheus \textit{P\textsuperscript{p}}}} \edtext{similantur}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | assimilantur \textit{P\textsuperscript{p}}}} \edtext{uterque}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}} | utraque \textit{λ} | vtrique \textit{αP\textsuperscript{z}mv}}}. \edtext{Similiter}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Sic \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{etiam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}V\textsuperscript{o}mv} | et \textit{P\textsuperscript{z}} | igitur \textit{G\textsuperscript{u}P\textsuperscript{q}} | \textit{om}. \textit{P\textsuperscript{p}}}} pedes quibus \edtext{vtimur}{\Cfootnote[nosep]{\textit{αλπmv} | utuntur \textit{P\textsuperscript{x}}}} diuersa \edtext{optinent}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}}}} \edtext{loca}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} in metro ut visum \edtext{est}{\Cfootnote[nosep]{\textit{γκπmv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}}}} \edtext{20}{\Cfootnote[nosep]{\textit{αλπmv} | 24° \textit{P\textsuperscript{x}}}}. +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ET ITA.} \edtext{Tunc}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | Nunc \textit{mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}}}} applicat ad propositum, \edtext{dicens}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} \textit{ \edtext{eodem modo in \edtext{consonantia}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | consonantiam \textit{γE\textsuperscript{a}mv}}} \edtext{euenire soni}{\Cfootnote[nosep]{\textit{γmv} | eueniet soni \textit{P\textsuperscript{y}} | euenit esoni \textit{κ} | euenire \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | aduenire eodem modo in consonantia \textit{P\textsuperscript{z}}}} et proprie dyapason, nam motus \edtext{sonorum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{causatiui}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | causatur \textit{P\textsuperscript{z}} | cantantium \textit{G\textsuperscript{u}} | cantanti \textit{V\textsuperscript{a}} | cantantiui \textit{M\textsuperscript{a}V\textsuperscript{m}} | cantui \textit{E\textsuperscript{a}} | canti \textit{P\textsuperscript{x}}}} proportionem habent \edtext{ad}{\Cfootnote[nosep]{\textit{κ} | ad se \textit{απmv}}} inuicem.} +\pend + +\pstart +\textbf{5} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{ALIARUM.}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | ALIORUM. \textit{πE\textsuperscript{a}}}} } Αssignat \edtext{secundo}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{πV\textsuperscript{z}}}} \edtext{causam partis alterius}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | causam alterius partis \textit{V\textsuperscript{m}V\textsuperscript{z}} | partem alterius \textit{P\textsuperscript{p}}}}, \edtext{dicens quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}, \textit{ \edtext{de numero aliarum consonantiarum \edtext{ad}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}V\textsuperscript{b}mv} | a \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}}}} dyapason quia sunt alterius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} proportionis ab ea, sunt \edtext{imperfecte}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{u}V\textsuperscript{o}mv}}} }, non enim sunt per \edtext{totum}{\Cfootnote[nosep]{\textit{ακπ} | tonum \textit{mv}}} ambientes \edtext{omnia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | tria \textit{P\textsuperscript{z}}}} signa .vii. uel .viii. \edtext{monocordi}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | monocordia \textit{P\textsuperscript{z}}}} \edtext{prima}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} sicut \edtext{dyapason}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}}. \textit{Sed potius reuersiue facte circa medium terminantur,} \edtext{ut}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | in \textit{E\textsuperscript{a}}}} dyatesseron \edtext{in quartoquarta}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | medio \textit{M\textsuperscript{a}V\textsuperscript{z}}}} \edtext{signo}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | signo et \textit{αP\textsuperscript{z}V\textsuperscript{o}mv}}} dyapente in quinto, ut visum \edtext{est}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}mv} | \textit{om}. \textit{P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}}}} .13°. \edtext{et .32°}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | et 12º \textit{V\textsuperscript{z}} | \textit{om}. \textit{π}}}. \textit{Et ideo non habent virtutem equaliter \edtext{ceu}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{u}P\textsuperscript{y}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}}}} dyapason, \edtext{uerum}{\Cfootnote[nosep]{\textit{αλmv} | sed \textit{π} | dicendum 8m. \textit{P\textsuperscript{x}}}} potius \edtext{inequaliter}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}mv} | in equalitatem \textit{P\textsuperscript{y}} | inequalitantur \textit{V\textsuperscript{m}V\textsuperscript{z}} | inequaliter licantur \textit{P\textsuperscript{x}}}} propter ipsas, \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} sensus \edtext{horret}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}v} | horum \textit{G\textsuperscript{u}} | haberent \textit{P\textsuperscript{z}}}} \edtext{auditus et}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | et auditus \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} corrumpitur.} \edtext{Sunt}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Sicut \textit{G\textsuperscript{u}}}} enim \edtext{respectu}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | respectum \textit{G\textsuperscript{u}P\textsuperscript{y}}}} dyapason \edtext{aspere \edtext{ac}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}mv} | et \textit{G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}}}} \edtext{horride}{\Cfootnote[nosep]{\textit{πP\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}mv}}} }{\Cfootnote[nosep]{\textit{αλπmv} | horride et aspere \textit{P\textsuperscript{x}}}}, quod declarat, quia \textit{sicut accidit \edtext{in rotis}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | rotis \textit{P\textsuperscript{z}} | in dochus \textit{E\textsuperscript{a}}}} cantantibus, \edtext{id est}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | id est in \textit{πP\textsuperscript{y}} | \textit{om}. \textit{V\textsuperscript{a}}}} cantibus \edtext{rotatiuis}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv}}} seu \edtext{conuersis}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}E\textsuperscript{a}mv} | conuersiuis \textit{P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | conuersiuus \textit{V\textsuperscript{a}}}}, \edtext{quod si aliquis}{\Cfootnote[nosep]{\textit{αλmv} | quia si aliquis \textit{P\textsuperscript{x}} | \textit{om}. \textit{π}}} eleuando sonum ultra \edtext{id}{\Cfootnote[nosep]{\textit{αλπmv} | illud \textit{P\textsuperscript{x}}}} quod debet, \edtext{ \edtext{saltem}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | saltare \textit{P\textsuperscript{z}}}} in \edtext{maius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | magis \textit{G\textsuperscript{u}}}} sursum ad aliquas notas \edtext{in}{\Cfootnote[nosep]{\textit{αλπmv} | ad \textit{P\textsuperscript{x}}}} quas \edtext{non}{\Cfootnote[nosep]{\textit{ακmv} | nunc \textit{π}}} debet}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} peruenire, \edtext{accidit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{sonum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} totum dissolui,} ut \edtext{apparet}{\Cfootnote[nosep]{\textit{ακπ} | patet \textit{mv}}} in organis \edtext{ita}{\Cfootnote[nosep]{\textit{ακπ} | \textit{om}. \textit{mv}}} \edtext{et}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | etiam et \textit{P\textsuperscript{y}} | \textit{om}. \textit{V\textsuperscript{a}}}} in aliis \edtext{consonantiis}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | consonantibus \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{ad}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | a \textit{πE\textsuperscript{a}M\textsuperscript{a}} | \textit{om}. \textit{γP\textsuperscript{y}mv}}} dyapason \edtext{contingit}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} suo modo et maxime in dyatesseron, \edtext{uel}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | seu \textit{P\textsuperscript{p}}}} \edtext{rotis}{\Cfootnote[nosep]{\textit{γλπP\textsuperscript{y}mv} | totis \textit{P\textsuperscript{x}}}}, \edtext{id est}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{instrumentis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in instrumentis \textit{P\textsuperscript{p}V\textsuperscript{z}}}} \edtext{illis}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} antiquioribus habentibus duas \edtext{acies}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | animas acies \textit{V\textsuperscript{a}}}} cordarum, \edtext{vnam}{\Cfootnote[nosep]{\textit{γπP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}m} | vna \textit{E\textsuperscript{a}M\textsuperscript{a}v}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{γλπP\textsuperscript{y}mv} | quidam \textit{E\textsuperscript{a}} | siquidem \textit{P\textsuperscript{x}}}} in vno \edtext{laterum}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | latere \textit{γP\textsuperscript{x}P\textsuperscript{z}}}} et reliquam in altero, \edtext{que}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | qui \textit{M\textsuperscript{a}}}} simul manibus tanguntur ambabus. \edtext{Nunc}{\Cfootnote[nosep]{\textit{ακmv} | Non \textit{π}}} autem si \edtext{inequaliter}{\Cfootnote[nosep]{\textit{αλπmv} | equaliter \textit{P\textsuperscript{x}}}} tetigerit eas, magis \edtext{pulsans}{\Cfootnote[nosep]{\textit{ακmv} | pulsans vnam quam aliam vel \textit{π}}} cordas vnius partis quam alterius, \edtext{adulteratur}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | adulterantur \textit{P\textsuperscript{y}} | adultantur \textit{V\textsuperscript{m}}}} \edtext{simphonia}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | symphoni et \textit{P\textsuperscript{y}}}}, primum tamen \edtext{melius et uerius}{\Cfootnote[nosep]{\textit{κ} | melius et uniuersalius \textit{αmv} | vniuersalius et melius \textit{π}}}. Dicit autem \textit{corruptio \edtext{sensui}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | sensuum \textit{V\textsuperscript{b}} | sensus \textit{G\textsuperscript{u}}}} } quia \edtext{dictum est}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | est dictum \textit{λ}}} quod musica non \edtext{solum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{rationi}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}} | rationem \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}mv}}} \edtext{innititur, ut}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | innititur, \textit{E\textsuperscript{a}}}} \edtext{sensit}{\Cfootnote[nosep]{\textit{αλmv} | sensuit \textit{P\textsuperscript{p}} | sensiunt \textit{P\textsuperscript{z}} | sentit \textit{P\textsuperscript{x}} | posuit \textit{G\textsuperscript{u}} | sensui \textit{P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{pictagoras}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | pythagoricis \textit{P\textsuperscript{u}} | pictagorici \textit{P\textsuperscript{z}}}}, \edtext{neque}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}V\textsuperscript{o}mv} | nunc \textit{P\textsuperscript{z}} | sed \textit{P\textsuperscript{u}}}} \edtext{tantummodo}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | tantum \textit{V\textsuperscript{z}}}} sensui, \edtext{sicut}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | sic \textit{P\textsuperscript{y}V\textsuperscript{m}}}} \edtext{aristoxenus}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{o}} | aristotenus \textit{P\textsuperscript{x}mv}}} , sed \edtext{utrumque}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}} | vtrunque \textit{mv} | utroque \textit{V\textsuperscript{m}} | uterque \textit{P\textsuperscript{x}}}} \edtext{contractat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | connatat \textit{V\textsuperscript{o}}}}. +\pend + +\pstart +\textbf{6} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AMPLIUS.} Ponit \edtext{aliam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} solutionem uel magis \edtext{pretactam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | pretactant \textit{P\textsuperscript{y}}}} confirmat et declarat \edtext{dicens}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | dicens quod \textit{V\textsuperscript{m}}}} \textit{ \edtext{rursus}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} in \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ypatem \textit{M\textsuperscript{a}}}} accidere \edtext{quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quod et \textit{P\textsuperscript{p}}}} habeat \edtext{vnum et eundem}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | unum et eiusdem \textit{P\textsuperscript{z}} | et eundum \textit{E\textsuperscript{a}P\textsuperscript{u}} | eundem \textit{P\textsuperscript{p}}}} finem \edtext{omnium}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | omnium \surplus{omnium} \textit{V\textsuperscript{a}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{z}}}} \edtext{peridorum}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}}}} siue \edtext{circuitionum}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | circuitionem \textit{V\textsuperscript{m}}}} existentium in sonis.} In \edtext{ipsa}{\Cfootnote[nosep]{\textit{γP\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{m}} | ipsam \textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{enim}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | eius \textit{P\textsuperscript{z}}}}, \edtext{tanquam}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv}}} \edtext{in}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | \textit{om}. \textit{G\textsuperscript{u}V\textsuperscript{o}}}} \edtext{principaliorem}{\Cfootnote[nosep]{\textit{αλπmv} | priorem \textit{P\textsuperscript{x}}}}, \edtext{terminantur}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}mv} | terminatur \textit{λP\textsuperscript{y}V\textsuperscript{a}}}} uel melius finem \edtext{perydorum}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}}}} id est \edtext{resonationum}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{z}} | resonationem \textit{V\textsuperscript{m}} | resonantium \textit{γmv}}} post \edtext{ictum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | dictum \textit{V\textsuperscript{a}}}} \edtext{remanentium}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | resonantium \textit{πE\textsuperscript{a}}}} diu in aere, quod \edtext{tinnitus}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}} | rinitus \textit{P\textsuperscript{x}}}} \edtext{potest dici}{\Cfootnote[nosep]{\textit{ακmv} | dici potest \textit{π}}}. Et ideo \edtext{vocatur}{\Cfootnote[nosep]{\textit{αλπmv}}} \edtext{magistra}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | nigram \textit{G\textsuperscript{u}}}}, ipsa \edtext{enim}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | eas \textit{P\textsuperscript{y}}}} \edtext{suscipit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | se concipit \textit{P\textsuperscript{z}}}} omnes et obtundit cum eius \edtext{sit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fit \textit{G\textsuperscript{u}}}} \edtext{proprius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | proprium \textit{πV\textsuperscript{a}V\textsuperscript{z}} | prius \textit{P\textsuperscript{y}}}} \edtext{antiphonizare}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | antiphonaria \textit{V\textsuperscript{o}}}} \edtext{ \edtext{et}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}} | atque \textit{αλmv} | ac \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{organizare}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv}}} }{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}}. \textit{Sed secunda corda, \edtext{correspondens}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}mv} | correspondet \textit{V\textsuperscript{a}}}} \edtext{ypati}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ypate \textit{G\textsuperscript{u}}}} per \edtext{oppositum}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | appositum \textit{E\textsuperscript{a}}}} omnino, est \edtext{neatis siue netes uel neatis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv}}}, \edtext{id est}{\Cfootnote[nosep]{\textit{απmv} | siue \textit{κ}}} resonantie \edtext{siue tinitus}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | sumitanter \textit{P\textsuperscript{z}}}}, pretacti.} Dupliciter enim accipitur \edtext{neate}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}} | neatis \textit{P\textsuperscript{z}}}} \edtext{.xlii.}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | 41° \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{apparens}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | apparens et \textit{M\textsuperscript{a}}}}, \edtext{2°}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{πV\textsuperscript{a}}}} \edtext{cuius}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | enim \textit{P\textsuperscript{y}}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quidam \textit{P\textsuperscript{p}}}} \edtext{ictus et}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} sonus \edtext{causatus}{\Cfootnote[nosep]{\textit{V\textsuperscript{b}V\textsuperscript{z}} | cantus \textit{E\textsuperscript{a}V\textsuperscript{o}mv}}} in aere. \textit{ \edtext{In idem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | Et idem \textit{G\textsuperscript{u}} | \textit{om}. \textit{γmv}}} \edtext{finit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | fuit \textit{G\textsuperscript{u}P\textsuperscript{y}} | sunt \textit{P\textsuperscript{z}V\textsuperscript{a}}}} cum sono qui \edtext{fit}{\Cfootnote[nosep]{\textit{π} | fiunt \textit{P\textsuperscript{x}} | fuit \textit{αλmv}}} ab ypate,} ex \edtext{ambabus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | ambobus \textit{γmv} | amborum \textit{π}}} \edtext{enim}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | enim sonis \textit{P\textsuperscript{p}}}} \edtext{consurgit}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | surgit \textit{V\textsuperscript{a}}}}, ut visum \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{sepius in}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}mv} | sepius \textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{simphonia}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}mv}}} dyapason. Et \edtext{merito}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}}, \edtext{quia}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} licet non eundem sonum \edtext{reddant}{\Cfootnote[nosep]{\textit{αλπmv} | reddeant \textit{P\textsuperscript{x}}}} secundum se. \edtext{Ymmo}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}}}} vna acutum \edtext{et}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} altera grauem. \textit{ \edtext{Tandem}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | Tamen \textit{V\textsuperscript{a}} | Et idem \textit{πE\textsuperscript{a}}}} cum ipsarum soni \edtext{coniungantur}{\Cfootnote[nosep]{\textit{γλP\textsuperscript{z}mv} | coniunguntur \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | iungantur \textit{P\textsuperscript{x}}}} ad inuicem, contingit fieri vnum et eundem sonum \edtext{omnifariam}{\Cfootnote[nosep]{\textit{αλπmv} | omnifaria \textit{P\textsuperscript{x}}}}, quemadmodum accidit \edtext{illis}{\Cfootnote[nosep]{\textit{αλπmv} | illi \textit{P\textsuperscript{x}}}} qui sonant instrumenta sub cantu cantantium. Uel quia \edtext{aliqui}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | aliquis \textit{P\textsuperscript{y}}}} \edtext{precinunt}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | precinit \textit{P\textsuperscript{y}} | ponunt et precinunt \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | precipiunt \textit{V\textsuperscript{m}}}} \edtext{et alii subcinunt}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | et aliqui subcinunt \textit{E\textsuperscript{a}} | alii succinunt \textit{P\textsuperscript{y}} | \textit{om}. \textit{G\textsuperscript{u}}}} licet,} \edtext{et}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | \textit{om}. \textit{πP\textsuperscript{y}}}} enim videantur discordare in principio, \edtext{concidunt}{\Cfootnote[nosep]{\textit{λ} | excidunt \textit{P\textsuperscript{x}} | concidunt tamen \textit{απmv}}} in \edtext{finem vnum}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | vnum finem \textit{G\textsuperscript{u}} | fine unum \textit{P\textsuperscript{x}V\textsuperscript{a}}}}. Et \edtext{illud est}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}mv} | id est \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}} | hoc est \textit{π} | idem \textit{V\textsuperscript{a}V\textsuperscript{z}}}} quod subiungitur, \textit{tales \edtext{namque}{\Cfootnote[nosep]{\textit{ακ} | enim \textit{πmv}}} \edtext{non}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | \textit{om}. \textit{C\textsuperscript{a}V\textsuperscript{o}}}} pariter et vna \edtext{fistulantur}{\Cfootnote[nosep]{\textit{κ} | fistulantur et cantant \textit{απmv}}}, sed \edtext{secundum}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{x}P\textsuperscript{z}}}} \edtext{alia et alia}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | aliam et aliam \textit{G\textsuperscript{u}P\textsuperscript{q}} | alia \textit{P\textsuperscript{z}}}}. \edtext{Si tamen}{\Cfootnote[nosep]{\textit{αλmv} | Tamen et \textit{π} | \textit{om}. \textit{P\textsuperscript{x}}}} quamuis \edtext{sint}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | sunt \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}} | sicut \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{m}}}} \edtext{alii}{\Cfootnote[nosep]{\textit{αλπmv} | alteri \textit{P\textsuperscript{x}}}} \edtext{et alteri}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}} | et aliquando \textit{γE\textsuperscript{a}mv} | tamen \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{concurrant}{\Cfootnote[nosep]{\textit{γP\textsuperscript{y}mv} | concurrunt \textit{κπE\textsuperscript{a}}}} \edtext{tandem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | in eundem \textit{P\textsuperscript{y}} | \textit{om}. \textit{π}}} \edtext{fine in vnum}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | in finem vnum \textit{πV\textsuperscript{b}} | finem in vnum \textit{E\textsuperscript{a}V\textsuperscript{a}} | finaliter in vnum \textit{V\textsuperscript{z}} | finem et vnum \textit{P\textsuperscript{y}}}} \edtext{quendam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | quidem \textit{P\textsuperscript{y}} | aliquando \textit{π}}} sonum, magis habent inducere delectationem quam \edtext{tristitiam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | tristitia \textit{V\textsuperscript{m}}}}, propter \edtext{hoc quod}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | quod dicere \textit{V\textsuperscript{a}}}} \edtext{differentie}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | dicere \textit{P\textsuperscript{z}}}} \edtext{seu}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{G\textsuperscript{u}}}} diuersitates que sunt in eis secundum principium reperte \edtext{sopiuntur}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | seperiunt \textit{P\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{y}}}} et concurrunt \edtext{demum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | deinde \textit{P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}}}} ad eundem finem \edtext{siue}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | seu \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{z}}}} terminationem. In eo enim, \edtext{ut}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | quod \textit{G\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{a}}}} \edtext{declaratum est}{\Cfootnote[nosep]{\textit{γκmv} | declaratum \textit{E\textsuperscript{a}P\textsuperscript{y}} | declaratum prius est \textit{π}}} \edtext{antea}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}, \edtext{quod}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{ex}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | et \textit{E\textsuperscript{a}}}} \edtext{differentiis}{\Cfootnote[nosep]{\textit{κ}}} diuersisque \edtext{extremis}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | ex terminis \textit{E\textsuperscript{a}}}} \edtext{efficitur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{vnum}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | vnum et \textit{πE\textsuperscript{a}}}} \edtext{quoddam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | quidem \textit{P\textsuperscript{y}}}} \edtext{commune}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} \edtext{proportionatum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}mv} | proportionaliter \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | proportionabiliter \textit{G\textsuperscript{u}}}}. \edtext{Cum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | Tamen \textit{M\textsuperscript{a}}}} dyapason \edtext{sit}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | fit \textit{G\textsuperscript{u}M\textsuperscript{a}} | sic \textit{P\textsuperscript{y}V\textsuperscript{z}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | huiusmodi \textit{γG\textsuperscript{u}P\textsuperscript{a}mv}}} \edtext{quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quoque \textit{P\textsuperscript{z}}}} \edtext{relinquitur}{\Cfootnote[nosep]{\textit{αλmv} | derelinquitur \textit{π}}} \edtext{ab ea}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{simphonum}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | simplex hominum \textit{P\textsuperscript{z}}}} delectabilissimum \edtext{extat}{\Cfootnote[nosep]{\textit{ακmv} | est \textit{π}}}, quod \edtext{ostenditur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ostendit \textit{V\textsuperscript{a}}}} quia secundum \edtext{eam organizare}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}mv} | organizare eam \textit{V\textsuperscript{a}} | organizare \textit{V\textsuperscript{z}}}} ex \edtext{oppositis}{\Cfootnote[nosep]{\textit{ακmv} | diuersis \textit{π}}} uocibus \edtext{causatur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | cantatur \textit{P\textsuperscript{z}V\textsuperscript{b}}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | in \textit{P\textsuperscript{z}}}} sonis \edtext{tandem in unum}{\Cfootnote[nosep]{\textit{κ} | in vnum tandem \textit{πE\textsuperscript{a}mv} | in unum tamen \textit{V\textsuperscript{a}} | in unum \textit{P\textsuperscript{y}}}} \edtext{redactis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | redactus \textit{P\textsuperscript{z}}}}. Et quia dyapason \edtext{ex}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | in \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | huiusmodi \textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{a}mv}}} \edtext{consistit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | existit \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, ut \edtext{expositum est}{\Cfootnote[nosep]{\textit{κP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | expositum \textit{α} | dictum est \textit{G\textsuperscript{u}P\textsuperscript{p}}}}, \edtext{sepius}{\Cfootnote[nosep]{\textit{κγπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} ideo \edtext{secundum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | per \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{ipsam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | huius \textit{λ}}} dictum est \edtext{solam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}mv} | solum \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} nullamque \edtext{aliarum}{\Cfootnote[nosep]{\textit{αλV\textsuperscript{o}mv} | aliorum \textit{G\textsuperscript{u}} | aliam \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}}}} \edtext{organizari}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}} | organizare \textit{G\textsuperscript{u}P\textsuperscript{p}mv}}},} \edtext{.20. \edtext{problemate}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | partes \textit{P\textsuperscript{x}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}}. +\pend + +\pstart +\textbf{7} \edtext{Nosce}{\Cfootnote[nosep]{\textit{ακπ} | Notandum \textit{mv}}} \edtext{quod}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} sicut se habet uox composita ad simplicem, ita dyapason ad \edtext{reliquas}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | alias \textit{V\textsuperscript{a}}}} consonantias.\edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{z}V\textsuperscript{z}}}} problema 40. et huius quidem expositio sufficiens iam 5to. apparebit parte repetitur uero ut memorie amplius comendetur. +\pend + +\pstart +\edtext{\subsubsection {Quadragesimum problema}\label{edition-text book-19a part40}}{\lemma{Quadragesimum + problema} \Cfootnote[nosep]{\textit{γmv} | «40m» (in mg.) \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | Quadragesimum. \surplus{Quadragesimum problema} \textit{P\textsuperscript{y}} | 39m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DELECTABILITER}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}} | PROPTER QUID DELECTABILIUS \textit{V\textsuperscript{m}} | PROPTER QUID DELECTABILITER AUDIUNT \textit{V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID DELECTABILITER AUDIUNT CANTANTES QUOSCUNQUE UTIQUE PRESCIENTES ATTINGANT CANTUS QUAM SI NESCIUNT? \textsuperscript{2}VTRUM QUIA MAGIS MANIFESTUS EST ATTINGENS QUEMADMODUM INTENTIONEM QUANDO COGNOSCUNT QUOD CANITUR? COGNOSCENTIBUS AUTEM DELECTABILE CONSIDERARE. \textsuperscript{3}AUT COMPATIENS EST AUDITOR CANTANTI NOTUM? CONSONAT AUTEM IPSO, CANTAT AUTEM OMNIS CONSONANS, QUI NON PROPTER ALIQUAM NECESSITATEM FACIT HOC \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} PROPTER QUID BIS PARACUTA AUT BIS IIII.OR NON CONCORDANT BIS DYAPASON AUTEM ITA. AUT QUIA QUOD QUIDEM DYAPENTE EST IN EMIOLA PROPORTIONE QUID UERO PER IIII.OR IN ENIPIRITIO EXISTENTIBUS AUT EMIOLIBUS TRIBUS CONSEQUENTER NUMERIS QUE EST EPITRITIO EXTREMA AD SE INUICEM NULLAM PROPORTIONEM HABEBUNT. NEQUE ENIM PARTICULARIA ERUNT NEQUE MULTIPLICIA DYAPASON AUT QUONIAM EST IN DUPLICI PROPORTIONE BIS. HOC FACTO IN QUADRUPLICI PROPORTIONE SI FIUNT EXTREMA AD INUICEM. QUARE QUONIAM CONSONANTIA RATIONABILEM HABENTIUM SONUM AD SE INUICEM EST RATIONEM AUT QUI QUIDEM HABENT BIS DYAPASON INTER DECISIONEM AD SE INUICEM SONI HABENT. QUI AUTEM BIS PER IIII.OR AUT PER QUINQUE NON HABENT QUICQUID DYAPASON CONSONABUNT UTIQUE ALII UERO NON PER EA QUE DICTA SUNT. \edtext{ \edtext{Et}{\Cfootnote[nosep]{\textit{αmv} | \textit{om}. \textit{λπ}}} \edtext{huius}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}} | huiusmodi \textit{γmv}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | quidem problematis \textit{V\textsuperscript{z}} | autem \textit{G\textsuperscript{u}P\textsuperscript{q}} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}}}} expositio \edtext{sufficiens iam}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}mv} | iam sufficiens \textit{P\textsuperscript{z}} | sufficienter iam \textit{G\textsuperscript{u}P\textsuperscript{q}} | iam \textit{V\textsuperscript{z}}}} \edtext{quinto}{\Cfootnote[nosep]{\textit{αλmv} | \textit{om}. \textit{π}}} \edtext{apparuit}{\Cfootnote[nosep]{\textit{γλπP\textsuperscript{y}mv} | apparebit \textit{E\textsuperscript{a}}}} \edtext{problemate}{\Cfootnote[nosep]{\textit{αλ} | capitulo \textit{mv} | \textit{om}. \textit{π}}}. \edtext{Repetitur}{\Cfootnote[nosep]{\textit{αλπ} | Reperitur \textit{mv}}} \edtext{uero}{\Cfootnote[nosep]{\textit{αλmv} | autem \textit{G\textsuperscript{u}P\textsuperscript{a}V\textsuperscript{o}} | ergo \textit{P\textsuperscript{p}} | igitur \textit{P\textsuperscript{u}} | enim \textit{P\textsuperscript{z}}}} ut \edtext{memorie amplius commendetur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{y}mv} | amplius memorie comendetur \textit{λ} | memorie commendetur amplius \textit{π}}}. \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{p}V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{αλπmv}}} Propter quid bis. Repetit 34. ut amplius exponat. Aut quia. Soluit Et primo assignat causam prime partis Et secundo secunde ibi dyapason .3° concludit in tantum ibi quare quoniam Primo querit quare quoniam dyapente est in sexquialtera proportione dyatesseron in sexquitertia. hiis itaque ita dispositis numerus ut 3us. etiam numeris consequenter reiterati ut tria et quatuor. ex quibus erat Epitrica ut dictum est proportio cum erant simplices in repetiti. Tunc si extrema huiusmodi duarum consonantiarum duplentur ad inuicem coniuncta nullam habebunt proportionem consurgentem inde quod probatur quia talia non reddunt nec superticularia neque multiplicia penes que ut visum est 13. proportiones accipiuntur musice. vnde apparet quod \hyperref[Ar]{aristotelis} consentit pictagoricis has ponentibus solum Et non concidit cum \hyperref[Pt]{ptolomeo} ponente proportionem compositam ex dyatesseron et dyapason consurgere ex multiplici et superparticulari. Si namque sumatur bis dyatesseron puta prima dyatesseron fit proportio 3. ad 4. et 2a 5. ad 4. Et coniungantur extrema: ut .3. ad 4. Nulla consurgit proportio pretactorum multiplicitatis aut superparticularis Similiter in dyapente si sumatur Exempli gratia Vna dyapente cum 2 comparantur ad 3 et 2a quando .6. ad .9. ita ut duo comparentur ad .9. modo eodem nulla consurgit proportio cum omnis ut sic constet in numero Epitrico. Emiolis duplari: triplari Et quadruplo ut ostensum est superius. etcetera Dyapason. Assignat causam 2e partis dicens quia dyapason se habet in dupla proportione si bis sumatur ea erit in quadruplici extremis comparatis ad inuicem proportionum maiorum et minorum Puta sumatur bis dyapason ut in vnaquaque comparetur vnum comparetur ad duo Et reliqua 2 ad 4 resultabit numerus quadruplus Iuxta quod predictum est bis dyapason bis Quare quoniam 3° concludit intentum dicens Et ideo quia consonantia est compositio quedam tonorum habentium et rationabilem et proportionalem proportionem ad inuicem Et hoc habet bis dyapason Non autem bis dyatesseron aut dyapente et reliqua Quod declaratur quia proportio quam habent soni ad inuicem Est habere inter se decisiones et confractionem quandam ad inuicem per quam sonsultant quidem proportionales armonici: ut bisdyapason quod non habet consonantiam per 4or. et quinque siue dyatesseron et dyapente Cunque ut dictum est tantum soni qui fuerunt secundum dyapason duplatum consonant alii vero minime: sicut ostensum est per ante dictam causam.\#Pq runs problem 40 into 41 just as \#Gu does. +\pend + +\pstart +\edtext{\subsubsection {Quadragesimumprimum problema}\label{edition-text book-19a part41}}{\lemma{Quadragesimumprimum + problema} \Cfootnote[nosep]{\textit{γmv} | «41m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{Quadragesimum primum.} Quadragesimumprimum. \textit{P\textsuperscript{y}} | Quadragesimumprimum problema etcetera. \textit{P\textsuperscript{x}} | \textit{om}. \textit{G\textsuperscript{u}M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID BIS PARACUTA}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}V\textsuperscript{o}} | PROPTER QUID BIS \textit{P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID BIS PARACUTA AUT BIS QUATUOR NON CONCORDANT, BIS DYAPASON AUTEM ITA? \textsuperscript{2}AUT QUIA QUOD QUIDEM DYAPENTE EST IN EMIOLIA PROPORTIONE, QUOD UERO PER QUATUOR IN EPITRITO? EXISTENTIBUS AUTEM EMIOLIBUS TRIBUS CONSEQUENTER NUMERIS, QUE EST EPITRICON, EXTREMA AD SE INUICEM NULLAM PROPORTIONEM HABEBUNT, NEQUE ENIM PARTICULARIA NEQUE MULTIPLICIA ERUNT. \textsuperscript{3}DYAPASON AUTEM, QUONIAM EST IN DUPLICI PROPORTIONE, BIS HOC FACTO, IN QUADRUPLICI PROPORTIONE SI FUERINT EXTREMA AD INUICEM. \textsuperscript{4}QUARE QUONIAM CONSONANTIA RATIONABILEM HABENTIUM SONUM AD SE INUICEM EST, RATIONEM AUTEM QUI QUIDEM HABENT BIS DYAPASON INTERDECISIONEM AD SE INUICEM SONI HABENT, QUI AUTEM BIS PER QUATUOR AUT BIS PER QUINQUE NON HABENT. QUI QUIDEM BIS DYAPASON CONSONABUNT, UTIQUE ALII UERO NON PER EA QUE DICTA SUNT \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} \edtext{Repetit trigesimumquartum ut amplius \edtext{exponat}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | exponatur \textit{P\textsuperscript{z}}}}.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv}}} +\pend + +\pstart +\textbf{2} \edtext{ \edtext{}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AUT.} Soluit et primo assignat causam prime partis, secundo secunde \edtext{secunda}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{o}} | secunda + ibi \textit{P\textsuperscript{z}V\textsuperscript{a}mv} | ibi secunda \textit{V\textsuperscript{b}} | ibi \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \textit{DYAPASON}, \edtext{3° concludit \edtext{intentum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{o}} | intentum ibi \textit{γP\textsuperscript{p}mv}}} }{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \textit{ \edtext{QUARE QUONIAM}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | QUARE \textit{E\textsuperscript{a}P\textsuperscript{z}}}} }. \edtext{ \edtext{Dicens}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | Dicit \textit{M\textsuperscript{a}V\textsuperscript{z}}}} causam \edtext{esse}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}v} | cesse \textit{m}}} }{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | Dicit primo causam esse \textit{V\textsuperscript{a}} | Primo querit quare \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}}}} \textit{ \edtext{quoniam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} dyapente \edtext{est}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} in \edtext{sexquialtera proportione}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}P\textsuperscript{u}V\textsuperscript{o}mv} | proportione sexquialtera \textit{P\textsuperscript{p}}}}, \edtext{dyatesseron in}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | dyatesseron \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}} epitrica. Hiis \edtext{igitur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | ergo \textit{P\textsuperscript{x}} | \textit{om}. \textit{V\textsuperscript{a}V\textsuperscript{m}}}} \edtext{ita}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | itaque \textit{V\textsuperscript{a}} | sic \textit{P\textsuperscript{p}}}} \edtext{dispositis}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | expositis \textit{P\textsuperscript{x}}}} \edtext{numeris}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}mv} | numerus \textit{κ} | numeris consequenter reiteratis ut tria ad 4. \textit{V\textsuperscript{a}}}}, ut \edtext{duobus}{\Cfootnote[nosep]{\textit{ακmv} | tribus \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} sexquialteris et tribus, \edtext{et}{\Cfootnote[nosep]{\textit{κ} | etiam \textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{numeris}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | numerus \textit{V\textsuperscript{m}}}} consequenter \edtext{reiteratis}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | reiterati \textit{E\textsuperscript{a}} | reiterari \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}}, ut tria ad quatuor, ex quibus \edtext{erat}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | erant \textit{M\textsuperscript{a}}}} epitrica, ut dictum \edtext{est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} proportio cum erant simplices \edtext{inrepetiti}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | repetiti \textit{P\textsuperscript{y}} | etiam repetiti \textit{P\textsuperscript{z}} | ut repetiti \textit{γ}}}, \edtext{tunc}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | termini \textit{V\textsuperscript{o}}}} si extrema \edtext{huius duarum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | huiusmodi duarum \textit{V\textsuperscript{b}mv} | harum duarum \textit{P\textsuperscript{p}} | duarum huiusmodi \textit{V\textsuperscript{a}}}} consonantiarum duplentur, ad inuicem \edtext{coniuncta}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | coniunctam \textit{V\textsuperscript{m}} | coniecta \textit{P\textsuperscript{x}V\textsuperscript{z}}}} \edtext{nullam}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in illam \textit{P\textsuperscript{x}}}} habebunt proportionem consurgentem. Inde quod \edtext{probatur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | prosequitur \textit{mv}}}, quia talia non \edtext{redduntur}{\Cfootnote[nosep]{\textit{ακmv} | reddunt \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{in}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}mv} | neque \textit{γλE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} superparticularia \edtext{neque}{\Cfootnote[nosep]{\textit{ακmv}}} multiplicia,} penes \edtext{que}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | quem \textit{V\textsuperscript{a}}}}, ut visum \edtext{est}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}V\textsuperscript{b}}}} \edtext{13°.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | .xix. \textit{mv}}}, \edtext{ \edtext{proportiones assumuntur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | assumuntur proportiones \textit{P\textsuperscript{y}} | proportiones accipiuntur \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} musice. Unde apparet quod \hyperref[Ar]{aristoteles}}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} consentit \edtext{pictagoricis}{\Cfootnote[nosep]{\textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | \hyperref[Pyth]{pictagoras} \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}}}}, has ponentibus solum, et non concidit \edtext{cum}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | causa \textit{P\textsuperscript{x}}}} \hyperref[Pt]{ \edtext{ptholomeo}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}m}}} }, ponente \edtext{fore proportionem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | proportionem fore \textit{V\textsuperscript{a}} | proportionem \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{compositam}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | compositum \textit{P\textsuperscript{x}} | expositum \textit{V\textsuperscript{a}}}} ex \edtext{dyatesseron et dyapason}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | dyapason et dyatesseron \textit{V\textsuperscript{z}}}} consurgere ex \edtext{multiplici}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | multiplicatione \textit{P\textsuperscript{x}}}} et \edtext{superparticulari}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}mv} | superpartienti \textit{E\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | superuenienti \textit{P\textsuperscript{x}V\textsuperscript{m}}}}. \edtext{Si namque}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | Si enim \textit{mv} | Si nam \textit{V\textsuperscript{a}}}} \edtext{sumatur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv}}} bis dyatesseron \edtext{puta prima dyatesseron}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}V\textsuperscript{a}}}} \edtext{sit}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | fit \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} proportio \edtext{trium}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv} | tria \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | tripla \textit{V\textsuperscript{b}}}} ad quatuor, \edtext{et}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{γP\textsuperscript{p}P\textsuperscript{x}mv}}} \edtext{ \edtext{secunda}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | secunda uero \textit{P\textsuperscript{x}mv} | secunda cessat \textit{V\textsuperscript{a}}}} \edtext{sex ad octo}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | sex .8. \textit{V\textsuperscript{a}} | sex ad 6to. \textit{P\textsuperscript{x}} | 5 ad 4 \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}}, \edtext{et \edtext{coniungantur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}V\textsuperscript{o}mv} | coniungant \textit{P\textsuperscript{y}}}} extrema, ut .3. \edtext{comparando}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}} | operando \textit{mv}}} ad \edtext{.8.}{\Cfootnote[nosep]{\textit{ακmv} | quatuor. \textit{V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}P\textsuperscript{z}}}} \edtext{nulla}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | nullo \textit{E\textsuperscript{a}}}} \edtext{consurgit proportio}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | consurget proportio \textit{P\textsuperscript{y}} | proportio consurgit \textit{mv} | contingit proportio \textit{V\textsuperscript{m}}}} }{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | secunda fit proportio 5a ad 4. nulla fit proportio \textit{P\textsuperscript{p}}}} \edtext{ \edtext{pretactarum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}V\textsuperscript{o}mv} | pretactorum \textit{P\textsuperscript{p}P\textsuperscript{u}} | quantitarum \textit{P\textsuperscript{z}}}} multiplicis \edtext{aut}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | autem \textit{P\textsuperscript{z}}}} superparticularis. \edtext{Similiter}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | Similiter et \textit{γλE\textsuperscript{a}mv}}} \edtext{in}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{a}V\textsuperscript{m}}}} dyapente, \edtext{ \edtext{ut}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} si \edtext{sumatur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv}}} exempli gratia vna dyapente}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}, puta cum duo \edtext{comparantur}{\Cfootnote[nosep]{\textit{λγE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{x}}}} ad tria, \edtext{et secunda}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et 3a \textit{P\textsuperscript{p}} | et secunda \surplus{et secunda} \textit{E\textsuperscript{a}}}}. \edtext{quando}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | quandoque \textit{V\textsuperscript{m}}}} \edtext{.6.}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | es \textit{P\textsuperscript{x}} | cessat \textit{V\textsuperscript{a}}}} \edtext{ad}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{.9., ita ut duo \edtext{comparantur}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | comparentur \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}mv}}} ad}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} .9.. \edtext{Modo}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Non \textit{P\textsuperscript{z}}}} \edtext{eodem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | eadem \textit{P\textsuperscript{p}}}} nulla consurgit proportio}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{cum omnis ut}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | omnis cum \textit{V\textsuperscript{a}}}} sic constet \edtext{in}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ex \textit{P\textsuperscript{y}}}} \edtext{numero}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} epitrico emiola duplari triplari et quadruplo, ut ostensum \edtext{est}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{E\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{anterius}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}} | anterius et \textit{E\textsuperscript{a}} | in anterius \textit{V\textsuperscript{b}mv} | in antedictis \textit{P\textsuperscript{y}} | superius \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}}}}.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}mv}}} +\pend + +\pstart +\textbf{3} \edtext{ \edtext{}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{DYAPASON.} Assignat causam 2e partis, dicens \textit{quia dyapason se habet in duplicidupla proportione, si bis \edtext{assumatur}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | sumatur \textit{P\textsuperscript{p}P\textsuperscript{u}}}} ea \edtext{erit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | habet se \textit{P\textsuperscript{p}}}} in \edtext{quadruplici}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | quatruplicibus \textit{V\textsuperscript{b}} | quatuor \textit{V\textsuperscript{a}}}} \edtext{extremis}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | in extremis \textit{P\textsuperscript{p}P\textsuperscript{u}}}} comparatis ad inuicem \edtext{proportionum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | proportionem \textit{P\textsuperscript{u}V\textsuperscript{m}} | proportione \textit{P\textsuperscript{z}V\textsuperscript{a}} | proportionatum \textit{P\textsuperscript{y}}}} \edtext{minoribus et maioribus}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | maioribus et minoribus \textit{V\textsuperscript{z}} | minoris et maioris \textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | maioris et minoris \textit{V\textsuperscript{a}} | minoris et ali[?]is \textit{P\textsuperscript{p}}}} }. \edtext{Puta}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Puta ut \textit{P\textsuperscript{y}}}} \edtext{sumatur}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{bis dyapason}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{ut in vna quarum}{\Cfootnote[nosep]{\textit{αmv} | ut in unaquaque \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | ut quarum \textit{κ}}} \edtext{comparetur vnum}{\Cfootnote[nosep]{\textit{ακV\textsuperscript{o}mv} | vnum comparetur \textit{P\textsuperscript{p}P\textsuperscript{u}} | comparatur vnum \textit{P\textsuperscript{z}}}} ad duo \edtext{et in}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | et \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | in \textit{V\textsuperscript{a}}}} \edtext{reliqua}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | reliquo \textit{V\textsuperscript{m}}}} duo ad \edtext{quatuor}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | .8 \textit{V\textsuperscript{z}}}}, \edtext{ \edtext{tunc}{\Cfootnote[nosep]{\textit{γκmv} | etiam \textit{E\textsuperscript{a}}}} si extrema comparentur ad inuicem ut vnum ad quatuor}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}P\textsuperscript{y}V\textsuperscript{o}}}} \edtext{resultabit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | resultat \textit{P\textsuperscript{z}}}} numerus quadruplus iuxta \edtext{quem}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | quam \textit{V\textsuperscript{z}} | quod \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{dictum}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | dictus \textit{P\textsuperscript{x}} | dignum \textit{P\textsuperscript{z}}}} est \edtext{bis dyapason}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | dyapason bis \textit{V\textsuperscript{a}mv}}} \edtext{siue}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}} | siue non \textit{V\textsuperscript{a}} | fieri \textit{mv} | sui in \textit{V\textsuperscript{o}} | \textit{om}. \textit{V\textsuperscript{b}}}} }{\Cfootnote[nosep]{\textit{ακmv}}} +\pend + +\pstart +\textbf{4} \edtext{ \edtext{}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{QUARE QUONIAM.} \edtext{Concludit intentum 3°}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | 3°. concludit intentum \textit{P\textsuperscript{p}P\textsuperscript{u}}}}, dicens \edtext{et}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | esse \textit{P\textsuperscript{p}}}} ideo \textit{quia consonantia est \edtext{compositio}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} quedam tonorum \edtext{habentium}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{rationabilem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}mv} | rationabile \textit{V\textsuperscript{b}} | rationalem \textit{P\textsuperscript{p}P\textsuperscript{z}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}}}} et \edtext{proportionatum}{\Cfootnote[nosep]{\textit{ακmv} | proportionalem \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} sonum \edtext{ad se inuicem}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ad inuicem \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{y}}}}, et hoc habet bis dyapason, non autem bis dyatesseron \edtext{aut}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | ut \textit{E\textsuperscript{a}}}} \edtext{dyapente}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | bis dyapente \textit{P\textsuperscript{x}}}} et reliqua. Quod \edtext{declaratur}{\Cfootnote[nosep]{\textit{γλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | declarat \textit{E\textsuperscript{a}P\textsuperscript{x}}}} quoniam proportio \edtext{quam quidem}{\Cfootnote{quam \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | quam siquidem \textit{ακ} | siquidem quam \textit{mv}}} habent soni ad inuicem \edtext{est}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | etiam \textit{P\textsuperscript{p}P\textsuperscript{u}}}} habere inter \edtext{se decisionem}{\Cfootnote[nosep]{\textit{γλP\textsuperscript{y}mv} | decisionem \textit{E\textsuperscript{a}} | se decisiones \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} et \edtext{confractionem}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | consurrectionem \textit{P\textsuperscript{x}}}} \edtext{ad inuicem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ad inuicem est habere \textit{P\textsuperscript{z}}}} quandam, per quam \edtext{resultant}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | resultent \textit{γE\textsuperscript{a}mv}}} \edtext{ipsi}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | quidam \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{proportionales}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}} | proportionabiles \textit{mv}}} armonici, ut bis dyapason, quod non habet \edtext{consonantia}{\Cfootnote[nosep]{\textit{γP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | consonantiam \textit{λE\textsuperscript{a}P\textsuperscript{y}} | \textit{om}. \textit{P\textsuperscript{z}}}} per quatuor \edtext{aut}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | aut per \textit{M\textsuperscript{a}} | ad \textit{V\textsuperscript{a}P\textsuperscript{u}}}} quinque siue dyatesseron \edtext{uel}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}mv} | siue \textit{P\textsuperscript{y}} | et \textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} dyapente. \edtext{Sed}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | Cumque \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} ut dictum \edtext{est}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}}}}, tantum soni qui \edtext{fuerint}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | fuerunt \textit{P\textsuperscript{y}P\textsuperscript{z}} | fluerunt \textit{M\textsuperscript{a}}}} secundum dyapason duplici \edtext{consonabunt}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | consonat \textit{P\textsuperscript{p}} | consonant \textit{P\textsuperscript{u}} | consonanter \textit{P\textsuperscript{z}} | \textit{om}. \textit{V\textsuperscript{z}}}}, alii \edtext{uero}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} minime, sicut ostensum \edtext{est}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}V\textsuperscript{z}}}} \edtext{per}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | propter \textit{P\textsuperscript{y}V\textsuperscript{b}mv}}} antedictam causam.} \edtext{}{\Cfootnote{etcetera. \textit{P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 42. problema 19e. particule. \textit{P\textsuperscript{x}}}} }{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}mv}}} propter quid bis paracuta autem bis iiii.or non concordant bis dyapason autem ita. Aut quia quod quidem dyapente est in emiolia proportione quod uero per iii.or in epyptrico existentibus autem emiolibus tribus consequenter numerus que est epitricon extrema ad se inuicem nullam proportionem habebunt. neque enim particularia neque multiplitia erunt dyapason quoniam est in duplici proportione bis. hoc factum in quadruplici proportione si fuerint extrema ad inuicem. quoniam consonantia rationabilem habentium sonum ad se inuicem est rationem aut qui quidem habent bis dyapason interpositionem ad se inuicem soni habent. qui autem quidem bis dyapason. et consonabunt utique alii uero non per ea que dicta sunt. +\pend + +\pstart +\edtext{\subsubsection {Quadragesimumsecundum problema}\label{edition-text book-19a part42}}{\lemma{Quadragesimumsecundum + problema} \Cfootnote[nosep]{\textit{γmv} | «42m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{Quadragesimum secundum:} Quadragesimumsecundum. \textit{P\textsuperscript{y}} | Quadragesimum + primum problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID SI QUIS}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | PROPTER QUID SI QUID ALTERA \textit{V\textsuperscript{m}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID SI QUIS ALTERA NITEM ACCIPIAT AUT YPATEM ACCIPIAT, YPATE SOLA UIDETUR SUBSONARE? \textsuperscript{2}AUT QUIA NEATE FINIENS ET DEPERDITA YPATE FIT? \textsuperscript{3}SIGNUM AUTEM POSSE AB YPATE NEATEN POSSE CANERE. SICUT ENIM EXISTENTE IPSA CAUSAM NEATE, SIMILITUDINEM ACCIPIUNT AB IPSA. QUONIAM AUTEM ET ECHO CANTUS QUIDAM EST, TACTUS EST UOCIS NEATIS FINIENTIS SONUS EXISTENS IDEM SONO YPATES MOUET CONUENIENTER, SIMILITUDINI YPATEM NITE UIDETUR MOUERE. NEATEN ENIM SCIMUS UBI MOUETUR ASSUMPTA. YPATEN AUTEM IPSAM UIDENTES INCOMPREHENSIBILEM EXISTENTEM ET SONUM IPSIUS AUDIENTES, HANC PUTAMUS SONARE. QUOD IN MULTIS NOBIS ACCIDIT, IN QUIBUS NEQUE RATIONE. NEQUE SENSU POSSUMUS CERTIFICARE CERTUM. \textsuperscript{4}AMPLIUS SI PERCUSSA NEATE MAXIME TENSA ACCIDIT IUGUM MOUERI NICHIL UTIQUE ERIT MIRABILE. MOTO AUTEM OMNES CORDAS PARITER MOUERI ET SONUM FACERE NON IRRATIONABILE. ALIIS QUIDEM IGITUR NEATIS SONUS ALIENUS EST ET FINIENS ET INCIPIENS, YPATE AUTEM FINIENS IDEM. NON APPOSITO PROPRIO SUO MOTU, ILLIUS UIDEBITUR OMNIA EORUNDEM ESSE NON EST INCONUENIENS. ERIT AUTEM MAIOR QUAM RELIQUARUM CORDARUM SONUS, QUOD HEE QUIDEM A NEATE SICUT IMPULSE MOLLITER SONUERUNT, NEATE AUTEM, TOTA SUI IPSIUS POTENTIA EXISTENS, IPSARUM FORTISSIMA EST. \textsuperscript{5}QUARE MERITO ET SECULARIUM IPSIUS MAIUS ERIT QUAM QUOD EST ALIARUM, QUARE BREUES MOUERI, SICUT IPSIS \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema quadragesimum + secundum etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} si quis cantu \edtext{aut tactu}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | aut tacta \textit{γ} | aut atactu \textit{P\textsuperscript{y}} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{altera}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | altam \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}} \edtext{suscipiat}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | suscipiet \textit{V\textsuperscript{a}}}} \edtext{nitem}{\Cfootnote[nosep]{\textit{κ} | nitorum \textit{E\textsuperscript{a}} | uocem \textit{P\textsuperscript{z}}}} \edtext{siue}{\Cfootnote[nosep]{\textit{ακmv} | aut \textit{π}}} \edtext{extremam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | extremam ut \textit{P\textsuperscript{z}}}}, quia \edtext{multiplex}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | iuxta \textit{P\textsuperscript{z}}}} ut \edtext{visum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | rismis quidem \textit{P\textsuperscript{z}} | dictum \textit{λ}}} \edtext{est}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{P\textsuperscript{y}V\textsuperscript{z}}}}, aut \edtext{pro et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | per \textit{P\textsuperscript{z}}}} ypatem accipiat, simul coniungens \edtext{alias}{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}mv} | alteras \textit{P\textsuperscript{x}} | ambas \textit{P\textsuperscript{y}}}} quidem \edtext{alteram}{\Cfootnote[nosep]{\textit{γP\textsuperscript{z}V\textsuperscript{z}} | altera \textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}mv} | altam \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} uocem, tunc \edtext{sola}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | solo \textit{E\textsuperscript{a}}}} \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ypatem \textit{M\textsuperscript{a}}}} sentitur ultimo subsonare,} \edtext{non}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | nota \textit{P\textsuperscript{p}P\textsuperscript{u}}}} quidem quod minorem sonum reddat, \edtext{sed}{\Cfootnote[nosep]{\textit{αmv} | seu \textit{π} | \textit{om}. \textit{κ}}} \edtext{sonat}{\Cfootnote[nosep]{\textit{ακmv} | at \textit{π}}} posterius cum sonus \edtext{eius}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | enim \textit{V\textsuperscript{m}}}} finitur, ipsa \edtext{enim}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | causa \textit{M\textsuperscript{a}}}} est \edtext{illa}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ista \textit{P\textsuperscript{y}V\textsuperscript{z}}}} \edtext{ex}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | in \textit{V\textsuperscript{m}}}} qua relinquitur \edtext{sonus, ille}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | ille, sonus \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{faticius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}} | \textit{om}. \textit{G\textsuperscript{u}}}} diutius \edtext{resonatio}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | resonantia \textit{G\textsuperscript{u}}}} dicta uel neate \edtext{seu}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | siue \textit{P\textsuperscript{z}}}} \edtext{tinitus}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}mv} | \sout{timitus} cantus \textit{P\textsuperscript{x}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}E\textsuperscript{a}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | AUT QUIA. \textit{γmv}}} } \edtext{Soluit primo assignans}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{a}mv} | Primo soluit assignans \textit{V\textsuperscript{b}} | Soluit et primo assignat \textit{λπE\textsuperscript{a}P\textsuperscript{y}}}} \edtext{causam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | causam et \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, .2° confirmat et declarat \edtext{ipsam magis}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | magis ipsam \textit{P\textsuperscript{p}P\textsuperscript{y}}}}. \edtext{Secunda}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}} | ibi secunda \textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}mv}}}: \textit{AMPLIUS}. Primo \edtext{igitur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ergo \textit{G\textsuperscript{u}}}} \edtext{causam dat}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | dat causam \textit{γπV\textsuperscript{z}mv} | dat causam causam \textit{P\textsuperscript{y}}}}, \edtext{dicens hoc esse}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | dicens ideo esse \textit{π} | huius esse dicens \textit{V\textsuperscript{a}} | huiusmodi dicens esse \textit{mv} | huiusmodi dicens hoc esse \textit{V\textsuperscript{b}}}} \textit{quoniam \edtext{cum}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} sonus \edtext{nites}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{o}} | vites \textit{P\textsuperscript{u}}}} finitur \edtext{deperditur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | disperditur \textit{P\textsuperscript{p}} | de proportione \textit{γ}}} et \edtext{occultatur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}mv} | hoc vtatur \textit{V\textsuperscript{a}}}} propter \edtext{resonationem}{\Cfootnote[nosep]{\textit{ακmv} | resonantiam \textit{π}}} \edtext{ypates}{\Cfootnote[nosep]{\textit{ακπ}}}, \edtext{ceu}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} maior motus \edtext{depellit minorem}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | minorem depulit \textit{P\textsuperscript{y}}}}, ea \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} \edtext{sola videtur posterius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | videtur posterius sola \textit{G\textsuperscript{u}P\textsuperscript{q}} | videtur sola posterius \textit{V\textsuperscript{a}} | uidetur posterius \textit{P\textsuperscript{z}}}} \edtext{subsonare}{\Cfootnote[nosep]{\textit{αλπmv} | resonare \textit{P\textsuperscript{x}}}} }. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{SIGNUM.} \edtext{Declarat 2°}{\Cfootnote[nosep]{\textit{ακπ} | Secundo declarat \textit{mv}}} per signum, dicens \textit{ \edtext{signum nobis ideo}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | signum nobis illud \textit{V\textsuperscript{z}} | signum nobis id \textit{α} | signum nobis hoc \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | signum nobis \textit{G\textsuperscript{u}mv}}} \edtext{demonstrans est}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | demonstrans esse \textit{V\textsuperscript{a}} | demorans est \textit{P\textsuperscript{x}V\textsuperscript{m}} | denotans est \textit{G\textsuperscript{u}P\textsuperscript{u}} | esse designans \textit{P\textsuperscript{p}}}} quoniam \edtext{neate}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | meatis \textit{P\textsuperscript{z}}}} potest amplius \edtext{subsonare}{\Cfootnote[nosep]{\textit{αλπmv} | subsentire \textit{P\textsuperscript{x}}}} \edtext{tanta}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}} | causata \textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}mv} | ca\expan{usa}ta \textit{(orig. \textup{cata})} \textit{P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}} | causatam \textit{M\textsuperscript{a}}}} ab \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ypatem \textit{M\textsuperscript{a}}}} diutius \edtext{remanendo}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | remanente \textit{G\textsuperscript{u}P\textsuperscript{q}}}} post tactum \edtext{corde}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | corde \surplus{quam neate alicuius alterius corde} \textit{P\textsuperscript{z}}}} \edtext{quam}{\Cfootnote[nosep]{\textit{αλπmv} | per quod \textit{P\textsuperscript{x}}}} neate \edtext{alicuius alterius corde}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | aliquis alterius cordis \textit{E\textsuperscript{a}}}}.} Unde cum ipsa \edtext{potissime}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | potissima \textit{G\textsuperscript{u}P\textsuperscript{y}}}} sit causa, \edtext{ut accidat}{\Cfootnote[nosep]{\textit{γλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | ut accidet \textit{P\textsuperscript{z}} | ne accidat \textit{E\textsuperscript{a}}}} neate, \edtext{omnes}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | quiaa \textit{P\textsuperscript{y}}}} relique corde \edtext{in terminatione}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | iteratione \textit{γP\textsuperscript{z}mv} | in q\expan{ua}n\expan{do} a co\expan{mmun}e \textit{(orig. \textup{qnacoe})} et \textit{E\textsuperscript{a}}}} \edtext{suorum sonorum}{\Cfootnote[nosep]{\textit{αλπmv} | sonorum suorum \textit{P\textsuperscript{x}}}} \edtext{suscipiunt}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} similitudinem ab \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | ypatem \textit{M\textsuperscript{a}}}}. +\pend + +\pstart +\textbf{4} Nosce quod \edtext{neate interdum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | interdum neate \textit{P\textsuperscript{y}}}} \edtext{sumitur}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} \edtext{pro hypate}{\Cfootnote{pro nete \textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}. Ut visum \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} ‘ \edtext{.13.}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | 23º. \textit{V\textsuperscript{b}}}} \edtext{et .39.}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{o}mv} | 239. \textit{E\textsuperscript{a}} | et .19º. \textit{λP\textsuperscript{z}}}}: est enim quasi corda iuuenilis et inferior accipitur \edtext{etiam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | enim \textit{G\textsuperscript{u}}}} pro resonatione secunda que \edtext{sentitur}{\Cfootnote[nosep]{\textit{ακπ} | retinetur \textit{γmv}}} diu post \edtext{percussionem}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | repercussionem \textit{P\textsuperscript{y}}}}, \edtext{ceu}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}}}} \edtext{hic}{\Cfootnote[nosep]{\textit{αλπmv} | hinc \textit{P\textsuperscript{x}}}}.\edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XIX .13 , 918b ll. 3–6 and XIX .39 , 921a ll. 7–31}}’ \edtext{Sicut}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | Sint \textit{E\textsuperscript{a}}}} \edtext{enim}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | est \textit{V\textsuperscript{m}}}} neate corda \edtext{est}{\Cfootnote[nosep]{\textit{αλπmv} | est cum \textit{P\textsuperscript{x}}}} inferior, ita \edtext{resonatio etiam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | etiam resonatio etiam \textit{V\textsuperscript{b}} | resonatio et \textit{G\textsuperscript{u}P\textsuperscript{q}} | etiam resonantia \textit{P\textsuperscript{y}}}} ypates est debilior sono priori, \edtext{sic ut}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | sic nunc \textit{P\textsuperscript{z}}}} \edtext{concidant}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | concidunt \textit{V\textsuperscript{b}}}}. +\pend + +\pstart +\textbf{5} Quod \edtext{autem}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | aut \textit{E\textsuperscript{a}}}} ita sit \edtext{ostenditur etiam}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}mv} | etiam ostenditur \textit{V\textsuperscript{b}} | ostenditur et \textit{P\textsuperscript{y}} | ostenditur \textit{V\textsuperscript{z}}}} per \edtext{echo}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{de quo dictum \edtext{est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} ‘ \edtext{.11a.}{\Cfootnote[nosep]{\textit{ακmv} | 14 \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}},\edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XI .23 , 901b ll. 18–19 ; XI .51 , 904b ll. 29–33}}’quod est quidam \edtext{cantus}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{y}mv} | tinitus \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | et intus \textit{E\textsuperscript{a}}}} seu sonus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{reflexus. Est enim \edtext{hic}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{z}mv} | huius \textit{V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{z}V\textsuperscript{m}}}} \edtext{echo}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{λγE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}}}} \edtext{cantus \edtext{aut}{\Cfootnote[nosep]{\textit{λπV\textsuperscript{b}mv} | autem \textit{E\textsuperscript{a}} | seu \textit{V\textsuperscript{a}}}} sonus}{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{x}P\textsuperscript{y}}}} uocis \edtext{siue}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | seu \textit{P\textsuperscript{y}}}} soni \edtext{neatis uel}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{γmv}}} \edtext{resonationis}{\Cfootnote[nosep]{\textit{αλπmv}}} \edtext{finientis}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | finis entis \textit{P\textsuperscript{x}}}} existens idem cum sono \edtext{ypates}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | ypate \textit{G\textsuperscript{u}}}} principaliori, quando \edtext{fuit}{\Cfootnote[nosep]{\textit{ακmv} | fuerit \textit{π}}} \edtext{tactus eius}{\Cfootnote[nosep]{\textit{κ} | eius tactus \textit{απmv}}}, \edtext{differens}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | differentiis \textit{P\textsuperscript{p}P\textsuperscript{x}}}}, \edtext{tamen}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | tamen a \textit{P\textsuperscript{p}V\textsuperscript{z}} | cum \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{m}} | tam \textit{E\textsuperscript{a}}}} \edtext{priori et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | priori \textit{P\textsuperscript{p}}}} \edtext{posteriori}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, fortiori et debiliori. Nam \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | causam \textit{V\textsuperscript{o}}}} \edtext{aliquid mouetur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | mouetur aliquid \textit{P\textsuperscript{p}}}} ita ut \edtext{decenter}{\Cfootnote[nosep]{\textit{αλπmv} | decenter et \textit{P\textsuperscript{x}}}} \edtext{adaptetur}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | aptetur \textit{P\textsuperscript{x}V\textsuperscript{a}}}} similitudini soni \edtext{qui}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}mv} | que \textit{V\textsuperscript{a}} | quo \textit{V\textsuperscript{o}}}} fit secundum \edtext{ypatem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}}, postremo \edtext{tunc}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | autem \textit{G\textsuperscript{u}} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{apparet}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{ac si}{\Cfootnote[nosep]{\textit{ακmv} | sicut \textit{π}}} \edtext{nite}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}} | uite \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{actu}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | acum \textit{V\textsuperscript{b}}}} tangeretur resonatio \edtext{siquidem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{ypates}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | ypate \textit{πE\textsuperscript{a}}}} videtur sono \edtext{principaliori netes}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} adaptari. \edtext{Tam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}mv} | Vum \textit{G\textsuperscript{u}V\textsuperscript{o}} | Illius \textit{P\textsuperscript{z}}}} \edtext{enim}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | causa \textit{E\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{immensus est}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | est immensus \textit{V\textsuperscript{a}} | immersus est \textit{M\textsuperscript{a}} | intensus est \textit{P\textsuperscript{y}}}} \edtext{ypates}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} sonus quod \edtext{deficiens}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{equiparatur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}mv} | equiparetur \textit{P\textsuperscript{y}}}} sono \edtext{netes}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv}}} principaliori. Quod ostenditur \edtext{quia}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | quod \textit{E\textsuperscript{a}}}} \edtext{neatem}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | neate \textit{P\textsuperscript{x}}}} alterius \edtext{corde}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | corde alterius \textit{P\textsuperscript{z}V\textsuperscript{o}}}} ab ypate scire dicimur \edtext{quando}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cum \textit{G\textsuperscript{u}P\textsuperscript{q}}}} tangitur \edtext{presignata}{\Cfootnote[nosep]{\textit{ακπ} | prelibata \textit{γmv}}} \edtext{corda et}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | corde \textit{M\textsuperscript{a}}}} \edtext{mouetur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}} ab ea altera. \edtext{Sed secus accidit circa ypatem}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} quoniam etiam si videmus \edtext{quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | per \textit{P\textsuperscript{u}}}} ypates non \edtext{comprehendatur}{\Cfootnote[nosep]{\textit{ακmv} | comprehenditur \textit{π}}} ita ut manifeste \edtext{tangi eam}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | eam tangi \textit{P\textsuperscript{u}V\textsuperscript{z}}}} \edtext{scimus}{\Cfootnote[nosep]{\textit{γκmv} | uidemus scimus \textit{P\textsuperscript{y}} | sentimus \textit{πE\textsuperscript{a}}}}, sonum \edtext{tamen}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{z}} | tamen autem \textit{mv} | tantum \textit{M\textsuperscript{a}V\textsuperscript{m}}}} audientes in \edtext{communi}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | communim \textit{P\textsuperscript{z}}}} \edtext{extimamus}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | existimamus \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} propter \edtext{ipsius}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | ipsam \textit{P\textsuperscript{u}} | eius \textit{P\textsuperscript{y}}}} \edtext{diuturnam}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}P\textsuperscript{x}mv}}} \edtext{resonationem}{\Cfootnote[nosep]{\textit{ακmv} | resonantiam \textit{π}}} fore ipsius. \edtext{Quod}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} declarat eo quod \edtext{id}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} non solum \edtext{hic accidit}{\Cfootnote[nosep]{\textit{αλmv} | accidit hic \textit{π} | huius accidit \textit{P\textsuperscript{x}}}}, \edtext{uerum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | sed \textit{P\textsuperscript{y}}}} \edtext{et in multis}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}mv} | etiam in multis \textit{λπ} | multis \textit{V\textsuperscript{a}}}} aliis rebus de quibus non habemus perfectam rationem \edtext{neque}{\Cfootnote[nosep]{\textit{ακmv}}} \edtext{sensum}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv}}} \edtext{perspicacem}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | perspicationem \textit{V\textsuperscript{a}} | perspicuitatem \textit{E\textsuperscript{a}} | perfectum seu perspicacem \textit{V\textsuperscript{z}}}}. ex quibus \edtext{possumus certificari omnino}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | possumus omnino certificari \textit{V\textsuperscript{a}} | certificari omnino \textit{P\textsuperscript{x}} | non possumus omnino certificari \textit{π}}} in talibus tunc accipimus \edtext{inde aliquam opinionem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ap rationem aliquam \textit{G\textsuperscript{u}}}} \edtext{estimatione debili}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}} | debili estimatione \textit{G\textsuperscript{u}P\textsuperscript{q}} | existimatione debili \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | ex terminatione debili \textit{M\textsuperscript{a}}}} \edtext{constrictam}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | constructam \textit{πE\textsuperscript{a}P\textsuperscript{y}} | coniectiua \textit{γM\textsuperscript{a}mv}}}. \edtext{Sic itaque}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | Siccam \textit{P\textsuperscript{y}}}} ypate \edtext{resonat}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | sonat \textit{γmv}}} pre aliis. Neate \edtext{etiam}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}, \edtext{que}{\Cfootnote[nosep]{\textit{απmv} | quam \textit{κ}}} ultimo \edtext{relinquitur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | reliquam \textit{V\textsuperscript{z}}}}, ipsius extat que \edtext{aliarum}{\Cfootnote[nosep]{\textit{ακmv} | aliorum \textit{π}}} \edtext{occultat}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}mv} | occidat \textit{V\textsuperscript{a}}}} et \edtext{deperdit}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | departem \textit{V\textsuperscript{a}}}} neatem. +\pend + +\pstart +\textbf{6} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AMPLIUS.} Secundo \edtext{confirmat}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | confirmat \surplus{confirmat} \textit{P\textsuperscript{y}} | declarat \textit{G\textsuperscript{u}P\textsuperscript{q}}}} causam predictam uel alteram subiungit, dicens quod \textit{non est mirabile \edtext{aliquod}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aliquid \textit{G\textsuperscript{u}P\textsuperscript{q}}}} si \edtext{contingat}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | contingit \textit{γmv}}} \edtext{iugum}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | iustum \textit{E\textsuperscript{a}} | istam \textit{π}}} moueri \edtext{subito}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | cito \textit{π} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{a}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{P\textsuperscript{u}}}} \edtext{situ suo}{\Cfootnote[nosep]{\textit{ακmv} | suo situ \textit{π}}} cum \edtext{ypate}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | ypatem \textit{M\textsuperscript{a}}}} \edtext{fuerit}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}V\textsuperscript{z}mv} | fuerint \textit{P\textsuperscript{x}} | fuit \textit{M\textsuperscript{a}}}} maxime \edtext{tensa}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | sensa \textit{V\textsuperscript{a}}}}. Si accidat quod \edtext{premissum est}{\Cfootnote[nosep]{\textit{γκmv} | premissum \textit{E\textsuperscript{a}P\textsuperscript{y}} | premisit \textit{π}}}, \edtext{neque etiam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | neque \textit{P\textsuperscript{y}}}} est \edtext{mirum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vicium \textit{G\textsuperscript{u}}}}. Si omnes \edtext{tunc corde}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}mv} | corde tunc \textit{P\textsuperscript{y}} | cum corde \textit{V\textsuperscript{b}}}} \edtext{alie}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{pariter moueantur}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{z}mv} | pariter moueatur \textit{V\textsuperscript{m}} | moueantur pariter \textit{π} | moueantur \textit{P\textsuperscript{x}}}} \edtext{et}{\Cfootnote[nosep]{\textit{απV\textsuperscript{z}mv} | in \textit{P\textsuperscript{x}V\textsuperscript{m}} | et in \textit{M\textsuperscript{a}}}} sonum \edtext{reddant}{\Cfootnote[nosep]{\textit{αλπmv}}} \edtext{cum iugum}{\Cfootnote[nosep]{\textit{ακmv} | coniugum \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | coniunctum \textit{G\textsuperscript{u}}}} cui \edtext{innituntur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}} | immittuntur \textit{P\textsuperscript{y}mv}}} \edtext{a}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | et \textit{V\textsuperscript{m}}}} \edtext{sua}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | suo \textit{M\textsuperscript{a}}}} mox \edtext{mouetur}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}mv} | mouentur \textit{V\textsuperscript{z}} | mouerunt \textit{M\textsuperscript{a}} | moueantur \textit{π}}} positione, licet tamen sic accidat \edtext{sonus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{neates}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} \edtext{qui}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | quibus \textit{P\textsuperscript{u}}}} fit ab aliis \edtext{cordis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{preterquam}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{z}mv}}} ab ypate \edtext{extraneus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | extraneus etiam \textit{P\textsuperscript{p}P\textsuperscript{u}} | extremus \textit{mv}}} \edtext{est et}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | esse \textit{E\textsuperscript{a}}}} \edtext{debilis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | debilis est \textit{V\textsuperscript{b}}}} in principio ac etiam in fine, \edtext{cum}{\Cfootnote[nosep]{\textit{κV\textsuperscript{a}mv} | cum primo \textit{P\textsuperscript{y}} | cum in \textit{πE\textsuperscript{a}V\textsuperscript{b}}}} \edtext{ypates}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | ypate \textit{P\textsuperscript{z}}}} \edtext{concidat \edtext{sonum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | sonat \textit{V\textsuperscript{a}}}}. Sed \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}P\textsuperscript{a}V\textsuperscript{b}mv}}} sonus incipiens et finiens idem permanet, non enim sono \edtext{apponitur seu adiungitur}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}mv} | adiungitur seu apponitur \textit{G\textsuperscript{u}P\textsuperscript{u}} | apponitur ceu adiungitur \textit{P\textsuperscript{y}} | adiungitur seu opponitur \textit{P\textsuperscript{x}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | concidat sonum sed huius sonus incipiens \surplus{dat sonum sed huius} \surplus{sonus incipiens} et finiens \surplus{sonus incipiens} \surplus{et finiens} idem permanet \surplus{et finiens idem} \surplus{permanet} non enim sono adiungitur \surplus{permanet non enim sono adiungitur} seu apponitur. \textit{P\textsuperscript{p}}}} aliarum, \edtext{seu}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}} | ceu \textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv}}} econtra, ipsa \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} \edtext{proportio}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | proprio \textit{V\textsuperscript{o}}}} \edtext{concitata}{\Cfootnote[nosep]{\textit{απV\textsuperscript{z}mv} | concita \textit{M\textsuperscript{a}}}} \edtext{motu}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | motum \textit{V\textsuperscript{z}}}} videbitur quod omnes soni \edtext{sint}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sunt \textit{G\textsuperscript{u}}}} \edtext{earundem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{cordarum aliarum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | aliarum cordarum \textit{V\textsuperscript{a}}}} \edtext{eius, cum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | ei, cum \textit{M\textsuperscript{a}} | cuius \textit{G\textsuperscript{u}P\textsuperscript{q}} | \textit{om}. \textit{V\textsuperscript{a}}}} in eam \edtext{concidant}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | concidunt \textit{V\textsuperscript{a}} | non concidant \textit{G\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{occultati}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}V\textsuperscript{z}mv}}}. \edtext{Quod}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{etiam, cum}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}mv} | cum etiam \textit{V\textsuperscript{a}} | est, cum \textit{E\textsuperscript{a}}}} \edtext{sit}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | sint \textit{G\textsuperscript{u}} | fit \textit{V\textsuperscript{m}}}} \edtext{soni}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}mv} | soli \textit{γ}}} ceteris \edtext{fortioris}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fortiores \textit{G\textsuperscript{u}}}}, \edtext{id}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} non \edtext{reputatur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | reparatur \textit{V\textsuperscript{c}V\textsuperscript{o}}}} inconueniens, quare tunc sonus \edtext{ipsius}{\Cfootnote[nosep]{\textit{ακmv} | eius \textit{π}}} \edtext{est}{\Cfootnote[nosep]{\textit{κ} | erit \textit{απmv}}} \edtext{maior}{\Cfootnote[nosep]{\textit{ακmv} | manifestior \textit{π}}} quam sonus aliarum cordarum. Nam \edtext{alie}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ille \textit{G\textsuperscript{u}}}} \edtext{quidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quidam \textit{P\textsuperscript{p}}}} impulse mollem \edtext{reddunt}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}} | reddiderunt \textit{γπE\textsuperscript{a}mv}}} sonum et paruum, ac si esset quedam neate ypates. Cuius \edtext{equidem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | eadem \textit{γmv} | eidem \textit{P\textsuperscript{z}} | quidam \textit{P\textsuperscript{p}}}} \edtext{est neate}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | est neates \textit{πV\textsuperscript{z}}}} tota, cum \edtext{extet}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}m} | extat \textit{P\textsuperscript{p}v} | existat \textit{G\textsuperscript{u}P\textsuperscript{u}}}} fortissima \edtext{virtute}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uirtutis \textit{P\textsuperscript{z}}}} ceterarum cordarum.} \edtext{Quod}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | Quod sicut \textit{P\textsuperscript{x}} | Quod sit \textit{λ} | Quid \textit{V\textsuperscript{o}}}} principalior ostendit \edtext{eius}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}} | ipsius \textit{αλmv}}} sonus, per iugum \edtext{siquidem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | enim quidem \textit{P\textsuperscript{z}}}} audio scabellum super quod \edtext{substentantur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}m}}} corde aut \edtext{illud}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}V\textsuperscript{m}}}} vniversaliter super quod \edtext{innixe}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | in nixeto \textit{P\textsuperscript{x}} | in nixe\textsuperscript{to} \textit{V\textsuperscript{m}} | nixe\textsuperscript{to} \textit{V\textsuperscript{z}} | inuise \textit{V\textsuperscript{a}mv} | in mese \textit{V\textsuperscript{b}} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{extenduntur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}} | coextenduntur \textit{P\textsuperscript{y}V\textsuperscript{a}mv} | coextenditur \textit{V\textsuperscript{b}}}}. Uel \edtext{per}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} iugum \edtext{intelligit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | intelligitur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{sinzeusim siue}{\Cfootnote[nosep]{\textit{V\textsuperscript{b}mv} | sinzeus in siue \textit{E\textsuperscript{a}} | Initeus in sui \textit{π}}} \edtext{coniunctionem}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{m}mv} | coniunctioni \textit{G\textsuperscript{u}} | coniunctione \textit{P\textsuperscript{z}} | coniectionem \textit{P\textsuperscript{x}V\textsuperscript{z}}}} duorumduarumduo \edtext{tetracordarum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}} | cetera cordarum \textit{P\textsuperscript{z}} | retrocordorum \textit{P\textsuperscript{y}}}} \edtext{in}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | et \textit{M\textsuperscript{a}}}} mese, ut videbitur \edtext{.44}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | in .44. innixe coexuntur \textit{πE\textsuperscript{a}}}}. +\pend + +\pstart +\textbf{7} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{MERITO.}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | QUARE MERITO. \textit{M\textsuperscript{a}} | QUINTO. \textit{P\textsuperscript{y}}}} } \edtext{Concludit}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | Ostendit \textit{M\textsuperscript{a}}}} tertio intentum, \edtext{dicens}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \textit{quare non immerito \edtext{secularium}{\Cfootnote[nosep]{\textit{απmv} | \textit{om}. \textit{κ}}} \edtext{ipsius ypates}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | ypates ipsius \textit{V\textsuperscript{a}} | unus ypates \textit{G\textsuperscript{u}} | ipsius compates \textit{P\textsuperscript{x}}}} \edtext{uel}{\Cfootnote[nosep]{\textit{αλπmv} | seu \textit{P\textsuperscript{x}}}} \edtext{condeterminatio}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | cum determinatio \textit{M\textsuperscript{a}} | conterminatio \textit{αmv} | confirmatio \textit{π}}} \edtext{seu}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | uel \textit{P\textsuperscript{x}V\textsuperscript{a}} | siue \textit{mv}}} finis,} solent enim musici, et \edtext{maxime}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}V\textsuperscript{a}}}} \edtext{psallentes}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | psallentis \textit{P\textsuperscript{z}}}}, \edtext{in diuinis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{in fine}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{dicere}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} seculorum amen. Est maius \edtext{et diutius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in diuinis \textit{G\textsuperscript{u}P\textsuperscript{q}}}} perdurans \edtext{quam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{secularium}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | secularum \textit{V\textsuperscript{a}} | seculorum \textit{P\textsuperscript{z}} | secularus \textit{V\textsuperscript{z}}}} reliquarum cordarum, \edtext{quapropter}{\Cfootnote[nosep]{\textit{αλπ} | quam propter \textit{mv} | per \textit{P\textsuperscript{x}}}} \edtext{reliquis sicut}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{m}mv} | sicut reliquis \textit{V\textsuperscript{z}} | reliquas sicut \textit{P\textsuperscript{x}} | reliquis sic \textit{π}}} \edtext{ipsis}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | ipsius \textit{P\textsuperscript{y}} | \textit{om}. \textit{π}}} existentibus breuis motus \edtext{in}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} ypate \edtext{longi}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | longum \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | longa \textit{P\textsuperscript{a}P\textsuperscript{z}} | longe \textit{G\textsuperscript{u}} | longius \textit{V\textsuperscript{z}}}} \edtext{neatem}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | neate \textit{πE\textsuperscript{a}P\textsuperscript{y}} | neatem diutius permanet \textit{V\textsuperscript{z}}}} \edtext{omnium}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | oppositum \textit{P\textsuperscript{z}}}} \edtext{conterminatur}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | conterminantur \textit{M\textsuperscript{a}V\textsuperscript{z}}}} in \edtext{ipsam}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | ipsa \textit{P\textsuperscript{y}V\textsuperscript{a}}}}. Et ideo \edtext{eam solam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}mv} | solam eam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | in eam solam \textit{P\textsuperscript{y}}}} accidit subsonare, \edtext{ut componatur \edtext{huius}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}P\textsuperscript{a}V\textsuperscript{b}mv}}} sermo. \edtext{Ipsa}{\Cfootnote[nosep]{\textit{λ} | illa \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{z}} | ista \textit{P\textsuperscript{p}P\textsuperscript{u}} | ita \textit{γmv}}} corda videtur \edtext{sola subsonare}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}} | subsonare sola \textit{V\textsuperscript{a}} | subsonare \textit{V\textsuperscript{b}}}} }{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{x}P\textsuperscript{y}}}} \edtext{ \edtext{seu}{\Cfootnote[nosep]{\textit{κ} | siue \textit{γπE\textsuperscript{a}mv}}} \edtext{post}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | per \textit{G\textsuperscript{u}}}} alias \edtext{resonare}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | cordas sonare \textit{V\textsuperscript{z}} | sonare \textit{G\textsuperscript{u}P\textsuperscript{q}}}} }{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}, cuius neate diutius \edtext{permanet}{\Cfootnote[nosep]{\textit{ακπ} | permaneat \textit{mv}}} post cessationem aliarum \edtext{neates}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | neatis \textit{P\textsuperscript{z}}}}, \edtext{talis quidem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | quidem talis \textit{G\textsuperscript{u}P\textsuperscript{q}} | tales quidem \textit{P\textsuperscript{y}V\textsuperscript{a}} | talis quod \textit{P\textsuperscript{z}}}}, \edtext{ut declaratum est, ypate}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | ut declaratum est est, ypate \textit{γV\textsuperscript{o}} | ypate sonum, ut declaratum est \textit{P\textsuperscript{z}} | ut declaratum est, ypate est \textit{mv} | ut declaratum, etiam in ypate \textit{P\textsuperscript{y}}}}. +\pend + +\pstart +\textbf{8} Nosce quod potest \edtext{causa huius}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | causa huiusmodi \textit{V\textsuperscript{b}mv} | causa eius \textit{M\textsuperscript{a}} | hoc causa \textit{P\textsuperscript{y}} | eam huius \textit{E\textsuperscript{a}}}} \edtext{breuitatis}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{a}} | breuiter \textit{λE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv}}} \edtext{assignari}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | talis assignari \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | asignari talis \textit{V\textsuperscript{a}} | signari \textit{P\textsuperscript{y}}}}, \edtext{quia}{\Cfootnote[nosep]{\textit{ακmv} | quod \textit{π}}} \edtext{ypate}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | Parypate \textit{G\textsuperscript{u}}}} \edtext{sonum reddit}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | reddit sonum \textit{V\textsuperscript{m}} | sonum reddat \textit{G\textsuperscript{u}}}} grauem, \edtext{qui}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | que \textit{G\textsuperscript{u}P\textsuperscript{u}}}} \edtext{extenditur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | extendit \textit{V\textsuperscript{a}}}} secundum longum \edtext{latum et \edtext{profundum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | profunditatem \textit{P\textsuperscript{y}}}}, \edtext{reliqua}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}} | relique \textit{E\textsuperscript{a}mv}}} uero ad ipsam \edtext{acutum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | accidit \textit{P\textsuperscript{z}}}}, qui secundum longum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}} | ceu \textit{γM\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{m}} | sicut \textit{P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{uisum est}{\Cfootnote[nosep]{\textit{γλπmv} | uisum e \textit{P\textsuperscript{x}} | uisum \textit{E\textsuperscript{a}P\textsuperscript{y}}}} ‘ \edtext{xia}{\Cfootnote[nosep]{\textit{ακmv} | prius \textit{π}}}.\edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XI .16 , 900b ll. 17–25}}’Tardius \edtext{autem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | aut \textit{γmv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{quietatur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quietatus \textit{P\textsuperscript{y}} | comoratur \textit{P\textsuperscript{z}} | commutatur \textit{G\textsuperscript{u}}}} \edtext{sonus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sonum \textit{G\textsuperscript{u}}}} aeris secundum plures moti dimensiones quam secundum \edtext{unam}{\Cfootnote[nosep]{\textit{ακmv} | unum \textit{π}}} cum \edtext{dictum etiam sit}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | etiam dictum sit \textit{V\textsuperscript{b}mv} | dictum etiam sit quod \textit{P\textsuperscript{x}} | etiam sit \textit{G\textsuperscript{u}V\textsuperscript{z}} | dictum est etiam \textit{P\textsuperscript{z}}}} \edtext{graue}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | graue et \textit{V\textsuperscript{m}}}} tarde et multum moueri \edtext{acutum}{\Cfootnote[nosep]{\textit{αλπ} | acuta \textit{P\textsuperscript{x}} | acutum uero \textit{mv}}} \edtext{econtra}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{z}}}} \edtext{uisum est sepius antea}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}mv} | uisum sepius antea \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{z}}}}. \edtext{}{\Cfootnote{etcetera. \textit{P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 43. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Quadragesimumtertium problema}\label{edition-text book-19a part43}}{\lemma{Quadragesimumtertium + problema} \Cfootnote[nosep]{\textit{γmv} | «43m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{quadragesimum tertium.} Quadragesimumtertium. \textit{P\textsuperscript{y}} | 42m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID DELECTABILE}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID DELECTABILE UNIUS CANTUS EST SI AD LYRAM ET FISTULAM CANTANT? \textsuperscript{2}AUT QUIA OMNE DELECTABILE MIXTUM DELECTABILI UNUM EST? \textsuperscript{3}FISTULA ENIM DELECTABILIUS EST LYRA, QUARE ET CANTUS HOC MIXTO LYRA DELECTABILIUS UTIQUE ERIT, QUONIAM MIXTUM IMMIXTO DELECTABILIUS EST, SI UTRORUNQUE SENSUM ALIQUIS SIMUL ACCIPIAT. \textsuperscript{4}UINUM ENIM DELECTABILIUS EST OXIMELLE. PROPTER ID QUOD MIXTA SUNT MAGIS IPSIS QUE A NATURA MIXTA QUAM QUE A NOBIS, EST ENIM ET UINUM QUOD EST MIXTUM EX ACUTO ET DULCI HUMORE. MANIFESTANT AUTEM ET GRANATA UOCATA MUZA. \textsuperscript{5}CANTUS QUIDEM IGITUR ET FISTULA MISCENTUR SIBI IPSIS PROPTER SIMILITUDINEM, SPIRITU ENIM UTRAQUE FIUNT. SONUS AUTEM LYRE, QUONIAM AUTEM NON SPIRITU FIT. \textsuperscript{6}AUT MINUS SENSIBILE QUAM QUI EST FISTULE INCOMMIXTIBILIS EST UOCE? FACIENS AUTEM DIFFERENTIAM SENSUI MINUS DELECTAT, QUEMADMODUM IN SAPORIBUS DICTUM EST. \textsuperscript{7}AMPLIUS FISTULA QUIDEM MULTA SUO SONO ET SIMILITUDINE OCCULTAT PECCATORUM QUE SUNT CANTUS. LYRE AUTEM SONI, EXISTENTES TENUES ET INCOMMIXTIBILES UOCI SECUNDUM SE CONSIDERATI ET EXISTENTES SIBI IPSIS MANIFESTUM FACIUNT CANTUS PECCATUM, QUEMADMODUM REGULE EXISTENTES IPSORUM. INIUSTIS AUTEM IN CANTU CULPATIS, COMMUNE EX UTRISQUE NECESSARIE PEIUS FIERI \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema .43m. etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} cantus vnius \edtext{cum altero}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | altero est \textit{P\textsuperscript{y}}}} \edtext{mixtus}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | nuptus \textit{P\textsuperscript{y}}}} \edtext{uel cantus vnicus}{\Cfootnote[nosep]{\textit{αλmv} | uel cantus unius \textit{P\textsuperscript{x}} | uel cantus uel \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | uel cantus \textit{P\textsuperscript{p}P\textsuperscript{q}} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{delectabilis}{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}mv} | delectabilius \textit{P\textsuperscript{x}} | laudabilis \textit{P\textsuperscript{y}}}} \edtext{et suauis existit}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | existit et suauis \textit{V\textsuperscript{m}} | uel suauis existit \textit{π}}}, puta, si \edtext{fuerit aliquis}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | aliquis fuerit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{cantans}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}} | cantus \textit{γmv}}} \edtext{in}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | in \surplus{in} \textit{E\textsuperscript{a}}}} sono lyre uel fistule?} \edtext{Et}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{z}}}} adhuc delectabilior \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | cum \textit{P\textsuperscript{y}}}} \edtext{cantus fistule}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sonus fistule siue cantus \textit{P\textsuperscript{p}}}} \edtext{quam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | uel \textit{P\textsuperscript{y}}}} lyre, \edtext{et}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{y}}}} per \edtext{se \edtext{et}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | \textit{om}. \textit{M\textsuperscript{a}V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{coniectus}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | coniunctus \textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}}}} \edtext{cantui}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv}}}, ita ut triplex \edtext{fiat}{\Cfootnote[nosep]{\textit{ακmv} | fiat cantus \textit{π}}} comparatio: puta, cantus simplicis \edtext{ad}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ad cantus \textit{V\textsuperscript{z}}}} \edtext{compositum, et simplicis ad simplicem}{\Cfootnote[nosep]{\textit{γκ} | compositum, et simplicitatem \textit{P\textsuperscript{y}} | simplicem \textit{πE\textsuperscript{a}mv}}}, \edtext{ut}{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}mv} | et \textit{P\textsuperscript{x}} | non \textit{P\textsuperscript{y}}}} \edtext{fistule ad lyram, et \edtext{compositi}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | compositum \textit{V\textsuperscript{m}}}} ad compositum, \edtext{sicut}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{o}mv} | ut \textit{P\textsuperscript{p}} | non \textit{P\textsuperscript{y}} | ac \textit{P\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{z}V\textsuperscript{b}}}} }{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} fistule et cantus ad lyram et cantum. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } Soluit et primo assignat \edtext{causam quare}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | causam et quare \textit{P\textsuperscript{z}} | quia \textit{P\textsuperscript{x}}}} cantus \edtext{vnius}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | vnus \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} cum sono alterius \edtext{uel}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | velut \textit{G\textsuperscript{u}}}} cantus \edtext{vnicus}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | musicus \textit{G\textsuperscript{u}}}} \edtext{sit}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}mv} | fit \textit{P\textsuperscript{y}V\textsuperscript{b}}}} delectabilis, \edtext{dicens prius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | prius dicens \textit{V\textsuperscript{b}} | dicens primo \textit{G\textsuperscript{u}V\textsuperscript{a}}}} causam esse \textit{quoniam delectabile \edtext{omne}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv} | esse \textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | etiam \textit{P\textsuperscript{z}}}} \edtext{commixtum est}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}mv} | quod mixtum est \textit{V\textsuperscript{a}}}}, et \edtext{vnitum}{\Cfootnote[nosep]{\textit{λG\textsuperscript{u}E\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}} | vnicum \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}} | mixtum \textit{γmv}}} ex diuersis}, ut declaratum \edtext{est}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}mv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{o}V\textsuperscript{z}}}} \edtext{.38}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | .18 \textit{V\textsuperscript{z}} | prius \textit{π}}}. Quod autem \edtext{sit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}} | sic \textit{V\textsuperscript{b}mv} | \textit{om}. \textit{π}}} \edtext{delectabile}{\Cfootnote[nosep]{\textit{αλπmv} | delectabilis dicens prius causam \textit{P\textsuperscript{x}}}} vnum existit, \edtext{cum tunc}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{z}mv} | tamen tunc \textit{V\textsuperscript{m}} | cum tamen \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | cum causa \textit{P\textsuperscript{z}} | cum \textit{G\textsuperscript{u}P\textsuperscript{x}}}} \edtext{vniformius}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}V\textsuperscript{o}mv} | uniformis \textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} \edtext{sensum moueat}{\Cfootnote[nosep]{\textit{ακmv} | moueat sensum \textit{π}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{FISTULA ENIM.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | FISTULA. \textit{G\textsuperscript{u}P\textsuperscript{q}}}} } Comparat 2° fistulam ad lyram \edtext{penes}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ponens \textit{P\textsuperscript{z}}}} \edtext{delectationem}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | delectationem et \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}}. \edtext{Secundo}{\Cfootnote[nosep]{\textit{αλπmv} | primo \textit{P\textsuperscript{x}}}} assignat \edtext{causam}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | aliam causam \textit{E\textsuperscript{a}}}} quare sonus fistule \edtext{est}{\Cfootnote[nosep]{\textit{γκmv} | sit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}}}} delectabilior \edtext{eo qui}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}mv} | eo quod \textit{P\textsuperscript{x}} | est quod \textit{P\textsuperscript{y}} | quam \textit{π}}} lyre. \edtext{Secunda}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | Secunda ibi \textit{V\textsuperscript{a}V\textsuperscript{z}mv} | Ibi secunda \textit{V\textsuperscript{b}} | Ibi \textit{π}}}: \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{z}mv} | a\expan{u}t\expan{em} \textit{(orig. \textup{āt})} \textit{P\textsuperscript{x}V\textsuperscript{m}}}} } \edtext{Dicit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | dicens \textit{P\textsuperscript{z}}}} \edtext{ergo}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}} | igitur \textit{λE\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{o}} | enim \textit{P\textsuperscript{y}} | \textit{om}. \textit{mv}}} \edtext{primo}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} quod \textit{fistula est delectabilius instrumentum \edtext{auditu}{\Cfootnote[nosep]{\textit{ακmv} | auditui \textit{π}}} quam lyra. \edtext{ \edtext{Unde}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}E\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} etiam cantus \edtext{commixtus}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} \edtext{ex}{\Cfootnote[nosep]{\textit{ακmv} | cum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} uoce et fistula \edtext{ \edtext{est}{\Cfootnote[nosep]{\textit{κ} | erit \textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{iocundior}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | ioculoxior \textit{V\textsuperscript{a}}}} \edtext{commixto ex}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | cum mixto et \textit{E\textsuperscript{a}}}} uoce et lyra}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}. Et hoc quia illud \edtext{quod}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | \textit{om}. \textit{γmv}}} \edtext{est mixtum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}} | mixtum est \textit{mv} | mixtum \textit{V\textsuperscript{b}} | \textit{om}. \textit{V\textsuperscript{a}} | est conmixtum \textit{πM\textsuperscript{a}}}} \edtext{delectabilius}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}mv} | delectabilius est \textit{λπE\textsuperscript{a}P\textsuperscript{y}}}} \edtext{eo quod}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | eo quod est \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{z}}}} simplex \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{immixtum}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}V\textsuperscript{z}}}}, \edtext{dummodo mixtura}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} utrorumque \edtext{mixtibilium}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}} | sensibilium mixtibilium \textit{P\textsuperscript{y}}}} sentiatur \edtext{utcunque}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | utrumque \textit{G\textsuperscript{u}P\textsuperscript{q}} | utique \textit{P\textsuperscript{z}}}} existens \edtext{tamen}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} in quadam \edtext{conmixtione}{\Cfootnote[nosep]{\textit{κ} | coniunctione \textit{γP\textsuperscript{y}mv} | soni notione \textit{πE\textsuperscript{a}}}}.} +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{UINUM.}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | UNUM. \textit{γmv} | VNDE. \textit{π}}} } Declarat \edtext{secundo id in}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{m}} | id .2°. in \textit{P\textsuperscript{y}V\textsuperscript{z}} | 2° illud in \textit{P\textsuperscript{x}} | 2° in \textit{γπmv}}} \edtext{mixtione}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} \edtext{nature et artis}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | nature id est artis \textit{P\textsuperscript{z}} | nature naturis \textit{κ}}}, dicens quod \edtext{ \textit{vinum} quod}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | unum quod \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{a}} | vnumquodque \textit{V\textsuperscript{b}mv} | illud quod \textit{G\textsuperscript{u}P\textsuperscript{q}}}} est simplex \edtext{arte}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | erit \textit{P\textsuperscript{y}}}}, \edtext{conmixtum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} \edtext{tamen}{\Cfootnote[nosep]{\textit{ακE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cum \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{natura}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | anima \textit{P\textsuperscript{z}}}}, \textit{ \edtext{est delectabilius}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | delectabilius est \textit{P\textsuperscript{y}V\textsuperscript{a}}}} \edtext{oximelle}{\Cfootnote[nosep]{\textit{γλG\textsuperscript{u}P\textsuperscript{y}mv} | exmilleus \textit{P\textsuperscript{x}} | ex melle \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{seu}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ceu \textit{P\textsuperscript{z}}}} \edtext{acetimelle}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | aceto melle \textit{P\textsuperscript{z}} | accetimellis \textit{V\textsuperscript{b}} | aceti \textit{E\textsuperscript{a}} | aceti et melle \textit{G\textsuperscript{u}}}} }, quod \edtext{est}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | est in \textit{γmv}}} arte \edtext{constructum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}} | constrictum \textit{P\textsuperscript{z}} | constructionem \textit{mv} | conmixtum \textit{P\textsuperscript{y}}}} ex \edtext{melle}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | melle et \textit{E\textsuperscript{a}G\textsuperscript{u}V\textsuperscript{z}}}} \edtext{aceto}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} et \edtext{aqua}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quia \textit{P\textsuperscript{z}}}}. \textit{Propter quod \edtext{vino}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | vinum \textit{M\textsuperscript{a}V\textsuperscript{m}} | modo \textit{P\textsuperscript{y}}}} ipsi sunt amplius \edtext{mixta}{\Cfootnote[nosep]{\textit{αλmv} | conmixta \textit{π}}} ea que sunt \edtext{nature}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | natura \textit{P\textsuperscript{y}} | uere \textit{P\textsuperscript{z}}}} \edtext{quam}{\Cfootnote[nosep]{\textit{αλπmv} | quod \textit{P\textsuperscript{x}}}} in \edtext{mixtione}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | commixtione \textit{P\textsuperscript{u}}}} artificiali per nos \edtext{constructa}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | considerata \textit{γ}}},} sicut \edtext{illa}{\Cfootnote[nosep]{\textit{ακmv} | ea \textit{π}}} que \edtext{oximellis}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}V\textsuperscript{z}} | oximelle \textit{γmv} | ex mellis \textit{πP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}}}}. In priori \edtext{causa}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | enim \textit{P\textsuperscript{y}}}} \edtext{uera extat}{\Cfootnote[nosep]{\textit{γκmv} | extat uera \textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | extat natura \textit{P\textsuperscript{y}} | existat vera \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{mixtio}{\Cfootnote[nosep]{\textit{ακmv} | commixtio \textit{π}}} in \edtext{oximelle}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | oximello \textit{V\textsuperscript{z}} | exmellere \textit{V\textsuperscript{m}}}}, \edtext{uero}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | nature \textit{P\textsuperscript{y}} | uero secundum \textit{π}}} \edtext{sensualis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | sensibilis \textit{V\textsuperscript{a}} | sensum \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{p}}}} tantum. \textit{Nam \edtext{vinum, quod}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | vnumquodque \textit{G\textsuperscript{u}P\textsuperscript{q}}}} est \edtext{mixtum quoddam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | quoddam mixtum \textit{π}}} \edtext{nature}{\Cfootnote[nosep]{\textit{ακmv} | naturale \textit{π}}}, \edtext{componitur}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | compositum \textit{G\textsuperscript{u}} | compositio \textit{M\textsuperscript{a}}}} ex humore acuto et dulci \edtext{mixtione}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | commixtione \textit{πE\textsuperscript{a}}}} \edtext{sufficienter}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sufficienti \textit{G\textsuperscript{u}}}}. \edtext{Circa}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}mv} | Certa \textit{λ} | Causata \textit{P\textsuperscript{y}}}} quod \edtext{manifestant}{\Cfootnote[nosep]{\textit{αλπmv} | manifestat \textit{P\textsuperscript{x}}}} \edtext{granata}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | grauata \textit{G\textsuperscript{u}} | generata \textit{P\textsuperscript{z}}}} nominata \edtext{musa seu}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | muza se \textit{P\textsuperscript{z}} | muca seu \textit{P\textsuperscript{x}}}} \edtext{messa}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | musa \textit{G\textsuperscript{u}}}} }, id est media, sunt \edtext{enim}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} tria specie: dulcia, \edtext{acida, et}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}} | acida \textit{mv} | acuta, et \textit{λ}}} media (\edtext{conmixta}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | commixti \textit{P\textsuperscript{u}}}} \edtext{ex}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{G\textsuperscript{u}}}} dulci et \edtext{acetoso}{\Cfootnote[nosep]{\textit{αλπmv}}} sapore). Et \edtext{ideo}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} magis delectant \edtext{quando}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | quam \textit{λ}}} in vno tertio \edtext{facta}{\Cfootnote[nosep]{\textit{αλπmv} | certam \textit{P\textsuperscript{x}}}} sunt \edtext{natura talia}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | naturalia \textit{G\textsuperscript{u}}}} quam si \edtext{miscerentur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ministrantur \textit{V\textsuperscript{a}}}} \edtext{arte}{\Cfootnote[nosep]{\textit{ακπ} | aere \textit{mv}}} dulcia \edtext{cum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{acidis}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | acetosis \textit{V\textsuperscript{z}}}}. \edtext{Quidam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}mv} | Quidem \textit{V\textsuperscript{a}V\textsuperscript{o}}}} quoque \edtext{habet}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | habent \textit{πM\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{z}} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{ex melle}{\Cfootnote[nosep]{\textit{ακmv} | oximelle \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | \textit{om}. \textit{V\textsuperscript{o}}}} loco \edtext{eius}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | est \textit{V\textsuperscript{z}}}} quod \edtext{ \edtext{expositum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | expositum est \textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | est expositum \textit{V\textsuperscript{z}}}} \edtext{ex melle}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}} | eximelle \textit{V\textsuperscript{m}} | oximelle \textit{αM\textsuperscript{a}V\textsuperscript{z}mv} | melle \textit{V\textsuperscript{o}}}}, quod non \edtext{sic}{\Cfootnote[nosep]{\textit{γλP\textsuperscript{y}mv} | sit \textit{P\textsuperscript{x}} | \textit{om}. \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{approbo}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | ambo \textit{P\textsuperscript{y}}}}, \edtext{quamuis id}{\Cfootnote[nosep]{\textit{γλE\textsuperscript{a}mv} | quam id \textit{P\textsuperscript{y}} | quamuis sic \textit{P\textsuperscript{x}} | quamuis \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | licet \textit{G\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{exposuerim}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}} | exposueram \textit{V\textsuperscript{a}} | exposuerint \textit{P\textsuperscript{y}mv} | expositum sit \textit{π}}} \edtext{quandoque}{\Cfootnote[nosep]{\textit{ακπ} | quoniam \textit{mv}}}. +\pend + +\pstart +\textbf{5} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{CANTUS.} Applicat ad propositum \edtext{concludendo}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}, dicens \edtext{itaque}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | itaque quod \textit{V\textsuperscript{m}} | ita \textit{P\textsuperscript{y}}}} \textit{cantus \edtext{in}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}} | et \textit{γP\textsuperscript{y}mv}}} fistula \edtext{commiscetur}{\Cfootnote[nosep]{\textit{κ} | commiscentur \textit{απmv}}} \edtext{sibi}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | sub \textit{P\textsuperscript{z}}}} ipsis propter similitudinem quam \edtext{habent}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}} | habent in \textit{E\textsuperscript{a}mv}}} ad inuicem. Quod ostenditur \edtext{quia}{\Cfootnote[nosep]{\textit{αλmv} | quoniam \textit{G\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{c}} | quando \textit{C\textsuperscript{a}V\textsuperscript{o}} | ex \textit{P\textsuperscript{x}}}} utrique, \edtext{ut}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | scilicet \textit{P\textsuperscript{y}}}} cantus et fistule, soni perficiuntur flatu ex ore, \edtext{namque}{\Cfootnote[nosep]{\textit{ακπ} | enim \textit{mv}}} prodeunt. \edtext{Sed}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}V\textsuperscript{o}mv} | Quod \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{c}} | \textit{om}. \textit{P\textsuperscript{p}}}} sonus lyre \edtext{non}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | non construitur \textit{P\textsuperscript{y}}}}, \edtext{sed}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{potius}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} tactu \edtext{perficitur}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}} | construitur \textit{λE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | instruitur \textit{V\textsuperscript{a}}}} rotatio.} Que autem similia sunt ad inuicem delectant amplius, cum \edtext{delitia}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}V\textsuperscript{m}mv} | delitie \textit{P\textsuperscript{x}V\textsuperscript{z}} | delectatio \textit{π}}} \edtext{causentur}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}} | causetur \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | causantur \textit{V\textsuperscript{z}} | tenetur \textit{P\textsuperscript{u}}}} ex coniunctione conuenientis cum \edtext{conueniente}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | conuenienti \textit{P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | conueniente ut \textit{M\textsuperscript{a}}}} ‘4° \textit{de \edtext{accidenti}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}} | accidente \textit{πP\textsuperscript{y}mv}}} }.\edtext{}{\Afootnote[nosep]{Gal. \textit{De morbo et acc.} IV .6 (The Greek original which d'Abano is here paraphrasing occurs in bk. I of the treatise called De symptomatum causis)}}’ +\pend + +\pstart +\textbf{6} \edtext{Nosce}{\Cfootnote[nosep]{\textit{ακπ} | Notandum \textit{mv}}} \edtext{quod mixtio}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quam connixtio \textit{G\textsuperscript{u}}}} \edtext{vini}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | vni \textit{P\textsuperscript{z}}}} \edtext{proportionatur sono}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | sono proportionatur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} composito \edtext{ \edtext{et}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{facto ex fistula}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | ex fistula facto \textit{P\textsuperscript{z}}}} et uoce, \edtext{que}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | quod \textit{V\textsuperscript{a}}}} autem \edtext{ex oximellis}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}} | oximellis \textit{M\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{o}} | oximell \textit{G\textsuperscript{u}P\textsuperscript{z}} | oximelli \textit{V\textsuperscript{z}} | oximel \textit{V\textsuperscript{b}mv} | ex melle \textit{E\textsuperscript{a}P\textsuperscript{u}}}} \edtext{simplici}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | simplicis \textit{M\textsuperscript{a}}}} \edtext{aut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | autem \textit{mv}}} \edtext{composito}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | compositi \textit{M\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} ex uoce et \edtext{lyra}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | lyra composito \textit{λ}}}, respectu alterius \edtext{qui}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | que \textit{G\textsuperscript{u}P\textsuperscript{q}V\textsuperscript{m}}}} \edtext{ex}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | est \textit{V\textsuperscript{m}}}} fistula. +\pend + +\pstart +\textbf{7} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } Soluit \edtext{assignans}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | assignando \textit{M\textsuperscript{a}} | et assignat \textit{π}}} \edtext{causam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | aliam causam \textit{π} | causam duplicem \textit{P\textsuperscript{y}}}} quare sonus lyre non \edtext{ut qui fistule est}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | ut qui fistule \textit{E\textsuperscript{a}P\textsuperscript{y}} | est ut qui fistule \textit{π} | ut que fistule est \textit{V\textsuperscript{m}}}} delectabilis. \edtext{Secunda: \textit{AMPLIUS}.}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | Secunda ibi: \textit{AMPLIUS}. \textit{V\textsuperscript{a}mv} | Ibi secunda: \textit{AMPLIUS}. \textit{V\textsuperscript{b}} | \textit{om}. \textit{π}}} \edtext{Dicit}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}V\textsuperscript{z}mv} | Dicens \textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}}}} \edtext{ \edtext{primo}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | prius \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv}}} \edtext{id}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ideo \textit{π}}} }{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | id prius \textit{V\textsuperscript{a}}}} esse \textit{quoniam sonus lyre minus \edtext{est}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{sensibilis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | sensui \textit{P\textsuperscript{z}}}} quam \edtext{sonus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} fistule, \edtext{quam minus}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | quare minus \textit{M\textsuperscript{a}V\textsuperscript{a}} | quamuis \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}, \edtext{enim}{\Cfootnote[nosep]{\textit{γπP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv} | eius \textit{M\textsuperscript{a}V\textsuperscript{m}} | ein \textit{E\textsuperscript{a}}}} \edtext{componibilis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | ponibilis \textit{C\textsuperscript{a}V\textsuperscript{o}} | comparabilis \textit{mv} | possibilis \textit{P\textsuperscript{z}}}} est cum uoce, \edtext{habet}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | hec \textit{πE\textsuperscript{a}}}} enim \edtext{differentiam}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | differentia \textit{E\textsuperscript{a}} | dicta \textit{π}}}, ut \edtext{iam}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} visum \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} ad ipsam. \edtext{Ex illo autem}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | Ex isto autem \textit{P\textsuperscript{p}P\textsuperscript{u}} | Ex illo \textit{V\textsuperscript{a}} | Et ideo \textit{P\textsuperscript{x}}}} quod differentiam \edtext{et \edtext{diuersitatem}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | diuersitate \textit{P\textsuperscript{x}}}} ad sensum habet}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | et diuersitatem habet ad sensum \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}} | habet et diuersitatem ad sensum \textit{G\textsuperscript{u}} | diuersitatem \textit{V\textsuperscript{a}}}} minor sentitur delectatio, sicut \edtext{apparuit}{\Cfootnote[nosep]{\textit{ακπ} | apparet \textit{mv}}} \edtext{in}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} saporibus arte \edtext{et natura mixtis}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | et natura in mixtis \textit{γE\textsuperscript{a}mv} | et natura compositis \textit{V\textsuperscript{z}} | commixtis et natura \textit{π}}}.} +\pend + +\pstart +\textbf{8} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AMPLIUS.}{\Cfootnote[nosep]{\textit{ακπ} | AMPLIUS. Amplius \textit{mv}}} } Assignat \edtext{causam secundam}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}} | secundam causam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | causam \surplus{dicens} secundam. \textit{P\textsuperscript{y}} | causam duplam \textit{γP\textsuperscript{x}mv}}}, \edtext{dicens}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | dicit \textit{P\textsuperscript{z}}}} quod \textit{fistula propter suum \edtext{sonum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | motum \textit{M\textsuperscript{a}}}} et eius similitudinem,} \edtext{quia}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | ut \textit{V\textsuperscript{m}}}} sua fortitudine soni \edtext{extollit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}} | excellit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{b}mv} | excedit \textit{V\textsuperscript{a}}}} uocem \edtext{cantantis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}}, \textit{ \edtext{obtegit multa peccata}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | peccata multa obtegit \textit{P\textsuperscript{p}}}} in \edtext{cantu}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cantu \surplus{cantu} \textit{P\textsuperscript{p}}}} contingentia. Sed soni \edtext{lyre}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}mv} | lyres \textit{V\textsuperscript{a}} | lyri \textit{E\textsuperscript{a}}}}, \edtext{quia}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} subtiles sunt et parui et \edtext{incommiscibiles}{\Cfootnote[nosep]{\textit{γP\textsuperscript{p}P\textsuperscript{z}mv}}} \edtext{uoci}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uoces \textit{G\textsuperscript{u}}}}, cum \edtext{secundum}{\Cfootnote[nosep]{\textit{κ} | per \textit{απmv}}} se \edtext{considerantur}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | consideratur \textit{M\textsuperscript{a}} | considerentur \textit{π}}}, \edtext{prout}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | cum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{in seipsis}{\Cfootnote[nosep]{\textit{γκπmv}}} \edtext{extant}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | extent \textit{G\textsuperscript{u}P\textsuperscript{q}}}} et non in aliis, \edtext{quibus}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | in quibus \textit{V\textsuperscript{a}} | qui hiis \textit{πE\textsuperscript{a}}}} \edtext{occultentur}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}E\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | occultantur \textit{γπM\textsuperscript{a}mv}}}, \edtext{manifestum est quod}{\Cfootnote[nosep]{\textit{κ} | manifestum quod \textit{E\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{o}} | manifestum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}} | aliam quam \textit{P\textsuperscript{z}} | Minor quia \textit{γmv}}} circa ipsos \edtext{peccatum}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | peccant \textit{M\textsuperscript{a}}}} \edtext{accidit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | accidunt \textit{G\textsuperscript{u}}}} in cantu, \edtext{nam}{\Cfootnote[nosep]{\textit{γP\textsuperscript{y}V\textsuperscript{z}mv} | non \textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}}}} in ipso, \edtext{sicut}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | sic \textit{V\textsuperscript{a}}}} in aliis \edtext{scientiis}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | sonis \textit{P\textsuperscript{y}P\textsuperscript{z}}}} sunt \edtext{canones}{\Cfootnote[nosep]{\textit{ακπ} | canonem \textit{mv}}} quidam per quos armonice canitur, a quibus \edtext{cum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | dum \textit{G\textsuperscript{u}}}} \edtext{receditur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | recedatur \textit{P\textsuperscript{y}}}} contingit in cantu peccare. Quare subditur quod \edtext{accidit}{\Cfootnote[nosep]{\textit{ακmv} | acutum \textit{π}}} \edtext{iniustis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | in musicis \textit{G\textsuperscript{u}} | in instrumentis \textit{P\textsuperscript{y}} | in tristis \textit{V\textsuperscript{o}} | in istis \textit{P\textsuperscript{z}V\textsuperscript{a}}}} non recte predictos canones \edtext{obseruantes}{\Cfootnote[nosep]{\textit{κ} | obseruantibus \textit{απmv}}} \edtext{alia}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | ac \textit{P\textsuperscript{y}}}} littera \edtext{multis ac}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | multis hac \textit{E\textsuperscript{a}} | multis autem \textit{P\textsuperscript{p}} | \textit{om}. \textit{G\textsuperscript{u}}}} melior, ut peccent et \edtext{culpentur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | culpent \textit{P\textsuperscript{y}P\textsuperscript{z}} | cohientur \textit{V\textsuperscript{o}}}} in cantu. Quod enim commune \edtext{existit}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | ex istis \textit{πE\textsuperscript{a}}}}, \edtext{ut ex}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{z}mv} | ex \textit{V\textsuperscript{m}} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{utrisque}{\Cfootnote[nosep]{\textit{αλπmv} | utriusque \textit{P\textsuperscript{x}}}} \edtext{confectum}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | cum factum \textit{M\textsuperscript{a}V\textsuperscript{b}}}}, puta uoce \edtext{et}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | non \textit{V\textsuperscript{b}}}} instrumento sicut lyra, \edtext{necessarie}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}mv} | necesse est \textit{M\textsuperscript{a}V\textsuperscript{z}} | necessa est \textit{V\textsuperscript{m}} | uocem \textit{P\textsuperscript{y}}}} deterius perfici} eorum \edtext{consonantia}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}} | dissonantia \textit{λE\textsuperscript{a}P\textsuperscript{z}} | discordantia \textit{P\textsuperscript{y}} | distantia \textit{γmv}}}, \edtext{contra}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | circa \textit{M\textsuperscript{a}P\textsuperscript{y}}}} \edtext{regulas}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | duas \textit{V\textsuperscript{a}}}} \edtext{armonicas}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | armonice \textit{V\textsuperscript{m}} | canonicas \textit{G\textsuperscript{u}}}} factum. \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{z}V\textsuperscript{z}} | sequitur 44m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Quadragesimumquartum problema}\label{edition-text book-19a part44}}{\lemma{Quadragesimumquartum + problema} \Cfootnote[nosep]{\textit{γmv} | «44m» (in mg.) \textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}} | Quadragesimumquartum. \surplus{quadragesimumquartum.} \textit{P\textsuperscript{y}} | 43m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{E\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID SEPTEM}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID SEPTEM QUIDEM MEDIA UOCATUR, OCTO AUTEM NON EST MEDIUM? \textsuperscript{2}AUT QUIA SEPTEM CORDARUM FUERUNT ANTIQUITUS CONSONANTIE, SEPTEM AUTEM HABET MEDIUM? \textsuperscript{3}AMPLIUS EORUM QUE SUNT IN MEDIO EXTREMITATUM, MEDIUM SOLUM PRINCIPIUM QUODDAM EST, EST ENIM ALTERA EXTREMITATUM DECLINANTIUM IN ALIQUA DISTANTIA PER MEDIUM QUOD PRINCIPIUM EST: HOC EST MEDIUM. QUONIAM AUTEM ULTIMA MEDIUM EST CONSONANTIE NEATE ET YPATE, HORUM AUTEM IN MEDIO RELIQUI SONI, QUORUM MEDIA UOCATA SOLA PRINCIPIUM EST ALTERIUS TETRACORDI, IUSTE MEDIA APPELLATUR. \textsuperscript{4}EORUM AUTEM QUE SUNT IN MEDIO QUARUNDAM EXTREMITATUM MEDIUM ERAT PRINCIPIUM SOLUM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema .44m. etcetera. \edtext{Repetit}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | Quare repetit \textit{E\textsuperscript{a}}}} 25° \edtext{et}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{utcunque}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | utrunque \textit{M\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{33m.}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}}, \edtext{dicens}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \textit{ \edtext{quare}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{.7.}{\Cfootnote[nosep]{\textit{αλπmv} | a \textit{P\textsuperscript{x}}}} dicitur \edtext{habere medium etcetera}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}.} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} } \edtext{Soluit}{\Cfootnote[nosep]{\textit{γλπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{x}}}} et \edtext{primo assignat}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | assignat primo \textit{G\textsuperscript{u}}}} causam, \edtext{et iam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | et inde \textit{V\textsuperscript{b}mv} | que iam \textit{π} | unde \textit{V\textsuperscript{a}}}} \edtext{apparuit}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | apparente \textit{E\textsuperscript{a}}}} 2°. Quia \edtext{mentionem fecerat}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | fecerat mentionem \textit{P\textsuperscript{y}}}} de medio, \edtext{ostendit}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | dicit \textit{P\textsuperscript{y}}}} \textit{ \edtext{quomodo}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quomodo autem \textit{G\textsuperscript{u}}}} \edtext{accipiatur medium}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}mv} | medium accipitur \textit{G\textsuperscript{u}} | accipitur medium \textit{V\textsuperscript{a}V\textsuperscript{z}} | accipiuntur medium \textit{V\textsuperscript{o}}}} \edtext{cum \edtext{dicitur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} .7. habere medium}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} } cuius \edtext{gratia problema}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | problema gratia \textit{P\textsuperscript{y}}}} \edtext{repetiit}{\Cfootnote[nosep]{\textit{ακE\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}mv} | repetit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}. +\pend + +\pstart +\textbf{3} \edtext{Secunda}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}} | Secunda ibi \textit{P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{z}mv} | Ibi secunda \textit{V\textsuperscript{b}} | Ibi \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \textit{AMPLIUS.} \edtext{Dicit}{\Cfootnote[nosep]{\textit{ακmv} | Dicens \textit{π}}} \edtext{igitur}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{b}mv} | igitur primo \textit{V\textsuperscript{a}} | \textit{om}. \textit{πE\textsuperscript{a}}}} quod \textit{vno modo \edtext{dicitur medium}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | medium dicitur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{quoddam principium}{\Cfootnote[nosep]{\textit{αλπmv} | principium quoddam \textit{P\textsuperscript{x}}}} \edtext{existens medium}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \surplus{inter duo extrema nam illud principium per quamdam distantiam equaliter declinat ab utroque extremorum dicitur} medium \textit{E\textsuperscript{a}} | \textit{om}. \textit{π}}} inter duo extrema, nam illud principium \edtext{quod}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} per quandam \edtext{distantiam}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | distantia \textit{P\textsuperscript{y}}}} equaliter \edtext{declinat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | determinat \textit{P\textsuperscript{p}P\textsuperscript{u}}}} ab utroque extremorum dicitur medium}, \edtext{sicut in aliqua consonantia est dare}{\Cfootnote[nosep]{\textit{γP\textsuperscript{y}V\textsuperscript{z}mv} | sicut aliqua consonantia est dare \textit{V\textsuperscript{m}} | sicut in alia consonantia est dare \textit{E\textsuperscript{a}M\textsuperscript{a}} | sicut in alico sonantia est dare \textit{P\textsuperscript{x}} | inter \textit{π}}} duo \edtext{ultima}{\Cfootnote[nosep]{\textit{ακmv} | extrema sicut in alia distantiam est dare .2. extrema \textit{π}}} \edtext{ut}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | quod \textit{V\textsuperscript{a}}}} vnus \edtext{sit sonus}{\Cfootnote[nosep]{\textit{ακmv} | sonus sit \textit{π}}} \edtext{cantus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}mv} | causatus \textit{P\textsuperscript{p}}}} ab ypate fortis existens, \edtext{secundus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | secundo \textit{V\textsuperscript{a}} | alius \textit{π}}} a \edtext{neate siue}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{nete}{\Cfootnote[nosep]{\textit{αλπmv} | a nete \textit{P\textsuperscript{x}}}}, inter quos est dare plures sonos medios \edtext{distantes ab extremis}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | ab extremis distantes \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} secundum \edtext{maius}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | magis \textit{απM\textsuperscript{a}mv}}} et minus, \edtext{ceu}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}G\textsuperscript{u}V\textsuperscript{o}}}} \edtext{inter vnum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | introductum \textit{P\textsuperscript{z}}}} et septem \edtext{que intermedia}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}mv} | inter que ueniunt media \textit{V\textsuperscript{z}} | que alias inter inde cum media \textit{V\textsuperscript{m}} | 5. intermedia \textit{P\textsuperscript{z}} | quia inde cum media \textit{P\textsuperscript{x}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{o}mv} | et \textit{V\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{y}P\textsuperscript{z}}}} .5. reliqua \edtext{dicantur}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | dicatur \textit{M\textsuperscript{a}} | dicuntur \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}}}} \edtext{media}{\Cfootnote[nosep]{\textit{ακπ} | mediam \textit{mv}}}. +\pend + +\pstart +\textbf{4} \edtext{Notandum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | Nota \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} quod \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | huiusmodi \textit{γG\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{p}mv}}} \edtext{medium dicitur principium}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | medium dicitur \textit{P\textsuperscript{z}} | principium medium dicitur principium \textit{P\textsuperscript{y}}}} eo quod \edtext{est}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{habitus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} quidam virtutis \edtext{qui}{\Cfootnote[nosep]{\textit{ακmv} | que \textit{π}}} principium extat \edtext{actuum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | actium \textit{V\textsuperscript{a}} | acutiuum \textit{G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}mv} | acutum \textit{P\textsuperscript{z}}}}, cum sit diuisibile habens quantitatem. \edtext{Est et}{\Cfootnote[nosep]{\textit{ακmv} | Est etiam \textit{π}}} aliud medium \edtext{uere}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{indiuisibile}{\Cfootnote[nosep]{\textit{ακmv} | indiuisibile natura \textit{π}}}; quale medium \edtext{dicitur}{\Cfootnote[nosep]{\textit{λ} | dicuntur \textit{απP\textsuperscript{x}mv}}} \edtext{solum illa habere}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}} | solum habere illa \textit{P\textsuperscript{y}} | solum illi habere \textit{γmv} | illa sola habere \textit{π}}}quorum \edtext{medium est principium alterius \edtext{tetracordi}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | tetracorda \textit{P\textsuperscript{z}}}}. Quod non appellatur uere principium, sed}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} medium magis, \edtext{sicut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | sic \textit{P\textsuperscript{z}V\textsuperscript{c}}}} positis .7. cordis, quarta, \edtext{quidem}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | quidam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}mv}}} ut mese, repetita cum tribus \edtext{superioribus \edtext{et inferioribus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{etiam}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ea \textit{P\textsuperscript{x}}}} tribus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | inferioribus et tribus superioribus \textit{P\textsuperscript{p}}}}, \edtext{constituuntur}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | constituitur \textit{P\textsuperscript{p}} | constituetur \textit{G\textsuperscript{u}} | constituunt \textit{P\textsuperscript{y}}}} \edtext{duo}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{tetracorda}{\Cfootnote[nosep]{\textit{λπV\textsuperscript{b}mv}}} tunc mese utrobique \edtext{uere}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} medium extat. \edtext{ \edtext{verbi gratia}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{c}mv} | verbi gratia si ordinantur \textit{G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} \begin{longtable}{P{0.31126760563380285\textwidth}P{0.5387323943661972\textwidth}} +\Panel{Ypate.}{label}{1}{l}\tabcellsep \\ +\Panel{Parypate.}{label}{1}{l}\tabcellsep \textsuperscript{}primum tetracordum.\\ +\Panel{Lychanos.}{label}{1}{l}\tabcellsep \\ +\Panel{Mese.}{label}{1}{l}\tabcellsep \\ +\Panel{Paramese.}{label}{1}{l}\tabcellsep \\ +\Panel{Paranete.}{label}{1}{l}\tabcellsep \textsuperscript{}secundum tetracordum. retracordium \\ +\Panel{Nete.}{label}{1}{l}\tabcellsep \end{longtable} Primum retrocordum \edtext{ \edtext{Et}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{o}}}} \edtext{huius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | huiusmodi \textit{γG\textsuperscript{u}P\textsuperscript{y}}}} \edtext{duo quidem}{\Cfootnote[nosep]{\textit{V\textsuperscript{b}} | quidem duo \textit{V\textsuperscript{a}} | secundo quidem \textit{E\textsuperscript{a}} | duo \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | .20. quidem \textit{P\textsuperscript{y}} | illius quidem \textit{M\textsuperscript{a}}}} \edtext{tetracorda}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{o}mv}}} secundum \edtext{sinzeusim ordinantur}{\Cfootnote[nosep]{\textit{γmv} | sinzeusim \textit{λπmv}}},}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} \edtext{cum \edtext{autem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{fuerint}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}mv} | fuerit \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{.8.}{\Cfootnote[nosep]{\textit{αmv} | quatuor \textit{π}}} corde secundum \edtext{dyazeusim}{\Cfootnote[nosep]{\textit{V\textsuperscript{b}}}} computantur.}{\Cfootnote[nosep]{\textit{απmv}}} }{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{m}V\textsuperscript{z}}}} +\pend + +\pstart +\textbf{5} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{EORUM.} \edtext{Tunc}{\Cfootnote[nosep]{\textit{ακπ} | Nunc \textit{mv}}} repetit \textit{medium prius horum}, \edtext{et}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | etiam \textit{λ}}} apparet sic igitur medium est \edtext{duplex}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}}: \edtext{vnum}{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} quidem geometricum \edtext{siue}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ceu \textit{V\textsuperscript{a}}}} quo ad nos \edtext{aut}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | autem \textit{P\textsuperscript{y}} | aliud \textit{P\textsuperscript{p}}}} \edtext{per abnegationem}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}mv} | paranegomon \textit{γ}}} extremorum, \edtext{aliud vero}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | aliud uero aliud vero \textit{V\textsuperscript{a}}}} arismetricum \edtext{seu}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | secundum \textit{P\textsuperscript{z}}}} \edtext{rei}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}} | rei uel \textit{γE\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}mv} | \gap{} uel \textit{M\textsuperscript{a}} | in uel secundum \textit{P\textsuperscript{y}}}} \edtext{per}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv} | pre \textit{V\textsuperscript{m}} | \textit{om}. \textit{V\textsuperscript{z}}}} indiuisibilem \edtext{equidistantiam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}mv}}} ab extremis. +\pend + +\pstart +\textbf{6} Apparet denique quod secundum \edtext{primum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | plurimum \textit{V\textsuperscript{z}}}} \edtext{medium}{\Cfootnote[nosep]{\textit{ακπ} | modum \textit{mv}}} potest dici \edtext{dyaocto}{\Cfootnote[nosep]{\textit{λγG\textsuperscript{u}mv}}}. Unde ‘primo \textit{musice}: in \edtext{octocordo}{\Cfootnote[nosep]{\textit{γλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | sexto corde \textit{P\textsuperscript{x}}}} \edtext{due semper}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | duo semper \textit{πE\textsuperscript{a}}}} \edtext{medie}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} reperiuntur, \edtext{et}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | etiam \textit{E\textsuperscript{a}}}} \edtext{non}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} vna \edtext{media}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} potest inueniri.\edtext{}{\Afootnote[nosep]{Boeth. \textit{De inst. mus.} Ι .20 (Friedlein p. 208, ll. 8–10)}}’ \edtext{}{\Cfootnote{etcetera. \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 45. problema. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Quadragesimumquintum problema}\label{edition-text book-19a part45}}{\lemma{Quadragesimumquintum + problema} \Cfootnote[nosep]{\textit{γmv} | «45m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{quadragesimumquintum.} Quadragesimumquintum. \textit{P\textsuperscript{y}} | 44m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID MULTI}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}} | PROPTER QUID MULTIPLICANTES \textit{π} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID MULTI CANTANTES SALUANT MAGIS RITHIMUM QUAM PAUCI? \textsuperscript{2}AUT QUIA MAGIS AD UNUM, AUT ET RECTOREM, INTENDUNT ET TARDIUS INCIPIUNT, QUARE FACILIUS IPSUM ADIPISCUNTUR? IN UELOCI QUIDEM IGITUR MAGIS FIT PECCATUM. \textsuperscript{3}ACCIDIT AUTEM DUCI INTENDERE MULTOS. APPROPRIATUS AUTEM NULLUS UTIQUE IPSORUM ILLUSTRABITUR, ELEUANS MULTITUDINEM. IN PAUCIS AUTEM MAGIS ILLUSTRANTUR, PROPTER QUΟD SECUNDUM SE IN SE IPSIS MAGIS EXERCITANTUR QUAM APUD DUCEM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema .45m. etcetera. Repetit \edtext{.22m}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | .22m. problema \textit{γmv} | 21m \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{γG\textsuperscript{u}}}} } Soluit et primo assignat causam \edtext{et iam visum est}{\Cfootnote[nosep]{\textit{γκmv} | ut iam visum \textit{P\textsuperscript{y}} | \textit{om}. \textit{πE\textsuperscript{a}}}}. Secundo \edtext{declarat}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | declarat in \textit{P\textsuperscript{p}}}} \edtext{assignando}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | et assignat \textit{V\textsuperscript{a}}}} \edtext{differentiam}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | differentias \textit{V\textsuperscript{a}}}} \edtext{inter}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} habentes ducem in cantu \edtext{et}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et inter \textit{P\textsuperscript{p}} | \textit{om}. \textit{P\textsuperscript{x}}}} non \edtext{habentes}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | habentem \textit{G\textsuperscript{u}P\textsuperscript{q}}}}. Cuius \edtext{causa}{\Cfootnote[nosep]{\textit{ακπ} | causam \textit{mv}}} \edtext{reiterauit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | reiterat \textit{P\textsuperscript{z}}}} sermonem: \edtext{2a}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}} | 2a ibi \textit{γP\textsuperscript{z}V\textsuperscript{z}mv} | ibi \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{\textit{ACCIDIT}}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ante \textit{P\textsuperscript{z}}}}. \edtext{Dicit}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}v} | Dicens \textit{G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}m}}} \edtext{2°}{\Cfootnote[nosep]{\textit{ακmv} | hoc \textit{π}}} contingere \edtext{quod}{\Cfootnote[nosep]{\textit{ακmv} | quia \textit{π}}} \textit{multi ad ducem \edtext{attendant}{\Cfootnote[nosep]{\textit{ακmv} | attendunt \textit{π}}} } ut eorum cantus \edtext{saluetur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | saluentur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} per amplius, quoniam cum \edtext{fuerint}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | fiunt \textit{P\textsuperscript{z}}}} \edtext{multi}{\Cfootnote[nosep]{\textit{αγκπ} | \textit{om}. \textit{mv}}}, \textit{nullus \edtext{ipsorum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | eorum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} determinatur, \edtext{ut}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | in \textit{E\textsuperscript{a}}}} \edtext{eleuando}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}} uocem \edtext{suam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} propter multitudinem, non paruam \edtext{poterit}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{illustrari}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | illuxiari uel illustrari \textit{V\textsuperscript{a}}}} et super \edtext{aliorum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | alios \textit{V\textsuperscript{a}}}} \edtext{uoces}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | uocem \textit{V\textsuperscript{m}} | uocens \textit{P\textsuperscript{z}}}} \edtext{suam extollere}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | suas extollere \textit{γmv} | suam vocem extollere \textit{G\textsuperscript{u}} | suam attollere \textit{P\textsuperscript{y}} | suam excellere \textit{P\textsuperscript{z}}}}, \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quia \textit{P\textsuperscript{p}}}} plurimi magis ualeant quam vnus \edtext{appropriatus}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | adappriatus \textit{P\textsuperscript{y}}}}. Sed in paucis cantantibus \edtext{id}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | illud \textit{P\textsuperscript{p}} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{poterit}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}} | potest \textit{P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}mv}}} sufficienter contingere, quare pauci cantantes plus \edtext{secundum}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{x}P\textsuperscript{z}}}} semet ipsos \edtext{exercitantur}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | excitantur \textit{M\textsuperscript{a}}}} et \edtext{singulariter}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | similliter \textit{V\textsuperscript{a}} | vniformiter \textit{G\textsuperscript{u}}}} \edtext{apparent}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | apparet \textit{G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}}}} in cantu suo \edtext{illustrari}{\Cfootnote[nosep]{\textit{κ} | illustrati \textit{απmv}}} quam \edtext{qui}{\Cfootnote[nosep]{\textit{αλmv} | que \textit{P\textsuperscript{x}} | \textit{om}. \textit{π}}} \edtext{apud}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv}}} ducem plures cantantes \edtext{existunt}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}} | existent \textit{mv} | \textit{om}. \textit{E\textsuperscript{a}}}}, \edtext{non enim}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | enim \textit{π} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{singulatim}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | sigillatim \textit{απV\textsuperscript{z}mv}}} sed ad ducem \edtext{exercitantur}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv}}}.} \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}} | amen \textit{mv} | dooo . \textit{P\textsuperscript{y}}}} Problema 46 huius precessit expositio .26°. et uerita illic iam apparuit cuiusdam apparentis contrarietatis inter .27m. et istud cum dictum sit ibidem difficilius acute cantare quam grauiter. hic autem videtur contrarium dici. sequitur 47. problema 19e. particule. +\pend + +\pstart +\edtext{\subsubsection {Quadragesimumsextum problema}\label{edition-text book-19a part46}}{\lemma{Quadragesimumsextum + problema} \Cfootnote[nosep]{\textit{γmv} | «46m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{quadragesimum.sextum.} Quadragesimumsextum. \textit{P\textsuperscript{y}} | 44m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID IN ACUTUM}{\Cfootnote[nosep]{\textit{V\textsuperscript{m}} | PROPTER QUID IN ACUTIS \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{2}PROPTER QUID IN ACUTUM DISSONANT PLURIMI? \textsuperscript{2}AUT QUIA FACILIUS ACUTUM DIMITTERE QUAM GRAUE? \textsuperscript{3}CANTANT IGITUR ACUTE MAGIS, ET IN QUO CANTANT PECCANT \textit{G\textsuperscript{u}M\textsuperscript{a}V\textsuperscript{a}mv}}}.} \edtext{ \edtext{Huius}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Huiusmodi \textit{V\textsuperscript{a}} | Cuius \textit{mv} | Huius problematis \textit{λ}}} \edtext{precessit}{\Cfootnote[nosep]{\textit{γλπP\textsuperscript{y}mv}}} \edtext{expositio}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | expositio ex \textit{P\textsuperscript{z}}}} .26°.. Et ueritas \edtext{illic iam}{\Cfootnote[nosep]{\textit{P\textsuperscript{y}V\textsuperscript{a}} | iam illic \textit{V\textsuperscript{b}mv} | illic \textit{λ} | hic iam \textit{πE\textsuperscript{a}}}} \edtext{apparuit}{\Cfootnote[nosep]{\textit{αλmv} | apparet \textit{π}}} \edtext{cuiusdam}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{apparentis}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | apparente \textit{V\textsuperscript{a}}}} contrarietatis inter \edtext{.37m}{\Cfootnote{.27m. \textit{ακπmv}}}, et \edtext{istud}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}V\textsuperscript{m}} | illud \textit{S\textsuperscript{c}mv}}} \edtext{cum}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | tamen \textit{G\textsuperscript{u}P\textsuperscript{q}}}} dictum sit \edtext{ibidem}{\Cfootnote[nosep]{\textit{αλmv} | ibi \textit{π}}} difficilius esse \edtext{acute cantare}{\Cfootnote[nosep]{\textit{αλmv} | cantare acute \textit{π}}} quam grauiter. Hic \edtext{autem}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} videtur contrarium \edtext{dici}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | dicere \textit{P\textsuperscript{z}}}}. \edtext{}{\Cfootnote{et cetera \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{αλπmv}}} +\pend + +\pstart +\edtext{\subsubsection {Quadragesimumseptimum problema}\label{edition-text book-19a part47}}{\lemma{Quadragesimumseptimum + problema} \Cfootnote[nosep]{\textit{γmv} | «47m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{quadragesimum septimum} Quadragesimumseptimum. \textit{P\textsuperscript{y}} | 45m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID ANTIQUI}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID ANTIQUI, SEPTEM CORDARUM FACIENTES CONSONANTIAS, RELIQUERUNT YPATEM, SED NON NITEM RELINQUERUNT? \textsuperscript{2}AUT NON YPATEM, SED NUNC PARAMESEN APPELLATAM, ABSTULERUNT ET TONILEM DISTANTIAM. UTEBANTUR AUTEM ULTIMA MEDIA DENSI IN ACUTUM, PROPTER QUOD ET MEDIAM IPSAM APPELLAUERUNT. \textsuperscript{3}AUT QUIA ERAT SUPERIORIS TETRACORDI FINIS, INFERIORIS AUTEM PRINCIPIUM, ET MEDIAM HABEBAT PROPORTIONEM TONO EXTREMITATUM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}?} Quadragesimumseptimum problema etcetera. \edtext{Repetit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | Repetit quoddam problema predictum \textit{P\textsuperscript{z}}}} \edtext{7m, et \edtext{apparuit iam}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | iam apparuit \textit{P\textsuperscript{y}} | apparet iam \textit{G\textsuperscript{u}M\textsuperscript{a}}}} \edtext{eius}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{expositio}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}P\textsuperscript{y}mv} | propositio \textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \sout{expositio} propositio \textit{V\textsuperscript{z}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | et apparuit iam ex ipso 7 \textit{P\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}V\textsuperscript{a}} | \textit{om}. \textit{E\textsuperscript{a}}}} } \edtext{Soluit}{\Cfootnote[nosep]{\textit{απmv} | Soluit assignans \textit{κ}}} \edtext{dupliciter}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | causam dupliciter \textit{M\textsuperscript{a}V\textsuperscript{z}}}}, \edtext{aliter tamen}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | aliter causam \textit{C\textsuperscript{a}P\textsuperscript{a}V\textsuperscript{o}} | et aliter \textit{P\textsuperscript{y}}}} quam prius, dicens \edtext{primo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{u}}}} quod \textit{non abstulerunt \edtext{ \edtext{de 7 cordo}{\Cfootnote[nosep]{\textit{λmv} | de 7º corde \textit{V\textsuperscript{a}} | de 7 cordis \textit{V\textsuperscript{b}} | de a cordo \textit{P\textsuperscript{x}} | decacordo \textit{P\textsuperscript{y}}}} \edtext{ypatem}{\Cfootnote[nosep]{\textit{γκπmv}}}, sed non pro neque cordam \edtext{appellatam}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}} | dictam \textit{mv}}} \edtext{paramese}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}mv} | paramesem \textit{λV\textsuperscript{a}V\textsuperscript{m}}}} seu \edtext{tritem}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}} | trite \textit{mv} | cetere \textit{V\textsuperscript{a}}}}. Sed abstulerunt}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}}, ut \edtext{propositum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | dictum \textit{P\textsuperscript{y}}}} est, \edtext{nitem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}} | nitem uel netem \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} et per consequens \edtext{toni}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}mv} | tonum \textit{V\textsuperscript{a}} | thonum \textit{V\textsuperscript{b}} | communi \textit{M\textsuperscript{a}P\textsuperscript{x}}}} \edtext{distantiam}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | distantia \textit{V\textsuperscript{a}}}},} \edtext{que}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | qui \textit{P\textsuperscript{u}}}} \edtext{attenditur}{\Cfootnote[nosep]{\textit{αλπmv}}} ab vna corda in aliam \edtext{siue}{\Cfootnote[nosep]{\textit{ακmv} | seu \textit{π}}} \edtext{ab}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} vna voce in \edtext{alteram}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}mv} | aliam \textit{λπE\textsuperscript{a}V\textsuperscript{a}}}}, \edtext{ceu}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{a}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} \edtext{ut re}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ut 20. \textit{P\textsuperscript{z}}}}. \edtext{Constituunt}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | Constituit \textit{V\textsuperscript{m}}}} enim due uoces \edtext{tonum}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv}}} ita quod vna corda \edtext{cassata}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | causata \textit{P\textsuperscript{z}} | cessata \textit{V\textsuperscript{a}}}} \edtext{tollitur uox vna}{\Cfootnote[nosep]{\textit{λγE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | tollitur vna uox \textit{G\textsuperscript{u}} | tolleri uox vna \textit{P\textsuperscript{x}} | coll\expan{er} \textit{(orig. \textup{coll'.})} mox una \textit{P\textsuperscript{y}}}}, \edtext{et}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} per consequens \edtext{tonus}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}mv} | totius \textit{P\textsuperscript{y}}}}, cum ex duabus \edtext{constet}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} uocibus. \edtext{Auferentes}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} autem \edtext{nete}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | nete quia \textit{G\textsuperscript{u}} | nete qua \textit{mv} | netem \textit{P\textsuperscript{z}}}}, \edtext{ne}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ut \textit{G\textsuperscript{u}}}} \edtext{armonie}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | armonice \textit{V\textsuperscript{z}}}} \edtext{destruerentur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | destruentur \textit{G\textsuperscript{u}V\textsuperscript{a}}}}, cum media corda \edtext{paramese}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv}}}, \edtext{puta}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} primo \edtext{modo medii}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | modo media \textit{πE\textsuperscript{a}}}} \edtext{dicto}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | dicta \textit{G\textsuperscript{u}P\textsuperscript{q}} | dicte \textit{P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{.44., \edtext{supplebant}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | supplebunt \textit{G\textsuperscript{u}P\textsuperscript{q}} | supplebantur \textit{E\textsuperscript{a}}}} \edtext{defectum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}} \edtext{nete}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{a}mv} | uocis \textit{P\textsuperscript{y}}}} \edtext{sublate}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}}. \textit{ \edtext{Utebantur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | Putabantur \textit{V\textsuperscript{a}}}} \edtext{enim}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}mv} | enim cum \textit{V\textsuperscript{a}} | \textit{om}. \textit{E\textsuperscript{a}}}} media, \edtext{scilicet paramese}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | paramese scilicet \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, loco \edtext{ultime}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}} | ultimo \textit{P\textsuperscript{y}mv}}}, \edtext{scilicet nete}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}mv} | videlicet nete \textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | paranete scilicet \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, quod \edtext{erat}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{cum}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | quod \textit{M\textsuperscript{a}V\textsuperscript{a}}}} \edtext{extendebant}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | extendant \textit{G\textsuperscript{u}}}} \edtext{eam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | eum \textit{C\textsuperscript{a}V\textsuperscript{o}}}} \edtext{in tantum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | tantum \textit{V\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{z}}}} ut sonum \edtext{redderet}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | reddent \textit{mv} | rediret \textit{P\textsuperscript{z}}}} \edtext{acutum}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | \textit{om}. \textit{E\textsuperscript{a}}}},} \edtext{ad modum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ut \textit{P\textsuperscript{p}}}} nete, ita quod \edtext{cum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{ypate}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ypatem \textit{V\textsuperscript{a}}}} \edtext{constituerent}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}mv} | constituerunt \textit{P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | construerent \textit{V\textsuperscript{b}}}} dyapason, sicut cum nete preexistente. Et merito quoniam \edtext{corda}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{extensior acutiorem reddit sonum}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | extensior reddit sonum acutiorem \textit{G\textsuperscript{u}} | exterior acutiorem reddit sonum \textit{V\textsuperscript{b}mv} | extentiora tuciorem reddit sonum \textit{E\textsuperscript{a}}}}, \edtext{grauior}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | grauiorem \textit{P\textsuperscript{y}}}} \edtext{autem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | uero \textit{V\textsuperscript{a}}}} tardiorem, \textit{quare \edtext{mediam}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | medium \textit{P\textsuperscript{y}}}} appellauere,} eo quod medium \edtext{habet virtutem}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | uirtutem habet \textit{V\textsuperscript{m}} | tenet virtutem \textit{P\textsuperscript{p}}}} \edtext{extremi}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | extremorum \textit{V\textsuperscript{z}}}} \edtext{ad ipsum comparatum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | comparatum ad ipsum \textit{P\textsuperscript{z}}}}. \edtext{Si}{\Cfootnote[nosep]{\textit{ακπ} | Scilicet \textit{mv}}} \edtext{namque}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | enim \textit{mv} | autem \textit{V\textsuperscript{z}}}} \edtext{minus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | uidetur \textit{P\textsuperscript{z}}}} \edtext{extensa}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | tensa \textit{V\textsuperscript{z}}}} plus tenet locum medii, amplius uero extremi, aut \edtext{erat}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | erit \textit{πV\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{policordum}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv} | pollicordum dum \textit{V\textsuperscript{m}} | policordium uel policorniam \textit{V\textsuperscript{a}}}} \edtext{diegeugeneum}{\Cfootnote[nosep]{\textit{mv}}}, id est \edtext{disiunctum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{z}mv} | disiectum \textit{V\textsuperscript{z}} | districtum \textit{P\textsuperscript{x}}}}, ubi \edtext{cordarum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | corde \textit{P\textsuperscript{z}}}} \edtext{reiterantur alique}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | alique \textit{P\textsuperscript{y}} | alique reiterantur \textit{π}}} uel duplantur, ut \edtext{apparuit}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{q}P\textsuperscript{y}mv} | apparebit \textit{C\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | apparebat \textit{P\textsuperscript{a}P\textsuperscript{z}S\textsuperscript{c}V\textsuperscript{c}} | apparente \textit{E\textsuperscript{a}}}} \edtext{3°}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}} | problemate 3º \textit{P\textsuperscript{z}} | 30 \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | .13 \textit{αmv}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AUT.} Assignat \edtext{aliam causam}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | causam aliam \textit{V\textsuperscript{m}}}}, \edtext{dicens}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | scilicet \textit{P\textsuperscript{z}}}} \textit{ \edtext{quia}{\Cfootnote[nosep]{\textit{αλπmv} | quod \textit{P\textsuperscript{x}}}} media \edtext{corda}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | cordarum \textit{G\textsuperscript{u}P\textsuperscript{q}}}},} \edtext{ut}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | uel \textit{G\textsuperscript{u}P\textsuperscript{q}}}} paramese virtute \edtext{quidem}{\Cfootnote[nosep]{\textit{ακmv} | quadam \textit{π}}} \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ut \textit{P\textsuperscript{z}}}} non distantia, ut tactum \edtext{}{\Cfootnote[nosep]{\textit{ακmv} | est \textit{π}}}, \textit{erat \edtext{finis tetracordi superioris et principium alterius}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | finis \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{b}} | inferius \textit{G\textsuperscript{u}}}} \edtext{tetracordi}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{b}V\textsuperscript{o}mv} | tetracordandi \textit{P\textsuperscript{u}} | tractandi \textit{P\textsuperscript{z}}}} \edtext{inferioris}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | differens \textit{P\textsuperscript{z}}}}, ut \edtext{uisum}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{z}V\textsuperscript{o}mv} | dictum est uel uisum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}}}}. \edtext{Que}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | Quia \textit{P\textsuperscript{y}}}}, secundum quod \edtext{existit media}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{z}mv} | media existit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | existit mediam \textit{γ} | ex illic media \textit{M\textsuperscript{a}} | est media \textit{P\textsuperscript{y}}}}, \edtext{habet}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | habent \textit{V\textsuperscript{m}}}} proportionem ad \edtext{extremitates}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | extremitatem \textit{V\textsuperscript{m}}}} ambas suo tono,} secundum quod \edtext{fuerit}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | fuerint \textit{G\textsuperscript{u}P\textsuperscript{z}} | \textit{om}. \textit{V\textsuperscript{m}}}} \edtext{isti}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | viri \textit{P\textsuperscript{z}} | \textit{om}. \textit{P\textsuperscript{p}}}} extremorum \edtext{comparata}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | comparata ad extrema \textit{E\textsuperscript{a}}}} uel \edtext{alteri}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | alter \textit{P\textsuperscript{p}} | alterius \textit{P\textsuperscript{z}}}}. Nam medium comparatum \edtext{ad}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{extrema}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | extremum \textit{γmv} | vnum extremorum \textit{π}}} videtur alterum, .5. \edtext{phisicorum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{a}mv}}} , aut \edtext{ordinabatur}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}mv} | ordinabitur \textit{P\textsuperscript{x}} | ordinabam \textit{γ}}} paramese \edtext{ante mese}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{z}} | ante mesem \textit{P\textsuperscript{z}V\textsuperscript{o}} | quoniam mese \textit{M\textsuperscript{a}} | aut in mese \textit{γmv}}}, ut \edtext{distantia}{\Cfootnote[nosep]{\textit{γλP\textsuperscript{y}mv} | destructa \textit{πE\textsuperscript{a}P\textsuperscript{x}}}} \edtext{etiam}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} fere \edtext{sit}{\Cfootnote[nosep]{\textit{γλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | fit \textit{E\textsuperscript{a}P\textsuperscript{z}S\textsuperscript{c}} | sic \textit{P\textsuperscript{x}}}} media. \edtext{Sic}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv} | Sicut \textit{V\textsuperscript{m}V\textsuperscript{z}}}} igitur \edtext{quia}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} paramese habet \edtext{uicem}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{z}mv} | nitem \textit{P\textsuperscript{x}V\textsuperscript{m}} | uocem \textit{P\textsuperscript{y}}}} extremorum ut medium, et quia \edtext{per eam}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | per eum \textit{G\textsuperscript{u}} | postea \textit{γmv}}} ambo \edtext{constituuntur}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | constituunt \textit{M\textsuperscript{a}}}} \edtext{tetracordi}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | tetracorda \textit{M\textsuperscript{a}}}} \edtext{virtute}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | uirtute autem \textit{V\textsuperscript{b}}}} \edtext{saltem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | saltim \textit{V\textsuperscript{a}}}}. \edtext{Siue}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}mv} | Sine \textit{M\textsuperscript{a}} | Seu \textit{V\textsuperscript{z}}}} \edtext{nete}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv}}} dubitatur, quia dictum est in septimo quod non \edtext{abstulerunt}{\Cfootnote[nosep]{\textit{αλπmv} | abstulerit \textit{P\textsuperscript{x}}}} \edtext{nitem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}} | nete \textit{V\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{p}}}}, \edtext{sed}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | secundum \textit{λV\textsuperscript{a}} | scilicet \textit{P\textsuperscript{z}}}} tertiam \edtext{id est tritem}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}} | id est trite \textit{G\textsuperscript{u}V\textsuperscript{a}} | ut tritem \textit{P\textsuperscript{p}} | id est netem \textit{κ}}} siue paramese. +\pend + +\pstart +\textbf{4} Dicendum quod antiquitus \edtext{fuit primitus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | fuit inuentus \textit{γmv} | fuit prius \textit{π}}} paramese quam nete \edtext{inuenta}{\Cfootnote[nosep]{\textit{ακπ} | inuentam \textit{mv}}}, \edtext{ceu}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{pretactum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | tractum \textit{P\textsuperscript{z}}}} \edtext{est}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}mv} | est in \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}}}} 13°. \edtext{deinde}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | Demum \textit{P\textsuperscript{y}V\textsuperscript{z}}}} \edtext{superueniens}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}V\textsuperscript{a}mv} | superuenientis \textit{V\textsuperscript{b}} | preueniens \textit{E\textsuperscript{a}} | perueniens \textit{P\textsuperscript{z}V\textsuperscript{o}} | veniens \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{tripandius}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}mv}}} , extrahens tertiam cordam ut \edtext{paramese}{\Cfootnote[nosep]{\textit{γG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}V\textsuperscript{m}mv} | paramesem \textit{E\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | paramesen \textit{P\textsuperscript{u}P\textsuperscript{y}} | paramese est \textit{P\textsuperscript{x}}}} \edtext{a}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{V\textsuperscript{z}}}} cordarum ordine, \edtext{netem}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | nete \textit{G\textsuperscript{u}} | uel netem \textit{P\textsuperscript{x}} | neque \textit{P\textsuperscript{z}}}} loco \edtext{illius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ipsius \textit{P\textsuperscript{z}}}} adiunxit ita \edtext{ut}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} primitus non \edtext{fuerit}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | fuit \textit{P\textsuperscript{z}V\textsuperscript{a}}}} nete, postea uero \edtext{adinuenta}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | adiuncta \textit{P\textsuperscript{z}}}} extiterit. Et sic \edtext{utrunque}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}P\textsuperscript{y}mv} | utraque \textit{λ}}} \edtext{uerificabitur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | uerificatur \textit{V\textsuperscript{m}}}} \edtext{particula}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}} | problema \textit{γπP\textsuperscript{y}mv}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}} | sequitur 48. problema 19e. particule. \textit{P\textsuperscript{x}}}} verbi gratia \begin{longtable}{P{0.3787128712871287\textwidth}P{0.4712871287128713\textwidth}} +\Panel{ypate}{label}{1}{l}\tabcellsep \\ +\Panel{paripate}{label}{1}{l}\tabcellsep \textsuperscript{}primum tena cordum\\ +\Panel{lychanos}{label}{1}{l}\tabcellsep \\ +\Panel{mese}{label}{1}{l}\tabcellsep \\ +\Panel{paramese}{label}{1}{l}\tabcellsep \textsuperscript{}45\\ +\Panel{Paramete}{label}{1}{l}\tabcellsep \\ +\Panel{nete}{label}{1}{l}\tabcellsep \end{longtable} Et huius 3us quidem cetra corda 2m. sinzeusim +\pend + +\pstart +\edtext{\subsubsection {Quadragesimumoctauum problema}\label{edition-text book-19a part48}}{\lemma{Quadragesimumoctauum + problema} \Cfootnote[nosep]{\textit{γmv} | «48m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{Quadragesimumoctauum} Quadragesimumoctauum. \textit{P\textsuperscript{y}} | 46m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID IN TRAGEDIA}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}} | PROPTER QUID IN TRAGEDIA CHORI \textit{V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID IN TRAGEDIA CHORI NON YPODORISTIUM NEQUE YPOFRIDISTIE CANTANT? \textsuperscript{2}AUT QUIA CANTUM MINIME HABENT HEE CONSONANTIE, QUO INDIGENT MAGIS CHORO? \textsuperscript{3}CONSUETUDINEM AUTEM CONSONANTIAM QUE QUIDEM EST YPOFRIDISTIUM OPERATIUUM, PROPTER QUOD ET IN GERIONEM EXITUS ET DEARMATIO IN HAC FACIEBANT. \textsuperscript{4}YPODORISTIUM AUTEM MAGNIFICUM ET STABILE, PROPTER QUOD ET CITHARISTISSIMA EST CONSONANTIARUM. \textsuperscript{5}HEC AUTEM UTRAQUE CHORO QUIDEM IN CONSONANTIA, EIS AUTEM QUE SUNT A SCENA MAGIS PROPRIA. ILLI ENIM HEROUM MUTATIUI, HII AUTEM DUCES ANTIQUORUM SOLI FUERUNT. \textsuperscript{6}PROPRII AUTEM HOMINES QUORUM EST CHORUS. PROPTER QUOD ET CONUENIT IPSI LAMENTABILIS ET QUIETUS MOS ET MELOS, HUMANA ENIM. \textsuperscript{7}HEC AUTEM HABENT ALIE CONSONANTIE, MINUS AUTEM ILLIS QUE EST YPOFRIGISTIUM, DIUINA UEL FURIOSA AUTEM ET BACHICHA. SECUNDUM HANC QUIDEM PATIMUR ALIQUID, PASSIUI AUTEM IMBECILLES MAGIS FORTIBUS SUNT, PROPTER QUOD ET IPSA CONUENIT CHORIS. SECUNDUM AUTEM EAM QUE EST YPODORISTIUM ET YPOFRIDISTIUM OPERAMUR QUOD NON EST PROPRIUM CHORO. \textsuperscript{8}EST AUTEM CHORUS CURATOR INOPERABILIS, BENIUOLENTIAM ENIM SOLUM PREBET QUIBUS ADEST \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema .48m. etcetera. Repetit \edtext{30m}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | 30. problema \textit{P\textsuperscript{z}V\textsuperscript{b}} | .3°. \textit{P\textsuperscript{x}}}} \edtext{ut amplius \edtext{exponat}{\Cfootnote[nosep]{\textit{ακmv} | apponat \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{dicens}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \textit{quare chori \edtext{secundum tragediam}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{y}mv} | secundum tragedia \textit{E\textsuperscript{a}P\textsuperscript{u}V\textsuperscript{o}} | sicut tragedia \textit{P\textsuperscript{p}} | secundum trocordia \textit{P\textsuperscript{z}}}} non cantant \edtext{cantum}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv}}} \edtext{ypodoristium}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}mv}}} \edtext{et multo minus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | et multo minus et \textit{P\textsuperscript{z}} | et multo minus \surplus{et multo minus} \textit{V\textsuperscript{a}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{ypofrigium}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}mv} | ypostigium \textit{P\textsuperscript{y}} | upotragium \textit{P\textsuperscript{z}}}}?} Que \edtext{autem}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | autem sint \textit{M\textsuperscript{a}}}} ista \edtext{exposita sunt}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | exposita \textit{P\textsuperscript{y}} | expositum est \textit{π}}} \edtext{.30°.}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | .3°. \textit{P\textsuperscript{p}P\textsuperscript{x}}}} \edtext{antea}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | antea sunt \textit{P\textsuperscript{y}} | \textit{om}. \textit{πV\textsuperscript{a}}}}. +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{ακπ} | AUT QUIA. \textit{mv}}} } Soluit et primo in communi \edtext{dicens}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}} | dicit \textit{G\textsuperscript{u}}}} causam esse \textit{quia \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | huiusmodi \textit{γG\textsuperscript{u}P\textsuperscript{a}mv}}} consonantie, puta \edtext{ypodoristie}{\Cfootnote[nosep]{\textit{κP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv}}} \edtext{ \edtext{ac}{\Cfootnote[nosep]{\textit{ακmv} | et \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{ypofrigie}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ypofrigistice \textit{P\textsuperscript{x}P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}}, non \edtext{habent}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | fiunt \textit{P\textsuperscript{z}}}} modum cantandi quo amplius indigent cantantes cantu chorico.} \edtext{Alie}{\Cfootnote[nosep]{\textit{λγG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | Alia \textit{E\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{namque}{\Cfootnote[nosep]{\textit{ακ} | enim \textit{πmv}}} consonantie proportione \edtext{indigent}{\Cfootnote[nosep]{\textit{αλπmv} | indiget \textit{P\textsuperscript{x}}}} \edtext{chori}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | proportione \textit{V\textsuperscript{a}}}}, et \edtext{alie}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{b}mv} | alia \textit{αλπ}}} \edtext{leges}{\Cfootnote[nosep]{\textit{αλπmv} | lege \textit{P\textsuperscript{x}}}} \edtext{comedice}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | comete \textit{V\textsuperscript{a}}}}, sub quibus \edtext{ypofrigius}{\Cfootnote[nosep]{\textit{κπmv}}} \edtext{continetur}{\Cfootnote[nosep]{\textit{λπV\textsuperscript{b}} | continentur \textit{P\textsuperscript{x}P\textsuperscript{y}} | continet \textit{V\textsuperscript{a}} | continere \textit{mv} | \textit{om}. \textit{E\textsuperscript{a}}}} cantus \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ex \textit{P\textsuperscript{z}}}} \edtext{ypodoricus}{\Cfootnote[nosep]{\textit{γκπmv}}}, ut apparuit \edtext{.15}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | 5º \textit{P\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{CONSUETUDINEM.}{\Cfootnote[nosep]{\textit{ακmv} | CONSUETUDINE. \textit{π}}} } \edtext{Solutionem declarat secundo}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | Secundo declarat solutionem \textit{mv} | solutionem declarat \textit{P\textsuperscript{p}P\textsuperscript{u}} | 2° declarat \textit{G\textsuperscript{u}}}} in \edtext{speciali}{\Cfootnote[nosep]{\textit{v} | sp\expan{eci}ali \textit{(orig. \textup{spali})} et \textit{π} | spirituali \textit{m}}}, \edtext{postea}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | primo \textit{P\textsuperscript{y}}}} notificat quid \edtext{sit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} chorus. \edtext{Secunda}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}} | Secunda ibi \textit{G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{z}mv} | ibi Secunda \textit{V\textsuperscript{b}}}} \textit{ \edtext{EST AUTEM}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | EST AUTEM CHORUS \textit{V\textsuperscript{z}}}} .} \edtext{Adhuc}{\Cfootnote[nosep]{\textit{αλπ} | Ad hoc \textit{P\textsuperscript{x}mv}}} \edtext{ostendit}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{u}mv} | .2°. ostendit \textit{P\textsuperscript{y}} | primo ostendit \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{quales}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | qualis \textit{E\textsuperscript{a}}}} \edtext{sint}{\Cfootnote[nosep]{\textit{ακmv} | sunt \textit{π}}} cantus \edtext{ypodoristii}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}} | ypodoristum \textit{V\textsuperscript{m}} | ypodorium \textit{P\textsuperscript{z}} | yporistii \textit{V\textsuperscript{a}mv}}} et \edtext{ypofrigii}{\Cfootnote[nosep]{\textit{κπmv}}}, et \edtext{quorum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | chorum \textit{γ} | \textit{om}. \textit{mv}}} secundo2a \edtext{chorici}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | chorico \textit{P\textsuperscript{z}} | qui chorici \textit{P\textsuperscript{p}}}}. \edtext{Secunda}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | Secunda ibi \textit{V\textsuperscript{a}V\textsuperscript{z}mv} | Ibi secunda \textit{V\textsuperscript{b}} | Ibi \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | \textit{om}. \textit{V\textsuperscript{o}}}} \textit{ \edtext{PROPRII AUTEM}{\Cfootnote[nosep]{\textit{ακmv} | PROPRIA AUTEM \textit{π}}} .} \edtext{Dicit}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | dicens \textit{G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}}}} primo quod ex consuetudine longa est \edtext{consonantiam}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}mv} | consonantia \textit{E\textsuperscript{a}V\textsuperscript{a}V\textsuperscript{m}}}} quandam \edtext{percipere in cantu}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in cantu percipere \textit{P\textsuperscript{p}}}} ab infantia, \textit{enim mox audiuntur.} \textit{Et \edtext{ideo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | non \textit{P\textsuperscript{z}}}} leges cantus \edtext{quidam fuerunt}{\Cfootnote[nosep]{\textit{ακmv} | quidem fuerunt \textit{π}}} appellati,} ut visum \edtext{est}{\Cfootnote[nosep]{\textit{γκπmv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}}}} 28. Que quidem \textit{consonantia consuetudinaria secundum cantum \edtext{ypodoristium}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{y}mv} | ypodoristi \textit{E\textsuperscript{a}}}} et \edtext{ypofrigium}{\Cfootnote[nosep]{\textit{κπ}}} \edtext{attenditur}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | artem dicitur \textit{P\textsuperscript{q}P\textsuperscript{u}}}} \edtext{maxime}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | maxima \textit{G\textsuperscript{u}P\textsuperscript{q}}}}, cum \edtext{operatiuus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | operatiuis \textit{P\textsuperscript{z}} | operatiuum \textit{mv}}} existat.} \edtext{Ipso}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | Ipsi \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} enim laborantes \edtext{incitantur}{\Cfootnote[nosep]{\textit{αmv} | exitantur \textit{P\textsuperscript{x}} | excitantur \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | exercitantur \textit{G\textsuperscript{u}P\textsuperscript{p}M\textsuperscript{a}}}} ad opus, ut \edtext{apparet}{\Cfootnote[nosep]{\textit{ακπ} | patet \textit{mv}}} in sono quem emittunt \edtext{antennas}{\Cfootnote[nosep]{\textit{P\textsuperscript{z}} | anthoras \textit{G\textsuperscript{u}} | ante nos \textit{V\textsuperscript{a}}}} in malos \edtext{eleuantes}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv}}}. \textit{Et ideo cantus qui \edtext{fuere}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | fuerunt \textit{G\textsuperscript{u}P\textsuperscript{x}}}} \edtext{antiquitus}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | antiquatenus \textit{P\textsuperscript{y}}}} apud \edtext{gerionem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | genortem \textit{P\textsuperscript{z}}}} et gentem \edtext{darmaticam}{\Cfootnote[nosep]{\textit{λP\textsuperscript{y}V\textsuperscript{b}mv}}} \edtext{faciebant}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | fatiebant \textit{G\textsuperscript{u}P\textsuperscript{y}mv}}} exitus tandem \edtext{et}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{terminationes}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | terminantes \textit{V\textsuperscript{a}} | terminationem \textit{P\textsuperscript{u}P\textsuperscript{y}}}} \edtext{in consonantia}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}} | in consonantiam \textit{γπE\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{z}mv} | consonantiam in \textit{P\textsuperscript{y}}}} } \edtext{ypofrigiam}{\Cfootnote[nosep]{\textit{κπmv}}}, sicut et \edtext{ditirambi}{\Cfootnote[nosep]{\textit{P\textsuperscript{z}S\textsuperscript{c}} | dyterambus \textit{G\textsuperscript{u}M\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | dyachitambum \textit{P\textsuperscript{x}} | dicti rambi. \textit{V\textsuperscript{b}mv}}} \edtext{demum}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | deinde \textit{αmv}}} \edtext{concidunt}{\Cfootnote[nosep]{\textit{ακmv} | decidunt uel concidunt \textit{π}}} \edtext{in ipsam}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{z}mv} | ipsam \textit{M\textsuperscript{a}} | in ipsa \textit{V\textsuperscript{m}}}}, ut uisum \edtext{est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{y}}}} \edtext{30°}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | 3° \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}}}}. +\pend + +\pstart +\textbf{4} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{YPODORISTIUM.}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}V\textsuperscript{z}mv} | YPODORISTI \textit{πE\textsuperscript{a}P\textsuperscript{y}} | YPODORISTUS. \textit{P\textsuperscript{x}V\textsuperscript{m}}}} } Ostendit secundo qualis \edtext{sit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} cantus \edtext{ \edtext{ypodoristium. Dicit quod}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}mv} | ypodoricis. Dicit quod \textit{P\textsuperscript{x}} | ypodoristus, dicens quod \textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}} | ypodorisi, dicens quod \textit{P\textsuperscript{z}} | dicens ypodoristium \textit{V\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | ypodorum \textit{P\textsuperscript{y}}}} \textit{ \edtext{ \edtext{cantus}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{ypodoristius}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}} | ypodoristicum \textit{mv} | ypodoristium \textit{P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{V\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{est}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | est est \textit{P\textsuperscript{p}} | fit \textit{G\textsuperscript{u}}}} \edtext{magnificus laudabilis uirilis stabilis}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}V\textsuperscript{o}mv} | laudabilis magnificus uirilis stabilis \textit{P\textsuperscript{p}P\textsuperscript{u}} | magnificus uirilis laudabilis stabilis \textit{P\textsuperscript{y}} | magnificus laudabilis et uirilis \textit{P\textsuperscript{z}} | laudabilis magnificus stabilis et virilis \textit{G\textsuperscript{u}}}}. Unde inter \edtext{ceteras}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | \textit{om}. \textit{V\textsuperscript{b}}}} consonantias \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} forte \edtext{citaricissimus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | cicurrissimus \textit{P\textsuperscript{p}} | ticurrissimus \textit{G\textsuperscript{u}} | acutissimus \textit{P\textsuperscript{u}}}}.} \edtext{Existit}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{quod propter}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}mv} | propter quod \textit{λ} | quam propter \textit{P\textsuperscript{p}}}} lidium \edtext{dictum sit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}mv} | sit dictum \textit{P\textsuperscript{p}}}} ut \edtext{uisum est}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv} | uisum \textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | apparet \textit{V\textsuperscript{z}}}} \edtext{30°}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}mv} | 3° \textit{P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}}}}, \edtext{et}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} in \edtext{hiis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} \edtext{indicatur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | duacatur \textit{V\textsuperscript{a}}}} \edtext{sue rationis maior}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{o}V\textsuperscript{z}mv} | rationis sue maior \textit{P\textsuperscript{q}V\textsuperscript{m}} | rationis sui maior \textit{G\textsuperscript{u}} | sue rationis maius \textit{P\textsuperscript{z}} | sue \textit{E\textsuperscript{a}}}}. +\pend + +\pstart +\textbf{5} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{HEC AUTEM.}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}M\textsuperscript{a}} | HIC AUTEM. \textit{P\textsuperscript{x}P\textsuperscript{z}} | HUC AUTEM. \textit{V\textsuperscript{m}} | HOC AUTEM. \textit{E\textsuperscript{a}} | HUIC AUT. \textit{V\textsuperscript{z}} | CUM AUTEM. \textit{V\textsuperscript{b}} | NON AUTEM. \textit{V\textsuperscript{a}mv}}} } Ostendit qualis sit cantus choricus \edtext{subdens}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} minorem, \edtext{dicens}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} quod \textit{hec utraque consonantia, \edtext{puta}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{ypofrigium}{\Cfootnote[nosep]{\textit{mv} | ypophrygius \textit{E\textsuperscript{a}} | ypofrigia \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}} | ypophigia \textit{V\textsuperscript{o}} | ypofrigii \textit{V\textsuperscript{z}} | ypofori \textit{V\textsuperscript{m}} | ypoforis \textit{P\textsuperscript{x}}}} et \edtext{ypodoristium}{\Cfootnote[nosep]{\textit{V\textsuperscript{z}mv} | ypodoristia \textit{πM\textsuperscript{a}} | ypodoristica \textit{P\textsuperscript{y}} | ypodorius \textit{E\textsuperscript{a}} | ypodoris \textit{V\textsuperscript{m}} | ypodotis \textit{P\textsuperscript{x}}}}, \edtext{relatione}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ratione \textit{V\textsuperscript{a}}}} cantus chorici \edtext{est}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | \textit{om}. \textit{G\textsuperscript{u}V\textsuperscript{m}}}} \edtext{uelut}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{z}} | ualde \textit{P\textsuperscript{y}} | ultima \textit{M\textsuperscript{a}} | universaliter \textit{P\textsuperscript{x}} | verus \textit{V\textsuperscript{a}} | \textit{om}. \textit{mv}}} \edtext{in}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | \textit{om}. \textit{γπE\textsuperscript{a}V\textsuperscript{z}mv}}} \edtext{consonantia}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | consonantiam \textit{M\textsuperscript{a}V\textsuperscript{m}} | consonantias velud consonantia \textit{V\textsuperscript{a}} | \textit{om}. \textit{mv}}}. Unde \edtext{est}{\Cfootnote[nosep]{\textit{ακmv} | est in \textit{π}}} \edtext{illis}{\Cfootnote[nosep]{\textit{κ} | istis \textit{π} | ipsis \textit{αmv}}} extranea, sed magis \edtext{propria}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | pro \textit{γmv}}} \edtext{duobus predictis}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{u}} | duabus predictis \textit{P\textsuperscript{z}V\textsuperscript{o}} | predictis duobus \textit{αmv} | duobus primis \textit{P\textsuperscript{p}}}} \edtext{cantandi modis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | modis cantandi \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}}}} est consonantia \edtext{ascema dicta, existens}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | dicta ascema, existens \textit{G\textsuperscript{u}P\textsuperscript{q}} | \textit{om}. \textit{V\textsuperscript{a}}}} ut visum \edtext{est}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}}}} prius \edtext{mutatiua}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}mv} | mutata \textit{π} | mutatam \textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | mutam \textit{P\textsuperscript{y}}}}. Et \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | huiusmodi \textit{γG\textsuperscript{u}P\textsuperscript{a}mv}}} quidem \edtext{consonantia}{\Cfootnote[nosep]{\textit{κ} | consonantie \textit{γπP\textsuperscript{y}mv} | consonant \textit{E\textsuperscript{a}}}} modi appellati \edtext{commutatiui}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv} | comutatum \textit{P\textsuperscript{z}}}} \edtext{erant}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} in \edtext{vsu}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}mv} | vsi \textit{V\textsuperscript{a}} | uisu \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} \edtext{apud}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | amplius \textit{P\textsuperscript{y}}}} \edtext{hereos}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}}}}, ipsi enim \edtext{soli}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | solum \textit{P\textsuperscript{y}V\textsuperscript{a}}}} fuerunt duces et gubernatores antiquorum,} \edtext{incitantes}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | incitando \textit{V\textsuperscript{a}} | excitantes \textit{π}}} ipsos in actus \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv}}} cantibus, ut in bellum uel aliud. \edtext{Et proprie}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | Et proprie in \textit{P\textsuperscript{p}} | Et proprium \textit{V\textsuperscript{b}} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{ypofrigium}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}mv} | ypophrygius \textit{E\textsuperscript{a}} | ypifrigis \textit{P\textsuperscript{x}} | ypofrigii \textit{M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{z}} | ypofri \textit{G\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}}}}, \edtext{operatiui}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}mv} | operatim \textit{πE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}V\textsuperscript{m}}}} \edtext{enim}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | enim sunt \textit{M\textsuperscript{a}} | est \textit{V\textsuperscript{a}}}} magis. +\pend + +\pstart +\textbf{6} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{PROPRII.}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | PROPRII AUTEM. \textit{V\textsuperscript{a}mv}}} } \edtext{Ostendit}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | dicit \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{qualis}{\Cfootnote[nosep]{\textit{αλπmv} | que qualis \textit{P\textsuperscript{x}}}} et quorum \edtext{sit}{\Cfootnote[nosep]{\textit{αλπmv} | sic \textit{P\textsuperscript{x}}}} cantus choricus, dicens primo quod \textit{homines singulares et priuati sunt \edtext{illi}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} quorum cantus est choricus,} et \edtext{propterea}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}M\textsuperscript{a}V\textsuperscript{z}mv} | propter hoc \textit{πE\textsuperscript{a}} | propter \textit{V\textsuperscript{m}}}} \edtext{fruuntur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | finitur \textit{π} | formatur \textit{V\textsuperscript{a}} | fortiter \textit{V\textsuperscript{b}mv}}} \edtext{hiis}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}V\textsuperscript{z}mv} | iis \textit{M\textsuperscript{a}} | illis \textit{P\textsuperscript{x}}}} \edtext{que}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | quem \textit{E\textsuperscript{a}}}} ipsius. \textit{ \edtext{Sibi namque}{\Cfootnote[nosep]{\textit{ακπ} | Si enim \textit{mv}}} \edtext{conuenit}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | competit \textit{πE\textsuperscript{a}}}} ut \edtext{sit}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} \edtext{lamentabilis}{\Cfootnote[nosep]{\textit{λπP\textsuperscript{y}V\textsuperscript{b}mv} | lemdabilis \textit{V\textsuperscript{a}}}}, \edtext{inducens}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | ut ducens \textit{P\textsuperscript{y}}}} \edtext{ \edtext{in pietatem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}mv} | in pietates \textit{V\textsuperscript{a}} | impietatem \textit{G\textsuperscript{u}V\textsuperscript{o}}}} homines, \edtext{etiam}{\Cfootnote[nosep]{\textit{γλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | et et \textit{P\textsuperscript{x}} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{agrestes}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv}}}, \edtext{et}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} quietus more}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | in \textit{P\textsuperscript{z}}}} \edtext{et}{\Cfootnote[nosep]{\textit{κ} | \textit{om}. \textit{απmv}}} \edtext{honestus}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | honesti \textit{V\textsuperscript{b}} | omestus \textit{V\textsuperscript{a}}}} et \edtext{melodiosus}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{a}mv} | melodiosos \textit{V\textsuperscript{b}}}} maxime, hec enim humana sunt et mansueta.} Et \edtext{ideo}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}mv} | \textit{om}. \textit{γP\textsuperscript{y}}}} \edtext{amatores tali}{\Cfootnote[nosep]{\textit{γκmv} | amatores tale \textit{P\textsuperscript{y}} | amatorabtali \textit{E\textsuperscript{a}} | admonitores tali \textit{π}}} \edtext{genere cantandi}{\Cfootnote[nosep]{\textit{ακmv} | cantandi genere \textit{π}}} vtuntur \edtext{in demulciendo}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}mv} | et demulciendo \textit{V\textsuperscript{m}} | inde multitudo \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{dominarum primitus animos suarum agrestes}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}V\textsuperscript{o}} | primitus agrestes animos suarum dominarum \textit{V\textsuperscript{z}} | primitus dominarum animos suarum agrestes \textit{P\textsuperscript{q}P\textsuperscript{u}} | primitus dominarum animos agrestes suarum \textit{G\textsuperscript{u}} | primitus dominarum animos suos agrestes \textit{γmv} | dominarum primitus animas suarum agrestes \textit{P\textsuperscript{p}P\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{7} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{HIC}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | HEC \textit{V\textsuperscript{a}V\textsuperscript{z}mv} | HOC \textit{πP\textsuperscript{y}V\textsuperscript{b}}}} \edtext{AUTEM.}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ETIAM. \textit{P\textsuperscript{p}P\textsuperscript{u}}}} } Ostendit \edtext{2°}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}}}} quod talia minus insunt \edtext{ceteris}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aliis \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{consonantiis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | consonantia \textit{P\textsuperscript{z}}}} \edtext{achorica}{\Cfootnote[nosep]{\textit{γP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | a chorico \textit{π}}}, dicens quod \textit{ \edtext{relique}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | reliqua \textit{V\textsuperscript{a}}}} consonantie} \edtext{prefate}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | prefacte \textit{P\textsuperscript{x}V\textsuperscript{a}} | pretacte \textit{λ}}} minus participant \edtext{cum}{\Cfootnote[nosep]{\textit{κ} | \textit{om}. \textit{απmv}}} predictis, \textit{nam \edtext{ypofrigia}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv}}} est diuina} \edtext{seu}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | et \textit{G\textsuperscript{u}P\textsuperscript{q}}}} legalis, ut apparuit .15. \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | uel \textit{mv}}} \edtext{.28.}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}P\textsuperscript{x}V\textsuperscript{o}mv} | .24. \textit{V\textsuperscript{m}} | .18º. \textit{V\textsuperscript{z}} | .26. \textit{G\textsuperscript{u}}}}, \textit{uel \edtext{furiosa}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}V\textsuperscript{z}mv} | furiosam \textit{V\textsuperscript{m}} | furioso \textit{P\textsuperscript{z}S\textsuperscript{c}}}} incitans \edtext{homines}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{in}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | ad \textit{π}}} tumultum \edtext{ \edtext{et}{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}mv} | uel \textit{P\textsuperscript{x}}}} \edtext{furiam}{\Cfootnote[nosep]{\textit{κγE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{q}mv}}}. \edtext{Est autem}{\Cfootnote[nosep]{\textit{κ} | Aut est \textit{γπE\textsuperscript{a}mv}}} }{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | aut \textit{P\textsuperscript{y}}}} \edtext{bachica}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}mv} | brachia \textit{P\textsuperscript{x}}}} } \edtext{praua}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}} | puta \textit{mv} | biana \textit{E\textsuperscript{a}}}} \edtext{solida}{\Cfootnote[nosep]{\textit{V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}} | solido \textit{mv} | stolida \textit{P\textsuperscript{y}V\textsuperscript{a}} | solitu \textit{P\textsuperscript{x}} | \textit{om}. \textit{πE\textsuperscript{a}M\textsuperscript{a}}}}, iuxta \edtext{illud}{\Cfootnote[nosep]{\textit{αλπmv}}} ‘noni \edtext{30e,}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}} | 30e 4º, \textit{V\textsuperscript{a}} | .34e, \textit{V\textsuperscript{b}mv} | regule, \textit{P\textsuperscript{x}}}} \edtext{propter quod}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | propter quid \textit{πM\textsuperscript{a}P\textsuperscript{y}}}} \edtext{bachici}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | arthici \textit{P\textsuperscript{x}}}} artifices ut \edtext{frequenter}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}} | frequentetur \textit{V\textsuperscript{b}mv}}} sunt mali.\edtext{}{\Afootnote[nosep]{Ps.Arist. \textit{Prob.} XXX .10 , 956b ll. 11–12}}’ \textit{Iuxta siquidem \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}} | huiusmodi \textit{G\textsuperscript{u}P\textsuperscript{a}V\textsuperscript{b}mv}}} consonantiarum \edtext{imperfectarum}{\Cfootnote[nosep]{\textit{γmv} | dictarum \textit{κ} | frigiarum \textit{π} | factarum \textit{E\textsuperscript{a}} | fictarum \textit{P\textsuperscript{y}}}} \edtext{modum}{\Cfootnote[nosep]{\textit{κP\textsuperscript{y}} | modo \textit{γE\textsuperscript{a}mv} | modos \textit{π}}} \edtext{patimur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | patiuntur \textit{P\textsuperscript{z}}}} \edtext{aliquid, cum autem patimur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{imbecilliores}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}v} | imbecilles \textit{V\textsuperscript{z}}}}, amplius fortibus \edtext{reddimur}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | redduntur \textit{M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}}.} \edtext{Et}{\Cfootnote[nosep]{\textit{ακπmv} | \textit{om}. \textit{E\textsuperscript{a}}}} ideo non possumus \edtext{cantum tenere}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | tenere cantum \textit{G\textsuperscript{u}} | tantum cantum tenere \textit{P\textsuperscript{z}}}} choricum, sed leges \edtext{facimus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | facilius \textit{P\textsuperscript{p}}}} \edtext{et}{\Cfootnote[nosep]{\textit{πγE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | ut \textit{M\textsuperscript{a}V\textsuperscript{m}} | aut \textit{P\textsuperscript{y}}}} \edtext{ascema}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}}, ut tactum \edtext{est}{\Cfootnote[nosep]{\textit{κγE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}}}} \edtext{.15°}{\Cfootnote[nosep]{\textit{ακmv} | .55° \textit{π}}}. Sed quia hiis opposite \edtext{sumus dispositi}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | dispositi sumus \textit{P\textsuperscript{z}} | sumus disposite \textit{V\textsuperscript{a}}}} \edtext{cum}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | ut \textit{V\textsuperscript{z}}}} \edtext{cantus}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | cantus \surplus{cantus} \textit{V\textsuperscript{m}}}} est \edtext{lamentabilis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | delectabilis \textit{P\textsuperscript{z}}}} \edtext{etcetera}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}V\textsuperscript{a}}}}, \edtext{tunc}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}V\textsuperscript{z}mv} | tunc .3. \textit{P\textsuperscript{x}} | tamen \textit{M\textsuperscript{a}}}} \textit{competit dispositio nostra et \edtext{potentia cantibus}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | predicta cantantibus \textit{P\textsuperscript{z}} | procantibus \textit{P\textsuperscript{y}}}} \edtext{choricis}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | choricum \textit{V\textsuperscript{m}}}}.} \edtext{Potest}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | Poterit \textit{V\textsuperscript{a}}}} enim ipsos \edtext{seruare}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | conseruare \textit{γ}}}, \edtext{quamuis}{\Cfootnote[nosep]{\textit{αλmv} | quam \textit{P\textsuperscript{x}} | licet \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | cum \textit{P\textsuperscript{z}} | \textit{om}. \textit{C\textsuperscript{a}E\textsuperscript{a}V\textsuperscript{o}}}} \edtext{extent}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}} | extant \textit{mv} | existunt \textit{V\textsuperscript{a}} | exterit \textit{G\textsuperscript{u}} | sint \textit{V\textsuperscript{z}}}} laboriosi, \textit{non \edtext{autem}{\Cfootnote[nosep]{\textit{αλπmv} | enim \textit{P\textsuperscript{x}}}} \edtext{conuenit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | cum nec \textit{P\textsuperscript{z}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sicut \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{dictum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}v}}} \edtext{est}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{ypofrigiam}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | ypofrigia \textit{απmv}}} \edtext{proprie}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | propria \textit{P\textsuperscript{y}}}} ipsis,} \edtext{operatiua}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}V\textsuperscript{z}} | operatam \textit{P\textsuperscript{q}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv} | operatiam \textit{G\textsuperscript{u}} | operava \textit{P\textsuperscript{p}} | temperatera \textit{E\textsuperscript{a}}}} \edtext{namque}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | enim \textit{G\textsuperscript{u}}}}, sicut expositum \edtext{est}{\Cfootnote[nosep]{\textit{πγP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}}}}. +\pend + +\pstart +\textbf{8} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{EST AUTEM.} Ultimo \edtext{manifestat}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | monstrat \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} quid \edtext{sit}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{z}mv} | est \textit{E\textsuperscript{a}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}}}} \edtext{ \edtext{chorus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}mv} | choris \textit{C\textsuperscript{a}V\textsuperscript{o}}}}, \edtext{dicens quod}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | et dicit quod \textit{G\textsuperscript{u}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{q}P\textsuperscript{u}}}} \textit{chorus est \edtext{uelut quidam}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | uelut quod \textit{G\textsuperscript{u}} | uniuersaliter quidam \textit{M\textsuperscript{a}} | sicut quidam \textit{mv} | quidam ualde \textit{P\textsuperscript{y}}}} \edtext{curator}{\Cfootnote[nosep]{\textit{ακmv} | curat \textit{π}}},} \edtext{studet}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | studens \textit{P\textsuperscript{z}}}} enim \edtext{remouere}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | remouetur de \textit{P\textsuperscript{z}}}} curas et \edtext{sollicitudines}{\Cfootnote[nosep]{\textit{γπE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | solicitudinem \textit{P\textsuperscript{y}}}} ab audientibus. \textit{Est \edtext{et}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | etiam \textit{π} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{inoperabilis}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | incomparabilis \textit{P\textsuperscript{y}}}},} non \edtext{enim}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | enim non enim \textit{P\textsuperscript{p}} | eos \textit{P\textsuperscript{x}} | eam \textit{V\textsuperscript{m}}}} \edtext{incitat}{\Cfootnote[nosep]{\textit{ακmv} | excitat \textit{π}}} ad \edtext{actus}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | actum \textit{P\textsuperscript{z}}}} \edtext{ut}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | et \textit{P\textsuperscript{y}}}} \edtext{ypofrigium}{\Cfootnote[nosep]{\textit{mv} | ypofrigius \textit{πM\textsuperscript{a}V\textsuperscript{m}} | ypofrigii \textit{P\textsuperscript{x}} | ypofrigia \textit{E\textsuperscript{a}V\textsuperscript{z}}}}, \textit{ \edtext{sed}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}mv} | licet \textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{solum}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}} | sonum \textit{mv} | actum \textit{P\textsuperscript{z}}}} \edtext{beniuolentiam et complacentiam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | benuolentiam \textit{P\textsuperscript{p}P\textsuperscript{u}}}} inducit quibus auditu \edtext{incurrit}{\Cfootnote[nosep]{\textit{πM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}} | occurrit \textit{γE\textsuperscript{a}mv} | occurat \textit{P\textsuperscript{y}}}}.} \edtext{Nihil}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}mv}}} enim post factum \edtext{relinquit}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | reliquid \textit{E\textsuperscript{a}P\textsuperscript{x}S\textsuperscript{c}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}}}} cum \edtext{solum}{\Cfootnote[nosep]{\textit{ακπ} | sono \textit{mv}}} \edtext{animos}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | animas \textit{V\textsuperscript{a}}}} demulcere \edtext{laboret}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}mv} | laborat \textit{V\textsuperscript{a}} | labores \textit{V\textsuperscript{b}}}}. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | sequitur 49m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Quadragesimumnonum problema}\label{edition-text book-19a part49}}{\lemma{Quadragesimumnonum + problema} \Cfootnote[nosep]{\textit{γmv} | «49m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | \surplus{xl. Nonum. doooo} Quadragesimumnonum. \textit{P\textsuperscript{y}} | 47m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID SONORUM}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID, SONORUM FACIENTIUM CONSONANTIAM, IN GRAUIORI EST MOLLIOR? \textsuperscript{2}AUT QUIA IN MELODIA SUA UOCE MOLLIS EST ET QUIETA, EA AUTEM QUE EST RITHIMI MISTIONE ASPERA ET MOTIUA? \textsuperscript{3}QUONIAM AUTEM GRAUIS QUIDEM SONUS MOLLIS ET QUIETUS EST, ACUTUS AUTEM MOTIUUS, ET HABENTIBUS IDEM MELOS, ERIT UTIQUE MOLLIOR GRAUIOR IN EODEM MELOS MAGIS. ERAT AUTEM MELOS IPSI MOLLE \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema .49m. etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} consonantia ex grauibus \edtext{causata}{\Cfootnote[nosep]{\textit{αλπmv} | canta \textit{P\textsuperscript{x}}}} \edtext{sonis}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sonus \textit{P\textsuperscript{p}P\textsuperscript{u}}}} est \edtext{mollior}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | melior \textit{πV\textsuperscript{a}}}} \edtext{et delectabilior}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | ac delectabior \textit{P\textsuperscript{z}} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{quam ex acutis}{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}mv} | acutis \textit{P\textsuperscript{z}}}} \edtext{constructa}{\Cfootnote[nosep]{\textit{ακπ} | constituta \textit{mv}}}?} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{AUT QUIA.} Soluit, \edtext{primo ostendens}{\Cfootnote[nosep]{\textit{αmv} | primo ostendit \textit{P\textsuperscript{x}V\textsuperscript{m}} | et primo ostendit \textit{πM\textsuperscript{a}V\textsuperscript{z}}}} \edtext{quare}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}mv} | quod \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}}}} consonantia \edtext{uocis}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | vocum \textit{πV\textsuperscript{m}}}} \edtext{grauioris}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}mv} | grauiori \textit{P\textsuperscript{x}V\textsuperscript{m}} | grauiore \textit{V\textsuperscript{z}} | grauior \textit{π}}} est \edtext{mollior}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}mv} | melior \textit{πV\textsuperscript{a}}}}. 2° adaptat \edtext{ad eam que sonorum}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}V\textsuperscript{z}mv} | eam que sonorum \textit{M\textsuperscript{a}} | que sonorum ad ea \textit{P\textsuperscript{x}}}} \edtext{illic}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | ibi \textit{πP\textsuperscript{y}}}}. \textit{QUONIAM \edtext{AUTEM}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} .} \edtext{Dicit causam}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}} | Dicit primo causam \textit{V\textsuperscript{a}} | Dicens causam \textit{P\textsuperscript{y}P\textsuperscript{z}} | Assignat causam dicens \textit{E\textsuperscript{a}}}} \edtext{ \edtext{esse}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{m}} | \textit{om}. \textit{V\textsuperscript{z}}}} quoniam huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | huius esse quoniam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | esse huius quoniam \textit{P\textsuperscript{z}} | esse quoniam huiusmodi \textit{γ} | esse quia huiusmodi \textit{mv}}} \textit{ \edtext{consonantia}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | consonantiam \textit{P\textsuperscript{y}}}} \edtext{in}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | est \textit{V\textsuperscript{a}}}} \edtext{melodia}{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}v} | melius \textit{P\textsuperscript{y}}}} propter \edtext{suam uocem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | vocem suam \textit{π} | suam \textit{V\textsuperscript{a}}}} \edtext{delectabilem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | delectationem \textit{V\textsuperscript{a}} | laudabilem \textit{G\textsuperscript{u}P\textsuperscript{q}}}} \edtext{ex qua}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}mv} | ex qui \textit{V\textsuperscript{o}} | in qua \textit{V\textsuperscript{a}}}} \edtext{construitur}{\Cfootnote[nosep]{\textit{κπP\textsuperscript{y}V\textsuperscript{b}m} | constituitur \textit{V\textsuperscript{a}v} | astruitur \textit{E\textsuperscript{a}}}} mollis \edtext{est et}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | et \textit{P\textsuperscript{z}} | est \textit{P\textsuperscript{y}}}} quieta, iuxta illud quod \edtext{prius dictum est}{\Cfootnote[nosep]{\textit{κ} | dictum est prius \textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | dictum est \textit{P\textsuperscript{z}} | dictum prius \textit{P\textsuperscript{y}}}} de cantu chorico. Sed fere per oppositum \edtext{consonantia}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | consonantie \textit{V\textsuperscript{a}}}} \edtext{rithimica ob suam \edtext{mixtionem}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} minus \edtext{consonam}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | consona \textit{πV\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{aspera existit}{\Cfootnote[nosep]{\textit{γκπmv} | asperexerit \textit{E\textsuperscript{a}} | aspera \textit{P\textsuperscript{y}}}},} \edtext{pungens auditum}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | auditum pungens \textit{V\textsuperscript{b}}}} \edtext{et immutans}{\Cfootnote[nosep]{\textit{λG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}V\textsuperscript{o}mv} | et mutans \textit{P\textsuperscript{x}} | \textit{om}. \textit{P\textsuperscript{y}}}} mox \edtext{subiecta}{\Cfootnote[nosep]{\textit{P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}} | subiuncta \textit{M\textsuperscript{a}} | subita \textit{απmv}}}, quasi \edtext{alteratione}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | alteratiua \textit{P\textsuperscript{z}}}} \edtext{nature}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | uero \textit{V\textsuperscript{a}}}} \edtext{preliatiua}{\Cfootnote[nosep]{\textit{λP\textsuperscript{y}V\textsuperscript{b}mv} | preliata \textit{π} | preliatam \textit{P\textsuperscript{x}}}}. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{QUONIAM.}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}} | QUONIAM AUTEM. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | QUANDO AUTEM. \textit{mv}}} } Applicat ad sonum, dicens \edtext{similiter}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | simpliciter \textit{P\textsuperscript{z}}}} \edtext{esse}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{z}mv} | est \textit{M\textsuperscript{a}V\textsuperscript{a}} | omne \textit{P\textsuperscript{x}}}} \edtext{in sono}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} \textit{quoniam grauis, ut dictum \edtext{est}{\Cfootnote[nosep]{\textit{γκπmv} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}}}} de uoce mollis, \edtext{est}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} \edtext{quietus et}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}mv} | et quietus \textit{γ} | quietus est et \textit{P\textsuperscript{z}} | et quietus et \textit{G\textsuperscript{u}mv}}} amenus, sed acutus \edtext{asper est}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}mv} | asper \textit{P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{z}}}} et \edtext{conmotiuus}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | commotus \textit{P\textsuperscript{x}} | commutiuus \textit{V\textsuperscript{m}mv} | comonens \textit{V\textsuperscript{a}}}}. \edtext{Unde}{\Cfootnote[nosep]{\textit{αλπmv} | vnde \textit{(\textup{\sic{Ui Unde}} a.c.)} \textit{P\textsuperscript{x}}}} posito quod \edtext{extat utrobique eadem}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | utrobique extat eadem \textit{V\textsuperscript{z}} | extet utrobique eadem \textit{απmv}}} melodia illa que \edtext{est grauior}{\Cfootnote[nosep]{\textit{κ} | grauior est \textit{P\textsuperscript{y}} | erit grauior \textit{γE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | erat grauior \textit{G\textsuperscript{u}}}} \edtext{mollior et}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}mv} | et mollior \textit{π} | melior est et \textit{P\textsuperscript{y}}}} \edtext{delectabilior}{\Cfootnote[nosep]{\textit{ακmv} | delectabilior erit \textit{π}}} in \edtext{eadem}{\Cfootnote[nosep]{\textit{γπP\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}m} | eodem \textit{E\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{m}v}}} melodia \edtext{magis}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | ea que est grauior \textit{P\textsuperscript{y}}}}, \edtext{nam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | non \textit{P\textsuperscript{z}}}} \edtext{melos}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv}}} \edtext{ipsius est}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | ipsi est \textit{mv} | ipsius \textit{V\textsuperscript{a}}}} \edtext{molle}{\Cfootnote[nosep]{\textit{λγπE\textsuperscript{a}mv} | melle \textit{P\textsuperscript{x}P\textsuperscript{y}}}} \edtext{quasi}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | id est \textit{G\textsuperscript{u}P\textsuperscript{q}}}} dulce.} +\pend + +\pstart +\textbf{4} \edtext{Nota}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | Notandum \textit{γmv}}} quod \edtext{cetera}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}mv} | certa \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{b}V\textsuperscript{o}} | omnis \textit{P\textsuperscript{y}} | ita \textit{V\textsuperscript{a}} | circa \textit{E\textsuperscript{a}} | et altera \textit{V\textsuperscript{z}}}} consonantia debet constare ex acuto et graui. Mollior tamen est \edtext{amenior}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}} | et amenior \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | et suauior \textit{M\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{z}} | amor \textit{P\textsuperscript{x}} | et amor \textit{E\textsuperscript{a}V\textsuperscript{m}} | et a motu \textit{γmv}}} cum \edtext{in}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | \textit{om}. \textit{V\textsuperscript{m}}}} graue \edtext{tendit}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | cedit \textit{M\textsuperscript{a}}}} \edtext{quam}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quem \textit{G\textsuperscript{u}} | antea \textit{P\textsuperscript{x}}}} \edtext{quando}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}mv} | cum \textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{z}}}} in acutum. \edtext{}{\Cfootnote{etcetera \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{z}} | sequitur 50m. problema 19e. particule. \textit{P\textsuperscript{x}}}} +\pend + +\pstart +\edtext{\subsubsection {Quinquagesimum problema}\label{edition-text book-19a part50}}{\lemma{Quinquagesimum problema} \Cfootnote[nosep]{\textit{γ} | Ultimum problema \textit{mv} | «50m» (in mg.) \textit{E\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{z}} | Quinquagesimum. \surplus{Quinquagesimum.} \textit{P\textsuperscript{y}} | 48m. problema. \textit{G\textsuperscript{u}} | \textit{om}. \textit{M\textsuperscript{b}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}}}} +\pend + +\pstart +\textbf{1} \textit{ \edtext{PROPTER QUID EQUALIUM}{\Cfootnote[nosep]{\textit{P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{m}V\textsuperscript{o}} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{z}} | \textsuperscript{1}PROPTER QUID EQUALIUM DOLIORUM ET SIMILIUM SIQUIDEM ALTERUM UACUUM FUERIT, ALTERUM UERO AD MEDIUM PLENUM, DYAPASON CONSONAT ECHO? \textsuperscript{2}AUT QUIA DUPLEX FIT ET QUE EST EX MEDIO EIUS QUE EST EX UACUO? \textsuperscript{3}QUID ENIM DIFFERT HOC QUAM IN FISTULIS? UIDETUR ENIM UELOCIOR MOTUS ACUTIOR ESSE, IN MAIORIBUS AUTEM TARDIUS AER OBUIAT. ET IN DUPLICIBUS TANTUM, ET IN ALIIS PROPORTIONALE. CONSONAT AUTEM DYAPASON ET DUPLEX ITER AD MEDIUM \textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{a}mv}}}.} Problema .50m. etcetera. \textit{ \edtext{Quare}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | Querit quare \textit{λ}}} \edtext{si}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | cum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} aliquis accipiat \edtext{duo}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | et \textit{P\textsuperscript{z}}}} dolia eiusdem \edtext{ \edtext{mensure}{\Cfootnote[nosep]{\textit{κmv} | materie \textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{quantitatis}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | quantitatum \textit{V\textsuperscript{m}}}} \edtext{et}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}} | \textit{om}. \textit{γE\textsuperscript{a}mv}}} \edtext{figure et}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | et \textit{P\textsuperscript{z}}}} \edtext{vniuersaliter}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | vniuersalis \textit{V\textsuperscript{a}}}} similitudinis omnis,} ‘in omnibus \edtext{enim}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | \textit{om}. \textit{γmv}}} \edtext{sit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | sunt \textit{P\textsuperscript{z}}}} equalitas nisi \edtext{in hiis in}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | in iis in \textit{M\textsuperscript{a}} | in \textit{P\textsuperscript{p}} | in hiis nisi in hiis in \textit{P\textsuperscript{y}}}} quibus \edtext{fit}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | sit \textit{E\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}}}} comparatio, \edtext{ut visum est}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}mv} | ut visum \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{o}}}} \edtext{}{\Afootnote[nosep]{.5°. \edtext{25°,}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}mv} | et 5º, \textit{E\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{z}} | \textit{om}. \textit{π}}} (Pietro expresses this idea in his commentary on problem 10 of particula 15. His reference to 5/25 is obscure.)}}’ puta quod \textit{ \edtext{vnum sit}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{o}mv} | sit vnum \textit{P\textsuperscript{u}} | vnum est \textit{P\textsuperscript{z}}}} \edtext{omnino}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | omnis \textit{P\textsuperscript{y}}}} \edtext{corpore}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{solido}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | solito \textit{V\textsuperscript{a}}}} ut liquore \edtext{aliquo}{\Cfootnote[nosep]{\textit{απV\textsuperscript{b}mv} | acuto \textit{λ} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{ \edtext{vacuum}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}mv} | vacuo \textit{V\textsuperscript{a}}}} \edtext{plenum, tamen aere}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | aere tamen plenum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | plenum, tamen aer \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{o}mv} | \textit{om}. \textit{M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{z}}}},} ‘ \edtext{idem \edtext{namque}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}} | enim \textit{mv} | tamen \textit{V\textsuperscript{a}}}} \edtext{apud vulgus est}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | est apud uulgum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}} | amplius uulgus est \textit{P\textsuperscript{y}}}} }{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}V\textsuperscript{m}mv} | \textit{om}. \textit{M\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{z}}}} uacuum \edtext{et plenum aere}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | et aere plenum \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{q}} | plenum tamen aere \textit{V\textsuperscript{m}V\textsuperscript{z}} | \textit{om}. \textit{G\textsuperscript{u}}}}, .7°. \textit{ \edtext{topicorum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} },\edtext{}{\Afootnote[nosep]{Arist. \textit{Top.} VII .1 , 152b , l. 20}}’ \textit{ \edtext{et}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} alterum sit semiplenum,} et \edtext{percutiantur}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{z}mv} | percutiatur \textit{E\textsuperscript{a}V\textsuperscript{m}}}} etiam \edtext{equaliter}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | aliqualiter \textit{P\textsuperscript{y}}}} \edtext{quocunque}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | quoque \textit{P\textsuperscript{z}}}} \edtext{modo}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | uel \textit{V\textsuperscript{a}}}} \edtext{ambo}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}mv} | \textit{om}. \textit{λ}}}, \edtext{uel}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | ut \textit{P\textsuperscript{z}}}} \edtext{clametur}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | clauetur \textit{P\textsuperscript{y}}}} in ipsis; \textit{tunc \edtext{echo}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{y}}}} resultans \edtext{ex}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{m}mv} | in \textit{V\textsuperscript{b}V\textsuperscript{z}}}} \edtext{hiis}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}mv} | ipsis \textit{V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{per refractionem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | per fractionem \textit{π} | prefatis \textit{V\textsuperscript{a}}}} ad parietes reddit \edtext{simphoniam}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv}}} \edtext{dyapasonicam}{\Cfootnote[nosep]{\textit{λmv} | dyapason sonicam \textit{V\textsuperscript{b}} | dyapason solidam \textit{V\textsuperscript{a}} | dyapason eam \textit{P\textsuperscript{p}P\textsuperscript{u}} | dyapason causa \textit{P\textsuperscript{z}V\textsuperscript{o}} | dyapason \textit{G\textsuperscript{u}}}}.} +\pend + +\pstart +\textbf{2} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{AUT.}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{z}V\textsuperscript{o}mv} | AUT QUIA. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}}}} } Soluit \edtext{et}{\Cfootnote[nosep]{\textit{ακmv} | \textit{om}. \textit{π}}} \edtext{dicit primo causam}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}P\textsuperscript{y}m} | primo dicit causam \textit{V\textsuperscript{a}} | id primo causam \textit{V\textsuperscript{o}} | primo dicens causam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} esse \textit{quia sonus causatus ex uacuo \edtext{uase}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{se habet}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | habet se \textit{P\textsuperscript{p}} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{ad sonum causatum \edtext{ex}{\Cfootnote[nosep]{\textit{ακmv} | a \textit{G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} semipleno \edtext{in}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}mv} | et \textit{V\textsuperscript{m}}}} dupla proportione}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | in proportione dupla ad sonum causatum a semipleno \textit{P\textsuperscript{p}}}} }, continet \edtext{enim}{\Cfootnote[nosep]{\textit{αλπmv} | omni \textit{P\textsuperscript{x}}}} bis \edtext{eius}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} \edtext{totum}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | tonum \textit{G\textsuperscript{u}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{ακπ} | quidem \textit{mv}}} uacuum \edtext{omne}{\Cfootnote[nosep]{\textit{απmv} | esse \textit{κ}}} id quod \edtext{semiuacuum}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}M\textsuperscript{a}V\textsuperscript{b}V\textsuperscript{z}mv} | semimatium \textit{V\textsuperscript{a}} | semiatiuum \textit{P\textsuperscript{x}} | soni uacuum \textit{P\textsuperscript{y}}}}. Dictum est \edtext{autem}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}mv} | enim \textit{π} | \textit{om}. \textit{V\textsuperscript{b}}}} \edtext{.13°}{\Cfootnote[nosep]{\textit{απmv} | 30. \textit{M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}} | .20. \textit{V\textsuperscript{z}}}} quod dyapason ex numero duplici nascitur. +\pend + +\pstart +\textbf{3} \edtext{}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}} | Deinde. \textit{V\textsuperscript{a}mv}}} \textit{ \edtext{QUID}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | QUOD \textit{P\textsuperscript{x}P\textsuperscript{z}}}} \edtext{ENIM.}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | IGITUR \textit{P\textsuperscript{y}}}} } \edtext{Secundo}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} remouet \edtext{dubitationem}{\Cfootnote[nosep]{\textit{αP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | dubium alias dubitationem \textit{G\textsuperscript{u}} | dubium \textit{M\textsuperscript{a}}}}, \edtext{quia crederet aliquis}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{quod}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}}}} ex sonis talium non \edtext{resultaret}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | resonaret \textit{E\textsuperscript{a}}}} \edtext{simphonia}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}V\textsuperscript{z}mv}}} sicut ex sonis \edtext{aliorum}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | aliarum \textit{E\textsuperscript{a}}}}. Et ideo \edtext{subdit}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | subdiderit \textit{E\textsuperscript{a}}}} quod \textit{non est aliqua differentia \edtext{quin}{\Cfootnote[nosep]{\textit{αλmv} | quando \textit{P\textsuperscript{x}} | quare \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | quasi \textit{G\textsuperscript{u}}}} ex \edtext{sonis}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | sono \textit{G\textsuperscript{u}}}} \edtext{istorum}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}V\textsuperscript{o}mv} | istarum \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | istis \textit{P\textsuperscript{y}} | istorum non \textit{P\textsuperscript{z}}}} \edtext{constituatur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | causetur \textit{V\textsuperscript{z}}}} \edtext{dyapason consonantia}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{z}mv} | dyapason secundum consonantiam \textit{P\textsuperscript{p}P\textsuperscript{u}}}}, \edtext{ceu}{\Cfootnote[nosep]{\textit{γM\textsuperscript{a}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{z}mv} | seu \textit{E\textsuperscript{a}V\textsuperscript{m}V\textsuperscript{o}} | sicut \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} ex sono fistularum et \edtext{huius}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | huiusmodi \textit{γG\textsuperscript{u}P\textsuperscript{a}P\textsuperscript{p}mv}}} instrumentorum \edtext{motorum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{z}}}} spiritu \edtext{seu}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}mv} | ceu \textit{P\textsuperscript{y}V\textsuperscript{a}}}} tactu.} Quod ostendit \edtext{inuentio}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | inuentor \textit{V\textsuperscript{b}mv} | inuentorum \textit{V\textsuperscript{a}}}} musice \edtext{malleorum}{\Cfootnote[nosep]{\textit{πE\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{a}mv}}} soni proportione, ut dictum \edtext{est}{\Cfootnote[nosep]{\textit{γκmv} | est in \textit{π} | \textit{om}. \textit{E\textsuperscript{a}P\textsuperscript{y}}}} \edtext{primo}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | prius \textit{V\textsuperscript{a}}}}, quod siquidem \edtext{contingere bene potest}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}mv} | contingere potest bene \textit{M\textsuperscript{a}} | bene contingere potest \textit{G\textsuperscript{u}P\textsuperscript{q}} | considero vnde ponit \textit{V\textsuperscript{a}}}} \edtext{cum}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | eam \textit{P\textsuperscript{z}}}} \edtext{ubique}{\Cfootnote[nosep]{\textit{γκP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} in talibus ratio \edtext{semper proportionis duplicis}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}} | proportionis duplicis semper \textit{π} | semper proportionis dupliciter \textit{γmv}}} \edtext{obseruetur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | bene obseruetur \textit{G\textsuperscript{u}P\textsuperscript{q}}}}. Quod ostenditur \edtext{quia}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}V\textsuperscript{b}V\textsuperscript{o}mv} | quia a \textit{P\textsuperscript{z}} | quod \textit{V\textsuperscript{a}}}} dyapason \edtext{causatur}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{ex}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | ab \textit{P\textsuperscript{y}}}} \edtext{acuto et graui}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}V\textsuperscript{o}mv} | graui et acuto \textit{P\textsuperscript{p}} | acuto \textit{P\textsuperscript{z}}}} quod \edtext{hic}{\Cfootnote[nosep]{\textit{λπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}} | huius \textit{P\textsuperscript{x}} | huic \textit{V\textsuperscript{b}mv}}} accidit, \edtext{nam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}mv} | est iam \textit{C\textsuperscript{a}P\textsuperscript{z}V\textsuperscript{o}}}} \textit{motus uelocior factus in semipleno angustia loci \edtext{percipitur}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv} | percipere \textit{V\textsuperscript{m}}}} \edtext{esse}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{a}}}} acutior, in maiori autem tardius mouetur et obuiat \edtext{aer}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | aeri \textit{κE\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{u}} | \textit{om}. \textit{V\textsuperscript{a}}}} } resistenti, \edtext{propter}{\Cfootnote[nosep]{\textit{αλπmv} | propter uel \textit{P\textsuperscript{x}}}} \edtext{plurimam}{\Cfootnote[nosep]{\textit{γλπE\textsuperscript{a}mv} | plurima \textit{P\textsuperscript{x}} | multam \textit{P\textsuperscript{y}}}} \edtext{quantitatem ipsius}{\Cfootnote[nosep]{\textit{ακmv} | ipsius quantitatem \textit{π}}} \edtext{motam}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv} | motum \textit{V\textsuperscript{c}V\textsuperscript{o}}}} et per longam distantiam ut visum \edtext{est xia}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{a}mv} | xia est \textit{V\textsuperscript{b}} | xia \textit{P\textsuperscript{y}} | est 41 \textit{π}}}, ita \edtext{quod}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | ut \textit{G\textsuperscript{u}}}} \textit{in \edtext{ \edtext{hiis}{\Cfootnote[nosep]{\textit{απV\textsuperscript{m}V\textsuperscript{z}mv} | iis \textit{M\textsuperscript{a}}}} que sunt dupla \edtext{ad inuicem}{\Cfootnote[nosep]{\textit{λπP\textsuperscript{y}} | in ad inuicem \textit{γE\textsuperscript{a}mv}}} et \edtext{in}{\Cfootnote[nosep]{\textit{γλP\textsuperscript{y}mv} | \textit{om}. \textit{πE\textsuperscript{a}}}} }{\Cfootnote[nosep]{\textit{αλπmv} | \textit{om}. \textit{P\textsuperscript{x}}}} \edtext{etiam}{\Cfootnote[nosep]{\textit{M\textsuperscript{a}P\textsuperscript{x}} | aliis \textit{V\textsuperscript{m}V\textsuperscript{z}} | aliis etiam \textit{απmv}}} \edtext{que}{\Cfootnote[nosep]{\textit{γκπP\textsuperscript{y}mv} | quod \textit{E\textsuperscript{a}}}} aliquam proportionem \edtext{numeralem habent}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}} | habent numeralem \textit{V\textsuperscript{b}mv} | habent \textit{P\textsuperscript{y}} | numeralem \textit{V\textsuperscript{a}}}} inter se consonat et \edtext{efficitur}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | conficitur \textit{V\textsuperscript{a}}}} \edtext{penes}{\Cfootnote[nosep]{\textit{απM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{z}mv}}} dupliciaduplaria dyapason. Cadit enim duplex \edtext{iter}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}V\textsuperscript{b}mv} | inter \textit{πP\textsuperscript{y}} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{et}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | est \textit{P\textsuperscript{z}} | \textit{om}. \textit{G\textsuperscript{u}P\textsuperscript{y}}}} \edtext{distantia}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{z}V\textsuperscript{o}mv} | distantiam \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}}}} \edtext{extremi}{\Cfootnote[nosep]{\textit{απP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | et fini \textit{M\textsuperscript{a}}}} ad medium,} ut in pleno, \edtext{vnum autem}{\Cfootnote[nosep]{\textit{ακmv} | vni autem \textit{P\textsuperscript{p}P\textsuperscript{u}} | vini aut \textit{G\textsuperscript{u}} | verum autem \textit{V\textsuperscript{o}} | autem numeri \textit{P\textsuperscript{z}}}} \edtext{in}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}}}} \edtext{semiuacuo}{\Cfootnote[nosep]{\textit{αλG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}}, cum alterum \edtext{contineat}{\Cfootnote[nosep]{\textit{γκG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}mv} | continet \textit{P\textsuperscript{p}} | \textit{om}. \textit{E\textsuperscript{a}}}} \edtext{pleni}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | pleni \surplus{pleni} \textit{V\textsuperscript{a}}}} medietatem. Secundum uero epitricaepitricam \edtext{dyatesseron}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | et dyatesseron \textit{P\textsuperscript{y}}}} et emiolaemioligi dyapente \edtext{et cetera}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}} | et illic \textit{γmv}}}, ut \edtext{monstratum}{\Cfootnote[nosep]{\textit{αG\textsuperscript{u}P\textsuperscript{p}V\textsuperscript{m}V\textsuperscript{z}mv} | manifestum \textit{P\textsuperscript{z}V\textsuperscript{o}}}} \edtext{est}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | \textit{om}. \textit{P\textsuperscript{y}}}} .13°. +\pend + +\pstart +\textbf{4} \edtext{Ex}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}mv} | Et \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}}}} hiis \edtext{utique}{\Cfootnote[nosep]{\textit{ακmv} | itaque \textit{π}}} \edtext{quam}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | quamuis \textit{G\textsuperscript{u}}}} \edtext{breuius}{\Cfootnote[nosep]{\textit{γκπmv} | breuiter \textit{P\textsuperscript{y}} | vermis \textit{E\textsuperscript{a}}}} \edtext{prodierunt}{\Cfootnote[nosep]{\textit{αM\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}mv} | prodierint \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}V\textsuperscript{z}} | producunt \textit{G\textsuperscript{u}}}} in \edtext{lucem}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | latem \textit{P\textsuperscript{z}}}} \edtext{utcunque}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{x}P\textsuperscript{u}V\textsuperscript{z}mv} | utrunque \textit{P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}}}} circa liberales artes, et \edtext{maxime circa}{\Cfootnote[nosep]{\textit{πP\textsuperscript{x}} | maxime \textit{αV\textsuperscript{m}V\textsuperscript{z}mv} | \textit{om}. \textit{M\textsuperscript{a}}}} \edtext{ \edtext{mathematica}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}V\textsuperscript{o}V\textsuperscript{z}} | mathematicam \textit{V\textsuperscript{b}mv} | mathematicas \textit{M\textsuperscript{a}} | methaphysica \textit{V\textsuperscript{a}}}} \edtext{problemata}{\Cfootnote[nosep]{\textit{λE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{o}} | probabilis \textit{γmv} | proposita \textit{P\textsuperscript{x}}}} }{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | problemata mathematica \textit{P\textsuperscript{p}}}}, grandi \edtext{textuali}{\Cfootnote[nosep]{\textit{G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{x}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}V\textsuperscript{z}}}} \edtext{caligine}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}V\textsuperscript{o}mv} | caligere \textit{P\textsuperscript{z}}}} cum eius \edtext{corruptione}{\Cfootnote[nosep]{\textit{ακπ} | corrupta \textit{mv}}} \edtext{inuoluta quandoque}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | quandoque inuoluta \textit{V\textsuperscript{a}} | inuoluta quando \textit{G\textsuperscript{u}}}}. \edtext{In quibus etiam}{\Cfootnote[nosep]{\textit{αP\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}mv} | In pluribus etiam \textit{M\textsuperscript{a}} | In quibusdam etiam \textit{π}}} quia plurimis \edtext{extranea}{\Cfootnote[nosep]{\textit{γκπE\textsuperscript{a}mv} | extra ea \textit{P\textsuperscript{y}}}} non \edtext{grandis}{\Cfootnote[nosep]{\textit{ακπ} | grandi \textit{mv}}} \edtext{utilitas}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}V\textsuperscript{b}} | utilitatis \textit{P\textsuperscript{y}} | subtilitas \textit{V\textsuperscript{a}mv}}} que \edtext{hodie}{\Cfootnote[nosep]{\textit{ακmv} | a plurimis \textit{π}}} \edtext{appetitur}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | apparetur \textit{P\textsuperscript{p}}}} \edtext{summe reperitur}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{o}mv} | reperitur \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{V\textsuperscript{a}}}}, quare \edtext{ipsa}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{a}V\textsuperscript{o}mv} | in ipsa \textit{V\textsuperscript{b}} | ea \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}} | \textit{om}. \textit{P\textsuperscript{z}}}} \edtext{celerius}{\Cfootnote[nosep]{\textit{ακG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}mv}}} \edtext{percurri}{\Cfootnote[nosep]{\textit{κ} | precucurri \textit{E\textsuperscript{a}P\textsuperscript{q}P\textsuperscript{u}P\textsuperscript{y}} | precurri \textit{P\textsuperscript{z}mv} | precurrari \textit{P\textsuperscript{p}} | precucari \textit{V\textsuperscript{o}} | procurari \textit{γG\textsuperscript{u}}}}. \edtext{Nunc}{\Cfootnote[nosep]{\textit{γπM\textsuperscript{a}M\textsuperscript{b}P\textsuperscript{y}mv} | Non \textit{E\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{m}V\textsuperscript{z}}}} \edtext{autem}{\Cfootnote[nosep]{\textit{κπE\textsuperscript{a}P\textsuperscript{y}V\textsuperscript{b}mv} | \textit{om}. \textit{V\textsuperscript{a}}}} \edtext{deinceps}{\Cfootnote[nosep]{\textit{γκE\textsuperscript{a}G\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | \textit{om}. \textit{P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}}}} circa \edtext{reliquas}{\Cfootnote[nosep]{\textit{αλP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | aliquas \textit{G\textsuperscript{u}}}} \edtext{partes}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}} | partes cum \textit{G\textsuperscript{u}} | partes si \textit{mv}}} \edtext{physice}{\Cfootnote[nosep]{\textit{E\textsuperscript{a}G\textsuperscript{u}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{b}V\textsuperscript{m}V\textsuperscript{o}}}}, \edtext{naturalemque}{\Cfootnote[nosep]{\textit{κG\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{z}V\textsuperscript{o}mv} | naturalisque \textit{V\textsuperscript{a}} | naturalesque \textit{E\textsuperscript{a}} | naturaleque \textit{P\textsuperscript{u}V\textsuperscript{b}} | naturaliaque \textit{P\textsuperscript{y}}}} maxime, problemata tam circa composita \edtext{quam}{\Cfootnote[nosep]{\textit{γE\textsuperscript{a}M\textsuperscript{a}P\textsuperscript{x}V\textsuperscript{o}V\textsuperscript{z}mv} | quam circa \textit{G\textsuperscript{u}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{m}}}} simplicia \edtext{existentia}{\Cfootnote[nosep]{\textit{κE\textsuperscript{a}P\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{y}P\textsuperscript{z}V\textsuperscript{a}V\textsuperscript{o}mv} | \textit{om}. \textit{G\textsuperscript{u}V\textsuperscript{b}}}} \edtext{tractabuntur}{\Cfootnote[nosep]{\textit{ακP\textsuperscript{p}P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{o}mv} | tractabunt \textit{G\textsuperscript{u}}}}. \edtext{}{\Cfootnote{et cetera. \textit{P\textsuperscript{u}P\textsuperscript{z}V\textsuperscript{b}V\textsuperscript{z}}}} \edtext{}{\Cfootnote{sequitur \textit{V\textsuperscript{z}} | amen. \gap{} Deo gratias amen \textit{V\textsuperscript{b}} | Explicit decimanona particula. \textit{P\textsuperscript{z}mv} | Explicit particula 19a deo gratias \textit{V\textsuperscript{a}} | Explicit particula xixa. sequitur .xx.ma \textit{P\textsuperscript{y}}}} +\pend + +\endnumbering +\backmatter +\newpage +\thispagestyle{plain} +\section{Back Matter} + +\pagestyle{fancy} + +\fancyhead[LE]{\thepage} +\fancyhead[CE]{Back Matter} +\fancyhead[RO]{\thepage} +\fancyhead[CO]{\rightmark} + +\subsection[{List of persons mentioned by Pietro}]{\centering\uppercase{\so{List of persons mentioned by Pietro}}}\label{back-historical-figures} +{\large \scshape{Historical figures}} +\begin{itemize} + +\item \label{Al} Aphrodisiensis, Alexander +\item \label{Ar} Aristoteles +\item \label{Ax} Tarentinus, Aristoxenus +\item \label{Av} Avicenna +\item \label{Bo} Boethius, Anicius Manlius Severinus +\item \label{Co} Colophonius, Hestiaeus +\item \label{Dam} Damascenus, Johannes +\item \label{Ga} Galenus, Claudius +\item \label{GAr} Aretinus, Guido +\item \label{Hip} Hippocrates +\item \label{Hor} Horatius Flaccus, Quintus +\item \label{Is} Hispalensis, Isidorus +\item \label{Mac} Theodosius, Macrobius Ambrosius +\item \label{Mu} Atheniensis, Musaeus +\item \label{Ni} Gerasenus, Nicomachus +\item \label{Ov} Ovidius Naso, Publius +\item \label{Phil} Cytherius, Philoxenus +\item \label{Phr} Phrynichus (tragicus) +\item \label{Pl} Plato +\item \label{Pt} Ptolemaeus, Claudius +\item \label{Pyth} Pythagoras +\item \label{Ter} Antissenis, Terpander +\item \label{Th} Antiochenus, Theophilus +\item \label{Ti} Locrus, Timaeus +\item \label{Ty} Milesius, Timotheus +\end{itemize} + +{\large \scshape{Mythical figures}} +\begin{itemize} + +\item \label{Cay} Cain +\item \label{Ju} Jupiter +\item \label{Mem} Memoria +\item \label{Mer} Mercurius +\item \label{Mos} Moses +\item \label{Or} Orpheus +\item \label{Tor} Torebus +\item \label{Tub} Tubal Cain +\end{itemize} + +\subsection[{List of titles cited by Pietro, with editions supplied}]{\centering\uppercase{\so{List of titles cited by Pietro, with editions supplied}}}\label{back-list-works-cited} +\begin{bibitemlist}{1} +\bibitem [d'Abano 1504]{AbCo} d'Abano, Pietro. \textit{Conciliator differentiarum philosophorum}. Venetiis: n.p., 1504. URL: \url{http://data.onb.ac.at/rep/10B710EE} +\bibitem [AlPr]{AlPr} Pseudo-Alexander of Aphrodisias. \textit{Problemata}. Ed. Robert W. Sharples and Sophia Kapetanaki as \textit{Pseudo-Aristoteles (Pseudo-Alexander), Supplementa Problematorum: A new edition of the Greek text with introduction and annotated translation}. Berlin: De Gruyter, 2006; trans. Pietro d'Abano in Vatican Biblioteca Apostolica reg. lat. 747, ff. 62r–104r, URL: \url{https://digi.vatlib.it/view/MSS\textunderscore Reg.lat.747} +\bibitem [Arist. De an.]{ArAn} Aristotle. \textit{De anima}. Ed. J. Decorte and J. Brams as \textit{De Anima}. \textit{Aristoteles Latinus Database} XII.1 URL: \url{http://clt.brepolis.net/ALD/pages/TextSearch.aspx?key=MIV11ANIM\textunderscore } +\bibitem [Arist. Cael.]{ArCa} Aristotle. \textit{De caelo} Ed. F. Bossier as \textit{De caelo et mundo}. \textit{Aristoteles Latinus Database} VIII URL: \url{http://clt.brepolis.net/ALD/pages/TextSearch.aspx?key=MGM11CAMU\textunderscore } +\bibitem [Arist. Eth. Nic.]{ArEth} Aristotle. \textit{Liber ethicorum ad Nicomachum}. Ed. R.A. Gauthier as \textit{Analytica posteriora (Iacobi Venetici translationis recensio)}. \textit{Aristoteles Latinus} XXVI.1–3. Leiden and Bruxelles: Brill and Desclée De Brouwer, 1972–1974, URL: \url{http://clt.brepolis.net/ALD/pages/TextSearch.aspx?key=MBUPIETN1\textunderscore } +\bibitem [Arist. Metaph.]{ArMet} Aristotle. \textit{Metaphysica}. Ed. G. Vuillemin-Diem as \textit{Metaphysica, lib. I-XIV. Recensio et Translatio Guillelmi de Moerbeka}. \textit{Aristoteles Latinus} XXV.3. Leiden, New York, and Köln: E.J. Brill, 1995, URL: \url{http://clt.brepolis.net/ALD/pages/TextSearch.aspx?key=MGM55META\textunderscore } +\bibitem [An. Post.]{ArPA} Aristotle. \textit{Analytica posteriora}. Ed. L. Minio-Paluello and B. G. Dod as \textit{Analytica posteriora (Iacobi Venetici translationis recensio)}. \textit{Aristoteles Latinus} IV.1–4. Bruges and Paris: Desclée De Brouwer, 1968, URL: \url{http://clt.brepolis.net/ALD/pages/TextSearch.aspx?key=MGM55ANPO\textunderscore } +\bibitem [Arist. Int.]{ArPe} Aristotle. \textit{Peri hermeneias}. Ed. L. Minio-Paluello and G. Verbeke as \textit{Periermenias (Peri hermeneias) (uel De Interpretatione)}. \textit{Aristoteles Latinus} II.2. Bruges and Paris: Desclée De Brouwer, 1965, URL: \url{http://clt.brepolis.net/ALD/pages/TextSearch.aspx?key=MGM11PEHE\textunderscore } +\bibitem [Arist. Ph.]{ArPh} Aristotle. \textit{Physica}. Ed. F. Bossier and J. Brams as \textit{Physica (translatio 'uetus')}. \textit{Aristoteles Latinus} VII. Leiden and New York: E.J. Brill, 1990, URL: \url{http://clt.brepolis.net/ALD/pages/TextSearch.aspx?key=MIV11PHYS\textunderscore } +\bibitem [Arist. Pol.]{ArPo} Aristotle. \textit{De politicorum}. Ed. Franciscus Susemihl as \textit{Aristotelis Politicorum libri octo cum vetusta translatione Guilelmi de Moerbeka}. Leipzig: Teubner, 1872. +\bibitem [Arist. Top.]{ArTo} Aristotle. \textit{Topica}. Ed. L. Minio-Paluello as \textit{Topica. Translatio Boethii, Fragmentum Recensionis Alterius et Translatio Anonyma}. \textit{Aristoteles Latinus} V.1–3. Bruges and Paris: Desclée De Brouwer, 1969, URL: \url{http://clt.brepolis.net/ALD/pages/TextSearch.aspx?key=PARBOTOPI\textunderscore } +\bibitem [ArPr]{ArPr} Pseudo-Aristotle. \textit{Problemata physica}. Ed. Carolus Ruelle, Hermannus Knoellinger and Iosephus Klek as \textit{Aristotelis quae feruntur Problemata physica}. Leipzig: Teubner, 1922. +\bibitem [AvCa]{AvCa} Avicenna. \textit{Canon medicinae}. Trans. Gerardus Cremonensis as \textit{Avicennae Arabum medicorum principis, Canon medicinae}. Venice: Iuntas, 1608. +\bibitem [BoAr]{BoAr} Anicius Manlius Severinus Boethius. \textit{De institutione arithmetica}. Ed. Godofredus Friedlein in \textit{Anicii Manlii Torquati Severini Boetii De institutione arithmetica libri duo, De institutione musica libri quinque}, 1–173. Leipzig: Teubner, 1868. +\bibitem [BoMu]{BoMu} Anicius Manlius Severinus Boethius. \textit{De institutione musica}. Ed. Godofredus Friedlein in \textit{Anicii Manlii Torquati Severini Boetii De institutione arithmetica libri duo, De institutione musica libri quinque}, 175–371. Leipzig: Teubner, 1868. +\bibitem [GaAc]{GaAc} Galen. \textit{De morbo et accidenti}. Ed. C. G. Kühn as \textit{De symptomatum causis libri iii} in \textit{Claudii Galeni opera omnia}, vol. 7 , 83–272. Leipzig: Knobloch, 1824. +\bibitem [GaPu]{GaPu} Galen. \textit{De differentia pulsuum libri iv}. Ed. C. G. Kühn in \textit{Claudii Galeni opera omnia}, vol. 8 , 493–765. Leipzig: Knobloch, 1824. +\bibitem [GaSa]{GaSa} Galen. \textit{De sanitate tuenda libri vi}. Ed. K. Koch in \textit{Corpus medicorum Graecorum} 5.4.2 , 3–198. Leipzig: Teubner, 1923. +\bibitem [HipAph]{HipAph} Hippocrates. \textit{Aphorismi}. Ed. É. Littré in \textit{Oeuvres complètes d'Hippocrate}, vol. 4 , 458–608. Paris: Baillière, 1844. +\bibitem [IsEt]{IsEt} Isidore of Seville. \textit{Etymologiae}. Ed. W. M. Lindsay in \textit{Isidori Hispalensis Episcopi Etymologiarum sive originum libri xx}, vol. 1. Oxford: Clarendon Press, 1911. +\bibitem [MacSS]{MacSS} Macrobius Ambrosius Theodosius. \textit{Commentarium in somnium Scipionis}. Ed. Franciscus Eyssenhardt in \textit{Macrobius}, 465–570. Leipzig: Teubner, 1868. +\bibitem [MasAph]{MasAph} Yuḥannā ibn Māsawaiyh. \textit{Aphorismorum libri}. Ed. Danielle Jacquart and Gérard Troupeau as \textit{Yuhannà ibn Màsawayh (Jean Mésué), Le livre des Axiomes médicaux (Aphorismi), édition du texte arabe et des versions latines avec traduction française et lexique}. Geneva: Droz, 1980. See also Biblioteca Apostolica vat. lat. 2460, f. 39r–42r, URL: \url{https://digi.vatlib.it/view/MSS\textunderscore Vat.lat.2460} +\bibitem [NiGer]{NiGer} Nichomachus (Dramatist). \textit{Geryones}. (Concerning this lost play, see URL: \url{http://www.apgrd.ox.ac.uk/ancient-performance/performance/491}) +\bibitem [Psalm]{Psalm} \textit{Liber psalmorum}. Ed. Robertus Weber in \textit{Biblia sacra iuxta vulgatam versionem}, 767–955. Stuttgart: Deutsche Bibelgesellschaft, 1994. +\bibitem [PtHar]{PtHar} Claudius Ptolemy. \textit{Harmonica}. Ed. I. Düring as \textit{Die Harmonielehre des Klaudios Ptolemaios} in \textit{Göteborgs Högskolas Arsskrift} 36 , 2–111. Göteborg: Elanders, 1930. +\bibitem [SePr]{SePr} Pseudo-Hermes Trismegistus. \textit{De sex rerum principiis}. Ed. Paolo Lucentini and Mark D. Delp in \textit{Corpus Christianorum, Continuatio Mediaeualis} 142. Turnhout: Brepols, 2006. (Sometimes attributed to Gilbert of Poitiers.) + +\end{bibitemlist} + +\end{document} From fb96dc4ea51d7cb64ff19f620ef5ad645ca47f6b Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Mon, 22 Jan 2024 11:30:36 -0600 Subject: [PATCH 04/25] fix: replace with "Other manuscripts from the Jean de Jandun redaction" should be in under , not under . --- edition.xml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/edition.xml b/edition.xml index afe9647..7402087 100644 --- a/edition.xml +++ b/edition.xml @@ -530,8 +530,8 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - Other manuscripts from the Jean de Jandun redaction + Other manuscripts from the Jean de Jandun redaction Ca Cambridge, Peterhouse 79, ff. From 184085d47f8c5460aa5762ae9a9a90ee61720bc3 Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Mon, 22 Jan 2024 11:32:20 -0600 Subject: [PATCH 05/25] update: add template to remove app with @exclude --- mutch.xsl | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/mutch.xsl b/mutch.xsl index 7d0538a..67fd197 100644 --- a/mutch.xsl +++ b/mutch.xsl @@ -20,6 +20,9 @@ + + + @@ -28,6 +31,7 @@ + From b5f96c47005a6a454ee823285291a9d48fc72705 Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Mon, 22 Jan 2024 11:32:42 -0600 Subject: [PATCH 06/25] update: to reflect changes in edition.xml --- pdf-edition.xml | 804 ++++++++++++------------------------------------ 1 file changed, 193 insertions(+), 611 deletions(-) diff --git a/pdf-edition.xml b/pdf-edition.xml index 2e12889..dd40969 100644 --- a/pdf-edition.xml +++ b/pdf-edition.xml @@ -493,8 +493,8 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - Other manuscripts from the Jean de Jandun redaction + Other manuscripts from the Jean de Jandun redaction Ca Cambridge, Peterhouse 79, ff. @@ -943,7 +943,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - + Primum problema .1. @@ -957,11 +957,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>PROPTER QUID DOLENTES ET DELECTANTES FISTULANTUR?AUT UT HII QUIDEM MINUS TRISTENTUR? ALII AUTEM MAGIS GAUDEANT . - - Propter quid dolentes etcetera. - Propter quid dolentes et gaudentes fistulantur - etcetera - Determinatis problematibus circa + Determinatis problematibus circa mathematicam mathematica methaphysica @@ -1234,7 +1230,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> hanc moyses - inuenisse + inuenisse tubal @@ -1266,7 +1262,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>Isidore of Seville, Etym. III.16.1 - + Sed greci @@ -2490,7 +2486,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Secundum problema 2m Secundum @@ -2513,10 +2509,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ETENIM EX OMNIBUS UOX UNIUSCUIUSQUE MULTIPLEX . - - Secundum problema - etcetera. - + Quare Querit quare @@ -2964,7 +2957,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Tertium problema 3m tertium @@ -2983,10 +2976,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Tertium problema - etcetera. - + Quare Querit quare @@ -4069,7 +4059,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> Cuiusmodi est huiusmodi descriptio - + dyatonici @@ -4279,28 +4269,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>canon canono canon dictus - ostendit. - - dyatonici - proslabanomenos - ypate ypaton - parypate ypaton - lychanos ypato dyatonici - ypate meson - lychanos meson - Mese - Trite sinezengium - Paranete sinezengium dyatonici - Nete sinezengium - Paramese - Trite dyazengium - paranete dyezengium dyatonici - zeze dyezengium - trite yperboleon - dyatonici - Nete yperboleon - - + ostendit. Deinde. @@ -4692,7 +4661,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Quartum problema 4m Quartum problema @@ -4715,10 +4684,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>HUIUS AUTEM UTIQUE CONSONANTIA QUEDAM CAUSA . - - Quartum problema - etcetera. - + Quare Querit quare @@ -5320,7 +5286,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Quintum problema 5m quintum problema. Quintum. @@ -5339,10 +5305,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ADHUC AUTEM ET CONSUETUM DELECTABILE MAGIS INCONSUETO . - - Quintum problema - etcetera. - + Quare Querit quare @@ -5710,7 +5673,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> et melodia et ystoria et siquidem cum habuerint - . + . Triplex enim tunc @@ -5738,12 +5701,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>delectantur delectatur - - triplex enim tunc delectatio - concurrit - triplex enim delectatio tunc concurit - triplex enim delectatio concurrit - , + , Deinde. unde secundo confirmat causam @@ -6200,7 +6158,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Sextum problema 6m sextum. @@ -6216,10 +6174,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Sextum problema - etcetera. - + Quare Querit quare @@ -6666,8 +6621,10 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>. Gal. De diff. puls. - I.8 (I.12 in Latin trans. by Burgundio of Pisa) Cf. Conciliator diff. - 83 + I.8 (I.12 in Latin trans. by Burgundio of Pisa) + Cf. + Pietro d'Abano Conciliator + diff. 83 Ceu @@ -6904,7 +6861,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Septimum problema 7m Septimum. @@ -6924,10 +6881,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>QUIA ACUTUM POTENTIA MAGIS, GRAUE AUTEM FACILIUS CANTATUR . - - Septimum problema - etcetera. - + Quare Querit quare @@ -7248,11 +7202,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> acutum acuta - cantare + cantare sed graue facilius, - + sicut pluries dicetur. Sic itaque ergo @@ -7603,7 +7557,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Octauum problema 8m octauum problema. @@ -7618,10 +7572,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>AUT QUIA MAIUS HOC GRAUE? OBTUSO ENIM ASSIMULATUR, HOC UERO ACUTO ANGULO . - - Octauum problema - etcetera. - + Quia Quare @@ -7765,7 +7716,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Nonum problema 9m nonum problema.Nonum. @@ -7785,10 +7736,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>TORES AUT LYRAS MULTAS NON EST DELECTABILE PROPTER ID QUOD DESTRUIT MELODIAM . - - Nonum problema - etcetera. - + Quare Querit quare @@ -8252,7 +8200,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Decimum problema 10m decimum problema. @@ -8270,14 +8218,8 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>AT UERO SED PROPTER OPUS IPSUM. UOX ENIM DELECTABILIS QUE EST HOMINIS, PERCUSSIUA AUTEM MAGIS INSTRUMENTA ORIS. PROPTER QUOD DELECTABILIUS AUDIRE QUAM UERNARE - . - PROPTER QUID SONANS ACUTIOR QUIA MINUS IMBECILLIOR EST - FACTA. - - - Decimum problema - etcetera. - + . + Quare Querit quare @@ -8782,7 +8724,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Undecimum problema 11m Undecimum. @@ -8790,18 +8732,14 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> -

+

PROPTER QUID SONANS PROPTER QUID SONANS ACUTIOR? AUT QUIA MINUS IMBECILLIOR FACTA EST . - - Undecimum - problema etcetera. - Propter quid sonans etcetera - + Quare Querit quare @@ -8904,7 +8842,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>

- + Duodecimum problema 12m @@ -8921,10 +8859,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>DUE NITE IN YPATE FIUNT . - - Duodecimum - problema. - + Quare Querit quare @@ -9115,7 +9050,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> licet possit tollerari series series tollerari - tamen iam exposita continens paramese + tamen iam exposita continens paramese planior et sauior @@ -9127,7 +9062,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>. - + Sed si Sed @@ -9339,7 +9274,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Tertiumdecimum problema @@ -9358,10 +9293,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>AUT QUIA MAXIME QUIDEM IN AMBOBUS EST AMBORUM MELODIA? SI AUTEM NON, NON GRAUE, MAIUS ENIM EST . - - Decimumtertium - problema etcetera. - + Quare Querit quare @@ -9454,7 +9386,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>arismetricis - + intuendum intuendum est @@ -9462,7 +9394,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - + Sunt autem secundum boecium in primis @@ -9519,7 +9451,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>superari subsuperparticulari - + et ex et @@ -9535,7 +9467,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>et superparticulari - , + , secunda ex multiplici superparticulari multiplici et superparticulari @@ -9979,7 +9911,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>duplex sexquialtera sexquialtera - , + , duplex sexquitertia @@ -9990,7 +9922,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>, duplex sexquiquarta, etcetera, - + et id ratione id rationem @@ -10014,7 +9946,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - + triplex sexquialtera, @@ -10539,7 +10471,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> una uox in grauitate uel seu - acuitate + acuitate se habuerit ad aliam sicut se habet ad aliam sicut @@ -10555,7 +10487,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>se hii· sed hii .

-

+

Iuxta uero emiolam @@ -11114,7 +11046,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ista videlicet ista in ista tolitua talis - . + . Γ. @@ -11756,153 +11688,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>sequitur 14m. problema 19e. particule. - - -
- - G - 1296 - ut - - - - - - - - - a. - 1152. - re. - Dyatonus - - - b. - 1034. - mi. - - - - c. - 972. - fa ut. - Dyatesseron. - - - d. - 864. - solre. - - - - e. - 786. - la mi. - - - - f. - 739. - fa ut. - - - - g. - 646. - solreut. - dyapason. - - - a. - 576. - lamire. - - - - b. - 554. - mi - - - - b. - 512. - fa. - - - - c. - 486 - solfaut. - dyatesseron dyapason. - - - d. - 432. - lasolre - dyapente dyapason. - - - e. - 384. - la mi. - - - - f. - 349. - faut. - - - - g. - 324. - solreut. - bis dyapason. - - - a. - - lamire - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-

+

- + Quartumdecimum problema @@ -11923,10 +11713,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Decimum quartum - problema etcetera. - + Quare Querit quare @@ -12248,7 +12035,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Quintumdecimum problema @@ -12280,10 +12067,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ENIM CANTAT IN SCENA AGONISTA ET MUTATOR, CHORUS AUTEM MINUS MUTATUR . - - Decimum quintum - problema etcetera. - + Quare Querit quare @@ -12440,7 +12224,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>altius alterius alterius perfectis - + cantus secunda EADEM AUTEM @@ -12458,7 +12242,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> dicens - + causam esse quoniam leges fuerunt cantus constituti ab agonizantibus et @@ -12619,7 +12403,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> Deinde. - + MAGIS ENIM EST @@ -12714,7 +12498,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - + ideo @@ -13380,7 +13164,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Sextumdecimum problema @@ -13399,10 +13183,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>DUE AD UNAM UOCEM FACTE DESTRUUNT ALTERAM . - - Decimum sextum - problema. - + Quare Querit quare @@ -13818,7 +13599,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Decimumseptimum problema 17m @@ -13838,10 +13619,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Decimum septimum - problema. - + Quare Querit quare @@ -14144,7 +13922,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>partium paruum - excessum non poterit excedentia + excessum non poterit excedentia manifestari vnius ad alterum, quare non contraphonizare contingit @@ -14163,7 +13941,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> moueri - . + . Unde relinquitur @@ -14187,7 +13965,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Decimumoctauum problema 18m @@ -14210,10 +13988,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Decimum octauum - problema etcetera. - + Quare Quare cum @@ -14306,11 +14081,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>per propter - proportionem duplam. + proportionem duplam. In antiphonis enim cordis ita se habet - + quod si altera cantetur cantetur simul @@ -14318,7 +14093,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - + siue tangatur tangetur @@ -14337,7 +14112,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>, - + ac si si @@ -14468,11 +14243,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>nete tunc vite - cantando et fistulando utrobique cantatur + cantando et fistulando utrobique cantatur vna quia media quia media - . + . Et ideo sola symphonia @@ -14563,7 +14338,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Decimumnonum problema 19m decimum nonum.Decimumnonum. @@ -14579,10 +14354,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Decimum nonum - problema etcetera. - + Consequenter @@ -14775,7 +14547,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Uigesimum problema 20m Uigesimum. problemaUigesimum. @@ -14803,10 +14575,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ITA AUTEM ET SONORUM MEDIA SICUT CONIUNCTIO EST ET MAXIME BONORUM, PROPTER ID QUOD MULTOTIENS INEST IPSIS SONIS . - - Uigesimum - problema. - + Quare Querit quare @@ -15177,7 +14946,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>et - primo in metrica, que est + primo in metrica, que est musica quedam quedam musica @@ -15190,7 +14959,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> quod musica - + omnes boni poete utentes hac parte musice metrica dicta, quam @@ -16059,7 +15828,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Uigesimumprimum problema 21m @@ -16079,10 +15848,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>AUT QUIA IN PLURI TEMPORE MULTUM EXHIBET, UELOX AUTEM ET ACUTUM LATET PROPTER UELOCITATEM ? - - Uigesimum primum - problema. - + Quare cantantes Querit quare cantantes @@ -16305,7 +16071,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Uigesimumsecundum problema 22m @@ -16322,10 +16088,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Uigesimum - secundum problema. - + Quare Querit quare @@ -16478,7 +16241,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Uigesimumtertium problema 23m @@ -16505,10 +16268,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>AMPLIUS IN TRIANGULIS PSALTERIIS EQUALI DISTENSIONE FACTA CONSONANT DYAPASON. HEC QUIDEM DUPLEX EXISTENS, ALIA UERO MEDIA LONGITUDINE . - - Uigesimum - tertium problema. - + Quare Quia @@ -16902,7 +16662,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> proportionato proportionate - ypate, ut sonus eius + ypate, ut sonus eius subgrauetur, et foramina per nitem @@ -16919,7 +16679,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> usque ad medium , - + ut in @@ -17181,7 +16941,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Uigesimumquartum problema 24m @@ -17199,10 +16959,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Uigesimum - quartum problema. - + Quare Querit quare @@ -17385,7 +17142,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> minus grauem. - + Sonus autem grauis grauis sonum @@ -17399,7 +17156,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>acuto - , + , sed et @@ -17520,7 +17277,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Uigesimumquintum problema 25m @@ -17536,10 +17293,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>PROPTER QUID MEDIA UOCATUR IN ARMONIIS, OCTO UERO NON EST MEDIUM? AUT QUIA SEPTEM CORDARUM ERANT ARMONIE ANTIQUITUS? SEPTEM AUTEM HABENT MEDIUM . - - Uigesimum - quintum problema. - + Quare Querit quare @@ -17835,7 +17589,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Uigesimumsextum problema 26m @@ -17854,10 +17608,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> AUT QUIA PEIUS GRAUI? PECCATUM PEIORIS OPERATIO . - - Uigesimum sextum - problema etcetera. - + Quare Querit quare @@ -18095,7 +17846,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Uigesimumseptimum problema 27m @@ -18119,10 +17870,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>MOTUS AUTEM IPSI OPERATIUI SUNT, OPERATIONES ENIM CONSUETUDINIS SIGNIFICATIO EST . - - Uigesimum - septimum problema etcetera. - + Quare Querit quare @@ -18586,7 +18334,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>sensibili sensibilis sensibiliter - , et + , et motus motus aeris @@ -18601,7 +18349,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>sensicun - . + . Operationes enim fiunt per eos eas @@ -18909,7 +18657,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Uigesimumoctauum problema 28m @@ -18928,10 +18676,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Uigesimum - octauum problema. - + Quare Querit quare @@ -19066,7 +18811,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>reddantur redduntur declaratum - manifeste + manifeste note uoce nete @@ -19242,7 +18987,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Uigesimumnonum problema 29m @@ -19261,10 +19006,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Uigesimum nonum - problema etcetera. - + Repetit 27m problema dicens .27. partem @@ -19440,7 +19182,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Trigesimum problema 30m Trigesimum. @@ -19460,10 +19202,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>AUT NON HABET CONUERSIUUM? SED A SCENA, IMMUTATIUA ENIM . - - Problema .30m. - etcetera. - + Quare Querit quare @@ -19719,7 +19458,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>maluafiati cuius cantus laudabilis - + tanquam @@ -19740,7 +19479,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>Pol. VIII, 1324b l. 12 - + unde .48. @@ -19960,7 +19699,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Trigesimumprimum problema 31m @@ -19978,9 +19717,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> AUT PROPTER ID QUOD MULTIPLICES SUNT TUNC CANTUS IN TRAGEDIIS METRORUM ? - - Pricesimum primum problema - + Quare Querit quare @@ -20083,7 +19820,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Trigesimumsecundum problema 32m @@ -20103,10 +19840,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ENIM ERAT . - - Problema 32m. - etcetera. - + Quare consonantia Querit quare consonantia @@ -20450,7 +20184,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Trigesimumtertium problema 33m @@ -20469,10 +20203,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> AUT QUIA GRAUE AB ACUTO FORTIUS ET MAGIS UOCALE ? - - Problema 33m. - etcetera. - + Quare Querit quare @@ -20554,7 +20285,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> Deinde. - MEDIA. + MEDIA. Remouet dubitationem dubium @@ -20585,7 +20316,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> quod - + corda media et principalis est corda media principalis est corda principalis et media est @@ -20774,7 +20505,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Trigesimumquartum problema 34m @@ -20793,10 +20524,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>AUT QUIA BIS PER ACUTOS NEQUE BIS DYATESSERON EST, QUOD AUTEM PER QUATUOR AUT PER QUINQUE ? - - Problema 34m. - etcetera. - + Quare Querit quare @@ -20828,7 +20556,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>simphoniam constituunt, dyapason uero concordat? Dicitur autem bis paracutos - + dyapente @@ -20872,7 +20600,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> Deinde. - + AUT. AUT QUIA. @@ -20952,7 +20680,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Trigesimumquintum problema 35m @@ -20984,10 +20712,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Problema 35m. - etcetera. - + Quare Querit quare @@ -21090,7 +20815,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ex parte - + quantitatis et qualitatis qualitatis et quantitatis @@ -21104,7 +20829,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> quod - + duplex nite @@ -21371,11 +21096,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>comparatio operatio - + totius ad totum, - + ut @@ -21406,7 +21131,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - + sed fit @@ -21419,11 +21144,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>erit est erunt - optima consonantiarum + optima consonantiarum dyapente .

-

+

Deinde. @@ -22230,7 +21955,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>

- + Trigesimumsextum problema 36m @@ -22253,10 +21978,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Problema 36m. - etcetera. - + Quare Querit quare @@ -22481,7 +22203,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Trigesimumseptimum problema 37m @@ -22511,10 +22233,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Problema .37m. - etcetera. - + Querit Quare @@ -23203,7 +22922,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Trigesimumoctauum problema 38m @@ -23236,10 +22955,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>QUAMUIS SENSIBILE SIT UTRISQUE EXTREMIS EX EQUALI POTENTIAM HABET IN CONSONANTIA PROPORTIO . - - Problema 38m. - etcetera. - + Quare Querit quare @@ -24128,7 +23844,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> ordinatio inordinatio - , que naturaliter + , que naturaliter delectabilis existit @@ -24137,7 +23853,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>. delectabilis - + Quod autem hoc sit delectabile ostenditur quoniam @@ -24147,14 +23863,14 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>complexionatum - + seu ceu siue mixtum, - + omne autem complexionatum complexionatum et mixtum @@ -24224,7 +23940,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>vtrisque utique - + extremorum postrimorum @@ -24242,7 +23958,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> remouet, dicens - + quodlibet quod @@ -24506,7 +24222,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Trigesimumnonum problema 39m @@ -24545,10 +24261,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Problema .39m. - etcetera. - + Quare Querit quare @@ -25229,10 +24942,10 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>causam partis alterius causam alterius partis partem alterius - , + , dicens quod - , + , de numero aliarum consonantiarum ad a @@ -26061,17 +25774,12 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> et cetera - - problema 40. - - - et huius quidem expositio sufficiens iam 5to. apparebit parte repetitur uero ut memorie - amplius comendetur. -

+ +

- + Quadragesimum problema 40m @@ -26096,21 +25804,8 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - PROPTER QUID BIS PARACUTA AUT BIS IIII.OR NON CONCORDANT BIS DYAPASON AUTEM ITA. AUT QUIA QUOD QUIDEM - DYAPENTE EST IN EMIOLA PROPORTIONE QUID UERO - PER IIII.OR IN ENIPIRITIO EXISTENTIBUS AUT - EMIOLIBUS - TRIBUS CONSEQUENTER NUMERIS QUE EST EPITRITIO EXTREMA AD SE INUICEM NULLAM - PROPORTIONEM HABEBUNT. NEQUE ENIM PARTICULARIA ERUNT NEQUE MULTIPLICIA DYAPASON - AUT QUONIAM EST IN DUPLICI PROPORTIONE BIS. - HOC FACTO IN QUADRUPLICI PROPORTIONE SI FIUNT - EXTREMA AD INUICEM. QUARE QUONIAM CONSONANTIA RATIONABILEM HABENTIUM SONUM AD SE - INUICEM EST RATIONEM AUT QUI QUIDEM HABENT BIS DYAPASON INTER DECISIONEM AD SE - INUICEM SONI HABENT. QUI AUTEM BIS PER IIII.OR AUT PER QUINQUE NON HABENT - QUICQUID DYAPASON CONSONABUNT UTIQUE ALII UERO NON PER EA QUE DICTA SUNT. - - + + Et @@ -26163,45 +25858,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>et cetera - - Propter quid bis. Repetit 34. ut - amplius exponat. Aut quia. Soluit Et primo assignat causam prime partis Et secundo secunde ibi dyapason .3° concludit in tantum ibi quare quoniam Primo querit quare - quoniam dyapente est in sexquialtera - proportione dyatesseron in sexquitertia. hiis - itaque ita dispositis numerus ut 3us. etiam - numeris consequenter reiterati ut tria et - quatuor. ex quibus erat Epitrica ut dictum est proportio cum erant simplices in - repetiti. Tunc si extrema huiusmodi duarum - consonantiarum duplentur ad inuicem coniuncta nullam habebunt proportionem - consurgentem inde quod probatur quia talia non reddunt nec superticularia neque - multiplicia penes que ut visum est 13. - proportiones accipiuntur musice. vnde apparet quod aristotelis consentit pictagoricis has ponentibus solum Et non - concidit cum ptolomeo ponente proportionem - compositam ex dyatesseron et dyapason consurgere ex multiplici et - superparticulari. Si namque sumatur bis dyatesseron puta prima dyatesseron fit - proportio 3. ad 4. et 2a - 5. ad 4. - Et coniungantur extrema: ut .3. ad 4. Nulla consurgit proportio pretactorum - multiplicitatis aut superparticularis Similiter in dyapente si sumatur Exempli - gratia Vna dyapente cum 2 comparantur ad 3 et 2a quando .6. ad .9. ita ut duo comparentur ad .9. modo eodem nulla consurgit proportio cum omnis ut sic - constet in numero Epitrico. Emiolis - duplari: triplari Et quadruplo ut ostensum est - superius. etcetera Dyapason. Assignat causam 2e partis dicens quia dyapason se habet in dupla proportione si bis sumatur ea erit in quadruplici extremis - comparatis ad inuicem proportionum maiorum et minorum Puta sumatur bis dyapason ut - in vnaquaque comparetur vnum comparetur ad - duo Et reliqua 2 ad 4 resultabit numerus - quadruplus Iuxta quod predictum est bis - dyapason bis Quare quoniam 3° concludit intentum dicens Et ideo quia consonantia - est compositio quedam tonorum habentium et rationabilem et proportionalem - proportionem ad inuicem Et hoc habet bis dyapason Non autem bis dyatesseron aut - dyapente et reliqua Quod declaratur quia proportio quam habent soni ad inuicem Est - habere inter se decisiones et confractionem quandam ad inuicem per quam sonsultant - quidem proportionales armonici: ut bisdyapason quod non habet consonantiam per - 4or. et quinque siue dyatesseron et dyapente Cunque ut dictum est tantum soni qui - fuerunt secundum dyapason duplatum consonant - alii vero minime: sicut ostensum est per ante dictam causam. - #Pq runs problem 40 into 41 just as #Gu does. -

+

@@ -26231,13 +25888,13 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>NON PER EA QUE DICTA SUNT . - + Repetit trigesimumquartum ut amplius exponat exponatur .

-

+

Deinde. @@ -26257,10 +25914,10 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - + QUARE QUONIAM QUARE - . + . Dicens Dicit @@ -26591,7 +26248,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>superius .

-

+

Deinde. @@ -26698,7 +26355,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>

-

+

Deinde. @@ -26821,24 +26478,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>19e. particule. - - propter quid bis paracuta autem bis iiii.or non concordant bis dyapason autem ita. Aut quia quod quidem - dyapente est in emiolia proportione quod uero - per iii.or in epyptrico existentibus autem - emiolibus - tribus consequenter numerus que est epitricon extrema ad se inuicem nullam - proportionem habebunt. neque enim particularia neque multiplitia erunt dyapason - quoniam est in duplici proportione bis. hoc - factum in quadruplici proportione si fuerint - extrema ad inuicem. quoniam consonantia rationabilem habentium sonum ad se inuicem - est rationem aut qui quidem habent bis dyapason interpositionem ad se inuicem soni - habent. qui autem quidem bis dyapason. et consonabunt utique alii uero non per ea - que dicta sunt. -

+

- + Quadragesimumsecundum problema 42m @@ -26876,10 +26520,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>QUARE MERITO ET SECULARIUM IPSIUS MAIUS ERIT QUAM QUOD EST ALIARUM, QUARE BREUES MOUERI, SICUT IPSIS . - - Problema quadragesimum - secundum etcetera. - + Quare Querit quare @@ -28198,7 +27839,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Quadragesimumtertium problema 43m @@ -28235,10 +27876,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Problema .43m. - etcetera. - + Quare Querit quare @@ -29269,7 +28907,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Quadragesimumquartum problema 44m @@ -29279,7 +28917,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> -

+

PROPTER QUID SEPTEM PROPTER QUID SEPTEM QUIDEM MEDIA @@ -29293,9 +28931,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>EORUM AUTEM QUE SUNT IN MEDIO QUARUNDAM EXTREMITATUM MEDIUM ERAT PRINCIPIUM SOLUM . - - Problema .44m. etcetera. - + Repetit Quare repetit @@ -29590,7 +29226,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> tunc mese utrobique uere - medium extat. + medium extat. verbi gratia verbi gratia si ordinantur @@ -29630,9 +29266,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - - Primum retrocordum - + Et @@ -29794,7 +29428,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>

- + Quadragesimumquintum problema 45m @@ -29804,7 +29438,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> -

+

PROPTER QUID MULTI PROPTER QUID MULTIPLICANTES @@ -29817,10 +29451,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Problema .45m. - etcetera. - Repetit + Repetit .22m .22m. problema @@ -29997,18 +29628,12 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>amen dooo . - - Problema 46 - - - huius precessit expositio .26°. - et uerita illic iam apparuit cuiusdam apparentis contrarietatis inter .27m. et istud cum dictum sit ibidem difficilius - acute cantare quam grauiter. hic autem videtur contrarium dici. sequitur 47. problema 19e. particule. -

+ +

- + Quadragesimumsextum problema 46m @@ -30029,7 +29654,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>CANTANT IGITUR ACUTE MAGIS, ET IN QUO CANTANT PECCANT . - + Huius Huiusmodi @@ -30092,7 +29717,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Quadragesimumseptimum problema 47m @@ -30115,9 +29740,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> ? - - Quadragesimumseptimum problema etcetera. - + Repetit Repetit quoddam problema predictum @@ -30745,43 +30368,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>sequitur 48. problema 19e. particule. - - verbi gratia - - ypate - - - - paripate - primum tena - cordum - - - lychanos - - - - mese - - - - paramese - 45 - - - Paramete - - - - nete - - -
Et huius 3us quidem cetra corda 2m. sinzeusim -

+

- + Quadragesimumoctauum problema 48m @@ -30818,10 +30409,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>EST AUTEM CHORUS CURATOR INOPERABILIS, BENIUOLENTIAM ENIM SOLUM PREBET QUIBUS ADEST . - - Problema .48m. - etcetera. - Repetit + Repetit 30m 30. problema @@ -31221,7 +30809,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> Ostendit secundo qualis sit - cantus + cantus ypodoristium. Dicit quod @@ -31233,7 +30821,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> ypodorum - + cantus @@ -32007,7 +31595,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Quadragesimumnonum problema 49m @@ -32028,10 +31616,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Problema .49m. - etcetera. - + Quare Querit quare @@ -32337,7 +31922,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>
- + Quinquagesimum problema Ultimum problema 50m @@ -32359,10 +31944,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - - Problema .50m. - etcetera. - + Quare Querit quare @@ -32423,9 +32005,9 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>25°, et 5º, - - Pietro expresses this idea in his commentary on problem 10 of particula 15. - His reference to 5/25 is obscure. + + Pietro expresses this idea in his commentary on problem 10 of + particula 15. His reference to 5/25 is obscure. puta quod vnum sit sit vnum @@ -32448,7 +32030,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>acuto - + vacuum vacuo @@ -32460,7 +32042,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> , - + idem namque enim From 0d7dbd4a8bfe3bba518f589bf7f34eea79051b68 Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Wed, 28 Feb 2024 14:15:53 -0600 Subject: [PATCH 07/25] Add # in front of some wits that were missing it --- edition.xml | 14 +-- pdf-edition.xml | 305 +++++++++++++++++++++++------------------------- 2 files changed, 151 insertions(+), 168 deletions(-) diff --git a/edition.xml b/edition.xml index 7402087..cbf4b52 100644 --- a/edition.xml +++ b/edition.xml @@ -1704,7 +1704,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> De caelo, II.9, 290b, l. 25 -

+ .

Musica uero humana mundana @@ -12211,7 +12211,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> >256. 2256 - duo milia ducenti .56. + duo milia ducenti .56. . Quorum @@ -13551,11 +13551,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> existentes - existentis + existentis acuti - acutii + acutii quia non concurrunt adeo in vnum, non sunt unius vinus @@ -17436,7 +17436,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> et perfectam et congruissimam congruissimam et perfectissimam - congruisima et perfectam + congruisima et perfectam congrauissimam et perfectam bene sonantem, et @@ -17458,7 +17458,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> horret orret - abhoret + abhoret oret honoret @@ -19620,7 +19620,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> medium habent - equidistans + equidistans equedistans eque distans equidistant diff --git a/pdf-edition.xml b/pdf-edition.xml index dd40969..dd081e8 100644 --- a/pdf-edition.xml +++ b/pdf-edition.xml @@ -472,7 +472,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ff. 179r-92r fourteenth century. - Pz + Pz @@ -492,7 +492,6 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - Other manuscripts from the Jean de Jandun redaction @@ -524,7 +523,6 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>fourteenth century. -

@@ -813,8 +811,8 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> Cohen 2012Cohen, David E.. Harmonic Mediation and the Triad: Gaffurio, Zarlino, Lippius and Pietro d’Abano’s Commentary on the Pseudo-Aristotelian <title>Problems. - Paper presented at the annual conference of the Music Theory Society of New - York State. New York, N.Y., March + Paper presented at the annual conference of the Music Theory Society of New + York State. New York, N.Y., March 31, 2012. Coucke 2008Coucke, Gijs. Philosophy between Text and Tradition The Reception of Aristotle's @@ -1120,7 +1118,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?><TEI <lem wit="#β #γ #κ #m #v">querebatur</lem> <rdg wit="#Ea" ana="#morphological">queratur</rdg> <rdg wit="#π" ana="#lexical #J">acquiritur</rdg> - </app>. Unde a poetis <persName ref="#Ju" instant="false" full="yes">iouis</persName> et <persName ref="#Mem" instant="false" full="yes"><app> + </app>. Unde a poetis <persName ref="#Ju">iouis</persName> et <persName ref="#Mem"><app> <lem wit="#β #κ #Ea #Gu #Pp #Pz #Vo">memorie</lem> @@ -1226,26 +1224,26 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?><TEI <rdg wit="#Pz" ana="#lexical #subtractive #J">Refertur</rdg> </app> <app> - <lem wit="#α #λ #Gu #Pp #Pu #Vo #m #v"><persName ref="#Mos" instant="false" full="yes">moyses</persName> + <lem wit="#α #λ #Gu #Pp #Pu #Vo #m #v"><persName ref="#Mos">moyses</persName> hanc</lem> - <rdg wit="#Pz" ana="#ordinal #J">hanc <persName ref="#Mos" instant="false" full="yes">moyses</persName></rdg> + <rdg wit="#Pz" ana="#ordinal #J">hanc <persName ref="#Mos">moyses</persName></rdg> </app> inuenisse <app xml:id="app-homt-1.1a" next="#app-homt-1.1b"> <lem wit="#α #λ #π #m #v"><app> - <lem wit="#Gu #Ma #Nu #Mb #Vm #Vz #m #v"><persName ref="#Tub" instant="false" full="yes">tubal</persName></lem> + <lem wit="#Gu #Ma #Nu #Mb #Vm #Vz #m #v"><persName ref="#Tub">tubal</persName></lem> <rdg wit="#Pp #Pu" ana="#lexical #J">aabal</rdg> - <rdg wit="#Py" ana="#additive"><persName ref="#Tub" instant="false" full="yes">tubal</persName> fratrem - <persName ref="#Cay" instant="false" full="yes">cayn</persName></rdg> + <rdg wit="#Py" ana="#additive"><persName ref="#Tub">tubal</persName> fratrem + <persName ref="#Cay">cayn</persName></rdg> </app> <milestone ed="#Pu" unit="column" n="B"/>de <app> <lem wit="#α #π #Ma #Vm #m #v">stirpe</lem> </app> - <persName ref="#Cay" instant="false" full="yes"><app> + <persName ref="#Cay"><app> <lem wit="#Pp #Pu #Py #Va #Vo #Vz">cayn</lem> @@ -1281,16 +1279,16 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?><TEI </app> <cit xml:id="cit-1.1b" prev="#cit-1.1a"> <quote rend="inline"><app> - <lem wit="#Py"><persName ref="#Pyth" instant="false" full="yes">pytagori samium</persName></lem> + <lem wit="#Py"><persName ref="#Pyth">pytagori samium</persName></lem> - <rdg wit="#Vb" ana="#morphological"><persName ref="#Pyth" instant="false" full="yes">pictagorius + <rdg wit="#Vb" ana="#morphological"><persName ref="#Pyth">pictagorius samium</persName></rdg> - <rdg wit="#Ma #Vz" ana="#morphological"><persName ref="#Pyth" instant="false" full="yes">pitagoram + <rdg wit="#Ma #Vz" ana="#morphological"><persName ref="#Pyth">pitagoram samium</persName></rdg> - <rdg wit="#Vm" ana="#morphological"><persName ref="#Pyth" instant="false" full="yes">pictagoram + <rdg wit="#Vm" ana="#morphological"><persName ref="#Pyth">pictagoram samium</persName></rdg> - <rdg wit="#π" ana="#morphological #subtractive #J"><persName ref="#Pyth" instant="false" full="yes">pictagoram</persName></rdg> + <rdg wit="#π" ana="#morphological #subtractive #J"><persName ref="#Pyth">pictagoram</persName></rdg> <rdg wit="#m #v" ana="#lexical">pythagorici samium</rdg> <rdg wit="#Va" ana="#lexical #subtractive">pitagorici</rdg> </app> sonitu <app> @@ -1368,7 +1366,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?><TEI <rdg wit="#Vm" ana="#morphological">que</rdg> <rdg wit="#Ea" ana="#morphological">quam</rdg> </app> causant orbes celestes, secundum <app> - <lem wit="#β #π #Ea #Vm #Vz"><persName ref="#Pyth" instant="false" full="yes">pictagoram</persName></lem> + <lem wit="#β #π #Ea #Vm #Vz"><persName ref="#Pyth">pictagoram</persName></lem> <rdg wit="#m #v" ana="#lexical">pithagoricos</rdg> @@ -1484,7 +1482,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?><TEI </app> <bibl corresp="#ArCa" default="false" status="draft"><author>Arist.</author> <title>De caelo, II.9, 290b, l. 25 -

+ .

Musica uero humana mundana @@ -1543,7 +1541,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> videtur - aristotelem + aristotelem a platonicis @@ -1928,7 +1926,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>traditionem introductione musice - guidonis + guidonis grauidons gradionis @@ -2055,10 +2053,10 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>boecium - pictagoram + pictagoram - primae pyctoragam + primae pyctoragam pythagoricos pictagoricas @@ -2178,7 +2176,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>igitur ergo - aristoteles more + aristoteles more consueto solito @@ -2300,11 +2298,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ut per vnum expressum - aliud aristoteles + aliud aristoteles audiat - aristoteles audiat + aristoteles audiat aliud - aliud audiat aristoteles + aliud audiat aristoteles recitatum @@ -2878,8 +2876,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> uox quedam quidem - #Gu scribe later changes to "quedam" in the dittographic - version of this clause + una constituitur multiplicium multiplicem @@ -2891,14 +2888,12 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ceu seu sicut - #Gu scribe later changes to "sceu" in the dittographic version - of this clause + tractus - #Py could be totus with a misplaced a-squiggle above the o, or - tractus with an o accidentally replacing the c. + tractum tracti @@ -3135,13 +3130,13 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>dicendorum contentorum et dicendorum quod antiquitus - a pictagora + a pictagora inuentum fuit instrumentum dictum monocordum - inuentum fuit a pictagora instrumentum dictum menocordum + inuentum fuit a pictagora instrumentum dictum menocordum a pictagoricis inuentum fuit instrumentum dictum monocordum a pitagoricis instrumentum inuentum fuit dictum @@ -3247,7 +3242,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> boecius - nichomacum + nichomacum @@ -3274,7 +3269,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>quatuor cordis. Quod durauit durabat - vsque ad + vsque ad orphei @@ -3361,7 +3356,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - dicitur mercurium + dicitur mercurium inuentorem dicitur mercurius inuentor fuisse. @@ -3472,7 +3467,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>Septimam Aliam uero - terpanterius lesbius + terpanterius lesbius @@ -3521,7 +3516,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>honorabilior honorabilis honor - vnde et iouem + vnde et iouem ypaton uocant @@ -3769,7 +3764,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> secundum + secundum thimotheum @@ -3881,7 +3876,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>essentialiores et necessariores septem videntur esse - , ita ut aristoteles + , ita ut aristoteles supra @@ -3951,10 +3946,10 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>ex trite ut numerus ut - boecius + boecius 18 cum - boecius cum - boecius + boecius cum + boecius 7 reiteratione ipsarum @@ -5909,7 +5904,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>omne ore esse - , aristoteles + , aristoteles talem et aliam @@ -6448,7 +6443,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>motus - oratii fuit + oratii fuit fuit oratii maxime.

@@ -7015,7 +7010,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> dicetur unde dicetur - quod + quod tripandius @@ -7349,8 +7344,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>acuto concordantibus acuto a cordantibus - #Pp and #Pu are ambiguous, because they use the character - "a" to represent "7." + sonis, cuius suis @@ -8239,7 +8233,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>auditui , unde - museus + museus muscis musicus dicitur @@ -8330,7 +8324,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>itaque uerbis - aristoteles + aristoteles eadem @@ -9259,11 +9253,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>12º xxiii° doooo - The added characters in Py seem to be space fillers, but - there's also a blank space of approximately 5 characters' width to their right, - before the start of "tertiumdecimum." Also, the blank space appears to be an - erasure, but the microfilm doesn't make reading the erased characters - possible. + in 12° . @@ -10320,7 +10310,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>quid - macrobium et boecium ex + macrobium et boecium ex omni numerorum modorum @@ -10831,8 +10821,6 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> nouenario - - nouenarum nouem , @@ -10891,7 +10879,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>uero nomen - + boecium @@ -11376,8 +11364,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>differentia .83a. differentiis 93. differentia sed - If the scribe of #Px uses tall s to mean 8 (as other places - suggest), then it is 83, not sed. + exposita. @@ -11402,7 +11389,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> quod - ptholomeus + ptholomeus @@ -11523,7 +11510,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>, quod et - videtur aristoteles sentire + videtur aristoteles sentire xli xiº 4° @@ -11584,7 +11571,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - + thimoteus @@ -11811,7 +11798,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> existentes - existentis + existentis acuti @@ -12193,8 +12180,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> . - This is a typical Jandun omission which #Vc also - omits. +

@@ -12562,7 +12548,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>.8. - filoxenus + filoxenus philoseus @@ -13153,8 +13139,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>patet - #Vc's scribe includes this representative Jandun - omission. + . etcetera @@ -13554,7 +13539,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>De inst. mus. I.8 (Freidlein 195, ll. 6–13) Videtur siquidem quantum facit ad sermonem - + aristoteles quod antiphonus sit delectabilior ex contrariis ualde distantibus consurgens ut ex @@ -14777,7 +14762,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> Notandum Nota - quod aristoteles + quod aristoteles multotiens dicit dicit multotiens @@ -14810,7 +14795,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> alie alii - . + . Pictagoras @@ -14830,10 +14815,10 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>et omni magis inherere - inherere aristotelem + inherere aristotelem inheretur adherere - , + , aristoxenus @@ -14848,7 +14833,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>sensui sensum , quos ambos - ptholomeus in eius + ptholomeus in eius pertheus in eius @@ -15207,7 +15192,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>quia - ouidii + ouidii ouii toni @@ -15224,7 +15209,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>aut que sunt autem sic que - + oracii et ideo @@ -15342,7 +15327,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>congruissimam et perfectam perfectam et congruissimam congruissimam et perfectissimam - congruisima et perfectam + congruisima et perfectam congrauissimam et perfectam bene sonantem, et @@ -15364,7 +15349,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> horret - abhoret + abhoret oret honoret @@ -15571,7 +15556,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>greci gramatici et potissime - galienus + galienus Gal' Galienus @@ -17365,7 +17350,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>medium habent - equidistans + equidistans equidistant @@ -17413,16 +17398,16 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>musice cum - estiacus colophonius + estiacus colophonius - ostiatus colophonius - estimatus colophimus - estimatus colofonius + ostiatus colophonius + estimatus colophimus + estimatus colofonius existimatus - colofonius - estyrginatus colophonius + colofonius + estyrginatus colophonius stiatiis elephinus @@ -17438,7 +17423,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> - , + , thimoteus @@ -17452,7 +17437,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>superveniens superveniens et - + milexius @@ -18450,8 +18435,8 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>nosce notandum quod causa - fundatur aristoteles - aristoteles + fundatur aristoteles + aristoteles fundatur @@ -19545,7 +19530,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>dicitur quidem siquidem dicitur dicitur - a + a chorebo @@ -19682,12 +19667,12 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>enim 7 uel triplat - quod aristoteles - boecius - quod aristoteles et - boecius - quod aristoteles - boecius + quod aristoteles + boecius + quod aristoteles et + boecius + quod aristoteles + boecius .31 . @@ -19710,10 +19695,10 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>

- PROPTER QUID CIRCA FRINICHUM + PROPTER QUID CIRCA FRINICHUM PROPTER QUID CIRCA - PROPTER QUID CIRCA PHRINICUM + PROPTER QUID CIRCA PHRINICUM FUERUNT MAGIS DULCE MELODIA? AUT PROPTER ID QUOD MULTIPLICES SUNT TUNC CANTUS IN TRAGEDIIS METRORUM ? @@ -19836,7 +19821,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> PROPTER QUID DYAPASON APPELLATUR, SED NON SECUNDUM NUMERUM DYAOCTO, QUEMADMODUM ET DYATESSERON ET DYAPENTE? - AUT QUIA SEPTEM FUERUNT CORDE ANTIQUITUS? POSTEA EXTRAHENS TERTIAM, TERPANDERUS NITEM + AUT QUIA SEPTEM FUERUNT CORDE ANTIQUITUS? POSTEA EXTRAHENS TERTIAM, TERPANDERUS NITEM APPOSUIT. ET IN HOC APPELLATA EST. DYAPASON, SED NON DYAOCTO, DYASEPTEM ENIM ERAT . @@ -19988,7 +19973,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>instrumentorum antiquitus tantum .5. .7. fuere instrumentorum antiquitus 7 fuere - . Postmodum superuenit + . Postmodum superuenit tripandius @@ -20474,7 +20459,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>mutantes - #Pp could be imitantes or mutantes + @@ -22056,7 +22041,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>capitulo - #Vc includes this passage. + .

@@ -22182,7 +22167,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> magistra magistram - #Px and #Pp could alternately read "nigram" + et regula @@ -22247,7 +22232,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>cuiustorum primitus corpus primo - #Nu's reading results from a dittographic cⳋ being blended with what should be tⳋorum = terminorum + tangit expositionem, dicens quod cum in uoce acutum acuta @@ -23030,8 +23015,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>triplex pretacta inducatur pretacta indicatur triplex triplex iudicatur pretacta - #Pp, #Pu, #Px, and #Vm could be either "iudicatur" - or "indicatur" + musica?

@@ -23971,7 +23955,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>complexionatum sit compositum ex utrisque - #Ca and #Pq also omit this passage. + extremorum excellentiis @@ -24013,7 +23997,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>. Et - ideo + ideo thimoteus @@ -24088,7 +24072,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> acuto acuta - . Plato + . Plato siquidem @@ -24205,7 +24189,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>conuenit continet - + thimotei @@ -24621,7 +24605,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>edocentur - boecii + boecii boni uero .10 @@ -25197,7 +25181,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>sensui - pictagoras + pictagoras pythagoricis @@ -25215,7 +25199,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>sicut sic - + aristoxenus aristotenus @@ -25833,7 +25817,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> apparuit apparebit - #Px shares #Ea's reading here. + problemate @@ -26042,18 +26026,18 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>assumuntur proportiones proportiones accipiuntur - musice. Unde apparet quod aristoteles + musice. Unde apparet quod aristoteles consentit pictagoricis - pictagoras + pictagoras , has ponentibus solum, et non concidit cum causa - + ptholomeo @@ -26328,7 +26312,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>etiam si extrema comparentur ad inuicem ut vnum ad quatuor - #Gu also omits this lemma. + resultabit @@ -26778,8 +26762,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> neate, omnes quiaa - #Py has the quia symbol with the squiggly-line "a" symbol above - it + relique corde in terminatione iteratione @@ -29812,7 +29795,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>cetere . Sed abstulerunt - #Vc also omits this passage + , ut propositum dictum @@ -30319,7 +30302,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>perueniens veniens - + tripandius @@ -32656,129 +32639,129 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> Historical figures - AlAlexander + AlAlexander Aphrodisiensis - ArAristoteles + ArAristoteles - AxAristoxenus + AxAristoxenus Tarentinus - AvAvicenna + AvAvicenna - BoBoethius, + BoBoethius, Anicius Manlius Severinus - CoHestiaeus + CoHestiaeus Colophonius - DamJohannes + DamJohannes Damascenus - GaGalenus, + GaGalenus, Claudius - GArGuido + GArGuido Aretinus - HipHippocrates + HipHippocrates - HorHoratius Flaccus, + HorHoratius Flaccus, Quintus - IsIsidorus + IsIsidorus Hispalensis - MacMacrobius + MacMacrobius Ambrosius Theodosius - MuMusaeus + MuMusaeus Atheniensis - NiNicomachus + NiNicomachus Gerasenus - OvOvidius Naso, + OvOvidius Naso, Publius - PhilPhiloxenus + PhilPhiloxenus Cytherius - PhrPhrynichus (tragicus) + PhrPhrynichus (tragicus) - PlPlato + PlPlato - PtPtolemaeus, + PtPtolemaeus, Claudius - PythPythagoras + PythPythagoras - TerTerpander + TerTerpander Antissenis - ThTheophilus + ThTheophilus Antiochenus - TiTimaeus + TiTimaeus Locrus - TyTimotheus + TyTimotheus Milesius Mythical figures - CayCain + CayCain - JuJupiter + JuJupiter - MemMemoria + MemMemoria - MerMercurius + MerMercurius - MosMoses + MosMoses - OrOrpheus + OrOrpheus - TorTorebus, filius + TorTorebus, filius Atys - TubTubal Cain + TubTubal Cain

@@ -32807,7 +32790,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?>J. Brams as De Anima. Aristoteles Latinus Database XII.1 URL: Arist. Cael. - Aristotle. De caelo Ed. + Aristotle. De caelo Ed. F. Bossier as De caelo et mundo. Aristoteles Latinus Database VIII URL: Arist. Eth. Nic. From 5d0dd1204ee4a0f56a313d64df52b10aa351b049 Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Wed, 28 Feb 2024 14:16:09 -0600 Subject: [PATCH 08/25] update XSLT to get to pdf-edition --- mutch.xsl | 3 +++ 1 file changed, 3 insertions(+) diff --git a/mutch.xsl b/mutch.xsl index 67fd197..5272f6c 100644 --- a/mutch.xsl +++ b/mutch.xsl @@ -38,4 +38,7 @@ + + + \ No newline at end of file From 257c885b69193a6d7d39e96cf3e3ab0f715a3e9e Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Thu, 8 Aug 2024 11:11:32 -0500 Subject: [PATCH 09/25] update: move ref tag at line 7540 The was inside of , which is allowable, but the itself should be inside of , since that is the information it provides as part of . --- edition.xml | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/edition.xml b/edition.xml index af6684e..d6d461b 100644 --- a/edition.xml +++ b/edition.xml @@ -7536,10 +7536,12 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> quod quid proportiones + - secundum auicenna + secundum auicenna + cadunt Date: Thu, 8 Aug 2024 11:15:02 -0500 Subject: [PATCH 10/25] update: ref tag at line 7536 The ref was inside of app, but the app should be inside of ref. --- edition.xml | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/edition.xml b/edition.xml index d6d461b..e12b21e 100644 --- a/edition.xml +++ b/edition.xml @@ -7536,12 +7536,10 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> quod quid proportiones - - secundum auicenna + secundum auicenna - cadunt >20.1–6 - - Boecius autem + + + Boecius autem Bouus autem + dyesim dicit diesim dicit From 90b3aee3cfe513d4fb11ad9dd1d75bb18ba9757b Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Thu, 8 Aug 2024 11:19:38 -0500 Subject: [PATCH 11/25] update: ref near xml:id app-13.12b moved ref outside of app --- edition.xml | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/edition.xml b/edition.xml index e12b21e..9385328 100644 --- a/edition.xml +++ b/edition.xml @@ -10432,19 +10432,21 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> + - Sunt autem secundum Sunt autem secundum boecium in primis principiis - arismetrice + arismetrice et musice numeri + quinque sumpte From 7b439f73f6a966d9e9f94a9ca3777114dadb9203 Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Thu, 8 Aug 2024 11:22:45 -0500 Subject: [PATCH 12/25] update: move ref at ~line 19800 ref should be outside of app --- edition.xml | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/edition.xml b/edition.xml index 9385328..803e7dd 100644 --- a/edition.xml +++ b/edition.xml @@ -19799,11 +19799,13 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> septem planetarum, - + + secundum - boecium, + boecium, + imitatione ymitatione From e70d0f46dc42d6052518e808223691e2de346a8a Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Thu, 8 Aug 2024 11:25:08 -0500 Subject: [PATCH 13/25] update: move ref at ~line 20348 ref should be outside of app --- edition.xml | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/edition.xml b/edition.xml index 803e7dd..46100d5 100644 --- a/edition.xml +++ b/edition.xml @@ -20357,18 +20357,20 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> actu acutum , - + + vt apparet vt patet in patet - + 2° 3º - de anima. + de anima. + Arist. De an. II. Date: Thu, 8 Aug 2024 11:27:11 -0500 Subject: [PATCH 14/25] update: ref at ~line 21293 ref should be outside of app --- edition.xml | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/edition.xml b/edition.xml index 46100d5..046925a 100644 --- a/edition.xml +++ b/edition.xml @@ -21290,12 +21290,13 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> II.1, 993b ll. 4–5 - + + vt ostensum est - + .18 18 rend="superscript">vo supra - . As cited in d'Abano's commentary on Book + . As cited in d'Abano's commentary on Book XVIII, Problem 8, where the paraphrased quotation begins with "nota" + Nam quod primitus discitur dicitur From 43151e9069deb9f004b60359615988f618600d9a Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Thu, 8 Aug 2024 11:28:28 -0500 Subject: [PATCH 15/25] update: move ref at ~line 23081 ref should be outside of app --- edition.xml | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/edition.xml b/edition.xml index 046925a..5ae25b8 100644 --- a/edition.xml +++ b/edition.xml @@ -23078,7 +23078,8 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> n="B"/>in principio a leuibus et debilibus incipit, non enim tunc est, operosa sed in fine, - + + vt @@ -23086,13 +23087,14 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> dictum dicatur - + 10a. 20. - + + Ps.Arist. Prob. X. Date: Thu, 8 Aug 2024 11:33:15 -0500 Subject: [PATCH 16/25] update: ref at ~line 25464 ref should be outside of app --- edition.xml | 12 ++++++++---- 1 file changed, 8 insertions(+), 4 deletions(-) diff --git a/edition.xml b/edition.xml index 5ae25b8..55335f7 100644 --- a/edition.xml +++ b/edition.xml @@ -24435,18 +24435,20 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> moueri cogitur moueri , - + + vt declaratum est - + xia iia - , + , + Arist. Prob. XI. fertur feretur , + vt visum est visum - .xi°. + .xi°. + Ps.Arist. Prob. XI. Date: Thu, 8 Aug 2024 11:35:09 -0500 Subject: [PATCH 17/25] update: ref at ~line 25567 ref should be outside of app --- edition.xml | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/edition.xml b/edition.xml index 55335f7..194f4a6 100644 --- a/edition.xml +++ b/edition.xml @@ -25564,19 +25564,21 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> naturam, naturam est, - + + vt visum est visum - particula + particula secunda 11a - . + . + Ps.Arist. Prob. II. Date: Thu, 8 Aug 2024 11:37:06 -0500 Subject: [PATCH 18/25] update: ref at ~line 26698 ref should be outside of app --- edition.xml | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/edition.xml b/edition.xml index 194f4a6..88598b5 100644 --- a/edition.xml +++ b/edition.xml @@ -26686,7 +26686,8 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> egritudo sit motus - + + ostensum differentia 7a @@ -26714,6 +26715,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> quarto problemate. + Ps.Arist. Prob. VII. Date: Thu, 8 Aug 2024 15:40:27 -0500 Subject: [PATCH 19/25] update: modifying position of some ref tags --- edition.xml | 30 ++++++++++++++++++++---------- 1 file changed, 20 insertions(+), 10 deletions(-) diff --git a/edition.xml b/edition.xml index 88598b5..38ad409 100644 --- a/edition.xml +++ b/edition.xml @@ -2498,14 +2498,16 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> gaudium et letitiam inducentia letitiam quod inducentia expedit audire? Vnde - + + alexander allexander - + + in problematibus - + et maxime et maxime et maxime @@ -2520,6 +2522,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> ad primam: + Propter quid @@ -7536,10 +7539,12 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> quod quid proportiones - - secundum auicenna + + + secundum auicenna + cadunt consiliatoris consiliatore - + differentia .83a. @@ -12936,6 +12941,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> exposita. + Pietro d'Abano Concil. diff. 83 @@ -24519,11 +24525,12 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> >armonica armonicam armonica sua - + taliter declarare alter declarare + dyapason esse optimam et perfectissimam consonantiarum consonantiam @@ -25649,7 +25656,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> 5a particula ille particula - + intelligenti dicta, intelligentis dicta, @@ -25676,6 +25683,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> considerare: puta consingulare: puta + modicum @@ -25861,13 +25869,14 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> vtcunque vtrunque - + + sicut videbitur sint videbitur - .vii°. + .vii°. xxixe. @@ -25878,6 +25887,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> , + Ps.Arist. Prob. XXVIII. Date: Thu, 8 Aug 2024 15:40:55 -0500 Subject: [PATCH 20/25] update xsl to remove 'singleton' entries in app --- mutch.xsl | 28 ++++++++++++++++------------ 1 file changed, 16 insertions(+), 12 deletions(-) diff --git a/mutch.xsl b/mutch.xsl index 5272f6c..f7b2472 100644 --- a/mutch.xsl +++ b/mutch.xsl @@ -11,24 +11,24 @@ - - - - - - - - - - - - + + + + + + + + + + + + @@ -38,6 +38,10 @@ + + + + From 55a07bef8e41a2bb5951c61b274c3e3a691837f8 Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Thu, 8 Aug 2024 15:41:15 -0500 Subject: [PATCH 21/25] add: edition-without-singletons.xml --- edition-without-singletons.xml | 25063 +++++++++++++++++++++++++++++++ 1 file changed, 25063 insertions(+) create mode 100644 edition-without-singletons.xml diff --git a/edition-without-singletons.xml b/edition-without-singletons.xml new file mode 100644 index 0000000..e72c270 --- /dev/null +++ b/edition-without-singletons.xml @@ -0,0 +1,25063 @@ + + + + + Expositio problematum Aristotelis, Particula XIX: De harmonia + Pietro d’Abano + Caleb Mutch + Medieval Academy of America + + TEI XML encoding: + Caleb Mutch + + + TEI XML encoding: + Samuel J. Huskey + + + + First Edition + + + The Digital Latin Library +
+ 650 Parrington Oval + Carnegie Building 101 + Norman + OK + 73019 + USA +
+ The University of Oklahoma + Norman, OK + 202? + + Creative + Commons Attribution-ShareAlike 4.0 International Licence (CC BY-SA 4.0) + + + + Library of Digital Latin Texts + + Edited by + Samuel J. Huskey + + ? + + + +

Born digital.

+ + + + + + Latin Letter Small B Squared; a.k.a. Flat, hard b (mi) + + + U+E9E1 + + + + Classes + combiningStaffPositions + + + + + Latin Small Letter Con + + + 9 + ꝯ + + + + +

+ + Ea, Gu, Pp, Pz, and Vz’s armoniac* emended to armonic* + Gu and Pq’s rigm* emended to rithim* + Nu's duppl* emended to dupl* + Gu’s *ypote emended to *ypate + Px, Py, and Pz's anthiphon* emended to antiphon* + Nu and Pp's mellodi* emended to melodi* + Pz's sinegengium emended to sinezengium + Gu, Py, and Vz's sesqui* emended to sexqui* + Ma, Va, and v's hi* emended to hii* + Px's "fati*" emended to faci* + Px and Py's sicud emended to sicut + Ma, Px, Py and Pz's velud emended to velut + Va's unique orthographical variants ignored + All: standardized spellings of lychanos, mese, and paramese + All: standardized spellings of dyatesseron, dyapente, and dyapason + All: lira* emended to lyra* + All: *ij and *ijs emended to *ii and *ijs + All: *cia, *cio, *cium, etc. emended to *tia, *tio, *tium, etc. + All: adinuicem emended to ad inuicem + All: probleuma* emended to problema* + All: Tironian et emended to et + All: ampersand emended to et + All: Tall s ( ſ ) emended to round s + All: contractions expanded + All: changes of hand/ink for problems' marginal numbering is ignored + +

+ + + + font-weight: bold + vertical-align:sub; font-size:50%; + display:block; font-size:100%; margin-left:3em; + padding-left:1em; margin-top:0; margin-bottom:0; padding-top:0; padding-bottom:0; + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ Preface +
+ I. Pietro d’Abano’s Expositio problematum Aristotelis +
+ 1.1 General +

The pseudo-Aristotelian Problems is an extensive + collection of questions and proposed answers concerning a wide range of subjects, + including biology, mathematics, and physics, divided topically into thirty-eight + sections. The nineteenth of these sections preserves the first substantial account of + ancient Greek music making and theorizing to have been rediscovered in the medieval + period. This material held great promise for medieval thinkers seeking to learn more + about the foreign world of ancient Greek music, whose legendary emotional power had + been lamentedly lost, and the text’s attribution to Aristotle imbued it with special + authority. Yet the Problems was also a challenging text to + decipher. Not only was the subject manner often unfamiliar, the manuscript tradition + of the Greek text is also corrupt in places. Furthermore, the first complete Latin + translation, made by Bartholomew of Messina (fl. 1258–66), observed the common + medieval practice of verbatim, indeed servilely literal, word-for-word translation. + For all these reasons, potential readers of the Problems + were in sore need of orientation and explanation.

+

Into the breach strode Pietro d’Abano (c. 1257–1316), who was a professor of + medicine with wide-ranging interests and expertise. Pietro composed his + Expositio, the first commentary on the entirety of the + Problems in the first decade of the fourteenth century, and there are + more than twenty extant manuscripts of it, as well as multiple early print editions. + His commentary also attracted the attention of his contemporaries, most notably Jean + de Jandun (c. 1285–1328), a philosopher and theologian of considerable importance + based at the University of Paris, who produced a revision of the entire + Expositio. Moreover, Pietro’s commentary on the problems of section + XIX, in particular, was the first widely circulated medieval attempt to interpret and + assimilate rediscovered knowledge about music in the ancient world, and his + explanations consequently became a touchstone for later generations of music scholars + who referred to the Problems, including Franchino Gaffurio, + Girolamo Mei, and Francisco de Salinas. Most recently, Claude Palisca has called + attention to Pietro’s anticipation of Renaissance modes of scholarship (1985), and David E. Cohen has demonstrated that Pietro’s + idiosyncratic interpretations of some of the problems concerning music played an + important role in the development of the music-theoretical concept of harmony (2012). Yet despite the inherent interest of Pietro’s + commentary as a site of cross-cultural engagement and its historical significance to + later music theorizing, his commentary on section XIX, on music, has been inaccesible + to scholars, for until recently it had not been published in any form since the + sixteenth century’s sadly unreliable print editions. Even that recent publication + (Meyer 2022), however, does not provide a proper + critical edition of the text, as it is based on a sixteenth-century print edition, + only considers half the extant manuscripts, and fails to distinguish between Pietro's + first version of his commentary and his later revision (see section 2.1). The present critical edition rectifies + that situation, establishing a base text informed by a stemmatic hypothesis of the + complete manuscript tradition. Furthermore, this edition is openly accessible, and it + presents a semantically encoded version of the text, allowing readers to select the + types of variants they wish to consider. As a result, it provides a better informed + version of Pietro's commentary and makes it more widely available than ever before. +

+
+ +
+ 1.2 Structure +

Each of the pseudo-Aristotelian problems follows a set structure. First, a + question is posed, such as at the start the first problem: Why do + those who are suffering and those who are rejoicing have pipes played for + them? (Propter quid dolentes et gaudentes + fistulantur?) Then one or more possible reasons are proposed, often + accompanied by additional explanation. For instance, the first problem continues: + Is it so that the former mourn less, but the latter rejoice + more? (Aut vt hii quidem minus tristentur, alii autem + vt magis gaudeant?) In his commentary Pietro follows a similar pattern. He + first paraphrases the opening question, and then addresses the remainder of the + problem, dividing it into between one and seven parts, depending on its length. He + signals the beginning of each successive division of the text with its first word or + two, followed by a partial or complete paraphrase. (These paraphrases are enclosed by + targeted "gloss" elements in the xml format, and they are italicized in the rendered + pdf.) Given the unidiomatic Latin of Bartholomew of Messina’s translation and the + common occurrence of obscure vocabulary, Pietro’s paraphrases provide an important + means of ingress to the text on their own. He often supplements these paraphrases + with additional explanatory material, both his own and by authors from antiquity. + In the latter case, he often provides cross-references to other pertinent passages + within the Problems (from both section XIX and other + sections), and he also inserts abbreviated quotations, most often from the + Aristotelian and medical corpora.

+
+ +
+ + +
+ II. The Textual Tradition +
+ 2.1 Introduction +

Establishing the best text of Pietro d’Abano’s commentary is no simple task, + for it survives in several different forms. By analyzing variants in the introduction + with which Pietro starts his commentary on the Problems, + Gijs Coucke has demonstrated that Pietro produced a revised version of his commentary + after the initial version was complete (2008, vol. 2, + xlii–xliv). About a quarter of the extant manuscripts derive from the initial version, + another quarter from the revision, and the remaining half of the manuscripts descend + from the revision made by Jean de Jandun (concerning which see Swaenepoel 2009). While these latter manuscripts do + not aid in the reconstruction of the text(s) Pietro himself wrote, they provide + important testimony as to the work’s reception in the Parisian university scene, and + consequently I have recorded variants from five selected manuscripts in the critical + apparatus. Coucke notes that “all manuscripts appear to have the identical explicit, + which refers to 1310 as the year in which Peter finished his Expositio” + (2008, vol. 2, xliv)—that presumably being the date + when the initial version was completed.

+

Further complicating matters, some of the manuscripts change affiliations + partway through the lengthy work. As Joan Cadden has observed, manuscript Pz + contains the first half of Pietro’s version and the second half + of Jean’s, and manuscript Ea has the converse + arrangement (2013, 228). Additionally, in his edition + of section IV of the Expositio, Coucke identifies manuscript Vb as deriving from Pietro’s revised version, whereas by + section XIX it hews more closely to the initial version. (Furthermore, manuscript Pq contains Jean’s version in sections IV and XIX, but by + section XXVII it appears to have changed to Pietro’s version [Coucke 2008, vol. 2, xxvi].) As a result, I have preserved Coucke’s + manuscript sigils, but not his labeling of families and conjectured sub-types. For + instance, Coucke labels Pietro’s first and second versions Pa and Pb, respectively whereas I call them α and κ. (This + change is made in part to avoid the confusing use of letters in Coucke’s Conspectus siglorum, where the manuscripts elsewhere labeled + as Pb are listed under + heading A, and those as Pa under heading B.)

+

In classifying the manuscripts I used Coucke’s findings on section IV as a + point of departure. I collated all the manuscripts’ versions of section XIX’s tenth + problem to test the validity of Coucke’s findings to section XIX. Then I collated all + the manuscripts representing solely either Pietro’s first or his second version (with + the exception of Mb, to be discussed below), along with + manuscripts Ea and Pz (since + their classification differs between sections IV and XIX), and four representative + manuscripts from the Jean de Jandun redaction.

+
+ +
+ 2.2 List of Sources +
+ Manuscripts + + Pietro's first version (α) + β + Consensus of Nu and Py, where Nu is extant + + + Nu + Nuremberg, Stadtbibliothek, Cent. III.38, ff. 61v–64v + before 1389 + + + Py + Paris, Bibliothèque Nationale man. lat. 6541 (accessed + 2022-01-03), ff. 179v–91v + fourteenth century. + + + + γ + Consensus of V<hi rend="superscript">a</hi> and V<hi rend="superscript">b</hi> + + + Va + Vatican, Biblioteca Apostolica lat. 2174 (accessed 2022-01-03), + ff. 72r–77r + fourteenth century. + + + Vb + Vatican, Biblioteca Apostolica lat. 2175 (accessed 2022-01-03), + ff. 107–16r + fifteenth century. + + + + + Ea + Erfurt, Bibliothek Amploniana fol. 15, ff. 136v–47r + early fourteenth century + + + + Pietro's revised version (κ) + + Px + Paris, Bibliothèque Nationale man. lat. 6540 (accessed 2022-01-03), + ff. 154v-64v + Fourteenth century. Italy. + + + λ + Consensus of Ma, Vm, + and Vz + + + Ma + Cesena, Malatestiana D.XXIV.2 (accessed 2022-01-03), ff. 96v–104r + before 1381. + + + Vm + Venice, Biblioteca Nazionale Marciana, lat. VI. 126, ff. 95r–100r + fifteenth century + + + Vz + Venice, Biblioteca Nazionale Marciana, lat. Z. 263, ff. 48v–70r + ca. fourteenth century, or after 1451 on the basis of watermark. + On paper, in one column + + + Mb + Cesena, Malatestiana S.VI.2/3 (accessed 2022-01-03), S.VI.3, ff. 38v–56r + 1381. A copy of Ma + + + + + + Jean de Jandun's redaction + + π + Collated manuscripts + + + Gu + Ghent, Bibliothéek van de Rijksuniversiteit, ms. 72 (accessed + 2022-01-03), ff. 234r–49v + fourteenth century. + + + Pp + Paris, Bibliothèque Nationale man. lat. 6542 (accessed + 2022-01-03), ff. 183v–94v + 1385. + + + Pu + Paris, Bibliothèque de l'Université 122, 114v–23r + fifteenth century + + + Pz + Paris, Bibliothèque Nationale man. lat. 6541A (accessed + 2022-01-03), ff. 179r-92r + fourteenth century. + + Pz + + + + + Pz2 is + responsible for the header, and writes in an ink that has faded + significantly. It may be the same scribe who wrote the large initials + which begin each problem. + + + + + + Vo + Vatican, Biblioteca Apostolica Ottobon. lat. 1764, ff. 147r–57v + fourteenth century + + + + + + Other manuscripts from the Jean de Jandun redaction + + Ca + Cambridge, Peterhouse 79, ff. + 76r–81v + fourteenth century + + + Pa + Paris, Bibliothèque Arsenal, 723, ff. 183v–97r + fourteenth century + + + Pq + Paris, Bibliothèque Nationale man. lat. 15454, ff. 127r–36r + fifteenth century + + + Sc + Seville, Biblioteca Colombina, 7.7.9, ff. 121r + ff. + fourteenth to fifteenth century + + + Vc + Vatican, Biblioteca Apostolica lat. 2176 (accessed 2022-01-03), + ff. 62r–65r + fourteenth century. + + + + +
+
+ Editions: Witnesses + + + m + + Illarius, Stephanus. Expositio succinta + problematum Aristotelis quam Petrus edidit Paduanus (accessed + 2022-01-03). Mantua: Paulus de + Butzbach, 1475. + + + + v + + Anonymous. Expositio preclarissimi atque + eximii artium ac medicine doctoris Petri de Ebano Patauini in librorum + problematum Aristotelis (accessed 2022-01-03). + [Venice]: Johannes Herbort, + 1482. + + + +
+
+
+ 2.3 Pietro d’Abano’s First Version +

The first version of Pietro’s commentary on section XIX of the Problems, which I label α, is found in five manuscripts: Nu, Py, Va, Vb, and Ea. + Manuscripts Nu and Py usually + carry the best version of this text. Unfortunately, Nu’s + codex has lost a number of pages, resulting in total loss of the text from a point + partway into problem 9 through problem 15, and again from the end of problem 38 + through the end of the section.

+

Manuscripts Va and Vb + are associated by shared error. The most salient of these occurs in problem 20, where + they repeatedly mistake discussion of the Greek language (oratio greca) for “grammatical speech” (oratio + gramatica). The scribe of manuscript Va + evidently prioritized speed over neatness of script and also had very idiosyncratic + orthography, regularly doubling single consonants or omitting one where they are + normally doubled. Given the ubiquity of these variants, I have omitted them from the + critical apparatus unless they are shared by other manuscripts. In his edition of + section IV, Coucke finds that Vb contains the second + version of Pietro’s commentary, but by section XIX there is little evidence of Vb sharing readings characteristic of that second version. In + addition, the sub-family represented by Va and Vb is particularly important for the commentary’s reception + history since the incunable editions of the text align most closely with them.

+

The situation is more complicated with manuscript Ea. Coucke assigns manuscript Ea to the Jean de + Jandun redaction, and in section XIX the manuscript adopts many (though not all) of + the omissions that characterize that redaction, and it sometimes shares readings with + Pz. Nonetheless, in non-omitted passages Ea’s text more closely resembles the manuscripts transmitting + Pietro’s first version. As a result, I primarily affiliate it with that family of + texts, with the proviso that the scribe of Ea evidently + consulted a Pz-related manuscript from the Jandun + redaction as well.

+
+
+ 2.4 Pietro d’Abano’s Second Version +

The second version of Pietro’s commentary, which I label κ, is also found in + five manuscripts: Px, Vm, Vz, Ma, and Mb. With respect to the fourth section, Coucke hypothesized + that manuscripts Px and Vb + (which in section IV transmits Pietro’s second version) most closely follow the + original form of the second version, that a further revised form of the second version + was the model for manuscripts Ma, Mb, and Pz, and that manuscript Vm shares common error with these latter three (Coucke 2008, vol. 2, xxxix). Only some of Coucke’s + observations hold true in section XIX, however. I agree that a revised version, which + I call λ, was the model for many of these manuscripts. As mentioned above, however, + manuscript Vb has switched its affiliation and now follows + Pietro’s first version, and Pz likewise has shifted to + Jean of Jandun’s redaction. Additionally, Coucke does not consider Vz, since it does not contain section IV.

+

The resulting picture is that Px follows the + original form of the second version, and that Ma, Mb, Vm, and Vz derive from λ, a revised version thereof. Coucke’s + hypothesis of a further revised source for Ma, Mb, and Pz (but not Vm) is not supported in section XIX, since there is good + reason to believe that Mb is copied either directly from + Ma or from another copy of Ma. For instance, in problem 2 the scribe of Ma + erroneously wrote unaa instead of una, and Mb’s scribe wrote unaa before deleting the superfluous a. Still stronger evidence of copying + is found in problem 3’s table of Greek note names, where Mb’s scribe was consulting a manuscript that breaks the word prollabamenos (recte: + proslambanomenos) into prolla and bamenos, as Ma does. We can tell + this because Mb’s scribe evidently thought the line break + divided two distinct words: in Mb, following prolla the rest of the line (about six characters’ worth) is + left blank, before the table of note names begins at the top of the next column with + bamenos. Furthermore, in problem 6 Mb’s scribe follows the word magnatis with the superfluous phrase vel huius est + inequale non eundem seruans tenorem ahead of where it should occur in the + text, and then repeats it in the correct place, following excellentis. In this case of homeoteleuton the -tis endings of magnatis and excellentis are nearly aligned in two successive lines of + Ma (f. 97v), so it is very likely that Mb’s scribe’s eyes skipped from the end of magnatis down a line to excellentis, and then erroneously copied the words that followed. In sum, + because my collation of Mb across the first ten problems + revealed no meaningful discrepancies with Ma, but rather + signs of direct copying, I conclude that it is not useful for establishing the best + text of Pietro’s second version.

+

Of the remaining manuscripts in sub-family λ, Vm + often preserves better readings than Ma and Vz. Zanetti dates Vz to about the + fourteenth century (1741, 121), but it may have + been copied later, as it is written on paper and is the only extant manuscript to be + copied in a single column. I have examined its watermark, which is a bellflower with + a five-petalled bell, two leaves that curl up, and a stem that curves sharply; it + closely resembles watermark DE4620-PO-127158, + which has been dated to 1447, in Rome, though its bell is straighter. Nonetheless, + the manuscript's unique readings are not obviously inferior to those of + Ma, so I have included its variants in the critical + apparatus throughout.

+
+
+ 2.5 Jean de Jandun’s Redaction +

The redaction undertaken by Jean de Jandun necessarily cannot help reconstruct + the best text of Pietro’s commentary, but it is still of some interest. This is in + part because Jandun is one of the most important thinkers in the + Latin Averroist tradition (South 2002, 372), + and consequently his understanding of the Problems and + Pietro’s commentary merits attention. Furthermore, due to the significant circulation + of Jean’s redaction in the environs of the University of Paris it is valuable for + understanding the Problems’ reception. As a result, I have + included readings from selected manuscripts of Jean’s redaction in my critical + edition, but have also tagged them so that readers may filter out readings only found + in that redaction.

+

Three broad feature of Jean’s redaction identified by Coucke in section IV also + occur in section XIX. First, the redaction is most saliently characterized by + omissions that either cover well defined text-units (paragraphs, + or entire (subordinate) clauses), or entail the removal of repetitive or superfluous + speech (2008, vol. 2: xxvii). Second, as a + whole the manuscripts of Jean’s redaction largely agree with those of Pietro’s first + version, but on occasion they follow his second version instead, as Coucke found + (xxx–xxxi). Third, as in section IV manuscript Vo appears to be most valuable for + establishing the text of the redaction (xxxiii). It has almost no unique errors of any + importance, but a brief passage in problem 9 (vtrobique + existente. Et hoc quia in cantu), which it alone omits, indicates that it + cannot be the direct (or at least the sole) model for the rest of the redaction’s + manuscripts.

+

Beyond these broad characteristics, however, further clarity is elusive. + Whereas Coucke found that manuscripts Pp and Vc are “contaminated,” since in section IV they complete the + omissions which are otherwise characteristic of Jean’s redaction (xxxi–xxxii), in + section XIX Pp never does so and Vc only sometimes does. Coucke then goes on to note of section IV (and he + observes that Delaurenti’s [then]-in-progress edition of section VII confirms the + same), that: The other representatives of + J [Jean’s redaction], however, are hardly differentiated, and among them the + relations are volatile and changing. Yet, the samples allow for a division of the + manuscripts along two main branches: (1) one of them is built around Vo, Ca and Ea; (2) another unites the distinct pair Pq Pu (xxxii). Broad + outlines of these relations among manuscripts are still present in section XIX: in the + first branch, Ca and Vo are + still closely related, but Ea now aligns better with + Pietro’s first version. In the second branch, moreover, frequent agreements of Pq with Gu and Pu with Pp also emerge. The + remaining manuscripts, Vc, Pa, + and Sc, do not clearly align with either branch.

+

Given that Jean’s redaction cannot help to establish Pietro’s text, I have not + included all its manuscripts in the apparatus. I follow Coucke (xxxiv) in selecting + manuscripts Vo, due to its paucity of errors, and Gu, because of its careful preparation and occasional unique + variants. I also selected manuscript Pz, on account of its + interest as it switches from Pietro’s second version to Jean’s redaction. Because + Coucke identified manuscripts Pu and Pq as constituting a differentiated branch in section IV, I + selected manuscript Pu, since by section XIX Pq closely matches Gu. And + finally I included manuscript Pp to help establish the + second branch’s readings. (Other manuscripts from Jean’s redaction are also + occasionally cited when they support variants that would otherwise appear unique.)

+
+
+ 2.6 Stemmatic Hypothesis +

+ +

+
+
+
+ III. Pietro d’Abano’s Practices of Quotation +

In section XIX of his commentary Pietro employs quotations in the same two ways + observed by Coucke in section IV: more literal quotations, which come immediately after + the source’s reference (usually cited by the work’s author, title, and book number, when + applicable), and loose paraphrases, which precede the reference (2008 vol. 2, lxi). To this general pattern we may add a more + specific observation: in section XIX Pietro’s more literal quotations draw exclusively + on Boethius and Isidore, and he uses them to lay out background information about the + discipline of music’s terminology and its received history. He does this most + prominently in problem 1, but also later, too, for example in problems 3, 7, and 16. + Pietro uses paraphrases, by contrast, largely to support or exemplify his interpretive + claims, and they come from a significantly wider range of sources, as will now be + addressed.

+

The sources with which Pietro engages in section XIX fall into three main + categories: the Aristotelian corpus, medical texts, and late-Antique writings on music. + Pietro cites sources from the first category most frequently. Cross-references abound to + passages within the Problems, from both section XIX and other + sections, and Pietro also cites other Aristotelian works that were well known in his + day, especially book VIII of the Politics. (Other + Aristotelian works with which Pietro engages in medical-focused sections of the Problems, such as the De generatio animalium and + De historia animalium [Coucke 2008, vol. + 2, lxii], make no appearance here.)

+

Given section XIX’s dedication to the subject of music, the extent to which + Pietro incorporates medical sources, the second category, undoubtedly speaks to his + training as a physician. Three of these treatises are by Galen, whom Claude Palisca + misidentified as an otherwise unknown author Balienus in a + chapter on Pietro (1985, 55). The other medical sources + range from the better known, such Avicenna’s Canon medicinae, + to the obscure, for instance the Aphorismi of + Yuḥannā ibn Māsawaiyh, which Pietro attributes to John of Damascus.

+

The number of texts in the third category, writings on music, is very small. + While Pietro makes reference to Macrobius and Ptolemy, he demonstrates first-hand + knowledge of only Boethius’s De institutione harmonica and + the section (III.15–23) of Isidore’s Etymologies which + concerns music. He also has at least passing familiarity with some aspects of medieval + music theory, as he makes reference to the Guidonian + tradition (traditio Guidonis) in problem 1 + and on occasion employs solmization syllables, but he displays no further awareness of + music-theoretical writing from after late Antiquity. (He is, however, certainly aware of + his day’s musical culture, as he discusses antiphonal singing and medieval instruments, + which are unmentioned in Boethius or Isidore.)

+
+
+ IV. Principles of Edition +
+ 4.1 Latin Translation by Bartholomew of Messina +

The textual tradition of Bartholomew of Messina’s Latin translation of the + pseudo-Aristotelian text is largely independent of Pietro’s commentary, as only six of + the twenty extant medieval manuscripts of Pietro’s commentary include the entirety of + Bartholomew’s translation. Furthermore, sixty manuscripts contain part or the entirety + of Bartholomew’s text, compared to only around thirty for the commentary (Coucke 2008 vol. 1, xxxvi; vol. 2, xxiii). As a result, a + critically established text of the Latin translation of section XIX is beyond the + scope of this edition, though I am presently preparing one for publication elsewhere. + For readers’ convenience, though, I have reconstructed the version of Bartholomew’s + translation which Pietro likely consulted and have included it as a variant. The + reconstruction is based on my draft critical edition, altered to reflect readings + found in Pietro's commentary.

+
+
+ 4.2 The Expositio problematum by Pietro d’Abano +

To constitute the text and the critical apparatus I have accounted for all the + manuscripts containing Pietro’s first and second versions of the commentary (except + for manuscript Mb, since it is a copy of Ma). I have also included a selection of manuscripts from + Jean of Jandun’s recension: Vo, Gu, Pp, and Pz. + Furthermore, readings from the two incunable editions are mentioned when they agree on + a unique reading or with variants found in other manuscripts.

+

In the edition’s text I aim to reconstruct Pietro’s second version of the + commentary, and consequently readings shared by manuscript Px and family λ are preferred. Where their readings diverge, if either Px or λ agree with multiple manuscripts from Pietro’s first + version, I prefer that shared text. Where the surviving manuscripts of Pietro’s second + version are corrupt, manuscript Py (and Nu, when not lacunate) is generally preferred.

+

With respect to orthography, I have largely preserved medieval spellings, + rather than changing them to classical Latin standards. (The most prominent exceptions + are that words ending with -cio, -cia, and the like have been changed to –tia, etc., + and the –ij and –ijs endings to –ii and –iis.) Because the digital critical edition + allows readers to choose whether to view orthographical variants, I have recorded most + spelling variances in the apparatus. Certain commonly occurring differences have been + silently normalized, however: + Ea, Gu, Pp, Pz, and Vz’s armoniac* emended to armonic* + Nu's duppl* emended to dupl* + Pp and Nu's mellodi* + emended to melodi* + Pz's sinegengium emended to sinezengium + Gu, Py, nd Vz's sesqui* emended to sexqui* + Ma and Va's hi* + emended to hii* + Px's fati* emended to faci* + Px and Py's sicud + emended to sicut + Pz, Px and Py's velud emended to velut + Va's ubiquitous unique orthographical variants + ignored + All: adinuicem emended to ad inuicem + All: probleuma* emended to problema* + All: lira* emended to lyra* + All: standardized spellings of rithim*, chor*, and antiphon* + All: standardized spellings of dyatesseron, dyapente, and dyapason + All: standardized spellings of lychanos, mese, and paramese + Gu’s *ypote emended to *ypate + All contractions have been silently expanded, including the ampersand and + Tironian et, and tall s has been changed to round s. + I have ignored all changes of hand and/or ink for the marginal numbering of the + problems.

+

Punctuation varies widely among the manuscripts. I initially adopted manuscript + Px’s punctuation, which is relatively sparse. Thereafter + I added further punctuation in keeping with modern practice, especially where it was + lacking at points of significant syntactic divisions. I followed a similar practice + with paragraph divisions, basing them on those found in Px, and adding others at moments clearly signaled by the text (such as new + thoughts introduced by nosce quod, notandum, and the + like).

+

Relatedly, it should be noted that in section XIX manuscript Va and the incunable editions mark the beginnings of new + paragraphs with deinde. In Coucke's edition of section + IV, however, he shows while that the manuscripts of Pietro’s second version (excepting + Vb, which Coucke assigns to the second version) use + deinde in that way, the remaining manuscripts do not. + The change of practice in Va is easily explained: a new + copyist takes over at f. 47r, at which point that use of deinde to mark new paragraphs begins. In the manuscripts from + Pietro’s second version, by contrast, that use of deinde gradually fades away, and seems largely to disappear + after problem 15 of section 11.

+
+
+
+ V. Bibliography + + + Cadden 2013Cadden, Joan. Nothing Natural is Shameful: Sodomy and Science in Late Medieval Europe. + Philadelphia: University of Pennsylvania + Press, 2013. + + Cohen 2012Cohen, David E.. Harmonic Mediation and the Triad: Gaffurio, Zarlino, Lippius and Pietro + d’Abano’s Commentary on the Pseudo-Aristotelian <title>Problems. + Paper presented at the annual conference of the Music Theory Society of New + York State. New York, N.Y., March + 31, 2012. + + Coucke 2008Coucke, Gijs. Philosophy between Text and Tradition The Reception of Aristotle's + <title>Problemata in the Middle Ages: Peter of Abano's Expositio + Problematum. Leuven: Ph.D. + dissertation, Katholieke Universiteit Leuven, 2008. + + Coucke 2009Coucke, Gijs. Needle in the Haystack: In Search of the Model of Peter of Abano's <title>Expositio + Problematum. Revue d'histoire des textes + 4 (2009): 179–213 + + + Klek 1922Klek, Joseph, + Knoellinger, Hermann, Ruelle, Charles Emanuel, + Pseudo-Aristotle. Aristotelis quae feruntur + problemata physica + Leipzig: Teubner, 1922. + + Kuksewicz 1985Kuksewicz, Zdzislaw. Les <title>Problemata de Pietro d'Abano et leur 'Rédaction' par + Jean de Jandun. Medioevo 11 (1985): 113–37 + + + Leemans and Coucke 2011Leemans, Pieter De, and + Coucke, Gijs. <foreign xml:lang="la">Sicut vidi et + tetigi</foreign>...: Ego-statements and Experience in Pietro d'Abano's + <title>Expositio Problematum Aristotelis. In + <foreign xml:lang="la">Expertus sum</foreign>: l'éxperience par les + sens dans la philosophie naturelle médiévale, ed. + + Thomas + Bénatouïl + + and + + Isabelle + Draelants + + , 405–26. + Florence, SISMEL, Edizioni del + Galluzzo, 2011. + + + Meyer 1922Meyer, Christian, + d'Abano, Pietro. Expositio problematum (XIX): Édition, + introduction et notes critiques et explicatives + Leuven: Leuven University Press, 2022. + + Palisca 1985Palisca, Claude. The Earliest Musical Humanists: Pietro d’Abano. Chap. 3 in + Humanism in Italian Renaissance Musical Thought. + New Haven, Yale University Press, + 1985. + + + Siraisi 1970Siraisi, Nancy. The <title>Expositio Problematum Aristotelis of Peter of + Abano. Isis 61, no. 2 (1970): 321–39 + + + South 2002South, James B. John of Jandun. In + A Companion to Philosophy in the Middle Ages, ed. + + Jorge + Gracia + + and + + Timothy + Noone + + , 372–76. + Malden, Mass., Blackwell, 2002. + + + Swaenepoel 2009Swaenepoel, Tine. Les deux versions des «<title ref="#ArPr">Problemata» de Pierre + d'Abano. Filologia mediolatina 16 (2009): 215–45 + + + Zanetti 1741[Zanetti, Anton Maria]. + Latina et italica D. Marci Bibliotheca codicum manu scriptorum per titulos + digesta. [Venice]: Apud Simonem Occhi + Bibliopolam, 1741. + +
+
+ + + +
+ Expositio problematum Aristotelis, Particula XIX: De harmonia +
+ + + + + + + + + + + + + + + + + + + Incipit + Incipit decimanona particula. + Incipit decimanona particula et cetera + De problematibus Aristotelis que sunt + circa Musicam l'armoniam particula .19a. + xix + Sequitur xviiii. + 20a + 20a particula + Incipit particula 20a de armonia continens problemata 47 + Aristotelis + problemata de hiis que sunt circa armoniam + particula 20m. + Capitulum primum + de problematibusarestotelis que sunt circa armoniam + vel musicam particula 19a. + + +
+ + + + Primum problema + + .1. + problema primum + +

+ PROPTER QUID DOLENTES + PROPTER QUID DOLENTES ET GAUDENTES + PROPTER QUID DOLENTES FISTULANTUR + + PROPTER QUID DOLENTES ET DELECTANTES FISTULANTUR?AUT UT HII QUIDEM MINUS TRISTENTUR? ALII AUTEM MAGIS + GAUDEANT + . + Determinatis problematibus circa + mathematicam + mathematica + methaphysica + methaca a.c. + + mathaca p.c. + + methaphysicam + methacam + + et orationes, determinat nunc problemata circa armonicam vel musicam, eo quod in + ipsa + ipso + est quidam amor sermonis, vt in + priori particula. Et primitus ad huius + + maiorem + amorem + + expositionem + premittantur + premittuntur + quedam communia, + sicut + scilicet + + quid est musica et que + ipsius + sint ipsius species + prius + ? Que secundum + + boecium + musice + 5° + boeciummusice + 4° + boeciummusicce + boecium raritate 4° + boecium + inprimomusice + + Boethius + De inst. mus. + V.2 (Friedlein p. 352, ll. 4–5) + + est armonica + armonica est + est armonice + Armonia est + facultas differentias + + acutorum et grauium sonorum sensu + + et + ac + ratione + acutorum sonorum et grauium sonorum ratione + perpendens. + Secundum vero + + ysidorum + + in + vt + + + + ethymologiis + + + + ethicis + + Isidore of Seville, Etym. + III.15.1 + est peritia modulationis, + sono + sonorum + + cantuque consistens. +

+

Dicitur etiam quod + sit scientia numeri ad sonos + proportionati + proportionatos + proportionatisrelati + . + Arist. + An. post. + 90a, 14–23 + + Que secundum + + ysidorum + + yrodorum + + dicitur a muso + + quasi a querendo + + quasi acquirendo + que acquerendo + id est acquirendo + , quia + per eam vis + per eam ius + per ea vix + per ius + paruis + + carminum + + querebatur + queratur + acquiritur + . Vnde a poetis iouis et + memorie + + + venem + + filias + + mutas + musas + unitas + + esse confictum + est + esse + + , nam + memoria soni + soni memoria + si memoria soni + non + teneantur, pereunt + teneatur, pereunt + teneatur, perit + , cum non + possint + + possunt + possit + scribi. + Isidore of Seville, Etym., + III.15.1–2 + + + A nonnullis + Amat nonnullis + nullus + Aut + + + vero dicitur + dicitur vero + dicitur + + + a moys + + amois + + + quod + que + est aqua, + quia + + olim primitus + primitus olim + olim amicus + olim tali primitus + + + inuenta fuit + fuit inuenta + + + in illa + et illa + in aqua + , et in + + ydriis + + + + + + siue instrumentis aquaticis similiter + + exercita + + ex certa + . + + Refert autem + + Refertur + + + moyses + hanc + + hanc moyses + inuenisse + + tubal + + + + + aabal + tubal fratrem + cayn + + de stirpe + + cayn + + + + + + + ante diluuium + + + + + . + Isidore of Seville, Etym. + III.16.1 + + + + Sed greci, + vt apparet per macrobium et + boecium + + bonum + , + dicunt eam + inuenisse + + + + + + + pytagori samium + + + pictagorius + samium + pitagoram + samium + pictagoram + samium + pictagoram + pythagorici samium + pitagorici + sonitu + malleorum + + , cum casu in publicum + exiret + ad fabros, et cordarum + demum impulsione + + deinde impulsione + deinde pulsione + . + Boethius, De inst. mus. + I.10 (Friedlein p. 196–7) + Macrobius, Comm. in somn. + Scip. + II.1 (Eyssenhardt p. 572–575) +

+

+ Diuiditur + Dicitur + autem musica iuxta + + eosdem + easdem + eo sedem + in mundanam, humanam, et organicam vel + instrumentalem. + Mundana + + + mundanam + + + vero + quidem + non + + + attenditur + + + intenditur + + in sono armonico, + quem + que + quam + causant orbes celestes, secundum + pictagoram + + + pithagoricos + pictagoricos + pitagoricos + cum aliis musicis, + differenter + + + + differuntur + drntur + + + commotos. + Sonum + enim + armonicum + causant, sed + + eum + eius + eum sed eum + non percipimus, dicunt, + propter quod + propter hoc quod + propter ea quod + preterea + + + in auribus nostris a principio + in auribus et nostris a principio + a principio nobis in auribus nostris + + + natiuitatis + natum + notum + + est + complantatus, vt + + in eris apparet + apparet in eris + in eis apparet + + + malleatoribus + + malleationibus + strepitum suum + vix percipientibus + consuetudine + + et ex consuetudine + + + quos + quod + quo + quorum + + + aristotelem impugnat + celi et mundi + + 2°. + aristotelem impugnat + + in + + 2° + <app> + <lem wit="#γ #Mb #Vm #Vo #Vz">celi et mundi</lem> + + <rdg wit="#Gu #Pp #Pu" ana="#subtractive #J">celi</rdg> + </app>. + aristotelem + in 2° + celi et mundi inpungnat. + + Arist. + De caelo, II.9, 290bl. 25 +

+

Musica vero humana + dicitur + que circa + concordantiam elementorum + concordantia elementorum + elementa + + diuersorum ad inuicem + in vno composito + non composito + + vel + compositionem + compositione + compositum + corporis versatur, per + eam + ea + enim natura spiritualis coniungitur + corpori et rationalis + corpori et in rationalis + rationalis + + + + concorditer + + concordie + cum + irrationali + + irrationabili + rationali + + coniungitur. Quod + + videtur + aristotelem + + a platonicis habitum ponentibus animam quandam + armonicam + fore consistentiam + esse consistentiam + . Vnde + + datum in afforismis + + dictum est in <app> + <lem wit="#Vb #Vm #Vz #m #v">afforismis</lem> + + + </app> + damascenus in afforismis + + + colligatio + + colicgio + + + anime et corporis + corporis et anime + secundum ordinis naturalis consonantiam + facta + factam + + + est + + , vt + substat + subsistat + , + Yuḥannā ibn Māsawaiyh, + Aph., (Vat. Lat. + 2460, + f. 39v, + ll. 7–8) + quare + huius + huiusmodi + + + musice + musice naturali + numeratione naturali + + + videntur scientie + scientie videntur + videntur hec scientie + numeri scientie + videntur sane + + supponi.

+

Instrumentalis vero dicitur que quibusdam exercetur armonicis instrumentis, que + predicamentis videtur + predicamentis videntur + videntur predicamentis + possunt videtur + + fore + + considerationis + speculationis + + contristationis + 9tātionis + + + + existens duplex + existens + dicendum + dd' + + existens dicendum + existens + + : nam quedam exercetur instrumento naturali, vt + hominis + homines + + voce, cum reliquis organis + locutionis + + locutiones + locutiuis + + , + aut + an + + artificiali. Et + id + illud + + + multipliciter: aut tactu vt + + viellis + + + + + vincul + , + vel + aut + + pulsu + ceu + seu + sicut + + + + cimbalis + + + + ebalis + , vel + + flatu + flatum + flacio + + + vt + sicut + in + + tubis, aut quasi + omni modo + omnino + + + sicut + vt + + fistulis.

+

+ Que + Qui + Dicitur + iuxta + + ysidorum + + + + + + diuiditur + diuidetur + dicitur + in armonicam metricam et + rithimicam + et rithimicam + rethoricam + . + Quarum + Quorum + + + armonica + + graue in sonis et acutum + graue et acutum in sonis + graue in sonis acutum + discernit. + Metrica + etricam + Matricam + + est que ratione probabili + cognoscit + mensuram + + mensuras + + mensuram cognoscit + diuersorum pedum vt + heroycum + + + + + + heronicam + + + iambicum + + + in abitio + + et + + heliacum + + + + + + + + + + . Rithimica + vero + vero est + est + + + que + + verborum incursionem + + inquirit + iungit + , vt + + aut + autem + + aut + aū + + an + + suauiter + vel + an + aut + non suauiter sonus + cohereat + + + adhereat + . + Isidore of Seville, Etym. + III.18.1–2 + +

+

Que + + siquidem + quidem + quedam + + + tria + tripliciter + + ad genus + videntur concurrere + + concurrere videntur + videtur concurrere + videntur currere + videntur concinere + + + cantilene + + + canticule. + caticlʼe + + + canticule + canule + + causa mille + , armonica tamen, vt + tactum + tactu + tactum est + dictum est + , + consonantiam + consonantia + grauis et acuti + attendit, + rithimica + rithimica vero + rithimicam vt tactum est + + + consonantiam + + consonantia + + terminationum, metrica vero temporum vt apparet in + + traditione + traditionem + introductione + musice + guidonis + + grauidons + gradionis + . et circa has + tres partes musice, et maxime + + duas + duos + et + + priores, dubitat + + aristoteles + + vtilitas + vnitas + volitas + + vero musice est, + Arist. + Pol. + VIII.5, 1339a, l. + 11 + quia delectat + animos + animas + + + excitat, et + exercitas et + exercitat et + et exercitat + exitat et + et + affectus mouet, et + + furiam + + furias + placat, + siluestrem + siluestres + siluestre + + mansuescere + + facit + + , vt apparet clangore, + namque + enim + tubarum et similium fortiores + redduntur bellatores. Similiter + lassatos et exercitio + + et laxatos exercitio + lasatas et exercitio + laxatiuo et exercitio + laxatos exercitio + lassatos exercitio + + laborioso + + detentos + + detento + reddit + faciles + facille + facilius + tollerare. Vnde + + <app> + <lem wit="#Ea #Ma #Nu #Pz #Va #Vo #Vz #m #v">politicorum</lem> + + </app> + 8°: + 8° + politicorum + palliticorum + duo + + musica habet delectationem naturalem propter quod omnibus + etatibus et omnibus + moribus + et moribus + horis + vsus ipsius est amicus. + Arist. + Pol. + VIII, 1340a, ll. 3–5 +

+

Recitat etiam + + + boecius + boecium + + + pictagoram + + + primae pyctoragam + pythagoricos + pictagoricas + + iuuenem + furentem in + combustionem + combustione + domus + riualis + + + in qua + sortum + scortum + continebatur melodiis musicis eius animum + sedasse + + + . + Boeth. + De inst. mus. + I.1 (Friedlein p. 185, l. 3) + Cuius + vtilitatem + subtilitatem + + tangit + + + politicorum + 8° + 8° + politicorum + aristotelis + 8° + politicorum + , + + ponitur + ponuntur + ponit + enim + vnum quatuor + quatuor + ibi quatuor + quatuor ibi + + + que debet + + que debent + quedam + + + adiscere + + + + puer + pueri + + : que sunt + littere + littera + lingue + + + + luctatiua + + + luctatio + luctatio + luctatio + licatio + iutatio + britatio + musica et + protractiua + + protractiua + p't'actā + + + protractura + pertractiua + porctiua + , + Arist. + Pol. + VIII, 1337b, l. 23 + + + ceu + seu + + scribere et pingere.

+

Querit + igitur + ergo + + aristoteles more + consueto + solito + + problema, dicens: Quare dolentes + et contristantes et + contristantes + et + contristantes + et tristantes et + et contristantes sunt + delectantes + gaudentesque + et gaudentes + gaudentes + + fistulas et + vniversaliter instrumenta + vniuersaliter omnia + instrumenta + + + + delectationem et gaudium inducentia + delectationem inducentia et gaudium + delectationem inducentia + gaudium et letitiam inducentia + letitiam quod inducentia + expedit audire? Vnde + + + alexander + + + + + et maxime + + quantum + + + ad primam + partem: + + Propter quid + coram patientibus fistule et + + tympana. + + tympane. + timpana et cetera. + + Ps.-Alex. Aph., Prob. + I.78 (Vat. reg. lat. 747, f. 75v) +

+

+ Nosce quod + + omnes passiones + licet omnes passiones + licet omnes + omnes passiones licet + omnes passiones sint + + + sint coniuncti + sint coniuncte + sint coniecti + sicut continetur + , + 1° + de anima + Arist. + De an. + I.1, 403a, l. + 25(Cf. 403a l. + 16) + ; quedam + + tamen se plus tenet + tamen se tenet + tamen se plus tenent + tamen plus se tenent + tamen plus tenent + se plus tenent + ex parte + corporis, vt dolere et delectari, alie vero ex parte + + anime vt gaudere et tristari; ita vt per vnum expressum + aliud aristoteles + audiat + aristoteles audiat + aliud + aliud audiat aristoteles + + + recitatum + + + + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens + causam esse vt + qui tristantur ac etiam + + dolent + doleant + + minus + contristentur + tristentur + + et doleant + propter + propter melodiam vel + iocunditatem inductam ex sonitu instrumenti. In + oppositis + oppositis vero + causa + extat + extet + existit + est + vt magis gaudeant et delectentur, si enim aliqui sunt iocundi addita causa iocunditatis, + vt + et + scilicet + fistulationis + armonice + armonia + + + amplius delectabuntur. + delectabuntur amplius. + magis iocundabuntur. +

+

Nosce quod + id + illud + potest contingere quia idem + potest esse + est + causa diuersorum aut + ratione + ratione diuersorum aut + ratione + dispositionis + susceptiui + susceptum + suscepti + susceptorum + subscopii + ; vel quia + diuersa + + dictum + dm + + diuersimode + dum + + + egeant + egeat + agat + + + eadem + eodem + eorum + + + + vel + et + + + ratione eius quod per se + aut + an + et + per accidens extat, + vt nauta per + sui + suam + + presentiam + + causa + causa est + est causa + salutis nauis, eius vero + absentia + + absentiam + absentia causa + + submersionis + + 2° + <app> + <lem wit="#λ #Gu #Nu #Pu #Vb #Vo">physicorum</lem> + + </app> + physicorum + 2° + . + Arist. + Phys. + II.3, 195a, l. 13 + + + + et cetera + sequitur 2m. problema. +

+
+ +
+ + Secundum problema + 2m + Secundum + Secundum + + +

+ PROPTER QUID LONGIUS + PROPTER QUID LONGIUS AUDITUR + + PROPTER QUID LONGIUS IDEM EADEM UOCE AUDITUR CUM ALIIS CANTANS ET CLAMANS + QUAM SOLUS? + AUT QUIA COADUNATE ALIQUID FACERE, AUT REPRIMERE + AUT IMPELLERE, NON TANTA PROPE SUNT QUANTUS NUMERUS. + SED SICUT LINEA BIPEDALIS NON DUPLUM SED QUADRUPLUM + ALIQUID SCRIBIT, ITA COMPOSITA PLUS + POSSUNT, AUT SECUNDUM NUMERUM AUT QUANDO FUERINT DIUERSA. + COADUNATIS IGITUR EXISTENTIBUS UNA FIT UOCIS + FORTITUDO ET SIMUL IMPELLIT AEREM. QUARE MULTIPLICITER PREIT, + ETENIM EX OMNIBUS UOX UNIUSCUIUSQUE + MULTIPLEX + . + + Quare vnus et idem numero + eadem + + + similiter voce cantans et + vociferans + + remotius auditur quando cum aliis + vna cantat et + una voce cantat et + una voce cantant vel + clamat quam si solus tantum cantaret aut vociferaret + + ? Non tamen adeo + + distantur + distantantes + distante + distant + distanter + + , sicut vnus post alium ordinatus distantia + vociferaret + vociferat + + + vt in + vt + in + et in + + + proicientibus + + lapidem successiue.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit + dicens primo causam esse + dicens causam esse primo + primo dicens causam esse + dicens causam esse + + quia + coniunctim + + coniuncti + coniunctum + coniunctus + + + aliquid + aliquod + ad + agere, puta + est reprimere + reprimere est + reprimere + + + coangustante + coangustantem + coangustare + coangustando + angustatis + + + an + aut + + + impellere + repellere + compellere + + + contendendo + + continendo + , vel + aliquid + aliquod + adeo + + + singulariter + simile + simpliciter + tale, non + tamen + + tantum + + + potest + per se vnumquodque, + + sicut quando plura + quantum quando duo + simul + + coniunguntur numerum + constituentia, dummodo + + ordinentur + ordinetur + in vnum + vt + velut + vel + nauis + tractus + + ostendit.

+

+ + Deinde. + + SED SICUT. Declarat secundo + dicens quod + + istud + illud + + apparet ex tali simili quoniam sicut linea duorum pedum non solum + duplum, sicut est potest + figurare + significare + firmare + + + intellecta moueri, sed + intellecta mouere, sed + intellectum ymmo etiam + + quadruplum et octuplum, secundum quod diuersimode + + mensurando + infundo + commensurando + + + applicatur + applicantur + + applicatur mensurando + , ita + vt + super + per + semper + + + plurem numerum habeat + plurem numeri habeat + pluralem numerum habeat + plures vnam habeant + potentiam, similiter et + + ad inuicem etiam + ad inuicem et + ad inuicem + in + quibuscunque + quibusdam + quibusdamcunque + aliis. Cum + autem + aut + plura + fuerint + fuerunt + + numero amplius possunt, + vel + vel quam + cum diuisa fuerint quocunque + alio + alio modo + + distinguente dummodo vnum + proportionaliter compossit + proportionaliter compos sit + proportionaliter composcit + proportionaliter possit + + + alteri + alteri coadunari + .

+

+ + Deinde. + + COADUNATIS. + Concludit tertio + + quod quando + quod + + aliqua plura numero vel specie aut qualitercunque diuisa + coniungantur + coniunguntur + ad inuicem + virtute + virtutem + virtute cum + virtute quod quantum + , + vtpote + vt potentia + vt puto + + + in voce vna + in voce + voce vna + in voce sua + ex omnibus + + contingit + contingitur + contingit simul + + + vocum + vocis + + + fortitudo + fortificando + + + simul + vel + + + + impellens + + implens + + + aerem + aera + . Et ideo + valde amplius + amplius valde + amplius + + + potest + potest amplius + ponit + preire + et + et in + + + longinquius + + + audiri quam vox vnius quod + ostenditur. Nam ex voce uniuscuiusque vox + quedam + quidem + + vna constituitur multiplicium + habens potentiam, + ceu + seu + sicut + + + + tractus + + + + tractum + tracti + optime + una + + + et diuisim + + denotat nauis + ostendit nauis + . Et hoc quidem + problema + partim + partium + + + + pertinet + pertinet enim + partini enim + + + + .xie. vt visum particule + .xie. vt visum est particule + .xie. particule, vt visum est + particule + vt visum est particule + .xie. vt visum est + .5e. particule, vt visum est + + Ps.-Arist. + Prob. + XI + + partimque isti. + + et cetera. + sequitur 3a. problema 19. particule. +

+
+ +
+ + Tertium problema + 3m + tertium + Tertium + + +

+ PROPTER QUID PARYPATEM + + PROPTER QUID MAGIS FRANGITUR + + PROPTER QUID PER YPATEM CANTANTES MAXIME RUMPIMUS NICHILOMINUS QUAM + NITEM ET SUPERIORA, CUM DISTANTIA PLURI? + AUT QUIA DIFFICILLIME HANC CANTANT, ET IPSA EST PRINCIPIUM? + ID AUTEM DIFFICILE PROPTER ELEUATIONEM ET + DEPRESSIONEM UOCIS. IN HIIS AUTEM LABOR, LABORANS AUTEM MAGIS + CORRUMPITUR + . + + Quare + + cum cantamus + cantamus + quando cantamus + causa cantamus + cum caneamus + cum teneamus + cantantes + secundum + notam + vocem + quam + illa + ista + corda representat que vocatur + ypotes + + + potissime interrumpimus cantum, non potentes + + ipsum continuare + continuare ipsum + ipsum continere + sicut + accepimus + accipimus + incepimus + + + pre sui + pro sui + prefui + difficultate. Et in nullo + minus + videtur + + + ymmo + + + + + + + in omnibus + in + etiam + + + magis frangimus + magis in omnibus frangimus + + cantum + + propter + per + ipsam quam per + + nitem + nucem + vitem + + + siue netem + seu netem + vel nectere + . + Et + + vniversaliter magis frangitur + cantus et difficilius seruatur quando + vtitur + vtuntur + vtimur + + + notis + votis + motis + per cordas superiores + + denotatis + denotatur + , et precipue quando distant inter + se maxime. Hoc autem + fit + fit in + fit instans + sit + instrumentis + cantando aut per notas illas que sunt in instrumentis + + + + proportionatas. + proportionatis. + proportionate. +

+

+ Notandum + Notandum quod + Nota + + ad intellectum eius quod + + hic + hic dicitur + huius + et + multorum + + in hac particula dicendorum quod antiquitus + a pictagora + inuentum fuit instrumentum dictum monocordum + + + + + inuentum fuit a pictagora instrumentum dictum menocordum + a pictagoricis inuentum fuit instrumentum dictum + monocordum + a pitagoricis instrumentum inuentum fuit dictum + monocordum + a pithagoricis inuentum fuit instrumentum + monocordum + , eo quod vnam + solam cordam + cordam solam + solam + haberet + taliter formatum + talem formatum + formatum taliter + taliter et formatum + taliter proportionatum + + + in + etiam + quo proportiones musice + .5e. cum + 53 + 59. + + + tonis + + rationes + + simplices prius cognosci + iubebat + iubeat + iubebant + videbantur + secundum diuersitatem loci + instrumenti tacti + + representante. + + representantem. + representatis. + + representatis + r'pn'tat' + + representare. + + + Deinceps + Deinde + + + inuenta sunt instrumenta + instrumenta inuenta sunt + sunt instrumenta + inuenta fuerunt instrumenta + cum pluribus cordis: + vt + vt cum + et + + duabus + + ceu rubeba + + + + seu rubeba + seu reubeba + seu rubeda + sicut rubeba + sicut rubeda + sicut rubula + que similiter organum + introductum + + introductorium + introductorum + existit. + Denique + Deinde + Deindeque + Demumque + Demum quia + Deinde quia + paulatim sunt cetere + adinuente + inuente + aduenientes + . Vnde + 1° + musice + ait + boecius + + nichomacum + + + + nichoantum + intomarum + inchoantum + inchoatam + dicere musicam + in principio fuisse + fuisse in principio + in principio fore + + simplicem + in tantum quod tota constabat + ex + in + + quatuor cordis. Quod durauit vsque ad + orphei + + + + tempus + + puta, quod + puta ex + ex + + + prima + prima quidem + et quarta corda + constitueret + constituerent + constabat + + + consonantiam duplam + consonantiam dupla + consonantiam + consonantia dupla + dyapason + dictam + dicta + . Medie quidem + + harum ad se inuicem + harum ad inuicem + tonum constituebant, + et ad + extremas + extremas partes + comparate + + + dyapente et dyatesseron, vt apparebit .13., + ita vt in + ita in + ita vt + hiis quatuor cordis + nichil + + dissonum + existeret + existere + existerit + existiterit + ad + imitationem + + + mutationem + immutationem + + + mundane musice + + musice mundane + antedicte que ex quatuor + + constat vt tactum elementis + vt tactum constat elementis + constat elementis vt tactum est + constat vt tactum est elementis + constat vt dictum est elementis + . Quarum quatuor + + cordarum + cordarum vt + + + + dicitur mercurium + inuentorem + dicitur mercurius inuentor + fuisse. Vnde adhuc + aliqua instrumentorum + aliquo instrumentorum + aliquod instrumentorum + alia instrumentorum + aliud instrumentorum + + videmus + tantum + quatuor cordas + habere + habentia + + vt + citaram + + + et + zigam + + zita + zigam vel mygam + . quintam vero cordam + chorebus + + + + + + thozebus + ciozebus + zozebeth + tozobus + + + achis filius + ac is filius + ac hiffilius + + + lidorum + + + lindorum + + rex + adiunxit, + hiagris + + + + yagris + + + + "According to Clement, Strom. 1. 76. 5, Agnis (Hyagnis) the + Phrygian—a legendary prehistoric figure—invented 'the trichord and the + diatonic scale'; but it is not entirely clear whether 'trichord' here is + adjectival, referring to a type of scale, or a noun, the instrument that bore + [the name 'trichord']" (M. L. West, Ancient Greek Music [Oxford: Clarendon + Press, 1992], 173, n. 43). + + + quidem + quidam + quid + + + phirs + + + + + furix + firix + sirix + phinix + + sextam + + apposuit + apponit + a + . + Septimam + Aliam + vero + terpanterius lesbius + + + + + + + + + + + + + crepander nilesbius + epauctus lesbius + + inuenit + + planetarum + ad planetarum + + + + septem + + + + similitudinem + + similitudine + . Inter quas grauissima erat, + ypate dicta + ypate dictas + ypatem dictam + + quasi maior et + + honorabilior + honorabilis + honor + vnde et iouem + + ypaton vocant + + + ypate vocant + ypatem vocat + + + id est + scilicet + et + autem in + + + supremum + + et consulem eodem + nomine nuncupantes + + nomine + propter dignitatis excellentiam. Septem vero fuisse cordas antiquitus + testatur + testabitur + testabatur + detestabatur + + .25. + + et 32. + et 33 + et 34° + 232 + et 25. et + 24. + 252. + 32. + + Et + attributa fuit + is + hiis + hec + ea + saturno propter tarditatem motus et grauitatem soni. + Parypate + + Parypaten + vero + 2a + 2o + + quasi iuxta + ypatem + + + collocata. + Lychanos 3a. + + ideo quia + ideoque + quia + + + lychanos digitus dicitur + + quem + quod + latini indicem vocant; greci vero + a lingendo lychanos + + a ligendo liginos + a lingendo diginos + alligendo lychanos + a ligando lychanos + . Et quia in + cantando + cantando ad + , hanc cordam + tertiam + + ab + ypate + + ypatem + , digitus + + hic + + + pertingit, quare ab ipso + lychanos appellatur. Quarta vero + dicitur mese + + + meser dicitur + + + quasi + que + + + + media quia + quia media + media + + inter primam et septimam + + vere + + vera + vero + + media est quarta. + Quinta + 5a vero + 5a est + paramese + quasi + id est + iuxta mediam collocata. + Septima quidem dicitur + Septima + dicitur + Septima + dicitur quidem + 6a vero dicitur + + nete + + quasi neate id est inferior. + Inter quam et paramese + + + Inter quam parame + et parame + quasi et parame + quasi paramese + + + est sexta dicta paranete quasi iuxta + netem + + + + sita + sitam + posite + + . + Paranese + + Paramese + Parapiese + autem quia 3a est a nete eodem vocabulo + trite + + tricte + trite id est trite + + id est + tertia dicitur. + Boeth. De inst. mus. + I.20 (Friedlein pp. 205–6, ll. 28–9) + + Fiat + igitur + ergo + + + talis cordarum + cordarum talis + talis + + + parygrafia + + + + + + + + secundum + thimotheum + + + + + + + + + + + precipuum in + + hac + hic + ac + + arte virum: + + vt + apparet + patet + + + + 2° + in 2° + 4° + + methaphysice + Arist. + Met. + II.1, 993b, ll. 15–17 + , incipiendo a superiori cordarum vocem grauissimam + reddenti + + ad inferius + + descendendo + vt + usque + et + ad ultimam acutissimam + + representantem: + + Hypate + prima. + + + Parypate + secunda. + + + Lychanos + tertia. + + + Mese + quarta. + + + Paramese + quinta. + + + Paranete + sexta. + + + Nete + septima. + +

+

+ Et + Est + + + iste + + quidem + siquidem + + + septem + videntur + + esse ceteris essentialiores + ceteris esse essentialiores + ceteris essentialiores esse + ceteris essentialiores + et necessariores + essentialiores et + necessariores septem videntur + esse + , ita vt aristoteles + + supra + ipsas non + tangat + tangit + vt apparebit ullam + ipsas solas tangat non nulli tamen + , + fueruntque + fueritque + fuerunt + fuerunt quia + fuerunt qui + consequenter + 8 + .9. et .10. + .8. + .9. + .10. + octo + nouem et decem dixerunt + iuxta illud + + + psalmiste + + psalmiste. + psale. + + psalmi + + in psalterio + decacordo. + Psalm + 143:9 (Psalm 144:9 in English translations) + Et + deinceps + + inde + deinde + demum + + in tantum + + creuit numerus + excreuit numerus + numerus excreuit + exercuit numerus + ex trite vt numerus + + vt + boecius + 18 cum + boecius cum + boecius + 7 + reiteratione + ipsarum + ipsorum + ipsas + + enumeret sub + dyatonico melo + + + dyacomcouiclo + ydyacomicomelo + et totidem sub + cromatico + + + + + + ac + 18 + .xxviii. + etiam + sub enarmonico + + + cum + variatione + + quadam + quedam + + + communi + + communis + + + + sine zeugnum + + + + + + + + + + et diateuzeugnum + et dyateuzegnu dyateuzeugnum + + + + + + + + + + + et dyageogimini + + . Non enim + plura tribus sunt + plura sunt tribus + sunt plura tribus + genera + melorum + + + quibus + omnis + omnes + omnibus + + + contexitur + cantilena. + + Cuius hec est descriptio + Cuius est huius descriptio + Quibus hec est + descriptio + Cuiusmodi est huiusmodi descriptio + + + + + dyatonici + + dyacommunia + + + proslabanomenos + + + + + + + ypate ypaton + + + + + + parypate ypaton + + parypatem ypaton + + + lychanos ypato dyatonici + + ypate meson + + meson + + + parypate meson + + + + lychanos meson dyatonici + mese + + trite sinezeugnum dyatonici + + + trite sinezeugium + trite sinezeugmen + trite sinegeumen + trite sinezeuium paramese trite diazeuium + paramete + + + paranete sinezeugium + + paranete sinezeumen diatonici + permete sinegeumen dyatonici + paranete sinezeugnum dyatonici + paranete sine ceugnum dyatonici + paramete inmeazegium dyatonici + + + + nete sunezeugium + + + + + + + + + + paramese + + + + + trite diezeugium + + + + + + trite diazeuium paramete + Ededie zeugium + + + + paranete dyezeugium dyatonici + + + + + + + + + + + nete dyezeugnum + + + + + + + + + + trite yperboleon dyatonici + + + trite ypereboleon + + trite yperboleon + + + paranete yperboleon dyatonici + + + + + nete yperboleon. + + "Of the 'moveable' notes whose positions varied in different + genera, Lychanos was treated as especially diagnostic of genus, and as a note-name + it is sometimes augmented or replaced by enharmonios, chrōmatikē, or diatonos, + depending on its actual station. The same happens more rarely with Paranētē" (M. + L. West, Ancient Greek Music [Oxford: Clarendon Press, 1992], 222). + Similis autem per omnia + figuratio extat + extat figuratio + est figuratio + figuratio + in + cromatico + + orematico + + + melo ac consimilis + melon ac consimilis + melo et consimilis + melcoris similis + melo et cuius similis + melo ac minus similis + in + enarmonico + armonico + , excepto + quod vt + quod + in prima + + subscribitur + describitur + scribitur + + + dyatonici + + + dyatonicum + dyatonicis + dyaconitus + + + ita + ita vt + + in secunda + + cromaticon + + + + tromaticus + cromatico + cormanticon + cormanticum + et in tertia + enarmonicum, ita vt omnes coniuncte liiii. + + sunt + sint + corde. Moderni autem in aliquibus ultra lxiiii. + + apposuere + apponunt + apposuerunt + vt medius + canon + canono + canon dictus + ostendit. + + + Deinde. +

+

+ AUT. + AUT QUIA. + Soluit + dicens + + dicit + causam esse quia + cum + + difficultate + ampliori + amplior + + cantus fit secundum + ypatem + + ypate + . Ipsa + enim est + est enim + est + enim + principium + + incipiendo + + incipiendo a + superius, vt + prescriptum + prescriptum est + descriptum est + ad quam. Si + perueniri debet + debet perueniri + perueneriet debet + + vocem oportet eleuare et ab + + ipsa + ipsam + versus + netem + + noctem + + + deuenire + peruenire + venire + , cum cantus perficiatur + sonorus + sonorum + ex contrariis eleuando et deprimendo vocibus.

+

+ + Deinde. + + ID AUTEM. + + Contingit + Concludit + Dicitur + propter hoc + quod + quia + contraria + sunt subitam + subitam sunt + sunt subiecta + sunt subicita + sunt subtila + + inducentia alterationem. In hoc vero + + intercidit + interdicit + labor et difficultas, + ubi autem huius + ubi huius + ubi autem hoc + ubi autem huiusmodi + magis accidit corrumpi sicut etiam in aliis apparet potentiis. Et ideo + + agonizantes + + + cantant leges et non choros + 15°. Per alias + vero cordas et proprie medias per oppositum cum difficultate cantatur + minime. + +

+

+ Circa predicta dubitatur + Dubitatur circa dicta + Dubitatur + quoniam videmus + plura + plurima + instrumenta habentia multo plures cordas + quam + que + + pretacte. + Rota + + Corda + enim habet xliiii. + vt + .22.as + in vno latere et in reliquo + totidem + medius + vero canon. + lxiiii. et de aliis + + similiter + + . Dicendum quod + ille + illi + plures reducuntur ad minores prius + + institutas + institutos + . + Quatuor + + 4 enim + Qua eticorum + superadditarum + sumuntur + + sumentur + pro vna + priorum + + priorum et + , ita vt xxviii. + cadant in .vii. notiores, + et + + + + .xliiii. + 24. + 28. + .10. et .44. + + + redeant + + redeunt + in .xi. et .lxiiii. in .xvi. Et similiter + de aliis taliter variatis. Sicut + + + + namque + enim + + + + + quatuor positi + sunt gradus + positi sunt quatuor gradus + 4or. sunt positi gradus + sunt positi quatuor gradus + positi sunt gradus + sunt gradus + + medicinarum + + prius in tegni, + + prius integri, + + Avic. + Can. med. + I, fen 2, 2.15 + + + deinde quoque + deindeque + deinde + + + quinto + simplicium vnusquisque + 4or simplicium vnusquisque + 5° + simplicium + + + diuisus est + est diuisus + diuisus est quilibet + + in + tres mansiones, vt + agnoscatur + agnoscantur + cognoscatur + quantum possibile + + particularius + particularis + per particularius + + complexio + + medicine + meclicine + medie + . Ita + posteriores + musici non solum cordis fuere + contenti quibus essentialiores et + integraliores + irregulariores + + denotarentur + proportiones. Verum vt + sonum + solum + amplius melodiosum + + construerent + constituerent + + inter + priores principaliores alias + adiunxere + adiuxerunt + , ne inter eas magna + + permanerent + permanerem + permaneret + + + interstitia + tristitia + in tristitia + . + + et cetera + sequitur 4m + problema. +

+
+ +
+ + Quartum problema + 4m + Quartum problema + Quartum + + +

+ PROPTER QUID SECUNDUM HANC + PROPTER QUID SECUNDUM PARYPATEN + + PROPTER QUID SECUNDUM HANC DIFFICULTER YPATEN, FACILE ETIAM DIUISIO + ALTERIUS? + AUT QUIA CUM REMISSIONE YPATE ET SIMUL POST + DIUISIONEM LEUE SURSUM PROICERE? + PROPTER HOC AUTEM UIDETUR ET QUE DICUNTUR AD VNAM + AD HANC QUAM CIRCA NITEM. + OPORTET ENIM CUM DIMISSIONE ET REMISSIONE UALDE + PROPRIA CONSUETUDINI AD + UOLUNTATEM. + HUIUS AUTEM UTIQUE CONSONANTIA QUEDAM + CAUSA + . + + Quare secundum + istam + illam + hanc + primam + cordam puta ypatem + difficulter + + cantatur + cantetur + ? Et ideo + dictum est + dictum + + + antea + ante + anima + + + secundum + secundum eam + interruptionem cantus + peruenire + peruenirem + prouenire + et licet cum difficultate + cantetur. Tamen diuisio siue distinctio istius corde a quacunque + + alia + aliam + + est facilis et manifesta et proprie ab inferioribus, vt nete + ac + + ei + ea + eis + etiam + propinquis.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit et prius ad + id + illud + quod + subdictum + subdictum est + subditum est + subditum + subductum + + secundo + + dicens + dicit + + + illud + id + ideo + + esse quia faciendo remissionem et quasi quandam + interpollationem + + cum cantus fiat cum ypate + simulque + fere statim post durationem + vel + et + + + diuisionem + dimissionem + + intonationis grauem, leue + fit + vocem sursum emittere, cum iam + aliqualiter cantans + cantans aliqualiter + + aliter cantans + cum nam aliqualiter cantus + + + quieuerit + quieuit + conuenerit + emittendo spiritum et + attrahendo + + mittendo + emittendo + sufficienter in vocis organa. + Et ideo + Et ideo non + Et ideo in + Ideo + percipi videtur + discretio + distinctio + in cantu facto per + ypatem + + + cum alia sibi opposita.

+

+ + Deinde. + + + PROPTER HOC. + PROPTER. + + Assignat causam prioris + premissi dicens + id + illud + + fore quia melodie que + + referuntur + feruntur + ad unam cordam, puta ad illam que est circa + netem + venem + vene + + vt + paranetem + + ac etiam paramese + aut etiam paranete + + + + facilime + + faciliter + + + cantantur + cantatur + , eo quod non interuenit multa diuersitas + vocum + vocis + secundum acutum et + grauem + + graue + , + sed tamen + sed cum + et inde + + licet + + per ypatem + + parypatem + cantetur + difficulter + + propter + grandem + gradem + magnam + grauem + notarum distantiam. Cum + + tamen + causa + + + + fit + sit + vt + tactum est + tactum + quadam dimissione et + remissione + reuersione + + quasi pausando ita + ea reddatur + ea redditur + propria valde consuetudini + per voluntatem + acquisite + + aquisittam + + + , + + quis enim sic eligit, tunc vtique consuetudine + per voluntatem acquisite. Quis enim sic eligit tunc vtique + consuetudine + inducta in cantando per + ypatem + + . + Secundum + Per + talem + dimissionem et remissionem + remissionem et demissionem + remissionem ad omissione + dimmisionem + dimisoonem + licet de se cantetur difficilime illo autem + modo + + minime, + quoniam + quod + quia + quando + consuetudo difficilima + etiam alleuiat + alleuiat etiam + etiam illeuiauit + + + + cuncta + puncta + cetera + iuxta illud + + + ypocratis + afforisticis + + + ypo. + affirmatio + yporetis amforisticis + iporcratis anpho. + ypoti. amplias + + assueti assuetos ferre labores et + reliqua + ceteram + . + Hipp. + Aph. + II.49 + + + + Dicit autem voluntatem quia + consuetudo proprie in habentibus rationem + acquiritur + + aquirimus + requiritur + + + apparens + vt apparet + + + + ethycorum + secundo + + + secundo + ethicorum + . + Arist. + Eth. Nic. + II, 1103a l. 17 +

+

+ + Deinde. + + + HUIUS AUTEM. + HUIUSMODI AUTEM + HUIUS ERGO + + + Subdit + Concludit + + tertio quod + etiam + illud + consonantia est + aliqua + alia + causa eius, + + quod + + + + per ypatem + parypatem + cantus + sepe + + non reputatur + + difficilius + difficilimus + difficilior + difficilis + difilis + nam consonantia + fessa + fesse + falsa + + + restaurantur + restauratur + + + vt visum et + et + vt visum est + vt visum est et + vt visum eius + + + vigorantur + vigorantur det + vigoratur + + + debilitata + debilitatem + et debilitata + et debilitatur + . + Εt + + ideo quesitum + ideo quiritur + queritur ideo + + + quare coram + infirmis + + secundum + alexander + + + fistule ac + tympana + + + tympana et cetera + . + secundum + + Ps.-Alex. Aph. + Prob. + I.78 (Vat. reg.lat. 747, f. 75v) + + + + + + Sic + + igitur + ergo + + + licet de se + de se licet de se + licet se + ita de se + + + difficulter + + difficiliter + + cantetur ypate per + + accidens, tamen non in tantum. Puta vel ratione consuetudinis interuenientis + aut + delectabilis + ipsius armonie, cum fuerit + + amicius + + ac amicius + animi eius + cum eius + cum eis + eius + aicius was likely mistaken for amici + eius + + + adiecta + adicta + adiuncta + + + opposita, et + quod + quia + distinctio + + maxime apparet in eo + qui secundum ipsam + cantu + cantum + cantat + causatur + . + + et cetera + sequitur 5a. problema 19e. particule. +

+
+ +
+ + Quintum problema + 5m + quintum problema. Quintum. + + +

+ PROPTER QUID DELECTABILITER + PROPTER QUID HABENTES ALIQUAM NOTITIAM + + PROPTER QUID DELECTABILITER AUDIUNT CANTANTES + QUOSCUMQUE, UTIQUE PRESCIENTES ADIPISCUNTUR CANTUS, QUAM QUOS NESCIUNT? + UTRUM QUIA MAGIS MANIFESTUS ADIPISCENS SICUT + INTENTIONEM QUANDO COGNOSCUNT QUOD CANITUR? HOC AUTEM DELECTABILE CONSIDERARE, QUIA DELECTABILE + DISCERE. HUIUS AUTEM CAUSA HOC QUIDEM ACCIPERE SCIENTIAM. HOC UERO UTI ET + RECOGNOSCERE IPSAM. + ADHUC AUTEM ET CONSUETUM DELECTABILE MAGIS + INCONSUETO + . + + Quare cum delectatione maiori audiunt homines cantatores ac etiam + sonatores + senatores + subatores + cantantes omnes + illos cantus + cantus illos + istos cantus + + quorum + preaudientes + audientes + plaudientes + + + habuere + habuerant + habuerunt + + + prius + aliquam cognitionem? Siue + sit + sint + + secundum verba, + vt + aut + ita + + + quod + quid + + aliquid de + ystoria + + + + + + gesti + gesta + iam + audiuerint + audierint + audiuerit + audierunt + , vel + demum + de modo + + cantandi, eo quod + + audiuerint + audiuerunt + audierit + audiuerit + alias, illum + + et + + + + consuetudinem aliquam inde acceperunt + acceperunt consuetudinem aliquam inde + consuetudinem inde acceperunt + acceperunt aliquam consuetudinem inde + consuetudinem aliquam acceperunt + quam illos cantus quorum audientes nullam + habuerunt + habuerint + + + precognitionem + cognitionem + omnino.

+

+ + Deinde. + + UTRUM. Soluit + et prius + et primo + primo + + + probabilius magis + probabile magis + magis probabiliter + dicens + illud + id + hoc + ideo + esse quoniam + quando homo aliquam prescientiam habuerit circa cantum + quem + quem quem + quam + + audiuit, adipiscitur + et attingit ei quod est + et adtingerit ei quod est + et attingit ei quod + ei quod est + + sibi + + magis + magis est + + + manifestum. Et hoc declarat + quemadmodum + + qm + qvam + + quod diu + + qdm + qvodammodo + + quando aliquis habuerit intentionem gesti quod cantatur + et hystoriam + + + + eius quodammodo + + sciuit + sciuerit + presciuit + , tunc + hoc + huic + hunc + + + intendere est + est intendere + intende est + intendetur est + delectabile + precognoscentibus + precognoscentiam + precognitionibus + , eo quod iocundum est discere + + aliquid + aliquod + adhuc + cuius non + perfecte habetur + habetur perfecte + + cognitio, + quod fit + vt fit + quod sit + quare sit + + iterum audiendo vel + considerare, vt continetur + .xl., ubi + id + illud + hoc + + + repetitur + repetetur + . Que + duo interueniunt cum quis habet cognitionem gesti aliquam, nam + ipse + + discit + discet + adiscit + dicit + dixit + in eo quod accipit scientiam cantus + illius, eo quod gestum + illud licet + illud hoc + illud + + aliqualiter + + esset + est + erat + fuit + + + scitum + situm + scituti + ab eo. Non tamen + + per modum melodie + promotionem die + toto omni die + per motionem die + vtitur autem et + considerat + considerant + consitus + + in eo quod audit + gestum cuius + habuit + habet + prius habuit + cognitionem. Et ideo videmus homines vt plurimum cum volunt amplius + + cantu + cantum + + delectari + facere + sibi + + ystoriam + + + gesti + enarrare + + + enarari + numerare + , tunc enim + dupliciter + dicitur + dicit dupliciter dicitur + + + delectantur + delectatur + + + + + et melodia et ystoria et siquidem + cum habuerint + . + Triplex enim tunc + + dilectatio + + concurrit + + consuetudinem audiendi predictum cantum + + aliquando + in + ita + amplius + amplius aliquando + + + delectantur + delectatur + + , + + Deinde. + unde secundo confirmat causam + prefatam + prefactam + .

+

+ ADHUC AUTEM + AD HOC AUTEM + ADHUC + . + + Dicit + Dicens + quod amplius ad hoc facit + si quod + si quid + que si + sicut + + + auditur fuerit consuetum, + auditur fuit consuetum, + auditur fuerit + audiui + + + quia + + + consuetum magis delectat quam oppositum, + cum sit + factum + facta + natura + quedam + quadam + et + nobis + a nobis + + + + conuenientia + conuenientiam + conuenientius + . Quod autem + + et + etiam + et quomodo + + + consueta + consuete + + covetia + convenientia + quod autem et quomodo consuetta + + + delectent + delectant + delectentur + , + + ostensum est + ostensum ostensum + ostensum + ostensum est in + + + sexto + 18e. + sexto + 16e. + 3e + 18e. + sexto + sexto et + octaue + , + Ps.-Arist. + Prob. + 18.6, 917a ll. 6–17 + et per oppositum + quid agant + quod agant + agant + quod agunt + quando audiunt + opposita, + et ideo + + + audientes qui + vnius + videntur + vuius + + + lingue sunt + lingue + + cantum + + alterius + anterius + alterius auertimus + minime nisi + consueti + delectantur, cum neque + ystoriam neque + + + + + + modum cantandi precognouerint + modum cantandi precognouerit + modum cantandi precognouerunt + modum precognouerunt + modum precantandi cognouerit + modum precanendi cognouerint + cantandi modum precognouerunt + cantandi precognouerunt + cantandi precognouerint + precantandi cognouerunt + . In opposito + autem secus + autem cetus + , + ceu + seu + sicut + cum + + + mihi + + + nichil + + + contingit + contigit + conuenit + + per omne cum ad gallos me + transtuli + + + . Vt + autem + aut + + + + id + illud + + + repetitum + repetitur + reperietur + repente + + + .xl. + 48°. + quarto + + + exponatur + exponitur + + + omne + ore + esse + , aristoteles + talem addit causam + dicens + + ideo esse + id esse + + quoniam + ille qui + illi qui + illud qui + ille + + + cantantem + cantant + cantationem + + compatitur ipsi et ab ipso + + afficitur + efficitur + , propter voces quas + exprimit + exprimunt + + que + + audienti + auditui + + videntur + denotare gaudium, et ideo consonat sibi + + id quod + illud quod + quod + ille + cantat + cantant + qui cantant + . + Et + cum + + quadam + naturali inclinatione + ad delectationem mouetur in seipso ceu ille mouetur + mouetur ad delectationem in se seu ille mouetur + in se mouetur ad delectationem + . Quando + enim + + natura + natatur + + + + vnius + unus + minus + + percipit + naturam alterius + congaudere + gaudere + congaudet + cum gaudere + + + + aut + et + vel + tristari vel se + purgare, natura etiam illius + + ad hoc mouetur + mouetur ad hoc + mouetur ad se hoc + agendum + + , vt + declaratum est + declaratum + + septima. Quare subdit in eius + + verificationem sermonis + sermonis verificationem + verificatione sermonis + quod omnis + cantans + cantus + consonat sibi et alium reddit consonum + et + affectum + affectantem + effectum + affectione + , dummodo illum cantum non exprimat propter + necessitatem + + veritatem + , vt + + sperans + superans + + + ita + ita vt + inde + + + victum + vitum + lucrari + ceu + seu + vt + + + ystriones + + + aut metu pene vel tristitia, et + huius + huiusmodi + + + propter que talia + propter que talia tam + propter talia que + propter quod talia + propter talia + + cantantes + non + + magne + magis + + + consonant + consonans + consonat + consonas + aliis + et + + maxime extraneis ab illo cantu + et sibimet ipsis + + minime. + + et cetera + sequitur 6m. problema 19e. particule. +

+
+ +
+ + Sextum problema + 6m + sextum. + Sextum. + + +

+ PROPTER QUID PARYPATE + PROPTER QUID RATIONABILE EST + + PROPTER QUID PAR YPATE SECUNDUM RATIONEM IN CANTIBUS TRAGICUM. + AUT PROPTER INEQUALITATEM? PASSIUUM ENIM INEQUALE, + ET IN MAGNITUDINE FORTUNE AUT TRISTITIE. EQUALE AUTEM MINUS PLORABILE UEL + ULULABILE + . + + Quare rationabile existit quod + genus cantandi tragicum + genus cantandi traycum + genus tragicum + + + per ypatem + per ypate + parypatem + cantetur? + + Nosce quod + Notandum quod + Nosce + + circa genus + armonicum + armoniarum vel armonicum + + + quodcumque + quod + t' + talis + + + duplicem maneriem cantandi constare, + quedam enim + quidem enim + que + + est + comedia altera tragedia. Est autem comedia + canticum + cantus + agreste que res priuatarum + et humilium personarum + personarum et humilium + et humilium + et habilium personarum + + comprehendit, et dicitur + a cosmos + acosinos + a cosinos + a camos + quod est + villa vel laus + villa + secundum aliquos. Grece tamen + mundus et + odi + odos + cantus quasi + mundanus + et vulgaris + cantus + + cantatus + , + de rebus enim + enim de rebus + de rebus + vulgaribus tractat et + affinibus + affinibus et + + + + cotidiane + + + + + locutionis + + locutioni + + locutioni cotidiane + . Vel dicitur + + a commessatione + + a conmiseratione + a commensuratione + a commesatione + a commensatione + a commessatione quia + accessatione + accensatione + post cibum, enim + + homines solebant + solebant homines + + ad + eam audiendam + conuenire. Tragedia vero + est modus carminis + est modus carminum + cantans + quo poete in luctibus regum vtebantur. + Dicta + Dictus + Dictum + a + tragos + + + treges + quod + est + dicitur + + + yrcus + + + et + odi + + odos + + + cantus + quod est cantus + + + quasi + in + et + inde + + + hyrcinus + + + + yranus + cantus. Et quia materia erat tristis + + feda + fetida + seda + , + huiusmodi + huius + + + animal + animalis + + vt + + yrcum + + + yrcus + hircus + hincus + + + pro munere + perminuere + provire + pro numero + + + poematis + poanatis + + + + accipiebant + accipiebantur + recipiebant + + + additur. Et + additur. Etiam + quod dicitur in + + + maneries a quibus 3° + maneries a quibusdam 3a + + + satira + + + dicta que carmine + construitur + constituitur + + + reprehensorio + reprehensoris + reprehensorior + reprehensionis + + + ceu + seu + sicut + + + modus + motus + + + oratii fuit + + fuit oratii + maxime.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse sumptam + ab inequalitate, vtrobique + enim + scilicet + videlicet + videt + inest quedam inequalitas, vt in cantu + tragico + + + + et + + per ypatem + parypaten + facto, propter + + eius esse + esse eius + eam esse + eius at esse + + supremum. Nam in + vnoquoque + vtroque + istorum est quedam passio et difficultas, quod autem + tale + tale est + , + siue + seu + ceu + Inequale seu + + + sit + fit + + in magnitudine + + fortune + fortitudine + ceu cantus magne letitie alicuius + magnatis + magnatis aut + magnatis et + magnatis vel huius est inequale non + eundem seruans tenorem + + probitatis, siue in magnitudine + + tristitie, sicut mortis alicuius excellentis + vel + + + + huiusmodi + huius + vt nuper domini ubertim dicens carraria vel hoc + , est inequale, + non eundem seruans tenorem. Quod + autem + aut + + est inequale + + et dissonum + rationabile est + rationabile erit + rationale est + est rationale + , vt cantu exprimatur + huiusmodi + huius + et huius + , vt pondus + meloticum + + + meloticus + + + + configeretur + + + + cum figeretur + contingeretur + velociter configeretur + velociter consigneretur + rei de qua existit. Tunc cantus consurgit + + eurithimus + onrichimius + + in rich enrichimus + enrichimus + + + + sicut de huius + sicut huius de + sicut de huiusmodi + + + pulsu scribitur + pulsi scribitur + cantu scribitur + + de differentiis + pulsuum + a + + galeno + + . + Gal. + De diff. puls. + I.8 (I.12 in Latin trans. by Burgundio of Pisa) + + Cf. Pietro d'Abano + Conciliator diff. + 83 + + + Ceu + Seu + in + bellis + becillis + + tubarum clangor bellantes concitat in furorem, in oppositis autem vt in choreis + oppositum + + expetitur + experitur + eproexperitur + , ac similiter in mortuorum lamentatione. Et + id + illud + hoc + est quod + + subditur + subdit + a contrariis probando + pretactum + pretactam + , + inquiens + in conueniens + quod illud + quod est equale in cantu et vnum conseruans tenorem non + est + + + + plorabile + proportionabile + + + aut + seu + + + ululabile + + amabilabile + lamentabile + , cum non sit quid passiuum, + propter quod non est conueniens ipsum + + + + parypatem + + + per ypatem + cuius est inequalitatem tenere sed per alias + cordarum + cordas + + + mitiores + + + anteriores + exponere.

+

+ Nosce + Notandum + quod + pondus est illud in + quo + quod + quid + proportiones + + secundum auicenna + + + + cadunt musice + musice cadunt + cadunt musice et + . + Avic. + Can. med. Book I, fen 2, 3 (p. 141 of 1608 ed.) + Hoc autem pondus + rebus expedit + rebus expetit + rebus accidit + expedit conformari rebus + circa quas + extat + extant + extitat + + configurari, + cum eo + quod eo + + exprimantur passiones que sunt in anima. + + + Voces enim + + sunt + + note passionum que sunt in + ea + anima + + + illeque rerum + + primo + <app> + <lem wit="#Gu #Ma #Pp #Px #Py #Vm #Vo #Vz #m #v">peryarmenias</lem> + + + + <rdg wit="#Va" ana="#lexical">pergere</rdg> + </app>. + Arist. + Peri herm. + I.1, 16a ll. 5–6 + Vnde si res fuerit + + alta + altera + + in signis + + contingit tragedia + tragedia contingit + + conuenit tragedia + conuenit tregedia + querit tragedi + + ipsam + exprimere. Si autem econtra comedia vt modus + coaptetur + coagiretur + coitetur + + rei + + ceu + seu + + proprietas subiecto. + + et cetera + sequitur 7m. problema 19e. particule. +

+
+ +
+ + Septimum problema + 7m + Septimum. + Septimum + + +

+ PROPTER QUID ANTIQUI + PROPTER QUID ANTIQUI CONSTITUENTES + + PROPTER QUID ANTIQUI SEPTEM + CORDARUM FACIENTES ARMONIAM YPATEM, SED NON NITEM RELIQUERUNT? + UTRUM HOC MENDACIUM, UTRAMQUE ENIM RELIQUERUNT, + TERTIAM UERO ELEUAUERUNT? + AUT NON, SED QUIA GRAUIOR FORTIFICAT ACUTIORIS + SONUM, QUARE MAGIS YPATE REDDIT ANTIFONUM QUAM NITE? + QUIA ACUTUM POTENTIA MAGIS, GRAUE AUTEM FACILIUS + CANTATUR + . + + Quare est quod antiquitus + constituentes + constitutos + constunentes + constitutiones + armoniam musicalem ex septem cordis + diuiserunt + dimiserunt + ypatem + non + + + + auferentes + + + ipsam ab armonia, non autem + relinquerunt + + + + nete + neten + netem + vocem + , + verum + + inde abstulerunt + namque abstulerunt + inabstulerunt + ?

+

+ + Deinde. + + UTRUM. Soluit et + prius + primo + + + problema + problemas + probatur + probabiliter + dicens + id + illud + illico + + + + non esse verum + non verum + + esse verum + + quod + premissum est + premissum + , quoniam non + seruauerunt solum + solum seruauerunt + seruauerunt + + + ypatem, + ymmo + + + + + vtramque + puta ypatem + ypatem + et + netem + + + nete + . Sed + + quam + quem + quid + abstulerunt fuit tertia, vt paramese vel lychanos, vtraque enim est tertia + eius quod est + + septem + 7a. + + esse + esse 7 + cordas. Vnde 32° + dicetur quod + tripandius + + + extrahens tertiam cordam a + septicordo + + cordo + + + netem + + + nutio + + + apposuit + apponit + apponunt + . Sic + ergo + igitur + + per + + interemptionem + interpretationem + intentionem + soluit.

+

+ + Deinde. + + + AUT NON. + AUT. + AUT QUIA. + Soluit + magis ad + orationem + oratio + rationem + + + secundo + 2a. + + + secundo magis ad + orationem + + + dicens + + dicit + + + nichil + alias + hoc + esse quod dicitur vt quod abstulissent + + netem + + + + + et + dimisissent + + dimisissentur + ad misissent + + stare + ypatem. Sed hoc dictum + + fortassis + + + ex hoc + + pullulauit + + + ex hoc pullulauit fortassis + , quia sonus + cordis + corde + grauis + vigorat + fortificat + figurat + fiat + sumitur + sonum acutioris. Suo enim multo tempore et duratione graue + substentat + + + + acutum + + ne + non + vt + cito + pereat + periat + persat + + cum breui tempore feriat. Propter quod + + ypate + ypatem + ypaton + + longo + tempore + + aere + aera + aerem + percutiente + quam + quem + quod + + + nete + + vite + + + reddat + + redeat + reddit + , + ob eius + ab eius + propter eius + + acuitatem, que + potentia + ponitur + vel fortitudine indiget in + cantando, + difficile namque + difficilime namque + difilime namque + difficile enim + + acutum cantare + sed graue facilius, + + + + sicut pluries dicetur. Sic + itaque + ergo + quia grauis corda sonum fortificat + acute et ad se + acute et a se + acute et acute a se + conuertit. et + quia + quia quia + + + + difficile acutum cantare + acutum cantare + difficilime acutam est cantare + difficilime est acutum cantare + difficilime acutum cantare est + + + , quis credidit ex hoc cum + + nete + + nitem + netem + voce + intensum + sonum non + + perciperet + percipet + percipiet + + proprium + quod esset sublata? Et fortassis aliquis leget + illud + istud + illud vt tactum multe + + QUIA ACUTUM. quod aliam solutionem + subiungat. + subiungit. + subiunget. +

+

+ Nosce + Notandum + quod + armonia que est + vna + trium + + partium vt tactum est musice + partium vt tactum musice + partium musice vt tactum est + partium + , proprie pertinet ad + comedos + + + comedias + comedras + + et + tragedos uel choros, et omnino ad eos + qui + que + precipue voce cantant. Ex ea + namque + enim + + + causatur + causatur talis + cantatur talis + armonia que est + + vocis + vocum + modulatio + et concordia plurium sonorum + vel + + coaptatio + coadapatatio + coactio + . + Simphonia + + est + vocis + vocum + modulatio + + temperata ex graui et + acuto accordantibus + + acuto concordantibus + acuto a cordantibus + + sonis, cuius quidem + contraria + contraria est + + + + dyaphonia + + + . + Euphonia + + + est suauitas + vocis + vocum + , hec autem melos + a melle et + amelo et + a melos a mellis + a melle + a mellis + + suauitate dicta. + Dyastema + + + + + + Dyafema + Dyaphonia + est + vocis + vocum + + spatium ex duobus uel pluribus sonis + coaptatum + coaptant + coadaptatum + . + Dyesis + + + est + spatia + spatium + + quedam + et + + deducens + deductiones + + + modulandi + + et vergendi + de vno in alterum sonum. + Isidore of Seville, Etym., + III.20.1–6 + + + + Boecius autem + + + dyesim dicit + + + dicit Dyesim + + + vnius + fore + fore unius + minus fore + fore + + + semitonii + + semitonium + . + Boeth. De inst. mus. + II.28 (Friedlein p. 260, ll. 21–24) + + + Tonus + est + est autem + autem + + + acuta vocis + vocis acuta + vox acuta + acuta + aucta acuta + vocis + arta vocis + alta vocis + acuta arta vocis + + enunciatio. + Αrsis + + + Resis + quidem vocis eleuatio, + tesis + + + + enthesis + + depressio. + Isidore of Seville, Etym., + III.20.7, 9 + Sic igitur ex + symphonia + + potest + haberi + habere + quod + antiphonum + + + antiphonori + + + vel + + antiphona + + anthima + sit quedam modulatio + vel + et + intonatio + contra + circa + que + quam + + + simphoniam + + , vt sonus qui + post + potest + prius + eam refrangitur auditum + demultiens + + denuntians + de multotiens + . + + et cetera + sequitur 8m. problema 19e. particule. +

+
+ +
+ + Octauum problema + 8m + octauum problema. + Octauum. + + +

+ PROPTER QUID GRAUIS + PROPTER QUID SONUS GRAUIS CORDE + + PROPTER QUID GRAUIS ACUTE FORTIFICAT SONUM? + AUT QUIA MAIUS HOC GRAUE? OBTUSO ENIM ASSIMULATUR, + HOC UERO ACUTO ANGULO + . + + + Quia + Quare + + + dixerat + dixatur + distrahit + + grauem cordam sonum fortificare acute, + + causam siquidem querit huius + causa siquidem querit huius + querit causam huius + dicens quare grauis + corde + corda + cordas + + sonus + + vigorat + + vigilat + eum qui acute?

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse + quoniam + illud quod est + graue + + + + maius + magis + + + est + + et fortius. Quod ostenditur quoniam angulo + + simulatur + + multiplicatur + si multiplicatio + si multiplicatur + + + obtuso + acuto + trianguli, qui quidem maior est et fortior + etiam + + + vigore acuto + acuto vt res + ostendunt + ostenduntur + ostendit + nature et artis, acutum vero + angulo + anguli + triangulo + + proportionatur acuto + + , + + ceu + seu + minori et debiliori. Quod autem + maius + magis + minus + maius est + + et fortius vigorat + quod + quam + quia + minus et debilius, + + huius + huiusmodi + quidem graue acuti respectu, quare ipsum vigorat, + vt .xii. etiam apparebit + vt 12. + apparebit + vt xii. at etiam + apparebit + vt 13º etiam + apparebit + + . + + et cetera + sequitur 9m. problema 19e. particule. +

+
+ +
+ + Nonum problema + 9m + nonum problema.Nonum. + + +

+ PROPTER QUID DELECTABILITER + PROPTER QUID DELECTABILIUS AUDIMUS + + PROPTER QUID DELECTABILITER UNITATEM CANTUS AUDIMUS SI QUIS AD FISTULAM + AUT LYRAM CANTAT ET AD CORDAS, ET + EUNDEM CANTUM CANTANT UTROBIQUE? + SI ENIM ADHUC MAGIS IDEM, POTIUS OPORTEBAT AD + MULTOS FISTULATORES ET ADHUC + DELECTABILITER ESSE. + AUT QUIA ADIPISCENS MANIFESTUS INTENTIONEM MAGIS + QUANDO AD FISTULAM AUT LYRAM? QUOD UERO AD MULTOS FISTULATORES AUT LYRAS MULTAS NON EST DELECTABILE + PROPTER ID QUOD DESTRUIT MELODIAM + . + + Quare + cum delectatione audimus + cantum vnitum + unitum + tantum munentum + seu in vnum + coniectum + coniunctum + , vt si quis cantat in fistula + vel + et + vel in + lyra et vniuersaliter in cordis + ceu + seu + + + in psalterio canone + in pulsatio canone + in psaltero causam + psalterio canone + et + huius + huiusmodi + instrumentis ex cordis multis compositis, dummodo vtrobique + cantet + causet + esset + eundem cantum? Quoniam si vnus cantus seu + + dantia + + concordantia + + + fieret in + fieret + fieret in vno + in + + instrumento et alius voce + cantantis + causantis + canentes + canentis + , + in + etiam + in etiam + + + illo + illum + non + consurgeret + consurget + + propter dissonantiam delectatio.

+

+ + Deinde. + + + SI ADHUC. + SI ENIM ADHUC. + + Quasi arguit in contrarium dicens quod + si unius + si huius + si huiusmodi + si talis + lilicius + + delectatio + contingat propter vnitatem cantus et + ydemptitatem + + + , tunc + oportebit + + magis delectari cum quis cantabit cum multis + + fistulantibus uel lyrantibus + lyrantibus uel fistulantibus + fistulantibus et lyrantibus + fistulationibus uel lyris + , cum magis + videantur + videatur + super vnum opus + + unitari + imitari + mutari + mundari + , + vt + sicut + vel + plures trahentes + nauem + nauim + + + imitantur + + mutantur + vnitantur + , vt melius trahant.

+

+ + Deinde. + + + AUT. + AUT QUIA. + + Soluit dicens causam esse + quia + quoniam + + cum + aliquis cantat + aliquis cantet + aliquis cante + + + singulariter + signanter + singulariter cantat + intentionem et maneriem cantus magis + vnitatur + vnitur + innitatur uel vnitatur + vnitatem + + vox + cum sono + instrumenti + quam + + quando + cum + + cantaret in diuersis instrumentis, + etiam + et + eodem cantu + vtrobique existente. + Et hoc + Et hoc et hoc + Et + quia in cantu + + + + quedam + + quidem + quid + qui + reseruantur proportiones vt dicetur + commensurate + + commemeratione + . Quibus + obseruatis + conseruatis + + iocunda + + consurgit + consistit + existit + + armonia, que quidem + corrumpitur + et + indelectabilis redditur cum + cantans + cantares + cantatis + ad multa + cantauerit + cantauit + instrumenta.

+

Quod autem + inductum + inductum est + aductum est + + + in + ad + contrarium prius non valet quia licet multi possint + + idem + id + ratione + cantare, non tamen eodem modo. + Non solum enim requiritur + Solum enim requiritur + Non enim solum requiritur + Non solum requiritur + Et non requitur solum + + + ydemptitas + + + + + ex parte illius quod cantatur et cuiuslibet cantantis ad se ipsum + ymo + + + + + + uniuscuiusque + uniuscuiusque et + ad alium + + et + + + ad omnes, ita quod ex omnibus resultent proportiones debite in cantu. Quod autem + subditur + subdit + subiecit + subicitur + subiecti + subieci + obicitur + de + nauis tractu + + tractu nauis + tractu nauis uel ligni + + + non huic + huic non + non habet huic + non hoc + + + similatur + + simulari + assimilatur + dicto, quoniam plurimi + + possunt simul idem + possunt idem simul + possint idem simul + + + vt + et + nauem eodem modo et + tempore + + + trahere vt audientes vocem + rectoris nauis. + Non + Vt + autem talis unitas potest in cantu plurium obseruari + + armonico + armonica + armonia + , cum + eum + enim + quo + + + ex pluribus + et contrariis + oporteat + + oportet + + + constituere + + ⳋstuere + constrvere + + construere + in + unum + unam + unum tonum alias + unitatem + . Tandem + + redditur + reditur + reductis + redditis + + quod + fit + sit + impossibile pluribus + + + entibus + + vocibus et + vocibus in + vocibus + instrumentis. + + et cetera + sequitur 10m. problema 19e. particule. +

+
+ +
+ + Decimum problema + 10m + decimum problema. + Decimum. + + +

+ PROPTER QUID NON DELECTABILIS + PROPTER QUID DELECTABILIUS SIT + + PROPTER QUID SI DELECTABILIS HOMINIS UOX QUE SINE + SERMONE CANTANTIS NON DELECTABILE EST UT UERNANTIUM, SED FISTULA AUT LYRA? + AUT NON ILLIC, SI NON IMMUTATUR, SIMILITER + DELECTABILE? + AT UERO SED PROPTER OPUS IPSUM. UOX ENIM + DELECTABILIS QUE EST HOMINIS, PERCUSSIUA AUTEM MAGIS INSTRUMENTA ORIS. PROPTER + QUOD DELECTABILIUS AUDIRE QUAM UERNARE + . + + Quare + si vox humana + est delectabilis + auditu + auditui + , unde + + museus + muscis + musicus + dicitur + + + <app> + <lem wit="#Ma #Vb #Vz #m #v">politicorum</lem> + + </app> + 8° + .8vo. + politicorum + policitorum + scilicet + politicorum + + + delectabilissimum + delectabili fine + quod delectabilissimum + est hominibus cantare, + Arist. + Pol. + VIII, 1339b, l. 22 + + cum + quis + qui + aliquis + cantat + etiam + et + + + non proferendo sermonem + omnino aut + insignificatium + insignium + insignita + insignibus + , + cur non est delectabilis + cur non delectabilis est + non delectabilis est + cur enim est delectabilis + + + vox alicuius uernantium + + vox uernantium + Videtur tamen + , + cum sit + cum non sit + crescit + + hominis vox, + et + eti + etiam + + lyre et fistule sonus est delectabilis? + Qui + Que + minorem communicationem + videtur cum homine habere quam vox ipsa humana. In hiis itaque uerbis + aristoteles + eadem + + + + succincte tetigit + + + tetigit succincte + succincte tangit + + + motiuum + + + quesiti et confirmationem + eius + quesiti + + .

+

+ Notandum + Nota + quod vernare + vocis + vocum + vocem + est expressionem facere in qua non + + manifestatur + manifestetur + aliqua + sensibilis + + subtilitas + diuersitas + extensione + + expressione + et + depressione vocis + diuersione + , ita quod eius + remaneat + remanet + maneat + equalitas, + ad modum quo + ver + vt + + + + equale ponitur a medicis + + ponitur equale a medicis + ponitur a medicis equale + . Est enim quasi + illud quod dicitur + illud + + + + bordonizare + + + + bordonizare et + + + quod + + per se + minime videtur + minime + minimam + delectationem inducere.

+

+ + Deinde. + + + AUT. + AUT QUIA. + AUT HEC. + + Soluit et + prius + primo + respondet ad confirmationem, dicens quod illic + scilicet in + fistula et lyra + + fistulis et lyra + + non est delectari, + quoniam similiter + similiter + + + in eis ita se habet vt + in eis ita se habet sicut + in eis similiter se habet vt + in eis se habet vt + in eis se habet + se habet vt + etiam se habet eis vt + + + in + + + + vernante + vernanti + vernantem + vernantis + + terminate + tiate + + , + quia + quoniam + si non + fiat + fiet + fieret + + immutatio soni secundum + ascensionem + + assentionem + immutationem + + et depressionem, vt + + inde + inde de + unde + + mundum + mdʼ + + + + consurgant + surgant + desurgant + desurgat + debite proportiones armonice, non + contingit + + conuenit + delectari ex + huius + huiusmodi + instrumenti sono. Sic + + igitur + ergo + uernare non est + delectabile + + delectatio + , eo quod + proportiones + + non proportiones + + + non cadunt in ipso melite + non cadunt mellite + in ipso mellite + in ipso melite + non cadunt in ipso melodice + in ipso non sunt mellite + non cadunt multipliciter + + auditum + + demulcentes + + demulceantes + .

+

+ + Deinde. + + + AUT UERO + AT UERO + AUT QUIA + . + Respondet + motiuo + + motoris + motois + + + motiuo + mto + + + motiuo + moto + + in + + + ipsius + ipsi + + + + causam dando + dando causam + dando causi + + dicendo + di.do + + quare vox humana cantantis sit delectabilis. Hoc enim est propter + operationem ex qua consequitur. In ipsa namque magis percutiuntur instrumenta oris ordinata ad + formationem + formationes + + cantus + delectabilis + quam + + in + ex + + uernare. Ex + huius + huiusmodi + + + namque + nam + enim + autem + + + maiori percussione + + percussione maiori + maiore percussione + instrumentorum + oris que + + horisque + fit in cantu, nunc in vocem + extollendo + + nunc + tunc + in deprimendo, modo vero medie conseruando resultat + cantus armonicus suauis valde. Et ideo + inquit + dicit + in quid + + delectabilius fore vocem + + hominis cantantis + cantantis hominis + etiam hominis cantantis + audire, cum + hic huiusmodi + hic huius + + hic huius + hc hui9 + + hoc huius + + contingat quam vocem + + + vernantis, ubi + minime. Vox etiam + hominis delectabilis + delectabilis hominis + delectabilis + quia consueta et quoniam + + potest + possunt + + + mutari + imitari + immitari + + + componi et contraponi + et contraponi + et componi + et potest contraponi + + + facillime + + + . + + et cetera + sequitur 11. + problema 19. particule. +

+
+ +
+ + Vndecimum problema + 11m + Vndecimum. + Vndecimum + problema + + +

+ PROPTER QUID SONANS + + + PROPTER QUID SONANS ACUTIOR? + AUT QUIA MINUS IMBECILLIOR FACTA EST + . + + Quare aliquis sonans sonitu uel voce acutior redditur et per consequens + alius + alii + autem + grauior?

+

+ + Deinde. + + + AUT. + AUT QUIA. + QUIA. + Soluit dicens causam esse quia + hic + sicut + + sonans est minus sonans quam illud + quod + quid + grauiter sonat. Quod autem sit minus ostenditur quia + fit + a virtute + + que + quia + facta est + imbecillior + + . Grauiter autem sonans a virtute + causatur fortiori + fortiori causatur + , propter quod + + dictum + dictum est + + + .xia. + quod pueri femine + + eunuchi + et eunuchi + eunuci et + + infirmi habent voces acutas, + Ps.Arist. + Prob. + XI.16, 900b, ll. + 15–17 + oppositi autem graues + propter + per + oppositum. + + et cetera + et cetera et cetera + sequitur 12m. + problema 19e. particule. +

+
+ +
+ + Duodecimum + problema + 12m + duodecimum problemaDuodecimum. + + +

+ PROPTER QUID CORDARUM + + PROPTER QUID CORDARUM GRAUIOR SEMPER SONUM ACCIPIT? SI ENIM OPORTET DIMITTERE + QUE EST CIRCA MEDIAM PARAMESEM CUM ALIA MEDIA, FIT MEDIUM NIHILOMINUS. SI + AUTEM MEDIA, UTRAQUE ALTA NON FUERIT. + AUT QUIA GRAUE MAGNUM EST, QUARE FORTE? ET INEST + IN MAGNO PARUUM, ET ASSUMPTIONE DUE NITE + IN YPATE FIUNT + . + + + Quare + Querit quare + que + de cordis + illa + + que grauioris + extat + est + + + toni + soni + semper accipit + sonum + tonum + et representat pre aliis ipsum vt + subiectum + sonum + + solum + som + + + proprietatem, + dum + cum + tamen equaliter fiat percussio et + + ad hoc + adhuc + , si oportet propter aliquam causam + vt + aut + + + defectum ipsius + + aut aliter + aliter + aut alteri + aliquando + + + dimittere paramese que est + iuxta mediam, scilicet iuxta mese + siue mediam uere + siue mediam ipso + siue mediam ipse + siue mediam ipsa + hec + hec + . Namque + + septem + id est + + cordarum + vt visum est media + vt visum media est + media vt visum est + vt visum est + + + + + cum + + + + alia + alio + aliqua + septima + quodammodo + media existente + existente media + existente + + quodammodo cum aliquo existente + vt lychanos, ita quod ea + sonum + sonus + + + non + nisi + + + constituatur in + constituat in + armonia. + Nihilominus ex + Nihilominus in + Nicomos ex + Nichilominus + Lichanos ex + extremis puta + + ypate nete parypate + + + ypate parypate nete + ypatem nete parypatem + ypanete parypate + ypate + + + etiam et + et etiam + et + etiam + + paranete, + sicut ex illis + tribus mediis + + resultat quoddam medium constitutiuum armonie, in quo grauior cordarum sonum preaccipit + aliis + acutis. Communis + + quidem + quidam + que + + littera circa + mediam partem + mediam partem habet + mediam + + + hoc tamen + habet causam + tamen + + licet possit tollerari series tamen iam exposita continens paramese + + planior et sauior + + sauior et planior + planior suauior + planior et senior + planior et sanior + planior est et uerior + . + + + + + Sed si + Sed + Et si + + + vtraque media + vtreque medie + vtraque medio + + + coniungantur + coniungatur + ad inuicem vtpote dicatur intermediarum, + sicut + vt + + + sunt + est + + lychanos mese paramese + + siue trite, non constituitur + sonus eleuatus, ita vt inde resultet grauis, + tanquam + + corde + + cordis + corda + grauioris reddentis sonum grauiorem, cum sonus + harum + earum + + + existat + existet + extat + + in medio inter + graue + grauem + et acutum. Sic itaque + videtur duo querere + puta + scilicet + + + quia + quare + grauior cordarum sonum + preaccipiat et + cur ex + cum cur ex + cum ex + cum + + extremis + + concursus + concursis + cum cursus + fiat in medium reddens grauem sonum non autem ex mediis.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse + quia + quod + quoniam + + + id + illud + + + quod + quod est + + graue magnum et forte diuque + perdurans preaccipit vigorem sui oppositi, talis siquidem est grauior cordarum ad alias, + etiam + et + in magno + continetur et + continetur + continuo et + continuo + + + occultatur + + + + parvuum, sicut in + superiori + siteriorum + siteriori + , taliter quod sonus duarum + + nitarum + + neten + notarum + ninctarum + assumptus est in sono vno + parypatem + + parametem + + + causato + + + . Ex quo habetur quod grauior cordarum + sonum preaccipit + preaccipit sonum + , + et quod + et + + + ex ultimis extremis + ex extremis ultimis + exultans extremis + + medium potest + + resultare + resultari + representare + , sicut apparebit + .23° + 22° + 12º + xxiii° doooo + + + in 12° + . + + et cetera + sequitur 13m. + problema 19e. particule. +

+
+ +
+ + Tertiumdecimum + problema + + + 13m + Tredecimum. + Tredecimum + problema + + +

+ PROPTER QUID IN DYAPASON + + PROPTER QUID IN DYAPASON ACUTI QUIDEM ANTIFONUM FIT GRAUE, HUIUS AUTEM ACUTUM + NON? + AUT QUIA MAXIME QUIDEM IN AMBOBUS EST AMBORUM + MELODIA? SI AUTEM NON, NON GRAUE, MAIUS ENIM EST + . + + Quare in proportione + illa + ista + + que dicitur dyapason vel proportio + dupla uel + totius, illud + tonus, illud + quod habet rationem acuti + + plerumque + plerumique + plurium + + + pertransit + + transit + in + grauem + graue + , + quod autem + quod autem hec + illud autem quod + + habet rationem grauis non permutatur in acutum?

+

+ Videndum + Videndum est + nunc + gratia eius + eius gratia + gratia huius + quod dicitur dyapason quot et que + sunt + sint + + proportiones + + musicales + musicale + musicales et + mussice + mutabiles + numeri + + + quomodo + penes quid + + + + sumantur + + , et + + quia originantur + quia organantur + dico quod originantur + ex proportionibus arismetricis + + intuendum prius illas. + + + + + + + Sunt autem secundum boecium in primis + arismetrice + + et musice + numeri + + + quinque + sumpte penes numerum inequalem. Quarum + tres sunt simplices + puta + + multiplex et submultiplex + multiplex submultiplex et + multiplex submultiplex + multiplex + , superparticularis et + + subsuperparticularis + + + , + superpartiens et + subsuperpartiens + + . Due autem composite quarum prima componitur ex multiplici et + + superparticulari + + superari + subsuperparticulari + + + + et ex + et + + + multiplici + supermultiplici + submultiplici + + + et subsuperparticulari + sup + et superparticulari + + + , + secunda ex + multiplici superparticulari + multiplici et superparticulari + multiplici superpartiente + multiplici similiter particulari + multiplicitati + et + submultiplici + submultiplici et + subsupermultipici et + + + subsuperparticulari + subsuperpartienti + subsuperpartiente + superparticulari + + + . + Boeth. + De inst. mus. + I.4 (Friedlein p. 191, ll. 6–10) + Boeth. + De inst. arith. + I.22 (Friedlein p. 46, ll. 6–17) +

+

Multiplex autem + est + est quando + + numerus maior minorem in se + continet + continens + pluries, vt + bis uel + bis + + ter aut + + quater + quater ter + quater uel multociens + + + et sic + aut + deinceps, vt + nichil + vel + desit + nichilque + + + exsuperet. + Huius + Hec + Huiusmodi + autem species sunt duplex + triplex + quadruplex et sic in infinitum. Duplex + quidem + + cum vnus numerus alium + vt vnus numerus alium + cum vnum numerum + bis continet que dicitur proportio dupla vt + quatuor ad duo. Triplex + cum vnus numerus continet + alium totum tribus + alium numerum tribus + alium tribus + alium numerum tribus totum + + + vicibus + modis + sicut + trinarius se + habet ad vnitatem + se habet trinarius ad vnitatem + + trinarius + + ad vnitatem se habet + .

+

Proportio autem + secunda + + value="2/1">dupla secundum + dupla + iuxta + aliam + alia + alium + inequalitatem, vt superparticularis cum eius + + opposita + oppositus + opponitur + opposatur + oporteat + , est cum maior numerus continet in se totum semel + + et + et adhuc + in + + vnam eius insuper partem, + vt aut + vt autem + vltra vt aut + + + dimidia + dimidiam + + + + vel + aut + + + + tertia + tertiam et + + ita deinceps. Cuius + + quidem + autem + + proportionis modi sunt sexquialtera, + + sexquitertia + sequitertia + sexquiquinta + sexquiquinta + uel epitrita + sexquiquinta uel + epitria + sexquinta uel epitrica + sexquiinta uel epitrita + sexquiinta uel epuctria + sexquitertia + , sexquiquarta et + huius + huiusmodi + . Sexquialtera + + seu emiola + + seu emialmlem + + seu enumerale + seu enucha + + + est cum quis numerus alium semel continet et insuper + + eius mediam partem + partem eius mediam + huius mediam partem + eius partem + , + vt + + ternarius + + se habet ad binarium + ternarius ad + binarium + se habet + tria se habent ad duo + . Sexquitertia + + cum + est qui + + semel et eius tertiam partem + + , vt + + quaternarius + quaternarium + quaternarius + adet + ternarius + ad ternarium + quatuor ad tria + sexquiquater + numerus ad quaternarium + 4 se habent + ad 3 + quaternarius + ad quaternarium + .

+

+ Superpartiens + + Superparticularis + + est + + quando + quoniam + quare + maior numerus continet minorem et insuper + + eius aliquas partes + aliquas eius partes + , vt + duas + 3as + 3es + + + tres et cetera. Cuius + species sunt + + species + + + superbipartiens + + ter bipartiens + superbipartiens et + subyparicus + subbipartiens et + + + supertripartiens + + triparties + + + + et cetera + et sic + + . + Superbipartiens + + + subipartiens + est cum numerus + continet numerum semel et eius + duas + partes, vt + quinarius ad ternarium se habet + quinare ad + ternare se habet + quinque ad + tria se habet + 5 ad 3 se habent + numerus + quinarius ad ternarium se habet + . + Supertripartiens + + Supertripartiens est + Superquiertiens + Superpartiens + Tripartiens + quando + semel continet + unus continet numerum semel + semel + + totum + + et + + + eius + + tres partes + tertiam + partem + , vt septem + + se habet ad + ad + + quatuor. Superquadripartiens + + et cetera, vt + etiam, sicut + + .ix. + + se habet ad .5 + + ad 5 se + habet + ad .5 + .

+

Compositarum vero multiplex superparticularis est + cum + + numerus + continet maior + maior continet + + + minorem + numerum minorem + minorem numerum + totum multotiens et insuper + aliquam + aliam + partem eius, vt medietatem uel tertiam + et + + huius + huiusmodi + . + Huius + Huiusmodi + autem + species sunt + sunt species + sunt + + + duplex + sexquialtera + + + + + duplex sexquin alta duplex sexquialtera + duplex sexquialtera + + sexquialtera + , + + duplex + sexquitertia + duplex + sexquitertia et + duplex + sexquialtera + , duplex sexquiquarta, et cetera, + + + + et + id ratione + id rationem + ideo ratione + rationem ratione + + + duplicitatis; + duplicis + ex parte + vero + + triplicitatis + triplicis + + + + + triplex sexquialtera, + + triplex sexquitertia + triplex + sexquitertia + duplex sexquitertia + triplex quitertia + + , + et cetera + triplex et cetera + triplex sexquiquarta + + + . Est + duplex sexquialtera + + quando + est quando + maior numerus + + continet minorem totum + minorem totum continet + minorem totum + minorem + minorem se totum + et insuper + eius partem mediam + partem eius mediam + eius medium + , vt + + .5. + quinarius + quinare + quinarium + + + se habet + se habent + + ad + .2 + binarium + binare + 3 + + 10 ad 4 + . + Duplex + sexquitertia + + Duplex + sexquialtera + 3a. + + + quando + est quando + quando ipsum + + continet totum et + ipsius + eius + + + tertiam + partem + partem 3am + , vt + septem se + habet + septem + ad .3. + Duplex sexquiquarta + et cetera + + Duplex + sexquiquarta + , + vt .ix. + + se habet ad + habet se ad + ad + quatuor. + Triplex + sexquialtera + Triplex + sexquitertia + + + + est quando + alter alterum continet totum + alter continet alterum totum ter + + + et + vt + + + adhuc + ad hoc + ad + + eius tertiam partem, + vt + decem + + quatuor + ad tria. + Triplex + sexquialtera + Triplex + sexquitertia + Quadruplex + sexquialtera + Triplex sexquiquarta + + quando + + + + quartam partem + continet + partem 4am. + continet + partem continet + continet + continet minorem numerum ter et 4am. partem + ultra totum, vt .13. ad quatuor.

+

Multiplex + superpartiens + est superpartiens + superparticularis + + + est cum + est quando + cum + maior numerus continet + minorem + minorem numerum + maiorem + plus quam semel uel multotiens et + + + pluries + plures + , cum hoc + ipsius + + partem + partes + + plures partes cum hoc ipsius + cum hoc plures eius partes + . Cuius etiam infinite sunt + species, vt + duplex superbipartiens, duplex supertripartiens, et cetera + duplex superpartiens, duplex supertripartiens, et cetera + duplex superpartiens, et desupertripartiens, + et cetera + duplex superpartiens, triplex + superpartiens, et cetera + duplex superpartiens et cetera, duplex + supertripartiens et cetera + duplex superpartiens, et cetera + duplex superparticularis + et + id + illud + + ratione + duplicitatis; ex parte + quidem + quidam + quid + vero + + triplicitatis erunt + + triplex + superbipartiens + triplex superpartiens + triplex subpartiens + triplex sibi partiens + , + triplex + supertripartiens + triplex superpartiens + + triplex superbipartiens triplex superbipartiens + , + et cetera + + . + Duplex + superbipartiens + + Duplex superpartiens + Duplex supertiens + est quando numerus maior continet minorem et insuper duas eius partes, vt octo + + se habet + habet se + se habent + + ad + triam + tria + tres + .3. uel .2 + . + Duplex + supertripartiens + + est quando + est + et cetera + , + vt xi. + + se habet + se habent + + ad + .3 + quatuor + . + Quadruplex + superbipartiens + + + Triplex + superbipartiens + Triplex + supertripartiens + + + est quando + quando + + + + et cetera, vt .15. + triplex + + + se habet + se habent + + ad quatuor. + Hee + + Hec + + + quidem + quidam + qua + sunt numerorum + inequalitates + inequales + ex quibus quinque resultant proportiones arismetrice cum suis oppositis antedictis.

+

Restat + quidem breuiter videre secundo + breuiter quidem videre secundo + quidem breuiter videtur secundo + breuiter 2° + videre + : + quot et que + que et quot + que et quot sunt + quod et que + + + ex hiis sint + sint ex hiis + ex hiis sunt + ex istis sint + ex hiis + + + consonantie siue simphonie + + consonantie + consonauere + musicales, et a + quibus + quibus proportionibus + + + sumantur + + summatur + sumuntur + + + arismetricis + arismetricum + . Secundum + quidem + quod + quid + + + macrobium et boecium ex + omni + numerorum + modorum + varietate pauci numeri + reperiuntur qui + conueniant sibi + conueniunt sibi + 9 aut 8 + ad consonantiam musicalem + constituendam + considerandam + custodiendam + . Sunt + autem + + + + hii + + hiis + + sex + omnes iuxta + quos + quas + quot + + + quinque + consonantie + consonantie quinque + constituuntur, et + + tonus + totus + totius + + ex quo + + constituunt + constituuntur + constituitur + + + dyatonum + + , scilicet + epitricus + + , + emiolus, duplaris, triplaris + + emi solus duplarum + triplarum + , + quadruplarus + + + quadruplum + quadruplaris quadriplum + , + epodous + + + epogdoii + epogdonium + .

+

+ Epitricus + + + + + + + vel + seu + et + + + sexquitertius + + + + sex quinitus + est + vt aliqualiter iam + unde iam aliqualiter + vel aliqualiter iam + + patuit cum maior numerus continet minorem totum et eius tertiam + partem, vt quatuor + + se habet ad + se ad + ad + + tria. Ex quo nascitur + + + simphonia + + uel consonantia + consonantia seu symphonia + simphonia consonantia + + + dyatesseron dicta id est + dicta dyatesseron id est + dyatesseron dicta + + per quatuor, que in + sexquitertia + proportione consistit + sexquitertia consistit proportione + sexquitertiam proportionem consistit + , vt cum una vox in grauitate + vel + seu + acuitate + + se habuerit ad aliam sicut + se habet ad aliam sicut + se habuerit ad ad aliam + sicut + ad aliam se habuerit scilicet + + quatuor ad tria + se + se hii· + sed hii + .

+

+ Iuxta vero + emiolam + + uel sexquialteram vt cum maior numerus + + + + minorem continet + continet minorem + minorem minorem continet + totum et + medietatem ipsius + ipsius medietatem + medietatem ipsi + medietatem + , + ceu se habet + ceu se habent + ceu + ceu se habet + vt + seu + + tria ad duo. Oritur consonantia dicta dyapente + uel + per + + + + quinque + + quandoque + quecunque + communionem + + + in quinto enim loco terminatur + in 5° + loco terminatur + in + monocordo + + + , sicut dyatesseron in + quatuor + quarta + quarto + 8o + + + ceu + + seu + + + cum + vt + + una + vox + + + se habuerit ad aliam in + grauitate et leuitate + et cetera.

+

Secundum + siquidem + quidem + 44. quidem + + duplarem numerum vel proportionem, vt quatuor + + se habet + se habent + + ad duo sumitur proportio dyapason siue per totum, terminat + enim et + et + enim uel + continet totum + + monacordum + + + et maxime primum, cadit enim super + octo + scilicet + 4 + incipiens + a gama greco + + a gama grece + in gama greco + agamo greco + agamatrico + .

+

+ Scilicet + .g. + + iuxta + vero triplarem + triplarem + vero + numerum + seu + siue + proportionem, vt cum numerus + se habet + se habeat + habeat se + + ad numerum + ceu + seu + sicut + vt + + tria + ad vnum, + componitur enim ex multiplici + et superparticulari + sicut se habet tria + ad vnum + sicut habet se tria ad unum + + , nascitur + simphonia + + + + composita + + vt + ex + + + dyapente dyapason + dyapente et dyapason + vt quando + vna + vnam + + vox excedit + alteram + aliam + et cetera. Iuxta vero numerum quadruplum, + cum + vt cum + est + vnus alium + quater + quadruplum + quadrupliciter + continet, vt quatuor + + se habet + se habent + + ad vnum oritur bis diapason.

+

+ Epogdous + + + + + + + Epogodus + est numerus qui + inter + intra + se minorem + concludit + conclaudit + claudit + continet + et insuper + octauam eius + partem + eius octauam + partem + + 8 eius partem + octauam + scilicet eius partem + , + ceu + seu + se + sicut + + nouem + + se habet + se habent + + ad octo. Ex + hoc quidem + numero + numerus + + + sonus + consurgit + + quem + quam + quomodo + musici + tonum vocant + vocant tonum + tonum vocarunt + tonum vocauerunt + tonum vocarent + tonum + , + qui + autem + + tono minus + + tono unus minus + + + + semitonum + + + + + dicitur + + , quod + non + non est + + + extimandum + existimandum + ex vtis + tonum + vere fore + fere fore + fore fere + sicut neque semiuocalem in + litteris + + . Non enim tonus naturaliter in duo + equalia + potest diuidi, cum + + constet + constat + constans + stet + ex numero + + nouenario + + + nouenarum + nouem + , + quod + + qui + + in duo + + diuidi minime potest equaliter + diuidi minime potest + diuidi minime equaliter potest + equalia diuidi minime potest + . + Vnde et + Vnde + Et + Et ideo + Vt + + + semitonium vocarunt + + vocauerunt semitonum + + sonum + tono + + tonum + minorem. Est autem + semitonum + + duplex + maius scilicet + scilicet maius + maius + et minus. + Maius videm dicitur apothomi + + + Minus quidem dicitur apothemi + amplius quidem dicitur + apothemi + Maius quidem dicitur + + apud vero + boecium + decisio, minus + autem + + dyesis + + + uel + limes + + + + lineis + , + quod + quid + qui + tam + paruo + paruum + distare a + tono + + toto + + deprehensum est quantum hii + duo + numeri distant: vt + + .243. + 242 + 283 + .343. + 2. + 43. + 12. 143. + + + et 256 + 256. + 2256 + . Quorum quidem + vnusquisque + + quisque + + + constat + constant + constituit + + ex duabus + vocibus + + puta + + prout + + vt mi, + est et + est etiam + + + ditonus + + + + + + , + qui + + ex duobus consurgit perfectis tonis + ex duo consurgit perfectus tonus + consurgens ex duobus tonis perfectis + ex duobus perfectis consurgit sonis + , et + + semidytonus + + semiditonis + semitonus + qui ex duobus non + integris + integer + + + . Vt + id autem + id + id aut + autem hec + per amplius + appareat + appareant + apparent + + + parigraphia + + + + + + + conscribatur + scribatur + + + ista + ista videlicet + ista in ista tolitua + talis + . + + + Γ. + 1296. + vt. + + + + + + + + + + a. + 1152. + re. + + + + b. + 1034. + mi. + dytonus. + + + c. + 972. + faut. + dyatesseron. + + + + d. + 864. + solre. + dyapente. + + + + e. + 768. + lami. + + + + f. + 739. + faut. + + + + + g. + 648. + solreut. + dyapason. + + + a. + 576. + lamire. + + + + + b. + 554. + mi. + + + + b. + 512. + fa. + + + + + c. + 486. + solfaut. + dyatesseron + dyapason. + + + d. + 432. + lasolre. + dyapente dyapason. + + + + e. + 384. + lami. + + + + f. + 366. + faut. + + + + g. + 324. + solreut. + bis dyapason. + + + + a. + 288. + lamire. + + + + b. + 277. + mi. + + + + b. + 256. + fa. + + + + c. + 243. + solfa. + + + + d. + 216. + lasol. + + + + + + + + +
+ + Pz's scribe writes two tables: one with columns one + and two (note letters and string lengths), and then a second with column three + (note names). Column four (interval sizes) is omitted. Pu's scribe writes the + interval names orthogonal to the rest of the table and does not indicate the notes + to which they apply. I have therefore omitted the names. (Vc does the + same.) + +

+ +

Sunt itaque consonantie quinque + + scilicet + + : dyatesseron, dyapente, dyapason, + dyapente dyapason, et + dyapente dyapason + dyatesseron et + et + + + bis dyapason. + Que quidem + Qui quidem + Siquidem + + + hiis + hii + + tonis et + + semitonis + + + + constituuntur, + dyatesseron + diatonici + dyatri + enim constat ex + duobus + tonis + et + + semitono + + + + + + + + non + + integro, dyapente tribus tonis et minore + semitono + + + + , + dyapason + + dyapason ex + + quinque + tonis et + semitonis duobus + minoribus + + duobus + semitonis minoribus + semitoniis duobus + , neque + + peruenit + per peruenit + prouenit + prout + ad .vi. + tonos perfecte. Ex quibus apparet quod dyatesseron et + dyapente + diapentesseron + diapentesseran + + consurgunt in + dyapason + diapasseron + + . + Dyapente dyapason + Dyapente dyapason que + Et in pentadyasson + ex .ix. + tonis + + et ex + ex + et + + + semitono + + semitonis + minori constat, + bis vero dyapason + + sed ipsa bis dyapason + ex .12. + perficitur tonis. + Et hec + Et huiusmodi + + + + + quidem + + + amplius sunt in + amplius sunt exposita in + + + + <app> + <lem wit="#Py #Vb #m #v">conciliatoris mei</lem> + + <rdg wit="#λ" ana="#lexical">conciliatoris nostri</rdg> + <rdg wit="#Ea" ana="#lexical">conciliatoris unde</rdg> + <rdg wit="#Px" ana="#subtractive">mei</rdg> + <rdg wit="#π" ana="#subtractive #J">conciliatoris</rdg> + </app> + + differentia .83a. + differentiis 93. + differentia sed + + + exposita. + + Pietro d'Abano + Concil. diff. 83 +

+

+ Nosce + Notandum + + quoque + + + ex musice + quinto + ex quinto + musice + + quod + ptholomeus + + + + thonus + + + sextam hiis + addit + sextam hiis addidit + sexta + hiis addidit + addidit + sextam + consonantiam compositam ex + dyatesseron et dyapason + dyatesseron dyapason + dyatesseron + , que constat ex + multiplici + multiplici et + + + superpartiente + superpartienti + superparticulare + superparticulari + superpartem + + + qua proportione + quam proportionem + secundum quam proportionem + in qua proportione + de qua proportione + + + se habet + se habent + habet se + habet + + octo ad .3.. Continet enim octo bis tria, propter + multiplicem proportionem ex qua + visum + visum est + consurgere dyapason, et duas + + eius partes + partes eius + eius partes eius + quod est tertia scilicet + duo + secundo + 32. + propter superpartientem + + a + ex + qua nascitur dyatesseron. + Boeth. + De inst. mus. + V.8–9 + + Communiter + tamen + + pictagorici + + + + musice + + + + institutores + + instructores + inpositores + + posuerunt omnes + proportiones + consonantias + musicales consurgere ex multiplici et superparticulari, nullamque ex + superpartiente + superpartienti + superparticulari + , quod videtur aristoteles sentire + xli + xiº + 4° + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse + quoniam in + quia in + + + ambobus scilicet + in + + graui et acuto + scilicet graui et acuto ambobus + + est melodia vtrorumque, vnum enim + alteri + altero + alter + alterius + + + coniunctum + + constitum + consitum + + melodiam + + reddit, quia graue et acutum sunt dissimilia + fieri ex dissimilibus + . + + + Et + + + + + thimoteus + + + + ethymous + thymolis + entimomus + recte: timaeus, methinks + + + quidem + qui + + + + extimauit + existimauit + musice primo melodiam uel consonantiam + fieri ex dissimilibus, non autem ex + similibus + consimilibus + + + . Si autem proueniat vtrorunque in vtrisque + concordia + concordiam + + non fit melodia, cum autem sic fuerit + + quod + quod quod + quia + graue + maius sit + sit maius + maius fuerit + maius fit + acuto et fortius, tunc quod est acutum + + assumit + + rationem grauis, ita quod acutum sentitur + sumit + + graue, + vt + nisi + enim + + cum + due + + + + + nite + + + concurrunt in + ypatem + + + . Dicitur autem melodia a melle, quoniam est consonantia + delectabilissima + + valde ex acuto + et graui + grauique + et graui est + + debite composita. + + et cetera. + sequitur 14m. + problema 19e. particule. + +

+
+ +
+ + Quartumdecimum + problema + + 13m. + problema. + 14m + QuartumdecimumQuartumdecimum. + + +

+ PROPTER QUID LATET DYAPASON + PROPTER QUID DYAPASON + + PROPTER QUID LATET DYAPASON ET UIDETUR UNIUS SONI ESSE, UT IN FINIKIO ET + IN HOMINE? QUE ENIM IN ACUTIS EXISTUNT NON UNIUS SONI, SED PROPORTIONALITER AD + INUICEM DYAPASON. + AUT QUIA SICUT IPSE ESSE UIDETUR SONUS PROPTER + ANALOGUM, EQUALITAS IN SONIS, EQUALE AUTEM UNIUS? HOC AUTEM IDEM IN FISTULIS + DECIPIUNTUR + . + + Quare dyapason cum sit proportio satis distans + quoniam dupla + quoniam duplo + quamdaperla + latet + in tantum + iterum + + quod videtur sonus ex ipsa + resultatus + resultatis + resultans + esse vnus et quasi vnum tonum simpliciter habere? Et hoc declarat sicut apparet + et cetera + eidem + + . Communiter + quidem + quid + + + + inuenitur littera + + littera inuenitur + inuenitur + + + in finitis + infinitatis + in infinitis + , + alia infantis + aliam infantis + alias infantis + alia infinitis + et alia infantis + + + + aliter finikio + aliter finibrio + alia finikio + + , sed forte debet + dicere in fidibus + dici in fidibus + habere in fidibus + esse in fidibus + infidibus + seu cordis. Et in homine similiter + + declarat + declaratur + ita quod + + per hoc + hoc + + + + tangat + tangit + duplicem melodiam + tactu + tacta + tactam + uel pulsu factam et + voce + note + . Soni siquidem + existentes + acuti quia non concurrunt adeo in vnum, non sunt + unius + vinus + minus + soni vt graues aut + sic + sunt + + compositi ex grauibus sed + in dyapason. Hoc accidit quoniam toni se habent proportionaliter ad inuicem ex graui + et + ex + acuto, + + est enim optima consonantiarum + + .35 + .xxv° + + tria + trium + 3. + ad + + quinto + + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse + quare + quia + quoniam + sonus apparet vnicus esse propter + anologiam + + et proportionem sonorum ad inuicem in dyapason, ex qua resultat equalitas + grandis in sonis. Quod autem equalitatem habet + + vnius + unus + + + soni existit + existit soni + , et non solum + hoc accidit + accidit hoc + accidit + in + sono voce facto + voce facto + sono uel voce + + aut pulsu, sed + etiam + + + in sono + flatu facto, + vel + vt + + in fistulis. In illis enim decipiuntur etiam vt in + + vocis sono + + voce sono + sonis + , propter + debitam enim tonorum + debitam enim sonorum + enim debitam tonorum + + consonantiam accidit plures tonos non discerni sed vnum apparere cum + diuersitates + + illic non extent + + illic non extant + illic quod extent + illic non existant + + + sensibiles + consimiles + + , + ceu + seu + videmus + ex + in + saporibus + composita ex + compositis ex + composita + conposita + diuersis in quibus vnus consurgit delectabilis et nullius excessus, + vt + vt qui + vt quod + + conficitur + decoctione + ex + + cucurbitis + + + + + cucurbite + , + cepis + sepis + , uel + alleis + + aliis + , cum + tamen vnum sit saporis insipidi et + alterum + alter + + acuti. + + et cetera + sequitur 15m. + probleme 19e. particule. +

+
+ +
+ + Quintumdecimum + problema + + 15m + Quintumdecimum. + Quintumdecimum + 14m. + problema: + + +

+ PROPTER QUID LEGES + + PROPTER QUID LEGES QUIDEM NON IN CONUERSIONIBUS FACIEBANT, ALII UERO + CANTUS CHORICI? + AUT QUIA LEGES QUIDEM AGONIZANTIUM FUERUNT? QUIBUS + UTIQUE MUTARI POTENTIBUS ET DISTENDI, CANTUS FIEBAT LONGUS ET MULTIFORMIS. + QUEMADMODUM IGITUR ET UERBA, ET CANTUS MUTATIONEM SEQUEBANTUR, SEMPER ALTERA + FACTA. + MAGIS ENIM CANTU NECESSE IMITARI QUAM UERBIS. + PROPTER QUOD ET DITIRAMBI, QUONIAM AUTEM IMITATIUI, FIEBANT. NON ADHUC HABENT + CONUERSIUOS, PRIUS AUTEM HABEBANT. CAUSA AUTEM QUONIAM ANTIQUITUS LIBERI + ROTABANT IPSI, MULTOS IGITUR AGONISTICE CANTARE DIFFICILE ERAT, QUARE IN + ARMONIA CANTUM DELECTABILITER. MUTARE ENIM MULTIS MUTATIONIBUS UNO FACILE QUAM + MULTIS ET AGONISTE ID EST CONSUETUDINEM SERUANT. PROPTER QUOD SIMPLICIORES + FACIEBANT SIBI MELODIAS. CONUERSIUUS AUTEM SIMPLEX, NUMERUS ENIM EST ET UNO + MENSURATUR. + EADEM AUTEM EST CAUSA ET PROPTER QUOD QUE QUIDEM A + SCENA NON CONUERSIUA, CHORI ENIM CONUERSIUA. QUI ENIM CANTAT IN SCENA AGONISTA ET MUTATOR, CHORUS + AUTEM MINUS MUTATUR + . + + Quare + antiquitus cantatores + constituerunt + quosdam cantus dictos leges non habentes conuersiones, sed alii cantus + + chorici + choris + conci corici + + et conuersiui + + fuere + fuerunt + finem + fide + + fuere chorici et conuersiui + ? Nosce quod per leges non in conuersionibus factas audio cantus simplices + + expansos + + expansus + in quibus + potius fit + fit potius + fit + + + commutatio + comitatio + connumeratio + uerborum quam cantus, ita quod in eis non constituantur + + circuli + circula + + conuersiui, sicut est cantus alicuius insignis + gesti + egesti + testi + . + + Choricos + Per choricos + autem cantus intelligo + + conuersiuos + conuersiuos cantus + versiuos + primis vtcunque + + oppositos + oppositis + , vt apparebit in causa. Est autem chorus + curator inoperabilis, beniuolentia enim + solum prebet + prebet solum + solus prebet + quibus adest + .xlviii. + + +

+

+ + Deinde. + + + AUT. + AUT QUIA. + CHORICOS. + Soluit et primo assignat causam quesiti. Secundo + ex hac infert + causam + causam etiam + + + cuiusdam + + + + alterius + altius alterius + alterius perfectis + + + cantus + secunda EADEM + AUTEM + ibi secunda EADEM AUTEM + secunda in EADEM AUTEM + secunda eadem + EADEM + . + Etiam + Et + + primo respondet ad primam partem dicens + + + causam esse quoniam leges fuerunt cantus constituti ab agonizantibus et bellatoribus, + ceu + seu + sicut + sunt cantus gestorum + + insignium + insignum + . Quas + quidem + quam + leges vt possent consequi recitando quod in eis continebatur + distendebant + diffe distendebant + descendebant + discebant + cantando, + nunquam + + inde quam + + faciendo conuersionem uel circulationem ad id + unde + + inceperant + inceperunt + ceperant + + + reddeuntes + redeuntes + . Propter quod + eorum + + cantus + fiebat + fiebant + longus et multarum manerierum, + secundum uerborum + prelatorum + prolatorum + prolapsorum + + diuersitatem. Nam secundum quod uerba gestorum + fiebant continue + + + altera + alta + alto + uel melius + + altera et diuersa mutatione similiter. + Et + + in cantu similem obseruabant mutationem, + vt + vt ad + et + + commutationem uerborum cantus + + comitaretur + + + cum comitaretur + comodaceretur + commutaretur + + + mutatio + imitatio + commutatio + , ad uerba enim amplius quam ad cantum attendebant. Propter quod + dicte sunt + dicta sunt + leges + cantus huius + cantus huiusmodi + cantus + + + a + + ad + legendo, + velut + vt + ultra + illud + visum + videret + in lectionibus et proprie + + diuinis + in diuinis + , vt apparebit + .xlviii. + .44. + .42. + , vna + + dictio + dicto + post aliam profertur non multum vocem + diuersificando + + diuersimode + .

+

+ + Deinde. + + + MAGIS + ENIM + EST + + . + + Tangit + + Tangit enim + Tanquam + causam + alterius + plures alterius + plus alterius + + partis, dicens quod in cantu + armonico + armonizato + + + sufficienter + sufficientis + non debet + + per oppositum accidere + per appositum accidere + per oppositum + hoc accidere per oppositum + , nam in eo quod dictum + + est + + , + in legibus + legibus + in lectionibus + amplius + oportet + + + + + imitari + + immutari + + cantum reddendo ipsum melodiosum quam uerba, cum cantus + sit magis + magis sit + fit magis + finis musici actus uerbis, ampliorem inducens delectationem, propter quod + dictum + dictum est + + 10°. quod vox delectabilis + est cantantis + cantantis est + est cantus + sine + sermone + sermonem + prouisione + + + etiam. Et + et cetera. Et + etiam. Et etiam + + + + + ideo quidam modi + cantandi dicti + ditirambi + + + + + + dicti dichitambi cantando + cantandi dictirambi + dicti Tytira ubi + + + + + fiunt + fuerunt + , cum quis + magis cantum imitatur + cantum ymitatur magis + magis imitatur cantu + cantum magis imitatur + magis cantus ymitantur + magis cantum immutatur + magis cantum mutatur + uerbis. Est autem + ditirambus + + + + + + + + dichitambis + ditrambis + dytiranbum + cantus qui concidit in + frigistum + + fixgistum + , unde + + + + 8° + politicorum + + scilicet politicum + + polliticorum + .8. + + + filoxenus + + + philoseus + filoserius + phylosherius + phiis + conatus in + dorista + corista + corialtera + facere + ditirambum + + + + + + + + + + dichitambis + distanbu + + + fabulas + fabulans + non fuit potens, sed ab + ipsa + ipso + illa + + natura decidit in + frigistum. + + + + Arist. + Pol. + VIII, + 1342b, + l. 9 + Hec autem .xlviii. + + erunt + fiunt + + manifesta adhuc. Siquidem + rediens + + rediens ad + leges + inquit + in quid + + quia + cantus huius dicti + cantus huiusmodi dicti + + + + leges fiebant vt dictum continue + vt dictum est leges fiebant continue + leges fiebant vt dictum est continue + faciendo + per mutationem + mutationem + . Secundum uerba ideo non sunt amplius conuersiui, sed + tamen + cum + antiquitus fuerunt. Cuius quidem + + causa + causa est + quoniam ab antiquo ipsimet liberi + nobilesque + + nobiles qui + nobiles + ignobilesque + faciebant cantus + + rotationes + rotatos + rotatiuos + recitatiuos + uel conuersiuos + + quoniam + quantum + quam + plures erant, et ideo difficile fiebat + eis + + eos + cantare agonistice uel + leges + legem + legere + facere. + + Choros + + Coram + autem faciebant siue cantus conuersiuos qui fiunt in choris, ubi sufficientes et quieti amplius + imitari conantur + + + + volunt imitari + melodiam quam + verba + verbo + . Propter + quod + + delectabile + cantare secundum armoniam + est cantare secundum armoniam + est secundum armoniam cantare + illam + commutatam + commutatiuam + commutationem + continentem + commitationem + connitatiuam + ubi pauci conueniebant. Nam + hii de facili + de facili hii + hii qui de facili + possunt mutare cantum pluribus + + mutationibus + mutatoribus + , + et id est quod dicitur: quod vni mutare cantum pluribus + mutationibus + + + facilius est quam + multis + multus + paucis + , quare agoniste cantantes uel leges consuetudinem + huius + huiusmodi + vt tactum + est + + + obseruant. + + Qui + Quod + Que + Sed + + + mutatione + mutationem + imitatione + + verborum + mutantur + imitantur + immutantur + , et ideo melodias valde simplices faciebant et + incompositas + compositas + , quoniam conuersiuus cantus quo vtebantur est numerus + quidem + quidam + + simplex, qui + vnitate + vnitatem + in unitate + musice + + tantum + mensurabatur + mensurabitur + mensurabilis est + mensurabis + + + , ita quod conuersio si + aliqua + alia + + erat ibi potius in simplicem + quam in + + compositum + compositam + compotum + , + referebatur + + , vt in numeris + dicimus + dicto + diuinis + illum numerum simplicem + + qui continue + + crescit + + mensuratus per vnitatem. Similiter et cantus potest + simplex dici + dici simplex + simpliciter dici + duplex dici + + + qui + que + + + contineatur + continetur + continuatur + + + per additionem solam + solum per additionem + per additionem soli + uerbi ad + ista + istam + verba + .

+

+ + Deinde. + + + EADEM. + EANDEM. + + Applicat + + istam + illam + causam + ad quesitum adhuc + ad quesitum ad hoc + ad quesitum aliud huic + , simile dicens quod + ista + illa + ita + eadem + causa est + est causa + causa + , + quia + quare + + + illi + ille + isti + iste + + cantus qui + a scena + scena + ascene + dicuntur non sunt conuersiui, chori + autem + aut + + + conuertuntur + + , quoniam + + ille + illi + qui + cantat + cantant + a scena est sicut + + agonistice + agonista + agoniste + + cantans + aut + + leges + legens + , + cantat enim + agonizantium + + + + + gesta + commutans + cantum secundum uerba vt + + agoniste + agonistice + agonistici + + + ceu + + + + + visum est + visum + + , una enim dictio indiget + aspiratione + inspiratione + expiratione + apparatione + , + alia vero + altera vero + alia + lenitate et + huius + huiusmodi + + consimili alteratione.

+

Sed + choricus + + cantus + minus + vnus + + + commutatur + + commutatus + alteratur commutatur + commitatur + , amplius enim vnum tenorem et circulum retinet + conseruatum + reseruatum + . + Notandum + Nota + quod a scena multas habet significationes, aliquando + namque + enim + + + idem est + idem + eadem est + ratione est + quod + umbra + nichilominus + inquimus + uel locus umbratus + et + vel + + + coopertus + + in + teatro + + intratio + + + dicitur + diuiditur + , + interdum + etiam interdum + in circulum + + totum + + teatrum + + tractum + , et + quandoque + quando + quoniam + recitatio operationis. + Vnde olim poete libros suos deferebant a scene vt + appropriarentur + approbarentur + apropinquiuarentur + + + . Dicitur + etiam + et + enim + tabernaculum + mercenariorum + + mercendariorum + + + coopertum + + + + asseribus + aceribus + . Hic autem + per + pro + + + ascena + + ascene + potest intelligi: locus + ubi colliguntur + in quo congregantur + homines vt gesta + librorum + liberorum + + + cantare audiant et + insignium + + + + et insignium cantare audiant + cantare audiatur et insignium + cantare audiante insignum + . + Et id etiam + .xxix. + 30º + + + et .xlviii. + et 38º + 28 + + + apparebit + patet + + + + . + + et cetera + sequitur 16. + problema 19e. particule. +

+
+ +
+ + Sextumdecimum + problema + + 16m + xvim.Sextumdecimum. + 15tum + problema. + + +

+ PROPTER QUID DELECTABILIUS + + PROPTER QUID DELECTABILIUS ANTIFONUM CONSONO? + AUT QUIA MAGIS MANIFESTUM FIT CONSONARE? + AUT QUANDO AD CONSONANTIAM CANTANT, NECESSE ENIM + ALTERAM CONSONARE? QUARE DUE AD UNAM + UOCEM FACTE DESTRUUNT ALTERAM + . + + Quare cantus antiphonus in quo + quedam extat resonantia + quedam restat consonantia + + vel + contra + circa + etiam + + + consonantiam + sonantia + consonantia uel etiam consonantia + + + tonorum + tenorum + super + tonos + tonis + chanos + cantus + est + delectabilior + delectabilis magis + + auditu quam sonus + qui est consonus + qui est sonus + + et vniformis in quo non sentitur + contra + circa + aliqua + + + resonantia + resonantiam + sonantia + . + + Apparentur + Apparent + Apparatur + + + + verbi gratia + + vt gratia + + + sicut si + duo + + succinant + + + subcinat + equaliter et tertius + precinat + + hic + hoc + + precinens + + contrasonat + consonat + et + antiphonizat + + + + + super illos + si super illos + super istos + gratia istos + contra illos + + + duos + duos + et cetera + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit + + + + + assignans + assignando + et assignat + + + duplicem causam + duas + causas + , dicens + id + illud + ideo + esse quoniam sonus + antiphonus + + + redditur manifestior et sensibilior sono consonante et vniformi. + Quod autem + sensibilius est sufficienter + scensibilius suficienter est + est sensibilius sufficienter + magis delectat, eo quod non est tale sicut apparet in tactu relatione aliorum sensuum.

+

+ + Deinde. + + + AUT QUANDO. + AUT QUESITI. + AUT QUIA. + AUT. + Assignat aliam causam, dicens quod quando + aliqui cantant + consonantiam facientes in qua + acutum non + excedat + excedit + graue aut econuerso, + necesse + tunc necesse + necessarium + est quod vox + vnius + unius vox + huius + + consonet omnino voci alterius, + + sed debet + si debet + sicut dicere + fieri consonantia. Si autem tertia + adueniens non + antiphonet + antiphonat + autem antiphonet + antiphanizet + , + ymmo + + + + sermo + + + consonizare + + consonare + uelit, oportet eam destrui, + quoniam + due voces + + equalis vigoris + vigoris equalis + equales vigoris + ad tertiam + + relate + relate et + + ad tertiam relate + equalis vigoris + + + destruunt + destruuntur + destruant + et occultant + + aliam + alteram + + penitus tertiam.

+

+ + Notandum + Notandum quod + + Nota + secundum + boecium + primo + musice + + + quod + + + consonantia est acuti soni grauisque + + mixtura + + mixtatio + suauiter + vniformiterque + et uniformiterque + et uniformiter quod + et vniformiter + auribus + accidens + accedens + . Sed dissonantia est duorum sonorum + sibimet + impermixtorum + + + ad + aurem + aures + + veniens aspera + atque + et + vtcunque + + iniocunda + percussio. Nam dum sibimet + + misceri + miseri + permisceri + conmisceri + + volunt et quodammodo + integri + integer + integra + + + vterque nititur + vtraque nititur + nititur vterque + peruenire, + cunque alter + cum alter + equaliter + alteri + officit + + efficit + ad sensum insuauiter, vterque + + transmittitur + + transmicteri + . + Boeth. + De inst. mus. + I.8 (Freidlein 195, ll. 6–13) + Videtur siquidem quantum facit ad sermonem + aristoteles quod antiphonus sit delectabilior ex contrariis valde distantibus consurgens vt ex ypate et + nete + + nete vel nite + , + consonans + consonant + consonatus + + autem + + quando + quoniam + + + + ex non adeo + non ex adeo + non ex ita + non adeo + + differentibus, sicut ex cordis + mediis + melodiis + , vt apparebit consequenter. + + et cetera. + sequitur 17; + problema 19e. particule. +

+
+ +
+ + Decimumseptimum + problema + 17m + decimum septimumDecimumseptimum. + 16tum. + Problema. + + +

+ PROPTER QUID QUINQUE + PROPTER QUID QUANDOQUE + + PROPTER QUID QUINQUE NON CANTANT ANTIFONAM? + AUT QUIA NON EADEM CONSONA CONSONANTIE, + QUEMADMODUM IN DYAPASON? ILLA ENIM IN GRAUI PROPORTIONALE, SICUT ACUTA + IN ACUTO, QUEMADMODUM IGITUR + EADEM EST SIMUL ET ALIA. QUE AUTEM IN DYAPENTE ET DYATESSERON NON HABENT, ITA + QUARE NON APPARET QUANDO ANTIFONE SONUS, NON ENIM EST IDEM + . + + Quare + quinque cantantes, uel + etiam + et + + + quatuor, + vnam non + vna non + non unam + cantant + antiphonam + antiphona + anphpuam + , + tres + + autem uel + aut + + sex possunt cantare?

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse quoniam + ipsa + ista + proportio + que + quam + + + habet + habent + + quinque ad inuicem non est + + proportio + concordia + debita que + consonet + consonat + conicet + et correspondeat tali consonantie in qua sit + + antiphonizare, + quemadmodum + + + + + + antiphonizare contingit + + contingit + + in dyapason, ubi est + proportio + dupla. Ipsa enim + habet proportionem + proportionem habet + habet proportiones + + + in graui + magnam + , graue enim proportionatum est graui in ipsa, sicut acutum acuto + et graue cum acuto + et + + + + etiam + + . Hoc autem non est in aliis. + Ymmo + + + + + + sicut + in sicut + sicut in + ipsa est eadem inter se et + proportionalis + + proportionaliter + vno modo ita, secundum alium modum habet + + quandam alietatem et + + alietatem et + + diuersitatem inter se, eo quod in ipsa est excessus + manifestus + + , etsi sit ad equalitatem reductus. Sed consonantie uel proportiones que sunt circa dyatesseron uel dyapente non sic + se habent + habent + se habet + . neque + enim + + in hiis + hiis + in eis + + + tantus + cantus + + est excessus, neque ad equalitatem + sit + sic + reductus. Et ideo sonus licet fiat antiphonus, secundum + istas + illas + + + duas + + proportiones non redditur manifestus. Non enim + est in ipso + + idemptitas + + + + cum quodam excessu sicut dictum est in dyapason euenire. Id autem + potest declarari + ex naturis, quia si debet cantari antiphona, oportet debitam proportionem + interuenire + ante venire + + + superantium ad superatos + sirantium ad frantos + et econtra secundum + graue et acutum. Sed id non accidit in quinque vocibus, + nam vel + quatuor + + antiphonizabunt vno + + antiphonizabunt + aut + tres + tribus + vel + + duobus + + , + non quidem + non quid + nunc quid + numquam + + quatuor + contra + vnum, quia vox eius oppositis + obtunderetur + obtundentur + obtundetur + omnino, ita + vt + quod + + + non + + possit + possint + sufficienter percipi. Neque tres contra duos, quoniam + propter + + paruum + + + partium paruum + excessum non poterit excedentia + manifestari vnius ad alterum, quare + non contraphonizare contingit + + + + contingit non contraphonizare + non contraphonizare + non contrasonizare contingit + non antiphonizare contingit + + + + cum id + cum illud + requiratur omnifariam + + + moueri + . Vnde relinquitur + + quod antiphonizare, vt apparebit + vt apparebit quod antiphonizare + quod antiphonizare + vt apparebit + + + + extet + existet + secundum dyapason proprie. + + et cetera + et cetera et cetera + sequitur 18; + problema 19e. particule. +

+
+ +
+ + Decimumoctauum + problema + 18m + Decimumoctauum. + decimum + octauum. + 17m. + Problema + + +

+ PROPTER QUID DYAPASON + + PROPTER QUID DYAPASON CONSONANTIA CANTATUR SOLA? ORGANIZANT ENIM SECUNDUM HANC, ALIAM NULLAM. + AUT QUIA SOLA EX ANTIPHONIS EST CORDIS, IN + ANTIPHONIS AUTEM ET ALTERAM SI CANTAT, IDEM FACIT. UNA ENIM QUODAMMODO + UTRORUNQUE HABET CORDAS, QUARE ET UNA CANTATA IN HAC CONSONANTIA CANTATUR + SYMPHONIA ET AMBO CANTANTES. + AUT HAC QUIDEM CANTATA. HAC UERO FISTULATA, + QUEMADMODUM UNAM UTRANQUE CANTANT. PROPTER QUOD SOLA CANTATUR, QUIA UNAM + HABENT CORDE UOCEM ANTIPHONAM + . + + + Quare + Quare cum + Querit quare + dyapason sola consonantiarum + cantatur maxime + maxime cantatur + cantanti maxime + maxime + + + consonans + sonans + consonantiarum + inter ceteras? Quod ostenditur + + quia + quoniam + secundum + ipsam + ipsas + cantantes + organizant + + + + voces + vocem + in altum + + leuantes + eleuantes + , + quod secundum + quia secundum + + + + nullam + nullam vero + nullum + ullam + aliarum + ita + sic + + + manifeste agere contingit.

+

+ + Deinde. + + + AUT + AUT QUIA + . Soluit dicens + + causam esse primam + primam causam esse + causam esse + causam esse primo + causam esse propriam + + quoniam ipsa sola constituitur ex cordis antiphonis seu consonantibus vt + graui acuto + per + propter + + proportionem duplam. + In antiphonis enim cordis ita se habet + + + + quod si altera + cantetur + cantetur simul + + + + + + siue + tangatur + tangetur + tangitur + , vt + media in quam + medio in qua + ambe + declinant + declinent + determinant + extreme vt apparebit, + idem fit + idem sit + iterum ad idem + , + + + + ac si + + ambe cantarentur + cantarentur ambe + ambe cantantur + ambe cantarent + ambo cantarentur + , + eo + ita + et + quod + illa + illam + ipsa + + vna + + habet + in se aliqualiter + aliqualiter in se + in se aliquam + + + vt in virtute + vt in unitate + vt virtute + virtute + + cordas vtrorumque sonorum puta grauis et acuti, quare accidit + in + et + ex + + + huius + huiusmodi + + consonantia quod vna cantata uel + pulsata cantetur et altera, ac si ambe + cantarentur, propter conuenientiam quam + habent + habet + in medio, + ceu ostendunt + ceu ostenduntur + seu ostendunt + sicut ostendunt + + pigmenta + ex diuersis optime constructa in saporem consurgentia + + delectamentum + delectatiuum + delectantium + delectatium + .

+

+ + Deinde. + + + AUT + AUT QUIA + QUOD + . + + Assignat aliam causam dicens + assignat aliam causam dicens causam + soluit dicens causam + + + ideo esse + esse ideo + id esse + esse + + + quia + quoniam + si vna cordarum cantetur vt ypate et altera fistuletur vt + nete + + nete tunc + vite + cantando et fistulando vtrobique cantatur + vna quia media + quia media + + . + Et ideo sola + symphonia + + cantatur + + , + quoniam + et propter hoc + corde + cantate + cantante + cantato + seu fistulate vnam habent vocem scilicet + antiphonam + + amptiipheniam + , de quo + planius + plenius + amplius + apparebit .19. + et .20. Omnia + enim hec + hec + enim hinc + + + problemata + problema + + + + concidunt, super eodem enim + fundantur + + fundatur + medio + concidunt + . Sic + ergo + igitur + + + ille + iste + + due + + solutiones + questiones + + ⳋones + communiones + + + + magis differunt + differunt magis + ratione modi quam rei, cum vna sit vocalis et + + altera vocalis et + alia + + instrumentalis. + + et cetera + sequitur 19; + problema 19e. particule. +

+
+ +
+ + Decimumnonum problema + 19m + decimum nonum.Decimumnonum. + 18m + problema. + + +

+ PROPTER QUID ANTIPHONIS + + PROPTER QUID ANTIPHONIS HOC SOLIS INEST? + AUT QUIA SOLE EQUALITER DISTANT MEDIO? MEDIETAS + IGITUR SIMILITUDINEM QUANDAM FACIT SONORUM. ET UIDETUR AUDITUS DICERE QUOD + IPSA ET QUOD UTREQUE ULTIME + . + + Consequenter querit + causam causae + causam + precedentis problematis, dicens quare in antiphonis cordis inest quod vna cantata + cantetur et altera + cantatur altera + , et quod idem + consonat + consonet + sonat + esse sonat + vtrobique + sicut si ambo + + cantarent + cantarentur + + + ?

+

+ + Deinde. + + + AUT. + AUT QUIA. + QUIA. + + Soluit dicens causam esse quia sole + huius + huiusmodi + cordarum antiphone in quibus + existit + estit + consistit + dyapason equaliter distant a + media corda, vt dicatur a mese + que + quod + est + vere + nete + media + vii. + enim + + + cordarum + corde + , vt visum + est + + . Illud + autem + aut + quod est medium conficit quandam + + similitudinem + similem + consonantiam + et conuenientiam sonorum cum + extremis, reddit + enim + cum + + + similitudinem fere sonum + similem fere sonum + media tacta, ac si tangerentur ambe ultime. Et hoc est quod dicit: auditus videtur + diiudicare + + + quod + ipsa + ista + + media cordarum et + quod + + + + vtreque + + vtrorunque + + extreme + constituant + constituunt + + vnum sonum. Et ideo in antiphonis solis accidit quod vna corda tacta uel cantata + + cantetur + cantentur + cantetur et + + + reliqua + relique + altera + , cum in + + medium + + mediam + + + concurratur + concurrant + concurrat + , quare dyapason + tantum + Sed + + inter alias + proportiones + concordias + + + sola ex + antiphonis est apparentius + apparentiis antiphonis est + antiphonis est apparentior + tonis. + + et cetera + sequitur 20. + problema 19e. particule. +

+
+ +
+ + Vigesimum problema + 20m + Vigesimum. problemaVigesimum. + 19mum. + problema. + + +

+ PROPTER QUID SI QUIS + PROPTER QUOD SI QUIS + NOSTRUM + + PROPTER QUID SI QUIS NOSTRUM MEDIAM MOUET, CONCORDANS ALIAS CORDAS, + UTITUR INSTRUMENTO, NON SOLUM QUANDO SECUNDUM MEDIE FIAT SONUM DEFICIT, ET + UIDETUR NON CONCORDANS, SED ET SECUNDUM ALIAM MELODIAM? SI AUTEM LICHANUM AUT + ALIQUEM ALIUM SONUM, TUNC UIDETUR DIFFERE SOLUM QUANDO ILLA QUIS UTITUR. + AUT RATIONABILITER HOC ACCIDIT, OMNES ENIM UTILES CANTUS MULTOTIENS MEDIA + UTUNTUR. + ET OMNES BONI POETE FREQUENTER AD MEDIAM OBUIANT. + QUAMUIS DISCEDANT, CITO REUERTUNTUR, AD ALIAM AUTEM ITA NEQUE UNAM. + QUEMADMODUM EX ORATIONIBUS: QUIBUSDAM ABLATIS + CONIUNCTIONIBUS, NON EST ORATIO GRECA, UT AUTEM ET UERO. ET QUIDAM AUTEM NON + DEFICIUNT, PROPTER ID QUOD HIIS QUIDEM NECESSARIUM EST ESSE UTI MULTOTIENS, SI + ERIT ORATIO, HIIS AUTEM NON. + ITA AUTEM ET SONORUM MEDIA SICUT CONIUNCTIO EST ET + MAXIME BONORUM, PROPTER ID QUOD MULTOTIENS INEST IPSIS SONIS + . + + Quare + + si aliquis + siquis + aliquis + + + nostrum + + modorum + scientium + pulsare + pulsaret + + + instrumentum + + + + tangat + tangit + + cordam mediam vt mese, vtitur instrumento tali modo ac si omnes + alias + + cordas extremas ad inuicem + concordantia + concordantes + reduceret, quod declarat? Non enim quando + media corda + corda media + tangitur sonus deficit + et videtur + videtur + vt videtur + et videtur videtur + non fieri + concordantia + concordia + in instrumento, sed quod plus est, + apparet + videtur + quod + tactus + cantus + + + istius corde + istius + illius corde + + + resonet + restent + insonet + in quandam melodiam. Id autem non contingit in aliis cordis extremis, sicut + est + est in + + lychanos, que est tertia post ypatem. Si quis enim sonum + causaret + causet + cantet + carent + per cordam hanc uel per aliam vt paramese vel paranete, + tunc + et cetera + + + solum + sonum + videtur differentia in sono et + dissimphonia + + + + + + dissymphoniam + disynphoniam + in disinphonia + + + causari + causare + + + quando + cum + quis vtitur tangendo illam cordam que + non + si + + est recte media. Vel aliter quod tunc + + solum + non + + est differentia sonorum + ad inuicem + + visa, qua + qua vissa + visa, quo + In secunda qua + + + discernitur quod vnus est delectabilior + altero + altera + alio + , quando + quis + + vtitur tali modo + vtitur modo + + destruitur tali modo + media corda recte taliter quod in + eam + ea + + + consonent + consonant + + due ultime, quod est difficile + + mihi + + minis + .

+

+ Notandum + Nota + quod aristoteles + + multotiens dicit + dicit multotiens + multotiens dicere + + videtur + eo quod + + huius + huiusmodi + scientia + consistit in sensu + in sensu consistit + + + et + vt + + auditu et ratione, + ceu + seu + sicut + + alie. + Pictagoras + + + tamen omne quod ipsius + + nitebatur + vtebatur + videbatur + + + rationi + ratione + rationem + et omni + magis + inherere + inherere aristotelem + inheretur + adherere + , + aristoxenus + + + + + + + + ar + aristoteles + vero + sensui + sensum + , quos ambos + ptholomeus in eius + + + pertheus in eius + ptolomeus in sua + + + armonica + + armonico + retorica + detestatur medium obseruans cum declinatione in rationem amplius. + Boeth. + De inst. mus. + V.3 +

+

+ + Deinde. + + AUT. Soluit per simile + in aliis repertum dicens + primo + pro + + + rationabiliter id + id rationabiliter + rationabiliter illud + illud rationabiliter + fieri quod in + quesito + quesito est + 5to est + + + proposito + propositum + propositum est + . Nam omnes cantus vtiles et laudati + attingentes + finem musice cuiuscunque multotiens + + vtuntur + vtitur + corda media + reducendo + + ceteras et maxime supremas + + et maxime super primas et ceteras + + + proportionaliter + proportionatas + proportionabiliter + + ad ipsam.

+

+ + Deinde. + + ET OMNES. Declarat + id + illud + + secundo + + et + + + primo in metrica, que est + musica quedam vt + apparuit + apparebit + , dicens quod + musica + + + omnes boni poete vtentes hac parte musice metrica + dicta, + quam + qua + + + + frequenter conuertunt se ad mediam cordam siue ad id quod proportionatur illi, quod si + accidat + accidit + + + recedere quandoque ab ea + quandoque recedere ab ea + quandoque ab ipsa recedere + , cito + + ad ipsam reddeunt + + redeunt ad ipsam + ad ipsam redit + + + tanquam + + ad perfectum, sed ad nullam + aliarum + aliorum + aliam + + + ita + + reuertuntur, + cum + + non vt + + hic tactum + hic tactum est + hic cantum + + + perficiat + proficiat + + huiusmodi + .

+

Nosce quod eximii poete tunc + obuiant ad mediam cordam et ad sibi + proportionale + proportionalem + proportionabilem + , quando + + apud + + nos + vsitate + + + + + construuntur + construunt + construant + constituunt + consciliunt + carmina in quibus sunt tempora + sillabarum + + ad inuicem + conproportionata + aproporpationata + proportionata + composita + proportionata + ex breui et + longo + longa + . + Sillaba + + + + namque + enim + breuis vnum + habet tempus + + , longa vero duo, + quale quod constructum + quale quod constructum est + + ex + + dactilo + + + + + + vicissim + + inessim + incisam + et spondeo + et + + non ex altero. Tantum + + neque in + exametro + + + + + trocheo, nisi in fine dactilo, + quidem + quodam + quod + + + nunquam + + tantum + + + + neque + spondeo in quinto + pede + ex spondeo in quinto + + aut + + iambo + + in ambo + + + ei + sibi + eius + opposito. Constat + namque + enim + + ex prima breui et ultima longa, + quo vtimur + quo vtuntur + continitur + licentia + quandoque + + poetica in principio + tertii pedis + .3ii. + + . Tunc + namque + enim + + + fit aliter + aliter fit + + vt cum + seceditur + sedetur + seccetur + descendit + se redditur + a media corda vel ab eo + quod sibi + consimile + simile + . Debent + + namque + enim + + carmina fore bene + cantatiua + cantantia + vt que + + ouidii + + ouii + toni + enim + eum + + non + + autem que sunt + autem que + aut que sunt + autem sic que + + + oracii + + et ideo + aliqui + aliquos + versus construunt + + dictos leoninos + leoninos dictos + leoninos + quasi + rithimicam + rithimos + rithimicis + rithimia + + + commiscentes + commiscente + commiscentis + consistentes + metrice.

+

+ + Deinde. + + QUEMADMODUM. Declarat secundo in + coniunctione + coniectione + iniunctione + orationis + prosaice + + + + dicens + id + quod sicut in aliquibus orationibus in quibus + + videlicet + scilicet + videt + + multa + coadunantur + + coadunata + , non constituitur + oratio + + greca + + gramatica + , que est orationum + + congruissima + cum grauissima + et perfectissima, remotis quibusdam + coniunctionibus + coniectionibus + + tanquam vinculis conuenientibus, puta vt + autem + aurem + vero + quidem + quedam + quod + quid + et + huius + huiusmodi + . Vnde et quidam + + construere volentes + + volentes construere + + orationem + + grecam + gramaticam + + + congruissimam et perfectam + perfectam et congruissimam + congruissimam et perfectissimam + congruisima et perfectam + congrauissimam et perfectam + bene sonantem, et ne sequatur vocalis + ad + post + + vocalem, + quod + que + quidam + + + grecus + gramaticus + creus + + + horret + + abhoret + oret + honoret + + etiam in scriptura, non + deficiunt + in + + huius + huiusmodi + + + coniunctionalibus + coniunctionibus + partium ligaturis, cum + oporteat + + + + eis + eos + ac eis + multotiens vti si + debet + debeat + oratio perfici conuenienter; in hiis autem + deficiunt + deficiunt, quandoque + + + ceu + seu + sceu + + et cantus, interdum recedunt a media corda. Quia quandoque non + sit + fit + necessarium + sepe vti + + vti sepe + sepe + , sicut in orationibus + minus + unus + viris + + + grecis + gramaticis + + aut alio modo, + velut + valde + uniuersaliter + ultra + sunt alie partes orationis preter est verbum + substantiuum + + substantium + subactium + + expressum + aut + vel + + + intellectum + subintellectum + in + omnibus + orationibus + . Vel aliter, quia coniunctiones sunt duplices, + quedam + quia quedam + + + namque + enim sunt + + + maxime + et maxime + valde + necessarie in oratione, cum + protenditur + protendentur + protenduntur + puta + et proprie si + et si proprie + et proprie .enim. + si + + + quia + que + + + aut + autem + et + huius + huiusmodi + similia + . Alie + vero + nec + vero nec + + quasi minime, vt + quidem siquidem nempe quippe + siquidem quidem nempe quippe + quidem siquidem nempe apparet + quippe nempe siquidem + + et + huius + huiusmodi + . Modo oratio + + perfecte + perfecta + + + greca + + gramatica + constituitur, quando vtitur + + hoc + hac + modo coniunctionis + duplici + 2a. + + , puta priori + + significatiua + significatio + + + et non significatiua + et non significatam + et non significam + + . Dico autem perfecte + + greca + + + gramatica + quia + greci + gramatici + et potissime + galienus + + Gal' + Galienus + + gallici + + + + maxime + et maxime + + + + vtitur + vtitur ista + vtuntur + + + huius + huiusmodi + + + ligamentis + ligamentalibus + ligamentationibus + + + sinchathegorematis + + + + + + + + + The word in question in συγκατηγόρημα: "a word in logick that + imports somewhat with another, as all, none, certain, etc. + which signify little of themselves, but add to the force of other words (N. + Bailey, An Universal Eytmological English Dictionary, 17th + ed. (London: T. Osborne et al., 1759)). + + + etiam + et + secundis, + vt et + et et + et + vt + + plura + + quandoque adiungat + quandoque adiungantur + quando adiungat + coniungat quandoque + vna puta: + ac et + a. et + Et ac + ac etiam et + , + nimirum + + + in nimirum + numerum + minimum + , quidem, + demum + deinde + . Tales + + autem + aut + + coniunctiones apud + + grecos + gramaticos + dicuntur + parapliromatice + + + + + + + + + + + + The word in question is παραπληρωματικός, i.e. expletive. Cf. + + , + id est + et + + + + completiue + complete + copulatiue + sermonis, + vtpote + vt puta + vt poete + + + di. ta. ra. ni. ge. + + + + di.ru. ru. ru. ge. + di ta ra ge + di. ca. na. ge. + et cetera.

+

+ + Deinde. + + ITA AUTEM. + Applicat ad propositum + tertio + 3 + + , dicens quod simili modo se habet + cordarum + corda + media uel + ei + enim + sibi + proportionale + in + et + sonis, + ceu + seu + sicut + + coniunctio in orationibus + gramaticis + gramaticalibus + gramatice + gramatico + et proprie + bonis seu grecis + grecis seu bonis + seu grecis + bonis ceu grecis + bonis ceu gramaticis + . Nam cordarum + + media + medio + melodia + est + proprie + propria + de numero bonarum + reddentium + cordarum reddentium + mellifluum sonum + + et + + + consonum extremis. Et quia + hiis + is + hiis + id + multotiens debet + + in esse sonis + esse in sonis + in esse sonus + inesse sonis + ideo + vt + + + + propositum est + propositum + multotiens, + cum possunt + cum post + compositum + vtuntur corda media secundum quod + ei + ea + et + est + + consonant extreme, et de hoc itidem + + .36°. apparebit consequenter + .36. apparebit. + apparebit consequenter + .36°. + + problemate. + + + et cetera. + et cetera. sequitur 21; problema 19e. particule. +

+
+ +
+ + Vigesimumprimum + problema + 21m + vigesimum. primum.Vigesimumprimum + Vigesimum + problema. + + +

+ PROPTER QUID CANTANTIUM + + PROPTER QUID CANTANTIUM GRAUIUS CANTANTES ACUTE CANTANTIBUS, SI + DISSONANT, MAGIS MANIFESTI FIUNT? SIMILITER AUTEM + ET RITHIMO: QUI IN GRAUIORI PECCANTES MANIFESTI MAGIS. + UTRUM QUOD PLUS TEMPUS GRAUI, HIC AUTEM MAGIS + SENSIBILIS? + AUT QUIA IN PLURI TEMPORE MULTUM EXHIBET, UELOX + AUTEM ET ACUTUM LATET PROPTER UELOCITATEM + ? + + + Quare cantantes + Querit quare cantantes + + de numero + grauius + grauium + + cantantium, si dissonent et + + errent + errarent + erteant + haberent + in cantu suo ab ordine debito, + magis redduntur + + + + manifesti + manifesto + manifeste + in suo errore quam illi qui cantant acutius? Et addit quod + + non solum accidit hoc + hoc non sollum accidit + non solum hoc accidit + in musica + armonica + armonia + + , que ex vocibus constat, sed etiam + in + ex + + + rithimica, que coherentiam et consonantiam + + verborum + vocum + + contemplatur: vtrum bene uel male + consonet + consonent + constent + . + Qui + Que + Quando + Quoniam + + enim + + peccant + potest causat + + in ipsa secundum grauius + magis manifestantur + magis manifestatur + quam si + peccarent + peccaret + secundum acutius.

+

+ + Deinde. + + UTRUM. Soluit et + assignat + + duplicem causam quasi + quasi duplicem causam + + consimilem, dicens causam esse quoniam graue + plus habet + habet plus + + + temporis quam acutum. Ubi + + autem + aut + plus est + + + + temporis + temporis et + , amplius potest peccari, + et + vt + + peccatum + similiter + magis percipi.

+

+ + Deinde. + + AUT QUIA. + + Assignat causam dicens + Soluit dicens + Dicens + Assignat aliam causam dicens + + + id + illud + hoc + ideo + esse + quia + quare + quod + + + in + et + + tempore maiori + + exhibet + + + + graue + grauem + tardum et multum sonum, + quare fit esse ipsius manifestum propter sui tarditatem. Sed uelox et acutum, quia in + minori tempore dat uelocem sonum + + , + ideo + acutum autem + latet propter eius uelocitatem, ita quod peccatum non perpenditur etiam inexistens notabiliter. + + et cetera + sequitur 22m. + problema 19e. particule. +

+
+ +
+ + Vigesimumsecundum + problema + 22m + vigesimum secundum.Vigesimum secundum. + 21mum. + problema. + + +

+ PROPTER QUID MULTI + + PROPTER QUID MULTI MAGIS CANTANTES RITHIMUM SALUANT QUAM PAUCI? + AUT QUIA MAGIS APUD UNUM ET RECTOREM INTENDUNT ET + GRAUIUS INCIPIUNT, QUARE FACILE IDEM ATTINGUNT? IN UELOCITATE ENIM PECCATUM + EST PLUS + . + + Quare multi cantantes melius + conseruant + consonant + seruant + + rithimum et vniuersaliter omnem + armoniam + armonicam + + quam acceperunt cantare quam pauci?

+

+ + Deinde. + + AUT. + + Soluit dicens + dicit + Dicit id + + causam esse + quoniam ipsi amplius intendunt et + ordinantur + ordinant + coadunantur + + ad vnum, tanquam ad + rectorem + Rethorem + regulam + terrorem + + + ouium + omnium + opposittum + , et grauius possunt incipere cum + fuerint + fuerunt + multi quoniam + vox vnius + fortificat et + substentat + + vocem alterius. Propter quod de facili possunt in vnum + deuenire + + illudque illesum conseruare in uelocitate. + Autem + Aut + + + + non contingit hoc + hoc non contingit + non contingit + hoc non conuenit + + + cum difficilius sit seruare acutum + quam graue + quam grauius + graue + , vt dicetur + .26°. + .36. + 36º + 26a. + , quare in uelocitate + magis contingit + contingit magis + magis conuenit + peccare, etsi peccatum + + plerumque sit + sit plerumque + plerumque fit + plurimumque sit + + magis latens vt etiam + alii ostendunt actus. Et + id + idem + ad + quidem .45°. + + repetitur + + reputetur + . + + et cetera + sequitur 23. + problema 19e. particule. +

+
+ +
+ + Vigesimumtertium + problema + 23m + vigesimum tertium.Vigesimum.tertium. + 22m. + problema. + + +

+ PROPTER QUID DUPLEX + PROPTER QUID DUPLEX UITE + + PROPTER QUID DUPLEX NITE YPATE? + AUT PRIMUM QUIDEM QUIA EX MEDIO CORDA CANTATA ET + TOTA CONSONANT DYAPASON? + SIMILITER AUTEM SE HABET IN FISTULIS, QUE ENIM PER + MEDIUM FORAMEN FISTULE CONSONANT PER TOTAM FISTULAM DYAPASON. ADHUC ET IN + ALIIS IN DUPLICI DISTANTIA ACCIPITUR + DYAPASON, ET ILLI QUI PERFORANT + FISTULAS ITA ACCIPIUNT. SIMILITER ET CUM DYAPENTE EMIOLIUM, QUIA QUI FISTULAS CONCORDANT IN YPATEM CERAM + PONUNT, NITEM AUTEM USQUE AD MEDIUM REPLENT. SIMILITER AUTEM ET PER DYAPENTE + EMIOLIO, ET PER QUATUOR + EPITRICA DISTANTIA ACCIPIUNT. + AMPLIUS IN TRIANGULIS PSALTERIIS EQUALI + DISTENSIONE FACTA CONSONANT DYAPASON. HEC QUIDEM DUPLEX EXISTENS, ALIA UERO MEDIA LONGITUDINE + . + + + Quare + Quia + + in + 12. + 13º + 21. + 2°. + + + dixerat + dixit + + duplicem + nitem + + vicem + + + constituere + ypatem? Ideo causam + huius + huiusmodi + eius + querit, dicens: quare duplex + + nite + + vite + constituit ypatem?

+

+ + Deinde. + + + AUT. + AUT PRIMUM. + + Soluit et primo ostendit quomodo ex duplici + nite + + nitem + vite + causetur + ypate + ypatem + + + in + + cantu, secundo + + in instrumentis + instrumentis in + + flatu, tertio + + ductu + in ductu + , + 2a + 2a + ibi + ibi 2a + + SIMILITER, + 3a + 3a ibi + + AMPLIUS, + dicens + dicit + dicens primo + dicit primo + causam esse + + ex hoc primitus sumendam + sumendam ex hoc + , quoniam quando media cordarum cuiuslibet + instrumenti + + cantatur + incantatur + , tunc et + omnes alie + alie omnes + omnes aut + + + coordinantur + + coadunantur + ad + ipsam + illam + mediam et + consonant + consonat + + + per eam, cum ex ea + per illam, cum ex ea + cum per eam + + + constituatur + constituitur + dyapason, vt + apparuit + apparebit + + + .20 + 2° + 3° + .

+

+ + Deinde. + + SIMILITER. + + Ostendit 2° similiter fore + Ostendit 2°. fore + similiter + Ostendit 2º + similiter + Ostendit 2º + fore + + in instrumentis + et + in + + + flatis + sufflatis + fistulatis + , dicens simili modo se habere in fistulis, in quibus sunt quedam + foramina habentia similitudinem cum cordis, + in eis enim + est + + + magnum foramen, cuius sonus grauis, + proportionatum + proportionatus + proportionatur + est proportionatus + + + ypate + ypati + ypatem + + et + + secundum + secundus + + vt medium, assimilatum mese et plura + parua. Super que + fistulantur + fistulentur + fistulatur + attributa + nete + + vite + , in quibus siquidem soni qui fiunt per medium + foramen + foramen dicit + foramen dicte + + fistule consonant et inducunt per totam fistulam secundum + aliqua eius + eius aliqua + aliqua enim + foramina omnia dyapason, cum in ipsum, + ceu + + seu + sicut + + in medium, + reducantur + reducuntur + reliqua. Similiter + et + + in aliis + id accidit + accidit id + illud accidit + accidit + instrumentis, in quibus predicta + potest + possunt + + + aptari + adaptari + foraminum similitudo, + nam + vero + non + in eis + etiam + in + + + + dyapason constituitur + constituitur dyapason + dyapason constituunt + + + in esse + inest + + secundum duplicem + distantiam: + puta vnius extremi ad medium vna, et alterius ad ipsum reliqua, uel quia ex numero + consurgit duplari. Quod ostenditur quia illi qui perforant fistulas + tali modo suscipiunt + + distantiam + distantia + vt inde + consurgat dyapason cum reliquis proportionibus. + Nam + Quam + + + taliter + + operantur + opponatur + : perforando et coaptando + vt secundum proportionem sexquialteram + + reddatur + addatur + + dyapente, quod declarat. Nam + qui + si qui + si + + + fistulas taliter + taliter fistulas + + + consonas + consonans + consonantes + faciunt vt consurgat dyapason apponunt + ceram + seram + uel aliquod + + viscosum glutinosum + + + glutinosum viscosum + viscosum siue glutinosum + + in foramine + maiori + maiore + + + proportionato + proportionate + ypate, vt sonus eius + subgrauetur, et foramina per + nitem + + + representata replent + cera + + ceram + cera et + cera vt + usque ad medium + + , + + vt eis + angustatis + + coangustatis + sonus reddatur acutior, ita vt possit duplex + + nite + + vite + in + ypatem + ypate + + + consurgere uel crescere + + concurrere + , cum vna exacuatur et + reliqua + altera + + + subgrauetur + sibi + sibique + + + appropinquantes + + + + appropinquent + + + vtcunque + ubicunque + vtrunque + vterque + vtrisque + eodem modo secundum + + debitam distantiam foraminum + debita distantia foraminum + debitam distantia foraminum + debita foramina + + cum + cere uel alterius + appositione + appone + oppositione + propositione + , ita quod etiam + + lignum + ligamen + + + submittunt + submittitur + subimmictunt + subimmittunt + + + subtile + + vtile + fistule + in foramen medium secundum sexquialteram proportionem, + seu + ceu + + emiolam faciunt dyapente. Similiter per + epitricam + + + + + + + distantiam + distantia + que est cum numerus continet + alium totum + totum alium + alterum totum + vt visum est + + et eius + in eius + 7 + etiam + + tertiam partem, vt + .4. ad .3. + + se + habet + habent + + + . Accipiunt per .4. + id est dyatesseron + grece + graue + .

+

+ + Deinde. + + AMPLIUS. Declarat + 3°. in instrumento + tactibili + tertio instrumento tactibili + 3°. in instrumento + tangibili + , dicens quod + insuper etiam + etiam insuper + + simili modo in psalteriis, que habent figuram triangularem, et in canonibus + facta + factam + + proportionali distensione cordarum + ipsarum + ipsorum + ex acuto et graui + consonant et adducunt + + adducunt et consonant + consonant et addunt + consonat vt adducunt + dyapason. In ipsa enim duplex corda, vt ypate et + nite + + vite + , + et alia + et aliam + taliter + in quam + + concidunt + concidat + conferat + constat + cum superat + que est + media + distantia + + vere + vero + + , + vt + et + a + mese. Vel aliter duplex nete concurrit in ypate: et constituitur tunc sonus + corde medie + medie corde + cordis medie + totidem medie + secundum distantiam vt + apparebit + apparebat + apparuit + + + vigesimo + vigesimo problemate + 22° + + . + + et cetera + sequitur 24. + problema 19e. particule. +

+
+ +
+ + Vigesimumquartum + problema + 24m + vigesimum quartvm.Vigesimumquartum. + 23m. + problema. + + +

+ PROPTER QUID IN TENUIBUS + + PROPTER QUID IN TENUIBUS MENTEM APPONERE, YPATE SOLA UIDETUR + CONTRASONARE? + AUT QUIA CONNATURALIS MAXIME FIT SONO SONUS QUI + EST AB IPSA PROPTER ID QUOD CONSONANS EST? SIMUL AUGERI AUTEM SIMILI UIDETUR + SOLUS. ALII UERO PROPTER PARUITATEM INMANIFESTI + . + + Quare + + cum + cum in + in + subtilibus cordis, vt nete et + paranete + + paranetum + , sonum acutum + et paruum + + + + + reddentibus + + + quis mentem id est rationem et sensum seu + auditum + aditum + + + apponit + apponet + apponitum + ? Hec enim scientia, vt + pretactum est + pretactum est constat est + pretactum + tactum est + , constat + in + + ratione et sensu. Tunc sola ypate sine aliis videtur + + antisonare + + antiphonizare + + + + sonitu reliquas + sonitu reliqua + soni cum reliquas + + superando, quod + prius dictum est + prius dictum est est + dictum est prius + + + antiphonare + + inantiphonare + + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + Soluit dicens causam esse quia sonus qui ab ipsa causatur principalissime efficitur connaturalis et + proportionalis + alii + alteri + + sono, propter hoc quod cum sua + + consonantia + contrasonantia + + est + etiam simul + simul etiam + et simul + etiam similis + + + consonans + + contrasonans + . + Quando + Quoniam + Contra + + + enim + est + sonus ipsius + cum sono alterius corde + inferiori + inferioris + sub medio + + existentis + existentibus + existente + + + construitur + constituitur + constitutus + , + consonantia + consonantia + est etiam simul sonsonans quando enim sonus ipsius cum sono alterius + corde inferioris sub medio existentis constituitur consonantia + vt iam patuit dyapason. Et similiter + solus sonus huius corde + solum sonus huius corde + solus sonus huius cordis + solus sonus huiusmodi corde + sonus huius corde solus + inter alios sonos videtur + augeri et + crementum + incrementum + in tonando accipere, quia ipsa reddit sonum sola grauiorem + aliis, alie vero acutum + + aut + et + autem + vt + minus grauem. + + + + Sonus autem + grauis + grauis sonum + + + ebetat + + + acute + + , + sed + + + soni + sonus + aliarum cordarum subtilium, quia sunt + parui + parue + praui + graui + , non + percipiuntur + percipitur + perciuntur + manifeste, propter quod + non apparent + non apparet + non apparebit + apparent non + + + consonare + contrasonare + . Stat + + igitur + ergo + enim + in hoc, + quia + quod + sonus + ypate + ypatem + parypate + fortis est, aliarum vero debilis. + Qui autem + Qui + Quia + + + huius + huiusmodi + + + + consonat + consonant + contrasonat + contra consonat + + debili cum eo quod recipit, + magnus + maior + + enim motus minorem debilitat et obtundit. + Huius + Huiusmodi + autem sonus + cordis + corde + licet sit fortior ceteris, quia tamen grauior et + dimensionatior + indimensionatior + dimensionationem + diuisionatorem + + sonum aliorum de facili + recipit + suscipit + et exaltat, ita vt dyapason + inducat + inducit + inducta + indicat + . + + et cetera + sequitur 25. + problema 19e. particule. +

+
+ +
+ + Vigesimumquintum + problema + 25m + vigesimum. quintum.Vigesimum quintum. + 24m. + problema. + + +

+ PROPTER QUID MEDIA + PROPTER QUID MEDIA VOCATUR + + PROPTER QUID MEDIA UOCATUR IN ARMONIIS, OCTO UERO NON EST MEDIUM? + AUT QUIA SEPTEM CORDARUM ERANT ARMONIE ANTIQUITUS? SEPTEM AUTEM HABENT MEDIUM + . + + Quare in armoniis quedam cordarum vt + mese + nete + + + appellatur + + appellantur + + media + recte + ratione + + .7. cordarum? Equaliter enim distat ab + eis + hiis + aliis + , sed octo + cordarum non est medium + directe + vt + + arismetricum + + + , sed potius geometricum. Et ideo octo cordarum + non vocatur aliqua media.

+

+ + Deinde. + + AUT. + Soluit dicens causam esse quoniam antiquitus, vt + visum est + visum + , non fuerunt nisi septem corde in instrumentis armonicis.Septem autem + medium habet + habet medium + medium habent + + + equidistans + + + equidistant + que distans + ab extremis, + puta + .4., vt + mese. Id autem factum + quia dyapason, que est optima consonantiarum, ordinatur amplius cum + fuerit medium verum in cordis inuenire. Et ideo + musice + primo + cum + estiacus colophonius + + + + ostiatus colophonius + estimatus colophimus + estimatus colofonius + existimatus + colofonius + estyrginatus colophonius + stiatiis elephinus + + + decimam + quartam + 4am. + 10am. + cordam .9. preexistentibus + addidisset + + + + , + thimoteus + + + + + + + + + + superveniens + superveniens et + + + milexius + + + + + + + + xiam. + + aliam + nullam + unam + + adiunxit, + Boeth. + De inst. mus. + I.20 (Friedlein, pp. 208–209) + ita vt signato + + vero + vt + sit + medio in hiis puta sexta + consonet dyapason.

+

+ Nosce + Notandum + , vt + indicatum + + iudicatum + dictum + + + est + + + superius, .7. + + antiquitus fuisse cordas + fuisse cordas antiquitus + fuisse cordas + + + septem planetarum, + + secundum + boecium, + + + imitatione + + + imitationem + immutatione + mutatione + , ita vt + suprema + + supra + earum ypate reddatur saturno propter tarditatem motus + Boeth. + De inst. mus. + I.20 (Friedlein 206, ll. 10–1, 15–6) + vtrobique. Infima lune + ceu + seu + sicut + nete ob eius velocitatem. Que autem + intermedio + intermedie + in medio + in intermedio + ordine planetarum + attribuantur + + atribuatur + attribuentur + attribuebantur + + + mediis + aliis mediis + medicinis + iuxta + eorum + earum + + + mediocrem + mediocrum + mediocritatem + cursum. Et id quidem .32°. + apparebit + + et magis + magis et + et maxime + + .44° + + . + + et cetera + sequitur 26. + problema 19e. particule. +

+
+ +
+ + Vigesimumsextum + problema + 26m + Vigesimumsextum. + vigesimum + sextum. + 25m. + problema. + + +

+ PROPTER QUID IN ACUTO + + PROPTER QUID IN ACUTO DISCORDANT PLURIMI? + UTRUM QUIA FACILIUS ACUTUM DIMITTERE QUAM + GRAUE? + AUT QUIA PEIUS GRAUI? PECCATUM PEIORIS OPERATIO + . + + Quare + plurimi cantantes + vna discordant + amplius + + + amplius discordant una + una discordant + in acuto quam + in + + graui?

+

+ + Deinde. + + UTRUM. + + Soluit + Soluit et + + + assignans + assignando + assignat + duplicem causam probabilem prius, dicens + id + illud + + ideo + esse + quoniam + quia + + + leuius est + leuius + facilius et leuius est + + + dimittere + + + acutum? Et recessus ab eo sepius contingit quam a graui propter breuitatem temporis + existentie + existentis + ex natura + ipsius, propter quod + dictum est + dictum + + + 22°. + 21°. + : quod in uelocitate peccatum + plus existit. Non tamen vt + expositum adeo est + expositum adeo + expositum est adeo + + manifestum + + vt + + + peccatum + in graui, propter quod + apparet hoc + apparet hic + hoc quod apparet + in nullo illi + aduersari + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit assignans + Soluit assignando + Assignat + aliam causam + necessariam magis + magis necessariam + , dicens + + id + illud + hoc + ideo + esse quoniam + + peccatum + pretactum + predictum + quod + committitur + + + + conuertitur + in acutum cantando + + deterius est + seu + difficilius quam peccatum quod + committitur + + in + graue + grauem + grauius + cantando + + . Cum + molestius + + molestius sit + cantare acuta quam grauia + .37.. + + Peioris autem + Peioris + Autem peioris autem + + seu + difficilioris actus peccatum + maius + maius est + + . + + Et + ideo + + + in ipso amplius accidit discordari. Quod enim difficilius agere magis + contingit + conuenit + + peccato + corrumpere + + corpore + , vt aurum arte construere. + Et id etiam .46. + + rescribetur + rescribetur capitulo + + + . + + et cetera + sequitur 27. + problema. +

+
+ +
+ + Vigesimumseptimum + problema + 27m + vigesimum septimum. + Vigesimumseptimum + 26m. + problema. + + +

+ PROPTER QUID AUDIBILE + + PROPTER QUID AUDIBILE SOLUM HABET SENSIBILIUM? ET ENIM, IN QUANTUM + ABSQUE RATIONE, CANTUS TAMEN HABET CONSUETUDINEM, SED NON COLOR, NEQUE ODOR, NEQUE HUMOR HABET. + AUT QUIA MOTUM HABET SOLUM UNIFORMEM, QUO SONUS + NOS MOUET? HUIUS ENIM ET ALIIS INEST, MOUET ENIM ET COLOR UISUM, SED + CONSEQUENTEM HUIUS SONO SENTIMUS + MOTUM. HEC ENIM HABET SIMILLIMA IN RITHIMIS ET IN SONORUM ORDINATIONE ACUTORUM + ET GRAUIUM, NON IN MIXTIONE. SED CONSONANTIA NON HABET CONSUETUDINEM, IN ALIIS + AUTEM SENSIBILIBUS HOC NON EST. + MOTUS AUTEM IPSI OPERATIUI SUNT, OPERATIONES ENIM + CONSUETUDINIS SIGNIFICATIO EST + . + + Quare audibili + tantummodo de numero sensibilium hoc inest + tantummodo hoc inest + de numero sensibilium + tantummodo sensibilium hoc inest + tantum de numero seu suum hoc inest + ? + + Quia + Qui + Quod + etiam in quantum est cantus sine + + ratione + solo + solummodo + sono + , + tamen + cum + tantum + auditus + sensibili + sensu + , quia hec scientia, vt visum + est + + , perficitur ratione et sensu. Quis + eum + cum + enim + + + reddit sibi + sibi reddit + reddit + consuetum, non autem + color odori aut sapori + + colori audiri aut sapori + color odori et sapori + colorem aut odorem aut saporem + coloris odoris aut saporis + id adest quod ea fiant consueta in tantum vt + que + + + + audibilia + audibili + .

+

+ + Deinde. + + AUT. Soluit et + primo tangit + tangit primo + primo assignat + + partem + cause + + + ratione + audibilium, .2° ex parte + eorum quibus acquiritur + + consuetudo + consuetudo ibi + consuetudo .2a + consuetudo .2a + ibi: + + MOTUS + AUTEM + ERGO + + . Dicit + igitur + ergo + primo id esse quoniam audibile solum habet motum vniformem, + propter + quod + quem + + sonus habet nos mouere. + + Mouet enim potentiam audiendi, cum sit virtus passiua, et eam deducit in + actum + actu + acutum + , + + + vt apparet + vt patet in + + 2° + de anima. + + Arist. + De an. + II.12, 424a l. 19 (Cf. 416b l. 33 and 419b l. 5) + + Sed hic modus mouendi + aliis etiam inest + aliis inest etiam + obiectis sensuum, nam color mouet + sensum + visum + sensum visus + + + et in + actum + acutum + deducit; et similiter odor et sapor. + Sed in auditu + + ultra hoc + ultra + universaliter + existit + quod + quia + + percipiendo sonum + sentimus etiam motum + etiam motum sentimus + percipimus etiam motum + sentimus et motum + quo mediante defertur ad aures quod + + etiam non solum + non solum etiam + etiam non + accidit in + sono + sono in + sono uel + sompno est + + communi, uerum etiam + similiter + + se + si + habet in rithimis et in + coordinatione + + + eo ordine + seu + coniunctione + coniectione + grauium sonorum et acutorum ad inuicem + vnius + vnus + humimus + quasi iuxta alium, vt non reddatur + vna + ulla + vera + recta + + commixtio. + Quia in ea + non id accidit + id non accidit + non accidit id + , cum sonus adeo vniformiter + + aerem et suauiter + et suauiter aerem + aera et suauiter + aerem + + + concitet + excitet + continet + + concurrit + ycurit + vt aures + universaliter + vel + nichil + percipiant + sensibile + + ex aeris motu. Et + ideo + + videmus infirmos + huius + huiusmodi + + adeo + melodioso + + + + melodiose + + + delectari + delectari sono + , non autem + priori + + priori scilicet difficiliori + + + + eum + + cum + + fugientes et maxime + galleatam + + + + galeanterra + habentes passionem seu + ouum + + animam + . + Et ideo consonantia + sic + sit + ac + armonica non recipit consuetudinem, quemadmodum neque alii pretacti + sensuum + sensum + sensu + , + cum nichil + + cum nichil aliud + vel naturaliter + sensibilius preter perceptionem speciei + sonabilis + sensibilis + subtilis + percipiatur ad auditum peruenire, quod + et + + in reliquis dictum est sensibus accidere. Sed in aliis + sensibus + sensibus pariter + sensibilibus + + , vt + + + color odor et sapor + color sapor et odor + sapor color et odor + + colore odore et sapore + colori odori et sapori + coloribus odoribus et saporibus + coloris odoris saporis + , non inest, vt + eorum sumantur + + sumantur eorum + eorum seruatur + species cum aeris motus + perceptione.

+

+ Nota + Notandum + quod sicut duplex + est mixtio + est vni visio + + , + vt + vna + + ad sensum quedam + + et alia + alia + + ad intellectum, id est uera et non uera, ita + et duplex grauis et acuti + duplex acuti et grauis + vt duplex grauis et acuti + et duplex est grauis et acuti + + permixtio, taliter vt ex + vna reddatur + una reddatur vna reddatur + vna tendatur + + + vera + vna + + consonantia, ex + altera vero + alia vero + apparens magis.

+

+ + Deinde. + + + MOTUS. + MOTUS AUTEM. + Τangit causam sumptam + ex secunda parte + ex alia parte + dicens cum + igitur + visibilia + + vt + + ad multum recurrant + ad organum cum + motu + motus + aeris + sensibili + sensibilis + sensibiliter + , et + motus + + sint + sicut + sic + + operatiui + + . + Operationes enim fiunt per + eos + eas + omnes + + + actiones proprie dicte, cum + + + proprium actionis + proprius actionis + proprium + + sit esse in motu, + + auctor + + auctorum + + .6. principiorum. + Ps.-Herm. Tris. + De sex re. princ. + II.1 + + + Et + + signum consuetudinis + + acquirende + acquirendo + uel acquisite sit operatio, nam + consuetudo est multotiens + aliquid + aliud + id + facere. + + 13° + .21a. + vt 13° + .21a. + 13 + .21a. + 13°. + 23e. + + Ps.-Arist. + Prob. + XXI.14, 928b ll. 25–26 + Consuetudo + siquidem + + + + adipiscetur magis + magis adipiscetur + in + audibilibus quam in ceteris + audibilibus quod in ceteris + audibilibus quam ceteris + ceteris audibilibus audibilibus quam in + ceteris + + + sensibilibus + sensibus + , + et id tangetur etiam 29 + et id tangetur et 29º + et id tangetur etiam 20° + + , + nosce + notandum + quod causa + fundatur aristoteles + aristoteles + fundatur + + + super + supra + hoc: quod + + generatio + + genera + genero + + + soni et vocis + vocis et soni + consistit in quodam + fieri et + motu et + + transmutari. Sunt + namque + enim + de genere successiuorum entium, cum + sunt + sint + in motu, et fiunt + tantum + color odor et sapor de manerie permanentium, que post factum + habent esse + esse habent + habet esse + esse remanent + et non prius. Quod + indicat + inducat + denotat + + + aristoteles, + + + quia singulariter de + anima + 2° + quia singulariter 2° + de anima + quia 2°. + de anima + quia similiter de alia sermo + + determinauit de modo generationis + + soni et vocis + vocis et soni + et vocis + + , + Arist. + De an. + II.8, 419b l. 9 + + et + Et modo inmutandi et + non aliorum, sed inde sensu et sensato. Cum + igitur modus + modus igitur + igitur motus + ergo modo + + generationis + soni et + soni + et + + + perceptionis + preceptionis + + + vt ad + ad + + multum + conueniat + conueniant + contingit + cum operatione + siue + seu + actione, que + fit + sit + sit in + mediante motu + qua + quam + que + quia + consuetudo vt + dictum + dictum est + + + acquiritur + + adquiratur ad + adquantur + + + visibilia + visibilis + audibilia + sensibilia + + pre aliis + sensibilibus + sensibus + sensibus uel sensibilibus + + + reddentur + redduntur + reddetur + consueta, vt + ostendunt + ostendit + + + eris + + et + nauium + + manifestum + + + malleatores + + + + + non audiendo, quod + + in + + illis + non + + non vt + + + acquiratur + acquiratur etiam + acquiratur audibilia + pre aliis sensibus redduntur consueta vt ostendunt quod in illis non + acquiritur + consuetudo + vtcunque + vterque + vtrumque + . + + et cetera + sequitur 28. + problema 19e. particule. +

+
+ +
+ + Vigesimumoctauum + problema + 28m + vigesimum octauum. + Vigesimum octauum. + 27m. + problema. + + +

+ PROPTER QUID LEGES + PROPTER QUID SECUNDUM LEGES + + PROPTER QUID LEGES APPELLANTUR QUAS CANTANT? + AUT QUIA PRIUSQUAM SCIANT LITTERAS, UIDERUNT LEGES + NON LATEANT, QUEMADMODUM IN AGATHUSIS AMPLIUS CONSUEUERUNT? ET POSTERIORIBUS + IGITUR CANTIBUS PRIMOS IDEM APPELLAUERUNT QUIDAM PRIMAS + . + + Quare + + illi + aliqui illi + cantus quos primitus + aliqui cantant + cantant aliqui + obliqui cantant + leges appellantur. + + Nosce + Nota + + quod + per leges hic audio cantus in quibus + mox aliqui + aliqui mox + statim aliqui + + edocentur cum incipiunt cognitionem habere, sicut illi qui ordinati sunt a lege vt + cantentur + cantetur + cantent + legaliter. + Tamen + Cum + , + vt visum + est + + + .15. + + , in laudem dei + + + ceu + seu + in lege nostra + + + docentur + + pueruli + + + salutationem virginis + vel + aut + + + huius + huiusmodi + cantare.

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit dicens + Soluit dicit + Dicit + causam esse quia cantantes leges + ceu + + seu + sicut + + + puerili + + pueri + antequam aliquid sciuissent de litteris et cantibus choricis, iam + viderant + viderunt + videant + leges seu + + audiuerant + + + + + scientes etiam + etiam scientes + scientes + scientes et + + + ipsas + ipsos + cantare ad hoc vt non lateant. + Sed + Sed vt + Seu + + + reddantur + redduntur + declaratum + manifeste + note + voce + nete + , + velut + ultra + illud + vel + volox + + volt' + volvit + + + + principia in scientia + et + vel + + + locus + velud + + ianue in domo + Arist. + Met. + II.1, 993b ll. 4–5 + + + vt ostensum est + + .18 + 18va. + problemate 8vo + supra + + . As cited in d'Abano's commentary on Book + XVIII, Problem 8, where the paraphrased quotation begins with + "nota" + + + + Nam quod primitus + discitur + dicitur + optime + imprimitur + + cum anima sit tunc + ceu + seu + sicut + tamquam + tabula rasa, et perfecte + retinetur, et + huius + huiusmodi + vnius + + quidem consuetudo + potissime fuit + fuit potissime + fuit + apud quosdam nominatos + + agathyrsos + + + + + + + + + . Quod autem + primum quis + primus quis + primum + primitus + adipiscitur prius + nomen + notum + non + + + suscipit + + suscepit + , + tanquam + + + + notum + motum + natum + cum anima nomen + imponatur + imponat + imponat vt + + + cognoscit + cognoscat + cognoscet + . Itaque cum + alii + aliis + , cantus vt + + chorici + theorici + siue conuersiui et vniuersaliter tragici, + sint + sunt + sit + sicut + posterius cantibus legalibus cantati, puta cum + sciuerint + sciuerunt + litteras et + fuerint + fuerunt + fuerit + adulti leges, primos cantus seu primas melodias quod idem est + + appellarunt + appellauerunt + , sicut scientie de sermone cum prius + instruantur in hiis pueri + instruantur in hiis puer + instruantur in eis pueri + dicuntur primitiue. + + et cetera. + sequitur 29. + problema 19e. particule. +

+
+ +
+ + Vigesimumnonum + problema + 29m + vigesimum nonum. + Vigesimumnonum. + 28m. + problema. + + +

+ PROPTER QUID RITHIMI + + PROPTER QUID RITHIMI ET CANTUS, UOX EXISTENS, CONSUETUDINIBUS + ASSIMILANTUR, SAPORES AUTEM NON, SED NEQUE COLORES ET ODORES? + AUT QUIA MOTUS SUNT QUEMADMODUM ET OPERATIONES? + IAM UTIQUE ACTIO QUIDEM MORALE ET FACIT CONSUETUDINEM, SAPORES AUTEM ET + COLORES NON FACIUNT SIMILITER + . + + Repetit + 27m problema dicens + .27. partem + dicens + .27m. + dicens + .27m. + particulariter dicens + problema + + quare rithimi, quantum ad speciem musice rithimicam, et cantus et vox + pronunciatiua + + + pronunciatam + + quantum ad armonicam + similitudinem + similem + + + + acquirunt + + adquirit + + + consuetudinis + consuetudines + consuetudinem + similitudinem consuetudinis + ? Redduntur enim consueti, sed sapores aut + + color uel odores + colores uel odores + odores vel colores + + non + proportionantur consuetudini.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse quia motus qui sunt circa sensibilia + auditus + + + + tanquam + + operationes existunt. Quod declarat quia sicut + videmus + nos videmus + in actione morali quod actus eius inducit consuetudinem et inclinationem ad + istud + + id + illud + + illud + id + uel ad + + illud + id + aliquid + agendum, ita + similiter + + est in + sensibus + sensibilibus + auditus. Ex multotiens + enim audire + audire enim + quidem audire + + + vnum + in vnum + nimium + cantum inducitur consuetudo, + qua + que + etiam + in + habituata cantus + ille + + iste + + reputatur delectabilis, + etiam + et + si non sit secundum ueritatem, non autem circa sensibilia aliorum sensuum, + vt declaratum, accidit + vt declaratum est, accidit + . Et hoc est + quod subditur + sapores + saporem + sapor + + qui sunt sensibilia; gustus et odores qui + olfatus + + olfaciunt + non id operantur, quod ex ipsis consuetudo + consimilibus + similiter + consimiliter + + + audibilibus + audibilis + adeoibilibus + audientibus + + acquiratur. + + et cetera + sequitur 30. + problema 19e. particule. +

+
+ +
+ + Trigesimum problema + 30m + Trigesimum. + trigesimum + problema. + 29m. + problema. + + +

+ PROPTER QUID NEQUE YPODORISTIUM + PROPTER QUID NEQUE + PROPTER QUID YPODORISTIUM + + PROPTER QUID NEQUE YPODORISTIUM NEQUE YPOFRIGISTIUM NON EST IN TRAGEDIA + ROTATIUUM? + AUT NON HABET CONUERSIUUM? SED A SCENA, IMMUTATIUA + ENIM + . + + Quare + + ypodoristium + + + + et + + ypophirgium + + + + + + cantare non + + est + + + + rotatiuum + + + rotatum + rota tantum + et conuersiuum in tragedia, ubi + + obseruentur + obseruantur + diuersitates sonorum secundum graue et acutum + ascensione + + + + et + ac + descensione per circulos casuum.

+

+ + Deinde. + + + AUT. + AUT QUIA. + QUANDO. + Soluit dicens causam esse quia + + huius + huiusmodi + cantare non + habent + habet + , vt expositum + est + + , + conuersiuum + masiuum + conuersionum + in quo magis + attenditur + + + ad cantus quam ad uerba. Sed potius + huius + huiusmodi + cantus est + immutatiuus + immitatiuus + imitatiuus + imutatiuus + , + qui + quod + quam + dicitur + ascena + + contentus sub legibus et comedia, vt visum + est + est in + + + .15., in + quo + + amplius + attenditur + + + ad verba quam ad + cantum + cantus + , et + id + illud + amplius apparebit + 48°.

+

+ Nosce + Notandum + vt apparet + + .8. + + <app> + <lem wit="#π #Ma #Nu #Px #Va #Vz">politicorum</lem> + + </app> + aristotelem + .8. + polliticorum + aristotelem + .8. + polliticorum quod + .8. + phisicorum + aristotelem + + Arist. + Pol. + VIII, 1324b ll. 12–18 + tangere tres + + cantus modos + modos cantus + cantus mentis + : precipue + phrigistium + + + + + philigistium + , + doricum + + doricum uel doristicum + choricum + , et + lidium + + . + Phrigistius + + + + Frigisticus uel phigistius + est + troianus + + , + qui + + que + est cantus + agrestis + + incitatiuus + et incitatiuus + imitatiuus + mutans + + + in + ad + + iram et passionem, + ceu + seu + + + qui + que + + fistule + in quam + in quem + in quo + in qua + in quod + inquit + nunquam + + + concidit decenter + ditirantibus + + + + + + + quid dithitambis + qui dithirambus + ex tyranbus + . + Dorista + Doristas + siquidem + maluaficiacus + + + + maluafiati cuius + cantus laudabilis + + + tanquam + + tam + + + stabilis + stabilis et + + + virilis + viribus + + , + + + Arist. + Pol. + VIII, 1324b l. 12 + + + + + unde .48. + unde .40. + unde 41. + + + magnificus + stabilis + stabilis et + stabilisimus + + + + + cytharicissimus + + + + + cithantissimus + omnium + + + Ps.-Arist. + Prob. + XIX.48, 922b l. 15 + + et + + ceu + seu + omnium + superhabundantiarum + + + + + + mediis + medius + laudatus in quo + pueruli + + sunt + edocendi + + . + Arist. + Pol. + VIII, 1324b ll. 12–18 + + Lidius + + + + + + quidem dicitur + dicitur quidem + siquidem dicitur + dicitur + a + chorebo + + + + + + + + lidorum + + rege. Qui omnibus laudabilior + est + + . + + Cum + Cum enim + + sit + aliorum + + medius + mediis + , tria in se continet quod medium + rationem habens + habens rationem + commune habens + virtutis quod decens + et + et quod + + possibile, + Arist. + Pol. + VIII, 1324b ll. 32–34 + que in cantu et maxime pverorum sunt obseruanda. Vnde + boecius + musice + .4. + si quis totas constitutiones + faciat + faciet + facit + acutiores uel + graues + grauiores + totas + remittat + + remittit + dyapason consonantie species, + efficiet + efficiat + + modos septem + + ceu + + seu + sunt + ypodorius + + + + + ypofrigius + + + + + ypolidius + + + ypodolius + + + dorius + chorius + polius + + + + frigius + + + + + + lidius + + + + + mixolidius + + + + + + Boeth. + De inst. mus. + IV.15 (Friedlein p. 342, ll. 10–14) + + ypermixolidius + + + + . Duplat + igitur + ergo + enim + 7 + uel triplat + quod aristoteles + boecius + quod aristoteles et + boecius + quod aristoteles + boecius + .31 + + . + + et cetera + sequitur 3.1; + problema 19e. particule. +

+
+ +
+ + Trigesimumprimum + problema + 31m + trigesimum.primum + Trigesimum primum. + Trigesimum + problema. + + +

+ PROPTER QUID CIRCA FRINICHUM + PROPTER QUID CIRCA + + PROPTER QUID CIRCA PHRINICUM + FUERUNT MAGIS DULCE MELODIA? + AUT PROPTER ID QUOD MULTIPLICES SUNT TUNC CANTUS IN TRAGEDIIS METRORUM + ? + + Quare est quod + apud phrinicum + + + apud plinitum + apud finitum + circa frinichum + apphimitum + id est caput frontum + , + qui + quod + est modus + cantantium + cantatiuum + cantantium uel cantuum + quorundam, + melodie + melodia + + + fuerunt + fiunt + finitur + magis suaues quam + apud + + amplius + + + alios + alias + ?

+

+ + Deinde. + + + AUT. + AUT QUIA. + APUD. + + Soluit dicens causam esse + quoniam + quia + + cantus + apud + + + + eum + cum + enim + fuerunt + multiplices et differenter + + compositi + appositi + propter quod + secundum plurimum fuerunt + + in tragediis + + metrorum + + metris + . Tales autem sunt suaues + maxime, cum eorum + sit + + sunt + principaliter + finis + + iocunditatem inducere. + + et cetera + sequitur 32. + problema 19e. particule. +

+
+ +
+ + Trigesimumsecundum + problema + 32m + Trigesimumsecundum. + trigesimum + secundum + 31m. + problema. + + +

+ PROPTER QUID DYAPASON + + PROPTER QUID DYAPASON APPELLATUR, SED NON SECUNDUM NUMERUM DYAOCTO, + QUEMADMODUM ET DYATESSERON ET DYAPENTE? + AUT QUIA SEPTEM FUERUNT CORDE ANTIQUITUS? POSTEA EXTRAHENS TERTIAM, TERPANDERUS NITEM + APPOSUIT. ET IN HOC APPELLATA EST. DYAPASON, SED NON DYAOCTO, DYASEPTEM + ENIM ERAT + . + + + Quare consonantia + Querit quare consonantia + + + dupla + dyapason siue per totum appellatur, + et non dicitur + non dicitur + + et omnino dicitur + + + dyocto + + + + + propter numerum + octonarium + + + octogenarium + , in + quem + quam + quod + videtur terminari + in + + parigraphia + + + + + + + proportionum? Terminatur + + enim + eius + super octo. Et + subdit + tangit + + + huius + huiusmodi + hic + eius + + + motiuum + + dicens + quemadmodum + quod deinde + + dicitur dyatesseron, quia finitur in 4° loco in predicta descriptione, aut quia fit in quatuor cordis musice. 5°. et similiter dyapente siue per 5°. + + terminatur + finitur + in 5° + + loco + + + + vel in 5. + + constat + stat + + cordis + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens causam esse cur dyapason dicitur et non + dyaocto + + + + dyoto + + quia corde + instrumentorum antiquitus .7. tantum fuere + antiquitus instrumentorum 7º. tantum fuere + instrumentorum antiquitus tantum .5. + .7. fuere + instrumentorum antiquitus 7 fuere + . Postmodum superuenit + tripandius + + + + , + qui + que + quia + + tertiam subtraxit cordam + + vt + + paramese cuius quidem loco + nitem + + + + + apponit + apposuit + , ita vt non videatur + mutasse + immutasse + numerum, sed + proportionem potius, et propter hoc appellata est dyapason, + quoniam + quia + ex tali mutatione + optima + + opposita + + + adinuenta est + est adinuenta + inuenta est + adiuncta est + consonantia. Non itaque dicitur + dyaocto, cum corde non + sunt + sint + nisi .7. Potius enim + dicendum esset + debent esse + deberet esse + deberet dici + dyaseptem, cum tantum isto numero + + + imitando + immutando + mutando + qui planetarum + + numerum vt visum est + vt visum est numero + numerum vt visum + numero vt visum + + + contineantur + contineant + + contineantur imitando numerum + planetarum vt visum est + . Quia + + tamen + tam + cum + + + corde prius .7. + prius corde .7. + corde .7. + prius + corde prius + + fuerunt + vt + + apparuit + apparebit + + , + pauciores + + paucitores + pluresque + demum + deinde + + + + adinuente + adinuenientem + adinueniendo + adueniente + , + tamquam + + + nomen stabilius, + elegerunt + + elegerant + potius dyapason dicere seu per totum et perfectum quam dyaseptem, tanquam nomen magis + denotatiuum + + denotatur + denominatiuum + determinatum + deuotatiuum + essentie ipsius. + + Et + Et hoc + Vt + + + tactum quidem + tactu quidem + quidem tactum est + + + .25. problema + 25° problemate + est hoc 25º problemate + est hoc prius + + + . + + et cetera + sequitur 33m. + problema 19e. particule. +

+
+ +
+ + Trigesimumtertium + problema + 33m + trigesimum tertium. + Trigesimum quartum tertium. + 32m. + problema. + + +

+ PROPTER QUID CONSONANTIUS + + PROPTER QUID CONSONANTIUS EST IN GRAUE QUAM A GRAUI IN ACUTUM? + UTRUM QUIA A PRINCIPIO FIT INCIPERE? + MEDIA ENIM ET PRINCIPALIS ACUTISSIMA PARACORDE. + HOC AUTEM NON A PRINCIPIO, SED A FINE. + AUT QUIA GRAUE AB ACUTO FORTIUS ET MAGIS UOCALE + ? + + Quare in cantu + maior extat + extat maior + maior existit + + consonantia si incipiatur ab acuto et + terminetur + terminatur + preterminetur + in + grauem + grauim + graue + , quam si a graui + preincipiens + incipiens + terminetur in acutum?

+

+ + Deinde. + + + UTRUM. + UTRUM QUIA. + Soluit + et assignat + assignando + duplicem causam dicens primo + id + illud + esse quia + contingit + + conuenit + incipere + a + in + principio rei in qualibet re, modo ipsum acutum + + tenet + retinet + + + locum principii + principium locum + locum principaliter + principium + in instrumento. Nam prime corde minores sunt ille + que + qui + qua + + + sonum reddunt + reddunt sonum + sonum reddunt sonum + reddunt + acutum, a quibus + oportet + + + incipere, vt ordo seruetur naturalis in arte.

+

+ + Deinde. + + MEDIA. + Remouet + dubitationem + dubium + , quia + crederet + diceret + aliquis + quod + + ab omni corda acuta + esset + esse + incipiendum. Vnde + id + + remouens + remouet + + dicens quod + + + + corda media et principalis est + corda media principalis est + corda principalis et media est + corda media est principalis et + et principalis est + + acutissima + seu + sive + fortissima + peracorde + peracordis + per .7. + cordas + , id est + cordis + corde + , iuxta ipsam + existentis + existentes + existentibus + . Vnde + hec + hoc + non est + + tangenda in principio + in principio tangenda + , sed potius in fine, propter eius excessum, + ista + ita + ita quod + siquidem aut est media positione recte + ceu + seu + sicut + mese, aut virtute + puta + pauca + sicut + + ypate, cum in mediam + + condescendit + + condescendat + cum nete, vt visum est + 20°.

+

+ + Deinde. + + + AUT. + AUT ET. + + Assignat + + aliam causam + causam aliam + aliam + dicens + id etiam + id + ideo + + esse + quoniam graue + incipiens ab acuto + ab acuto incipiens + descendens ab acuto + + + fortius + + est. Diutius enim + permanet + + + et magis vocale existit quam econuerso. Hoc autem facere magis est + + connaturale + contra naturale + contra naturalem + cum naturale + + + ac + hoc + etiam + morale + mortale + + + quam + quod + quidem + suum contrarium. + Videmus enim in operibus nature quod ipsa in principio a leuibus et + debilibus incipit, non enim tunc est, operosa sed in fine, + + + vt + + + dictum est + dictum + dicatur + + 10a. + + + + Ps.Arist. + Prob. + X.45, 895b l. 27- to 896a l. 4 + Et ideo est videre optimos cantatores naturam + imitantes + + + + mutantes + + + + hoc + + seruare + obseruare + + + , quod in acuto leuiter incipientes + in + + + + grauem + graue + postea conterminant, et non econtra concordant. + + et cetera + sequitur 34. + problema 19e. particule. +

+
+ +
+ + Trigesimumquartum + problema + 34m + trigesimum quartum. + Trigesimumquartum. + 33m. + problema. + + +

+ PROPTER QUID BIS QUIDEM + PROPTER QUID BIS + + PROPTER QUID BIS QUIDEM PER ACUTOS. ET BIS DYATESSERON NON CONSONAT, BIS + DYAPASON AUTEM? + AUT QUIA BIS PER ACUTOS NEQUE BIS DYATESSERON EST, + QUOD AUTEM PER QUATUOR AUT PER QUINQUE + ? + + Quare + + bis paracutos seu bis paracuta + bis paracuta seu bis paracutos + bisperacuta + bis paraclitos seu bis paracuta + id est bis dyapente et bis dyatesseron + siue bis per quatuor + id est dyatesseron + + non consonant + + et + id est + + + simphoniam + + constituunt, dyapason vero concordat? Dicitur autem bis paracutos + + dyapente, quia constat ex + duobus + duabus + + acutis + et + + vno + vna + non + graui + seu + siue + ceu + breuibus et + longo, more + dactili + + + + + + + .

+

+ + Deinde. + + + + AUT. + AUT QUIA. + Soluit dicens causam esse quoniam + bis paracutos + + + + + vel bis dyapente + vel + et + + + bis dyatesseron + dyatesseron + non est dare, quod constituant + aliquam + aliqualiter + + consonantiam, + quoniam + illud + id + quod per quatuor se habet aut per + quinque licet proportionem + + constituant + constituat + constituant aliquam consonantiam + et per consequens consonantiam, vt per quatuor + quoniam illud quod per + 4 + vt per quatuor + dyatesseron + vel + vel per + + quinque dyapente. + + Quando enim + Quando + epsa enim + Quoniam + + + minus extremum prime, et + minus extremum prime ad + extremum prime minus + minus + + + extremum magis + extremum maius + + 2e comparantur ad + inuicem nulla consonantiarum resultat inde, vt videbitur .41°., ubi repetitur + + idem + id + inde + amplioris expositionis gratia. + + et cetera + sequitur 35. + problema 19e. particule. +

+
+ +
+ + Trigesimumquintum + problema + 35m + trigesimum quintum. + Trigesimum quintum. + 34m. + problema. + + +

+ PROPTER QUID DYAPASON + + PROPTER QUID DYAPASON OPTIMA CONSONANTIA EST? + AUT QUIA IN OMNIBUS TERMINIS RATIONES SUNT, + ALIORUM AUTEM NON IN OMNIBUS? QUONIAM AUTEM DUPLEX NITE YPATES. QUOT NITE DUE YPATEM UNUM, ET QUALIS YPATE DUO NITE QUATUOR, ET + SEMPER ITA. + MEDIE AUTEM EMIOLIA. QUOD ENIM PER QUINQUE + EMIOLIUM NON IN OMNIBUS NUMERIS EST. NON + ENIM UNUM MINUS, MAIUS TANTUM AUTEM ET ADHUC MEDIUM. QUARE NON TOTA AD TOTA + COMPARANTUR, SED INSUNT PARTES. + SIMILITER ET IN EO QUOD EST PER QUATUOR SE HABET, EPITRICON ENIM EST QUANTUM INCIDERE QUOD ET ADHUC IN QUATUOR + EPITRICON EST. + AUT PERFECTISSIMA QUE EST EX UTRISQUE, ET QUIA + MENSURA MELODIE? PER TOTUM ID QUOD FERTUR QUE EST SECUNDUM MEDIUM MOTUS + FORTISSIMUS, INCIPIENTE AUTEM ET FINIENTE MOLLIOR. QUANDO AUTEM FORTISSIMUS + MOTUS, ET UOX ACUTIOR EIUS QUΟD FERTUR, PROPTER QUOD ET CORDE TENSE ACUTIUS + SONANT, UELOCIOR ENIM MOTUS FIT. + SONUS AUTEM AUT AERIS AUT ALIUS CUIUSDAM MOTUS, + CAUSA QUE EST PER MEDIUM PORUM ACUTISSIMUM OPORTET FIERI. QUARE SI HOC NON + ACCIDIT, NON ERIT MOTUS ALICUIUS + . + + Quare dyapason est optima et dulcissima consonantiarum?

+

+ + Deinde. + + + + AUT. + AUT QUIA. + Soluit + et assignat + + assignando + dicit et assignat + dicens + + duplicem causam, + + secunda + .2a. + ibi + + AUT. + + Adhuc + Ad hoc + Item + + primo dat causam + + + + quare + quare est + optima consonantiarum + + , dicens + + illud + id + ideo + esse quoniam proportiones + secundum + per + quas + constituitur huius consonantia + constituitur huiusmodi consonantia + huius consonantia constituitur + + + sumuntur + + sumitur + ex omnibus terminis summis numerorum. + + Multi enim sunt + Multi sunt enim + Et multi enim sunt + modi quibus + corde + ad inuicem comparate + + hanc efficiunt + efficiunt hanc + hac efficiunt + + + consonantiam + + consonantia + . Quod declarat tam ratione substantie quam + + ex parte + + + + + quantitatis et qualitatis + qualitatis et quantitatis + quantitatis qualitatis + quantitatis et qualiter + quantitatis + , dicens + primo + primo esse + sermo + quod + + + + duplex + + nite + + nitem + , cum accepta fuerit, + assumit rationem + + + rationem assumit + affruat nomen et rationem + et substantiam + ypates + + ypatos + compates + . Et + similiter + sit + dicitur + + ratione + + + quantitatis, vt + querenti + querente + conuenienti + + + quot + quod + + + nite + + + + constituunt + constituerunt + ypatem + vnam + unum + veram + + + dicendum, + quoniam + quod + + due, et secundum + quale etiam + etiam quale + qualem etiam + quale scensiam + + due + + nite + + netes + vite nete + + sunt, + qualis + quales + qualis qualis + est ypate + vna, et quatuor + + nete + + eodem modo sunt + + due + ypate + ypate due + due ypates + due + ipates + duo + ypate + , + et sex + tres + et 6. et 3. + 26. + 3. + 2. + 63. + . + Et + + + + ratione substantie ac + ratione substantie et + ratione substantie + ratione substantie Et ratione substantie + accidentis considerando et ita semper + + procedendo + + protendendo + + due + + nite + + netes + + vnam constituunt ypatem.

+

+ + Deinde. + + MEDIE. Ostendit quod dyapente et + dyatesseron non est optima + consonantia + consonantiarum + , primo dicens quod + proportio + medietatis + equalitatis + + est + + emiola + + ennola + . Et exponit, + dicens quod illud quod + dicens quod id quod + + dicens quod illud + + est + + per + pro + quod + + quinque est + emiolum + + + emidelium + , et tale non reperitur in omnibus numeris; + + ymmo + + + + + + in nullis ita + nullis ita + in nulla + vt dicatur omnis et perfecta, + vt dyapason dicitur perfecta + + , consonantia. Non enim + + perfecte totum + totum perfecte + perfecte + + + comprehendit + comprehendunt + apprehendit + numerus maior minorem; + ymmo + + + + duorum + + numerorum + minorum + vnus + est sicut quid + est sicut qui + est sicut quem + quidem est sicut + maius + et aliud + et alius + alius + et aliud sicut + minus, eo quod talis consonantia consistit in proportione sexquialtera, in qua + vnum continet + alium totum + aliud totum + ad totum + totum aliud + + semel + tantum et eius medietatem. Propter quod in hac consonantia non + fit + sit + + comparatio + + totius ad totum, + + + + + vt + quod + + vnus numerus + vnius numeri + minus numerus + + + bis quod + bisque + vel quod + + + totum + totus + mensuret + alterius + + alterum + + , + + + + + sed + fit + comparatio + + + totius ad partes, quare non + erit + est + erunt + optima consonantiarum dyapente.

+

+ + + Deinde. + + SIMILITER. Ostendit consequenter + quod dyatesseron non est optima consonantiarum + + , dicens + + quod in + + quando + + illa + + consonantia + + consonantiarum + que est per quatuor vt dyatesseron eodem + modo se habet. Non + enim est + tamen est + enim + optima consonantiarum, cum + non fiat + non sit + enim non + + + comparatio + compositio + totius ad totum, quoniam + epitricam + + + + + + proportionem esse + proportionem + proportio esse + + + quoddam + quoddam enim + quod + est, quantum interuenire, vt cum maior numerus continet minorem totum et amplius cum hoc + epitritio + epitricus + epitricon + est in + quatuor, id est continet super hoc eius tertiam + partem, ex quo + consonantia + consona + resonantia + + resultat + quaterna. Et sic non fit comparatio totius ad totum, sed totius ad partem, vt dictum + est + est in + in + dyapente.

+

+ + Deinde. + + + AUT. + AUT QUIA. + AUTEM. + + Assignat aliam causam, uel + quod + per + + + + dictum + dictam + dictum est + confirmat per amplius, dicens + primo quod + primo + prima + + consonantia ex hiis vtrisque composita, puta ex dyatesseron et dyapente, est perfectissima. Ipsa enim vt + dictum est + dictum + + .13. + ex hiis + + duabus + + + constat proportionibus, cum dyapason sit fere + sex + sexto + >sexta + + tonorum + + simphonia + + + . Et + dyatesseron ex duobus tonis et + semitonio + + semitonis + + + constet + constat + , + ac + ad + et + dyapente ex + tribus + tribus + tonis + duobus + + + et semitonio + + + semitonis + , que + + coniuncta + coniecta + + .6. + tonos fere constituunt. Dico autem fere + eo quod + + semitonium + + + + vel limes aut + aut limes uel + vel limes ac + + + dyesis + + + + minor est + tono.

+

Quod autem sit perfectissima ostenditur, quoniam mensura extat et ratio + omnium melodiarum est. + + Namque + Enim + simplicissima, vt ratio mensure + perquirit + requirit + per quare + , + + + xº apparens + vt apparet in + .10. + .10e. + .4°. + apparens + 4°. + mensure perquirit .4°. apparens + + methaphysice. + Arist. + Met. + X, 1052b ll. 34–37 + Vnde + 2° + + musice + mathematice + musice dixit + + boecius: + + dyapason + + dyapente + est + maxima + maxime + + max + maxime + + consonantiarum + et simplicitate + simplicitate + et simplicitati + notissima. + Boeth. + De inst. mus. + II.18 (Freidlein 250, ll. 6–8) + + Quod + Quid + autem sit mensura apparet quia motus illius consonantie que secundum medium + existit fortissimus est per totum + id per + id + per + quod fertur siue sit in principio siue in fine. In medio + namque + nam + enim + + + constat virtus + consistit virtus + virtus constat + totius, dyapason enim ex + + cordis + corde + + + conficitur + efficitur + perficitur + extremis et ad inuicem + confractis + constructis + et mediis, non autem alie consonantie. Et + quamquam + + vt + dictum est + predictum est + dictum + dicunt quidem + + predicta consonantia + sit perfectissima. Tamen + quando + quia + que + motus quo causatur + fuerit + fortissimus et uelocissimus, efficietur hec + dulcior + + delectatior + consonantia quam quando fuerit + minus + minis + fortis et uelox, eo quod tunc vox eius quod mouetur erit acutior + sonus, autem + sonus + et sonus autem + + + is + hiis + alius + aeris + similiter + + dulcior + obtuso + obtusus + aperenso + , propter quod corde tense uelociter sonant, eo quod motus earum est uelox cito pertransiens. Cum enim corda + fuerit + fuerit quia + fiunt qua + + + tensa + tense + , + non + vt + + potest in tantum + moueri et vagari a medio sicut si fuerit + relaxata + + laxata + .

+

+ + Deinde. + + SONUS. + + Et + + quia fecerat + mentionem + + de sono ultimo, vnde causatur ostendit, dicens sonum esse aut motum aeris in se aut + causa + causam + + cuiusdam alterius quod in aere mouetur. + Cuius + Cum + autem fuerit causa motus + qui + qui + + + per medietatem pori uel meatus existit tunc et + acutissimum oportet sonum fieri in poro. + + + Sic enim aer + Aer enim sic + Sicut enim aer + constringitur + et fortissimo motu + velocissime + velocissime + velocissimo + + et velocissimo motu fortissimo + et fortissimo motu + et fortissime + + + + cogitur moueri + moueri cogitur + moueri + , + + + vt declaratum + est + + + xia, + + + + Arist. + Prob. + XI.15, 900b ll. 10–12 + et sonum tunc reddit acutum. Et ideo instrumenta perforantur, + que foramina + quod foramina + etiam + + si + + claudantur + clauduntur + minime sonant. Quare + contingit + + concludit + conuenit + + + quod + + quando non + est + erit + + porus per medium, vt + dictum + dictum est + , existens, non causabitur maneries + + alicuius soni + aliqua soni uel alicuius + .

+

Sciendum + + ptolomeum + + + + per tholomeum + per + thm + tholomeum + + per thimotheum + perchium + in + armonica + armonicam + armonica sua + + taliter declarare + + dyapason esse optimam et perfectissimam + consonantiarum + consonantiam + , fere siquidem + vna + + existit + vocula + notula + , vnum quodammodo sonum componens, puta + ceu + seu + + + + + si denario + si denarius + denarius + aliquis numerorum + addatur + ad + addarum + + , vt duo, semper + remanet + remanebit + + + + + denarius + binarius + + integer illesus, + Boeth. + De inst. mus. + V.10 (Freidlein 360, ll. 6–10) + Cf. Ptol. + Harm. + I.7 N.B. Ptolemy actually says that the octave is a homophone, not a concord. + + + non enim ultra ipsum numerus quis eleuatur, + + vt visum est + vt visum + vt insum + + .15. + Arist. + Prob. + XV.3, 910b ll. 23–30 + Quod + tamen non + non tamen + tamen + contingit in ceteris proportionibus, nam si tribus + duo + coniungantur statim fiunt + .5. et + mutatur + mutantur + mutant + species numeri. + Sed si + Sed si tu + Sed + Si + + + duo addas + + addas duo + duo + addat + duo + addis + duo addit + duo + additur + + + denario + + denar. + denarium + + denarium + + .12. + + faciens + facies + etiam faciens + , + et + + + + vtrique + vterque + vtrumque + + + numerus + videtur + + integer + + conseruabitur + conseruari + , et similiter + si addas + + ternarium + ternarius + ternarios + denario + et ceteros eodem modo. + Similiterque + Similiter quia + Similiter quoque + Similiter + dyapason + simphonia + + symphoniam + + + + quancunque + quantumcunque + + consonantiam aliam + sumat + + suma + seruant + , seruat suam consonantiam + + neque + + + + immutat + inmutatur + imitatur + , vt ex + consona + consonantia + reddat + se + sed + dissonam, quod in aliis non accidit + simphoniis + + + . + + et cetera. + sequitur 36. + problema. +

+
+ +
+ + Trigesimumsextum + problema + 36m + trigesimum sextum. + Trigesimumsextum. + 35m. + problema. + + +

+ PROPTER QUID SI QUIDEM + PROPTER QUID SI QUIDEM MEDIA + + PROPTER QUID SI QUIDEM MEDIA MOUEBITUR ET ALIE CORDE SONANT, SI AUTEM + ITERUM HEC QUIDEM MANET ALIARUM AUTEM QUEDAM MOUEATUR MOTA SOLA SONAT? + AUT QUIA CONCORDARE EST OMNIBUS HABERE SE AUTEM + QUODAMMODO AD MEDIAM OMNIBUS, ET ORDINATIO QUE EST UNIUSCUIUSQUE UTIQUE PER + ILLAM EST? ELEUATA IGITUR CAUSA CONCORDANDI ET CONTINENTIS, NON ADHUC + SIMILITER APPARERE EXISTERE. UNA AUTEM DISCORDANTE EXISTENTE MEDIA AUTEM + MANENTE, RATIONABILITER QUOD EST SECUNDUM IPSAM DEFICIENS, ALIIS ENIM EXISTIT + CONCORDARE + . + + + Quare + Querit quare + + si media cordarum moueatur alie corde consonant illi, sed si postea fiat quod media + immobilis permaneat + + immobilis permaneat immobilis + + et quedam de numero + aliarum a media + armoniarum aliarum + aliarum + + + moueatur + moueantur + solum illa que + + fuerit + fuit + sint + mota sonat, + + ita quod + itaque + + + neque + + in + alia sonat + + propter motum ipsius, neque + etiam + in + + + media.

+

+ Nosce quod + huius + huiusmodi + de huiusmodi + de huius + + + problemate + problematis + + iam sermo aliqualiter precessit in + 20a. + secundo + + + problemate + capitulo + + + + .

+

+ + Deinde. + + AUT. Soluit dicens causam esse + quoniam media cordarum concordat et consonat cum omnibus + cordis + cordis aliis + . Quod ostenditur quoniam concordare cum omnibus + + nichil + + + non + + + aliud + ad + + est quam se habere aliqualiter + + ad mediam + ad medium + + + + omnis + omnes + , + ordinatio enim + + enim ordinatio + + + vniuscuiusque + + uniustus quia + aliarum cordarum per illam existit. Quod probatur quoniam + ipsa + ista + illa + + media remota ex instrumento, non amplius erit sentire cordam + aliquam que + existat + existit + extat + ratio concordandi alias concorditerque retinendi. Sed vna aliarum remota ita quod causa existat discordandi dummodo media cordarum + recte maneat + remaneat + , sicut debet, illud quod erat + deficiens, vt corda ablata, + suppletur + + per mediam, ita quod + + illa + ista + remota adhuc + + aliis cordis inerit + inerit aliis cordis + cordis non erit + concordare et consonantiam reddere per virtutem medie. Media enim est vt + magistra + + et regula + et 2a + + + + aliarum omnium + omnium aliarum + aliorum omnium + omnium ceterarum + . + + et cetera. + sequitur 37. + problema 19e. particule. +

+
+ +
+ + Trigesimumseptimum + problema + 37m + trigesimumseptimum + Trigesimumseptimum. + 36m. + problema. + + +

+ PROPTER QUID QUOD EST IN UOCE + PROPTER QUID QUOD + + PROPTER QUID QUOD EST IN UOCE ACUTO EXISTENTE MODICUM, GRAUI AUTEM + SECUNDUM MULTUM GRAUE? QUIDEM ENIM PROPTER MULTITUDINEM GRAUE, ACUTUM AUTEM + PROPTER PAUCITATEM UELOX EST. + MOLESTUM MAGIS CANTARE ACUTA QUAM GRAUIA, ET + PAUCI ASCENDENTIA POSSUNT CANTARE, + ET LEGES DIRIGUNT, ET ACUTI DIFFICILES DIMITTERE PROPTER ID QUOD TENSI + SUNT. + MINUS OPUS MODICUM MOUERE QUAM MULTUM, + QUARE ET AEREM. + AUT IDEM ACUTE SONANS ESSE NATURA ET ACUTE CANERE, + SED NATURA QUIDEM ACUTE UOCIS OMNIA PROPTER IMBECILLITATEM PRO EO QUOD NON + POTEST MOUERE MULTUM AEREM, SED MODICUM. MODICUS AUTEM UELOCITER FERTUR. IN + CANTANDO AUTEM ACUTUM POTENTIE SIGNUM, QUOD QUIDEM ENIM UELOCITER FERTUR, + PROPTER QUOD ET ACUTUM POTENTIE SIGNUM. PROPTER QUOD ET QUI SUNT BONI HABITUS + ACUTE UOCIS, ET MOLESTUM QUE ELEUANTUR CANTARE, GRAUIA AUTEM DEORSUM + . + + + Querit + Quare + Contingit + quesitum cuius + + terminorum primitus + + cuiustorum primitus + corpus primo + + tangit expositionem, dicens quod cum in voce acutum + existat secundum modicum temporis, graue + autem secundum multum. + Nam graue + + causatur propter multitudinem aeris moti qui tarde mouetur, acutum vero propter paucitatem ipsius, ex + qua + quo + uelocitas causatur, + + sicut ex multitudine tarditas, + + vt visum est .xia + vt visum .xia + vt visum est 11a particula. + + + Ps.Arist. + Prob. + XI.16, 900b ll. 24–28 +

+

+ + Deinde. + + MOLESTUM. + Secundo + format quesitum, dicens quare magis + difficile + difficile est + cantare + illa + ea + que sunt acuta quam + ea + illa + que sunt grauia. Quod ostenditur + quoniam + quia + pauci sunt + qui possunt cantus + qui possint cantus + + + ascendentes + cantare maxime, cum sint acutissimi. Et ideo + huius non + huiusmodi non + tales non + cantant, sed potius dirigunt leges, legales enim cantus constituunt. Sunt enim + tanquam + + graues remissi faciles ad cantandum, vt visum est + + .15 + in 15 + . Et non solum difficile + est in acutum tendere et + + seruare + seruant + reseruare + + cantus, sed etiam + difficile + difficile est + + + mox cessare a cantibus acutis, eo quod + tensi + remissi + sunt valde + ceu + + seu + + + equum + + + extensum + et uelocissime currentem + molestum + + est + + confestim sistere, atque + similiter nauem uelocissime + nauem similiter uelocissime + nauem uelocissime similiter + similiter manere uelocissime + nauem uelocissime + + + inpulsam + + .

+

+ + Deinde. + + MINUS. Tertio arguit in contrarium, quasi dicat + quod + quia + + minus + + est + sit + opus et sic + maior + maior opus + minor + virtus requiritur ad mouendum illud quod est modicum + quam quod + quod quam + quam quod est + quare illud quod est + quam ad + multum, non videtur quod acutum mouere + cantando + euitando + + + sit + fit + difficile, cum sit modicum, et graue facile, quia multum + ymmo + + + econuerso, quare sicut est. Universaliter in aliis ita + etiam videtur esse + videtur esse + videtur etiam + in aere + qui + que + + est subiectum sonorum, eius enim medium + proprium + proprie + propositum + est ipse in quo causatur et recipitur primitus.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit dicens + causam esse + sumendam + + + + ex hoc, quia + idem videtur esse naturaliter acute sonare et + acute cantare + acuto cantare + sonare + , + et non + non + + + differt + + differunt + dicent + + nisi + secundum quod + quod + sicut + + + superius differt + differt superius + superius + ab inferiori. + Hoc autem + assumit + + + + vt + + declaret + declararet + + per + + id + illud + quod + est + + in voce + vniversaliter + similiter + videtur + + sic esse in sono. Vnde subdens + + ait + + autem + aut + + + + omnia + omnis + naturaliter acute + + vocis + vocem + vox + + fieri propter debilitatem suam, eo quod non + possunt + possint + multum aerem mouere, qui + + grauis vocis est causa + est causa grauis vocis + grauis vocum est causa + grauis netis est causa + grauis est causa + . Sed modicum possunt, + modicus + motus + + autem aer motus uelociter fertur, + + + vt visum est + .xi°. + + + + Ps.Arist. + Prob. + XI.13, 900a ll. 21–27; 21, 901a ll. + 31–32 + + Sepe atque + Sepe at quia + Sepe ac + Aut quia + acutum sic uelociter mouetur si quis cantauerit secundum acutum. Signum quidem + ex hoc + suscipitur + accipitur + sumitur + concipitur + + cuiusdam vigoris + in + + eo quod mouet aliquid uelociter, quod non fieret nisi vigor adesset. Et ideo ex + hoc + hac + + + confirmatione + confirmatiue + concluditur quod illi qui sunt bone complexionis quorum pulmones non + redundant + + redundat + exundant + + humiditatibus superfluis + existere + existunt + esse + vocis acute eo quod organum est + exsiccatum + + + excitatum + + solidum. Et quia difficile est cantare que eleuantur, cum acuta extollantur, ipsa + fiet + fiat + cantare difficile, nam + + eleuare + elleuare est + eleuantur + contra naturam, + + + vt + visum est + visum + + particula secunda. + + + + Ps.Arist. + Prob. + II.38, 870a l. 34 + Et quia grauia + naturaliter tendunt + tendunt naturaliter + naturaliter + deorsum, quod nobis magis + naturale, + ideo facile fit + facile fit ideo + ideo facile sit + facile igitur fit + + ipsa cantare. Sic igitur + + soluitur + soluit + + solo + solummodo + + solum + adquesitum, + neque + + + + ambiguitas + + relinquitur + + relinquatur + aliqua + que + quia + + in + + + .xia. particula + particula .11a. + 5a particula + ille particula + + + intelligenti dicta, + intelligentis dicta, + intellecto dicta, + multa dicta, + + quoniam + + in acute cantare siue sonare + in acutis cantare siue sonare + acute cantare siue sonare + in acuto cantare siue sonare + + + duo fit + duo sit + est duo + + considerare: puta + + modicum + aerem motum et quantum ad hoc videtur quod + acutum + acute + mouere sit facile, + Ps.Arist. + Prob. + XI.14, 900a ll. 34–36 + cum + id + illud + + debiles agant et + impotentes + + + . + Est et + Et est + Est + Est etiam + + considerare quod illud + modicum + aeris velociter mouetur, et + + quia quod + quod + quia + + + huius + huiusmodi + non + fit + sit + nisi a + constanti + constante + virtute. + Ideo + Item + Ergo + + + acutum + acute + mouere denotat constantiam + virtutis, et difficultatem per consequens, quare apparuit + + + .xiiii°. + 24º + .34°. + + xi°. + pveros + + voces acutiores + acutiores voces + acutiores + habere + senioribus + senibus + , propter + consistentiam + constantiam + + calidi + + virtuosi + unctuosi + . + Ps.Arist. + Prob. + XI.14, 900a l. 33 to 900b l. 8 + + + et cetera. + et cetera et cetera. + sequitur 38. + problema. +

+
+ +
+ + Trigesimumoctauum + problema + 38m + trigesimum octauum. + Trigesimumoctauum. + 37m. + problema. + + +

+ PROPTER QUID ET RITHIMO + PROPTER QUID IN RITHIMO + + PROPTER QUID ET RITHIMO ET CANTU ET OMNINO CONSONANTIIS GAUDENT + OMNES? + AUT QUIA MOTIBUS QUI SUNT SECUNDUM NATURAM + GAUDEMUS SECUNDUM NATURAM? + SIGNUM AUTEM PUEROS CONFESTIM NATOS GAUDERE IPSIS. + PROPTER CONSUETUDINEM AUTEM MODIS CANTUUM GAUDEMUS. + RITHIMO AUTEM GAUDEMUS PROPTER MOTUM ET ORDINATUM + NUMERUM HABERE ET MOUERE NOS ORDINATE MAGIS. MAGIS PRIUS ENIM EST ORDINATUS + MOTUS NATURA INORDINATO, QUARE ET SECUNDUM NATURAM MAGIS. + SIGNUM AUTEM LABORANTES ENIM ET BIBENTES ET + COMEDENTES ORDINATE SALUAMUS ET AUGEMUS NATURAM ET UIRTUTEM, INORDINATE AUTEM + CORRUMPIMUS ET STUPEFACIMUS IPSAM. + EGRITUDINES ENIM ORDINATIONIS CORPORIS NON SECUNDUM NATURAM MOTUS SUNT. + CONSONANTIA GAUDEMUS QUONIAM COMPLEXIO EST + CONTRARIORUM HABENTIUM PROPORTIONEM AD INUICEM. PROPORTIO AUTEM ORDINATIO, + QUOD ERAT NATURA DELECTABILE. COMPLEXIONATUM AUTEM INCOMPLEXIONATO OMNE DELECTABILIUS ALITER. + QUAMUIS SENSIBILE SIT UTRISQUE EXTREMIS EX EQUALI + POTENTIAM HABET IN CONSONANTIA PROPORTIO + . + + Quare omnia, + ita + quod + vt + + etiam bruta + + vtcunque + vtrunque + + + + + sicut videbitur + sint videbitur + + + .vii°. + + xxixe. + 29e particule + et 9e. + , + + + + Ps.Arist. + Prob. + XXVIII.7, 949b l. 37- to 950a l. 16 + + exultantur + + exultant + + + rithimo + rithimi + + et cantu + ac + ac etiam + et + + vniuersaliter + + consonantiarum + consonantiam + consonantia + auditu in hiis, siquidem + + verbis + + + + triplex pretacta indicatur + triplex pretacta inducatur + pretacta indicatur triplex + triplex iudicatur pretacta + + musica?

+

+ + Deinde. + + + AUT. + AUT QUIA. + QUONIAM. + Soluit + primo dans causam vniversaliter dicens + primo vniversaliter dicens + dicens primo + causam fore communem, + quoniam + quia + quare + + + gaudemus naturaliter + + naturaliter gaudemus + gaudere naturaliter + gaudemus vniuersaliter + giludomus naturaliter + motibus naturalibus, + cum + que + + + in temperamento + temperamento + in temperato + quodam consistant. Sicut enim + excellentie sensibilium corrumpunt + + sensus + sensum + , + + vt apparet de + anima + 3°., + vt apparet 3º + de anima, + vt patet 3° + de anima, + + Arist. + De an. + III.13, 435b l. 15 (Cf. 426a, l. 30) + + ita et + ita etiam + ita vt + et + itaque + + + ipsorum + conmensurationes + eos custodiunt, + + vt + sicut + + + etiam + et + + + + tactum est + tactum + tactus est + + in principio + huius + huiusmodi + + particule. + Ps.Arist. + Prob. + XΙΧ.2, 917b ll. 22–29 +

+

+ + Deinde. + + SIGNUM. + Declarat secundo quomodo in vnoquoque + + trium + cum + + + predictorum + predictorum sicut + motus secundum naturam + existat + existit + existant + + et per consequens gaudere fiat + + ex eo + + et eo + + . + Primoque + Primo quid + Primo quod + Primo + manifestans in + tactu + cantu + sensu + + + dicens + dicit + + + huius + huiusmodi + hoc + signum esse quoniam pueri mox cum fuerint nati accidit ipsis gaudere + cantu tum + cantu cum + cantu tamen + tamen + cantatum + + + propter + per + musicam naturaliter + ipsis + + inditam + + + indicatiua + . Anima enim + + maxime nostra + nostra maxime + maxime + magis uel maxime + ad similitudinem + numeri consoni + numerum consoni + numerius soni + + + constricta + constructa + constituta + + + existit + existat + est + , + + vt apparet per + vt patet per + vt + per + + + damascenus + + + damascenum + dictum + in <app> + <lem wit="#β #Ea #Vb #Vo #m #v">afforismis</lem> + + + + + + <rdg wit="#Pz" ana="#additive #J">amphorismis suis</rdg> + </app>. + Yuḥannā ibn Māsawaiyh + Aph. (Vat. Lat. + 2460, + f. 39v, + ll. 10–11) + Quare + + primo + de <app> + <lem wit="#α #π #Vz">regimine sanitatis</lem> + <rdg wit="#Ma #Px #Vm #m #v" ana="#lexical"><choice> + <abbr>re. sa.</abbr> + <expan instant="false">re<ex instant="false">gimine</ex> sa<ex instant="false">nitatis</ex></expan> + </choice></rdg> + </app> + pueri + familiariter dispositi sunt ad musicam. + Gal. + De san. tu. + I.7 + + Tum + Cum + Tamen + etiam propter consuetudinem quam + adipiscimur + adispiscitur + adypiscimus + adipiscuntur + deinceps + ex + + maneriebus + + + + cantuum + + + gaudere accidit, quidam enim gaudent vno cantu, alii + vero + autem + + alio secundum quod consueti + fuerunt + fuerint + audire a natiuitate. Quod autem infantes + huius + huiusmodi + cantibus + delectentur + + delectantur + , id sciunt nutrices industriose que modis cantuum et + motuum + motum + motibus + + + quibusdam + quidam + communium + , cum hii + + tristentur + tristantur + et plorant, ipsorum animos + demulciunt + + demulcent + , quiescere facientes et gaudere, cum ostensum sit hanc esse potentiam musice. Vnde + + eodem + eodem modo + + primo: + nutrices tribus + modis consolantur et ad + sompnum + + ad sompnum + prouocant pveros: vt appositione + mamillarum + + + ad os, melodia vocis, et motu. + Gal. + De san. tu. + I.7 +

+

+ + Deinde. + + + RITHIMO. Secundo dat causam + RITHIMO. Dat causam + RITHIMUS. Secundo dat causam + RITHIMO. Declarat secundo + RITHIMO. Secundo declarat + causam + AC HUIC. Dat causam 2° + + + rithimo quare + quare rithimo + rithimo + + + fit + sit + + gaudere quod + secundo + + signo manifestat + manifestat + signo ibi + signo manifestat secunda ibi + signo inanimat + + + SIGNUM AUTEM + SIGNO AUTEM + DIGNUM AUTEM + + , + dicens causam esse + dicit causam esse + dicens causam dicens causam + esse + + + + quare + quia + quoniam + + gaudemus rithimo. + Est + + + propter + motum suauem et numerum ordinatum eius et proportionatum clausularum vnius + + cum + + altera concordantium + quos + quas + + + habet + habet est + hoc + . Que + autem huius + autem huiusmodi + aut huius + ab huius + nos habent mouere amplius paulatiue et ordinate, nam motus ordinatus et vniformis prior est + natura + nature + + + opposito + apposito + apposita + , + + ceu + seu + sicut + habitus + priuatione + priuationem + priuationis + . + Ordinatum + Ordinatus + Ordinatam + + + enim habet + rationem + + ratione + equalitatis, + inordinatum + inordinatam + id est ordinatus + vero + inequalitatis + rationem inequalitatis + + in cardinalitatis + ī cartis + + . Omne + autem + enim + + inequale + reducitur ad equale, + vt + sicut + + ad primum et perfectum, + vt + et + + + probatum est + probant + arismetrici et musici. Et ideo concluditur quod naturaliter magis + debeamus gaudere + debemus gaudere + rithimo et + iocundari + iocundiori + iocunditati + , + tanquam + + ordinato.

+

+ + Deinde. + + SIGNUM AUTEM. + Declarat + id + illud + + + + signo + 2° + 2º signo + dicens quod + huius + huiusmodi + signum in + regimine + + vite + + + sumitur tale, quia nos + exercitantes + + et + . + + + + laborantes bibentesque + laborantesque bibentes + elaborantes bibentesque + laborantes et bibentes + + + et + ac + atque + + + comedentes + + + + conmensurate + mensurate + + + et + ac + ordinate, + + + vt precipit + precipit + + regimen + + galeni + + caloris + + <app> + <lem wit="#Ma #Px #Va #Vm">sanatium</lem> + + <rdg wit="#π" ana="#lexical #J">sanitatem</rdg> + </app>, + Gal. + De san. tu. + V.2 + + saluamus et augmentamus + nostram naturam siue complexionem + naturam nostram siue complexionem + naturamque nostram siue complexionem + nostram siue coniunctionem + nostram complexionem siue naturam + , quantum ad corpus magis + et virtutem + ad virtutem + + + + quo ad animam plus. Per oppositum vero cum indebite ac inordinate vtimur + + + regimine sanitatis corrumpimus ac + stupefacimus + naturam nostram + nostram naturam + naturam + + et virtutem. Quod + ostenditur + quia + egritudines + sunt motus cuiusdam ordinationis et concursus corporis nostri non secundum naturam + verum + sed + preter + naturam existentis + naturam existentes + naturam existentem + naturas + . + Quomodo + Quomodo autem + Quomodo autem quod + + + egritudo sit motus + + + ostensum differentia 7a + ostensum est differentia 7 + ostensum differentia 7a alia + visum est prima + + problemate quarto. + + Ps.Arist. + Prob. + VII.4, 886b ll. 5–6 +

+

+ + Deinde. + + + CONSONANTIA. + CONSONANTIAM. + Assignat tertio causam delectationis consonantie, dicens + causam huius + huius causam + causam huiusmodi + causam + esse, quare + + gaudeamus + gaudemus + consonantia, quia ipsa + causatur + cantatur + ex coniunctione + contrariorum habentium proportionem ad inuicem secundum acuitatem et grauitatem. + Confranguntur + Confrangantur + Confrangitur + Cum frangantur + + enim oppositorum excellentie ita vt ex eis resultet vnum medium + contemperatum + + contemperamentum + contemperatiuum + temperatum + + + ac + et + proportionatum extremis, + ceu + seu + seu seu + Sicut + opposita ostendunt contrariorum excellentium in copulatione ad inuicem + qualitatum + qualitatis + . In + huius + huiusmodi + hac + autem proportione + copulationis + complexionis + + + saluatur + + seruatur + + ordinatio, que naturaliter + + + delectabilis existit + est delectabilis + delectabilis + . + + delectabilis + Quod autem hoc sit delectabile ostenditur quoniam habens consonantiam est complexionatum + + + seu + ceu + siue + mixtum, + + + omne autem + complexionatum + complexionatum et mixtum + + + + + est + delectabilius + delectabilis + quam incomplexionatum + + + + vel + seu + et + simplex, aliter tamen et aliter, quoniam multo magis est delectabile + cum in simplicibus + cum simplicibus + + + + vt + et + id est + + in elementis primis remaneant excellentie, in complexionatis + + autem + aut + vero + + + + consurgunt + confringantur + refranguntur + et ad medium + reducte sunt + sunt reducte + deducte sunt + ducte sunt + .

+

+ + Deinde. + + QUAMUIS. Remouet + 2° + dubitationem + dubium + , quia crederet aliquis + eo quod + quod + quia + complexionatum compositum est ex vtrisque + + extremorum + non + posse delectabile fore. Quod remouet, dicens + + + + + quodlibet + quod + quia licet + + + sit complexionatum + si complexionatum + complexionatum + complexionatum sit compositum + ex vtrisque + + + + + extremorum excellentiis + excellentiis extremorum + extremorum excellentibus + extremorum non posse delectabile + fore excellentiis + + constitutum. + + Nichilominus + + tamen est delectabile, quoniam ipsum constituitur ex + contrariis et inequalibus + inequalibus et contrariis + , et non ex + omnino + non + + similibus et equalibus, sic enim non + posset + possunt + potest + adeo mouere. + Et + + ideo + thimoteus + + + + + + + + + consonantiam fieri + ait ex dissimilibus + ex dissimilibus ait ayt + aut ex dissimilibus + vt ex similibus + ex dissimilibus + in vnam et eandem vocem venientibus, nam in vocibus que nulla equalitate discordant nulla + omnino + + extat + + existit + consonantia, + cum ea sit vt tactum + est + + dissimilium inter se vocum + sed dissimilitudo. neque similiter si acutum + iungatur + + in vnum + redacta concordia. Si enim grauis graui + misceatur, nulla + fit + sit + consonantia sed dissimilitudo, + neque similiter si + + similiter nec si + si autem similiter + ne similiter si + acutum iungatur + acuto. Plato + siquidem + + voluit taliter consonantiam + voluit talem consonantiam + voluit taliter consonantia + voluit dicere taliter consonantiam + voluit tradere taliter consonantiam + in + aure + aere + autem + + + causari + causare + , + necesse + necessario + vocem + + quidem + ait sonum + velociorem + + velocem tunc + + esse acutiorem, qui cum precesserit + grauem + graue + ingreditur + celeriter + + + + in aurem + aurem + maiorem + ipsius ledens + extremitatem intrinsecam. Et ideo quasi pulsus + cum tanto + cum canto + a tanto + + + motu + + modi + + + retro reuertitur + reuertitur + retrouertitur + , et quia + iam + ipse + + + pigrescit exire, obuiat graui subintranti et sibi commiscetur + + consonantiam + consonantias + consonantia + + constituens + musicalem. Id tamen vt + + visum est + visum et + visum + dictum est + dictis non conuenit + + thimotei + + + + + + + . + + et cetera + sequitur 39m. + problema 19e. particule. +

+
+ +
+ + Trigesimumnonum + problema + 39m + trigesimum nonum: + Trigesimumnonum. + 38m. + problema. + + +

+ PROPTER QUID DELECTABILIUS + + + PROPTER QUID DELECTABILIUS EST SECUNDUM CONSONANTIAM EO QUOD EST UNIUS + UOCIS? + AUT ET ANTIFONUM QUIDEM CONSONUM EST DYAPASON? EX + PUERIS ENIM IUUENIBUS, ET NUMERUS FIT ANTIFONUM, QUI DISTANT COMMUNIS SICUT NITE + AD YPATEM. CONSONANTIA AUTEM OMNIS + DELECTABILIUS SIMPLICI SONO, PER QUE + AUTEM DICTUM EST, ET HORUM DYAPASON DELECTABILISSIMA QUIDEM QUAM UNIUS SONI EST + SIMPLICEM HABET SONUM. ORGANIZANT AUTEM IN DYAPASON CONSONANTIA. + QUIA QUEMADMODUM IN METRIS PEDES HABENT AD SE + IPSOS RATIONEM EQUALEM AD EQUALEM, + AUT DUO AD UNUM, AUT ALIQUEM ALIUM, + ET ITA IN CONSONANTIA SONI PROPORTIONEM HABENT + MOTUS AD SE IPSOS. + ALIARUM AUTEM CONSONANTIARUM IMPERFECTE, QUE + ALTERIUS REUERSIUE SUNT IN MEDIUM FINIUNT, PROPTER QUOD POTENTIA NON EQUALES + SUNT. EXISTENTES AUTEM INEQUALES PER CORRUPTIONEM SENSUI. QUEMADMODUM IN ROTIS + IN DISSOLUENDO MAIUS SALTANS SONANTIBUS EST. + AMPLIUS YPATE ACCIDIT EUNDEM FINEM PERIODORUM, QUI + SUNT IN SONIS, HABERE; SECUNDA AUTEM NEATIS ICTUS AERIS YPATE EST. FINIENS AUTEM IN IDEM, NON IDEM FACIENTIBUS UNUM ET COMMUNE OPUS ACCIDIT + FIERI, QUEMADMODUM SONANTIBUS SUB CANTU. ETENIM HII ALIA NON PARITER + FISTULANTUR, SI IN IDEM CONUERTANT DELECTANT MAGIS FINE QUAM CONTRISTANT + DIFFERENTIIS QUE SUNT AD FINEM, IN EO QUOD FIT EX DIFFERENTIBUS COMMUNE + DELECTABILISSIMUM EX DYAPASON. ORGANIZANT AUTEM EX CONTRARIIS UOCIBUS; PROPTER + HOC IN DYAPASON ORGANIZANT + . + + Quare cantus et vniuersaliter sonus, existens secundum consonantiam, que est + copulatio + + compositio + quedam + suauem + suaue + consuauem + et mixtum reddens sonum, delectabilior est quam cantus et + omnino sonus qui + sonus qui omnino + vniversaliter sonus qui + non sonus qui + fuerit vnius vocis et percussionis, et uniuersaliter dyapason ad alias consonantias?

+

+ + Deinde. + + AUT. Soluit et primo assignat + causam vnam + vnam causam + , secundo alteram uel priorem confirmat. + secunda + ibi + ibi secunda + secunda ibi + + AMPLIUS. Adhuc + prius dat causam + primo dat causam + dat causam + prime partis, + dicens + dicens primo + primo dicens + + + id + illud + ideo + hoc + id ideo + esse quoniam + dyapason est + antiphonum + archifonum + archisonum + + quoddam + + consonum + sonum + cum sonum + cum sonu + . + Secundum enim ipsam + Secundum ipsam enim + Enim secundum ipsam + + + solam + solum + + + fit + sit + + antiphonizare, vt + apparuit + apparebit + , et + organizare + + organizare vt apparuit + et organizare + agonizare + cum sit ex pluribus + + sonis uel vocibus consonantibus + vocibus et consonantibus sonis + sonis uel vocibus contrasonantibus + + coaptata. Ipsa + enim + enim est + vt dictum est + optima consonantiarum, + ac + et + quia + suauissima ex vocibus acutis pverorum et grauibus iuuenum + consurgit. Fit enim numerus + quidam et proportio consonum reddens + antiphonum + + + . + Alias + + + + Alii + Aliquando + Aliter + Vel + + + et + et cetera + etiam + + + viris fit + fit viris + iuris fit + viris + et tunc iuuenibus veniat + + indeterminatio + in determinationem + + + de li + de lii + + delectabili + deli + + ly + pueris, prior tamen scriptura melior. Qui + siquidem + sic quidem sit + + differunt + + ab + ad + inuicem ratione + acuitatis et grauitatis + grauitatis et acuitatis + + + vocis + uas + + + acquisite + + secundum + sed + tempus, quanta est differentia + communis uel vniversalis + universalis uel communis + communis et vniversalis + et ultime + ad ypatem communem + dyapente communem + dyapente causam + + + supremam + + supremamque + extremam + . Que quidem + due + secunde + corde tacte reddunt consonantiam delectabilem, cum sonus earum sit compositus. Omnis autem consonantia delectabilior + + est + est magis + + quam sonus + simplex. Et ideo dictum + est + + prius quod dyapason de numero sonorum est delectabilissima + per respectum + per respectu + et per respectum + in respectu + ad sonos simplices + et + + vt + + vnum tantum. Vnde secundum eam + + solum + + sonum + + + vt prescriptum est + prescriptum est + prescriptum + vt scriptum est + + + organizare + + + accidit + .xviii. + 18° + hiis + igitur + , quod in alia consonantiarum non contingit. Dicit autem + communis + numerus + + + + quia + quod + + ypate et nete sicut + + et + est + + + aliarum quedam preponuntur + et alie supponuntur, repetuntur enim cum determinatione + cum + + plures + septem + enim + id est + ponuntur corde vt + policorda + + + policorde + + + edocent + edocet + edocentur + + + boecii + boni + vero + .10 + + .

+

+ + Deinde. + + + QUIA QUEMADMODUM. + QUEMADMODUM. + QUARE QUODDAM. + Declarat + deinde id + id deinde + illud deinde + demum id + id demum + dictum id + deinde + , dicens hoc esse quia sicut in carminibus pedes + obtinent + + optinet + oportunt + + debitam proportionem ad inuicem, vt sit proportio aut equalis ad + equale + equalem + equalia + , vt + dicatur + dicitur + + in + dactilo + + + + + + constante ex tribus sillabis equalium + ex tribus + sillabis equalium constante + constantem ex tribus sillabis equalium + + constare ex tribus + sillabis equalium + + + + non + vt + et + + + tandem + tamen + tantumdem + temporum, quia ex prima longa, que + est + + + duorum temporum, et duabus breuibus, quarum + alter vterque + alter vtram + alterum vtraque + altera vtraque + ad alter vtraque + + vnius, + ubi + vt + et + nisi + + + duo ad vnum + unum ad duo + duo + + + comparantur + comparatur + operantur + , vt + due breues ad vnam + longam, vel econtra, + + ceu + seu + sicut + in + anapesto + + + apeston uel anapasco + huic opposito, uel secundum alium + quendam + quamdam + quidem + modum sicut vna + sillaba + duorum temporum ad aliam consimilem, ceu + in spondeo. Aut + vnam longam + ad + et + alteram breuem vel econtra + + , + velut + vt + vel + in + trocheo + + + + et + iambo, spondeus siquidem + sono proportionatur + proportionatur sono + sonus proportionatur + graui et iuuenum voci. + Tribrachus + + + + Tribati + Tribitus + Attributus + + + vero + quidem + est + + + + constans ex tribus + breuibus + ex + tribus breuibus constans + + acute, sed + dactilus + + + + + + anapestus + trocheus et iambus + + similantur + + assimilantur + + + vterque + + vtraque + vtrique + . + Similiter + Sic + + + etiam + et + igitur + + pedes quibus vtimur diuersa + optinent + + + loca in metro vt visum + est + + + 20.

+

+ + Deinde. + + ET ITA. + + Tunc + Nunc + + applicat ad propositum, dicens + + eodem modo in + consonantia + consonantiam + + + euenire soni + eueniet soni + euenit esoni + euenire + + aduenire eodem modo in consonantia + et proprie dyapason, nam motus sonorum + + causatiui + causatur + cantantium + cantanti + cantantiui + cantui + canti + proportionem habent + ad + ad se + inuicem.

+

+ + Deinde. + + + ALIARUM. + ALIORUM. + Αssignat + secundo + + + + causam partis alterius + causam alterius partis + partem alterius + , dicens quod, + de numero aliarum consonantiarum + ad + a + + dyapason quia sunt alterius + + proportionis ab ea, sunt + imperfecte + + , non enim sunt per + totum + tonum + ambientes omnia signa .vii. uel .viii. + + monocordi + + monocordia + + prima sicut dyapason. Sed potius reuersiue facte circa + medium terminantur, vt dyatesseron + in quarto + medio + + + signo + signo et + dyapente in quinto, vt visum + est + + + .13°. + + et .32° + et 12º + + . Et ideo non habent virtutem equaliter + ceu + seu + sicut + dyapason, + verum + sed + dicendum 8m. + potius + inequaliter + in equalitatem + inequalitantur + inequaliter licantur + propter ipsas, + namque + enim + sensus + horret + + + horum + haberent + + + auditus et + et auditus + corrumpitur. Sunt enim + respectu + respectum + dyapason + aspere + ac + et + + + horride + + + + horride et aspere + , quod declarat, quia sicut accidit + in rotis + rotis + in dochus + cantantibus, + id est + id est in + + cantibus + rotatiuis + + + seu + conuersis + conuersiuis + conuersiuus + , + quod si aliquis + quia si + aliquis + + eleuando sonum ultra id quod debet, + saltem in maius sursum ad aliquas notas in quas non debet + + peruenire, accidit + sonum totum dissolui, vt + apparet + patet + in organis + ita + + + + et + etiam et + + in aliis + consonantiis + consonantibus + + + + ad + a + + dyapason contingit suo modo et maxime in dyatesseron, vel + + rotis + + totis + , id est + + instrumentis + in instrumentis + + illis antiquioribus habentibus duas + acies cordarum, + vnam + vna + + + quidem + quidam + siquidem + in vno + laterum + latere + et reliquam in altero, que simul manibus tanguntur ambabus. Nunc autem si inequaliter + tetigerit eas, magis pulsans cordas vnius partis quam alterius, + adulteratur + adulterantur + adultantur + + + simphonia + + symphoni et + , primum tamen + melius et uerius + melius et uniuersalius + vniuersalius et melius + . Dicit autem corruptio + sensui + sensuum + sensus + quia dictum est quod musica non solum + + rationi + rationem + + + innititur, vt + + innititur, + + + sensit + sensuit + sensiunt + sentit + posuit + sensui + + + pictagoras + + + pythagoricis + pictagorici + , + neque + + nunc + sed + + tantummodo sensui, + sicut + sic + + + aristoxenus + aristotenus + + + + + + + , sed + vtrumque + vtrunque + vtroque + vterque + + contractat.

+

+ + Deinde. + + AMPLIUS. Ponit aliam solutionem uel magis pretactam confirmat et declarat dicens + rursus in ypate accidere quod habeat + vnum et eundem + unum et eiusdem + et eundum + eundem + finem + omnium + omnium omnium + + + + peridorum + + + + siue + circuitionum + + circuitionem + existentium in sonis. In + ipsa + ipsam + + enim, + tanquam + + + + in + + + principaliorem, + terminantur + terminatur + uel melius finem + perydorum + + + id est + resonationum + + resonationem + resonantium + post ictum + + remanentium + resonantium + diu in aere, quod + tinnitus + + + + rinitus + + potest dici. Et ideo vocatur + + magistra + + nigram + , ipsa enim + + suscipit + + se concipit + omnes et obtundit cum eius sit + + proprius + proprium + prius + + + antiphonizare + + antiphonaria + + + + et + atque + ac + + + organizare + + + + + . Sed secunda corda, + correspondens + + correspondet + + ypati per oppositum omnino, est + neatis siue netes uel neatis + + + + , id est resonantie + siue tinitus + + + sumitanter + , pretacti. Dupliciter enim accipitur + neate + + neatis + + + .xlii. + 41° + + apparens, + 2° + + + cuius + quidem + ictus et sonus + causatus + + + cantus + in aere. + In idem + Et idem + + + + finit + fuit + sunt + cum sono qui + fit + fiunt + fuit + ab ypate, ex + ambabus + ambobus + amborum + + enim + consurgit, vt visum est + + sepius in + sepius + + + + simphonia + + dyapason. Et + merito + + , quia licet non eundem sonum reddant secundum se. + Ymmo + + + + vna acutum et altera grauem. + Tandem + Tamen + Et idem + cum ipsarum soni + coniungantur + coniunguntur + iungantur + ad inuicem, contingit fieri vnum et + eundem sonum omnifariam, quemadmodum accidit illis qui sonant instrumenta sub cantu cantantium. Vel quia aliqui + + precinunt + precinit + ponunt et precinunt + precipiunt + + + et alii subcinunt + + et aliqui subcinunt + alii succinunt + + licet, + et + + enim videantur discordare in principio, + concidunt + excidunt + concidunt tamen + in + finem vnum + vnum finem + fine unum + . Et + illud est + id est + hoc est + idem + quod subiungitur, tales + namque + enim + + + non + + pariter et vna + fistulantur + fistulantur et cantant + , sed + secundum + + + + alia et alia + aliam et aliam + alia + . + Si tamen + Tamen et + + quamuis + sint + sunt + sicut + + alii + + et alteri + et aliquando + tamen + + + + concurrant + concurrunt + + + tandem + in eundem + + + + fine in vnum + in finem vnum + finem in vnum + finaliter in vnum + finem et vnum + + + quendam + quidem + aliquando + sonum, magis habent inducere delectationem quam tristitiam, propter hoc quod + differentie + seu diuersitates que sunt in eis secundum principium reperte + sopiuntur + + seperiunt + + et concurrunt + demum + deinde + ad eundem finem + siue + seu + terminationem. In eo enim, + vt + quod + + + declaratum est + declaratum + + declaratum prius est + + antea, quod + ex + + differentiis + + diuersisque extremis + efficitur + + vnum + vnum et + + quoddam + + commune + + + + + proportionatum + proportionaliter + proportionabiliter + . Cum dyapason + sit + fit + sic + + + huius + huiusmodi + + quod + + relinquitur + + derelinquitur + + ab ea + + simphonum + + + simplex hominum + delectabilissimum extat, quod ostenditur quia secundum + eam organizare + + organizare eam + organizare + ex oppositis vocibus + causatur + cantatur + + et sonis + tandem in unum + in vnum tandem + + in unum tamen + in unum + + redactis. Et quia dyapason + ex + in + + + huius + huiusmodi + + + consistit + + existit + , vt + expositum est + expositum + dictum est + , sepius ideo + secundum + per + + ipsam dictum est + solam + solum + nullamque + aliarum + aliorum + aliam + + + organizari + + organizare + , + .20. + problemate + + .

+

+ Nosce + Notandum + + quod sicut se habet vox composita ad simplicem, ita dyapason ad reliquas consonantias. + + et cetera + + +

+
+ +
+ + Quadragesimum + problema + 40m + Quadragesimum. + Quadragesimum + problema + 39m. + problema. + + +

+ PROPTER QUID DELECTABILITER + PROPTER QUID DELECTABILIUS + PROPTER QUID DELECTABILITER AUDIUNT + + PROPTER QUID DELECTABILITER AUDIUNT CANTANTES QUOSCUNQUE UTIQUE + PRESCIENTES ATTINGANT CANTUS QUAM SI NESCIUNT? + VTRUM QUIA MAGIS MANIFESTUS EST ATTINGENS + QUEMADMODUM INTENTIONEM QUANDO COGNOSCUNT QUOD CANITUR? COGNOSCENTIBUS AUTEM + DELECTABILE CONSIDERARE. + AUT COMPATIENS EST AUDITOR CANTANTI NOTUM? CONSONAT AUTEM IPSO, CANTAT + AUTEM OMNIS CONSONANS, QUI NON PROPTER ALIQUAM NECESSITATEM FACIT + HOC + . + + + + Et + + + + huius + huiusmodi + + + quidem + quidem problematis + autem + + expositio + sufficiens iam + + iam sufficiens + sufficienter iam + iam + + quinto + apparuit + + problemate + capitulo + + . + Repetitur + Reperitur + + + vero + autem + ergo + igitur + enim + vt + memorie amplius commendetur + amplius memorie comendetur + memorie commendetur amplius + . + + et cetera + + +

+
+ + +
+ + Quadragesimumprimum + problema + 41m + Quadragesimum primum. + Quadragesimumprimum. + Quadragesimumprimum problema et cetera. + + +

+ PROPTER QUID BIS PARACUTA + PROPTER QUID BIS + + PROPTER QUID BIS PARACUTA AUT BIS QUATUOR NON CONCORDANT, BIS DYAPASON AUTEM ITA? + AUT QUIA QUOD QUIDEM DYAPENTE EST IN EMIOLIA PROPORTIONE, QUOD UERO PER QUATUOR IN EPITRITO? EXISTENTIBUS AUTEM EMIOLIBUS + TRIBUS CONSEQUENTER NUMERIS, QUE EST EPITRICON, EXTREMA AD SE INUICEM NULLAM + PROPORTIONEM HABEBUNT, NEQUE ENIM PARTICULARIA NEQUE MULTIPLICIA ERUNT. + DYAPASON AUTEM, QUONIAM EST IN DUPLICI PROPORTIONE, BIS HOC FACTO, IN QUADRUPLICI PROPORTIONE SI FUERINT EXTREMA AD + INUICEM. + QUARE QUONIAM CONSONANTIA RATIONABILEM HABENTIUM + SONUM AD SE INUICEM EST, RATIONEM AUTEM QUI QUIDEM HABENT BIS DYAPASON + INTERDECISIONEM AD SE INUICEM SONI HABENT, QUI AUTEM BIS PER QUATUOR AUT BIS PER QUINQUE NON HABENT. QUI QUIDEM BIS DYAPASON CONSONABUNT, + UTIQUE ALII UERO NON PER EA QUE DICTA + SUNT + . + + Repetit trigesimumquartum vt amplius exponat. +

+

+ + + Deinde. + + AUT. Soluit et primo + assignat causam prime partis, secundo secunde + secunda + secunda + ibi + ibi secunda + ibi + + DYAPASON, + 3° concludit + intentum + intentum ibi + + + + + QUARE QUONIAM + QUARE + . + + Dicens + Dicit + causam esse + Dicit primo causam esse + Primo querit quare + + + quoniam dyapente est in sexquialtera proportione, + dyatesseron in + dyatesseron + + + epitrica + + . Hiis + igitur + ergo + + + + ita + itaque + sic + + dispositis + + numeris + numerus + numeris consequenter + reiteratis vt tria ad 4. + , vt + duobus + tribus + + sexquialteris et tribus, + et + etiam + + numeris consequenter + reiteratis + reiterati + reiterari + , vt tria ad quatuor, ex quibus erat + + epitrica + + , vt dictum est proportio cum erant simplices + inrepetiti + repetiti + etiam repetiti + vt repetiti + , tunc si extrema + huius duarum + huiusmodi duarum + harum duarum + duarum + huiusmodi + consonantiarum duplentur, ad + inuicem + coniuncta + coniunctam + coniecta + + nullam habebunt proportionem consurgentem. Inde quod + + probatur + prosequitur + , quia talia non + redduntur + reddunt + + + in + neque + superparticularia + neque + + multiplicia, penes que, vt visum + est + + + + 13°. + .xix. + , + + proportiones assumuntur + + assumuntur proportiones + proportiones accipiuntur + musice. Vnde apparet quod aristoteles + + consentit + pictagoricis + + + + pictagoras + + + , has ponentibus solum, et non concidit cum + + ptholomeo + + + + + , ponente + fore proportionem + proportionem fore + proportionem + + + compositam + compositum + expositum + ex dyatesseron et dyapason consurgere ex multiplici et + superparticulari + superpartienti + superuenienti + . + Si namque + + Si enim + Si nam + + + sumatur + + bis dyatesseron + puta prima dyatesseron + + + + sit + fit + proportio + trium + tria + tripla + ad quatuor, + et + + + + + secunda + secunda vero + secunda cessat + + + sex ad + octo + sex + .8. + sex ad + 6to. + 5 ad 4 + , + et coniungantur extrema, vt .3. + + comparando + operando + + ad .8. + + + nulla + + consurgit proportio + consurget proportio + proportio consurgit + contingit proportio + + secunda fit proportio 5a ad 4. nulla fit + proportio + + + + pretactarum + pretactorum + quantitarum + multiplicis aut superparticularis. + Similiter + Similiter et + + + in + + dyapente, + + vt + + si + sumatur + + exempli gratia vna dyapente + + , puta cum duo + comparantur ad tria, + et secunda + et 3a + et secunda et + secunda + . quando + + .6. + es + cessat + + ad + + .9., ita vt duo + + comparantur + comparentur + ad + + + .9.. Modo + eodem nulla consurgit proportio + + + cum omnis vt sic constet in + numero + epitrico + + emiola + + + + + + duplari + triplari et + quadruplo + + + , vt ostensum + est + et + + + + anterius + anterius et + in anterius + in antedictis + superius + . +

+

+ + + Deinde. + + DYAPASON. Assignat causam + 2e partis, dicens quia + dyapason se habet in + duplici + dupla + proportione, si bis + assumatur + + sumatur + ea erit in + quadruplici + + quatruplicibus + quatuor + + + extremis + in extremis + comparatis ad inuicem + proportionum + proportionem + proportione + proportionatum + + + minoribus et maioribus + maioribus et minoribus + minoris et + maioris + maioris et minoris + minoris et aliis + . Puta + + sumatur + + + bis dyapason + + vt in vna quarum + vt in unaquaque + vt quarum + + + comparetur vnum + vnum + comparetur + comparatur vnum + ad duo + + et in + et + in + + reliqua + duo ad quatuor, + tunc si extrema comparentur ad inuicem vt vnum ad quatuor + + + + resultabit + numerus quadruplus iuxta + quem + quam + quod + + + dictum + dictus + dignum + est + bis dyapason + dyapason bis + + + siue + siue non + fieri + sui in + + +

+

+ + + Deinde. + + QUARE QUONIAM. + + Concludit intentum 3° + 3°. + concludit intentum + , dicens et ideo quia consonantia est compositio quedam tonorum habentium + + rationabilem + rationabile + rationalem + et + proportionatum + proportionalem + sonum + ad se inuicem + ad inuicem + , et hoc habet bis dyapason, non autem bis dyatesseron aut + dyapente et reliqua. Quod + declaratur + declarat + quoniam proportio + quam quidem + quam + quam siquidem + siquidem quam + habent soni ad inuicem + est + etiam + habere inter + se decisionem + + decisionem + se decisiones + et confractionem + ad inuicem quandam, per quam + resultant + resultent + + + ipsi + quidam + + + proportionales + proportionabiles + armonici, vt bis dyapason, quod non habet + consonantia + consonantiam + + per quatuor + + aut + aut per + ad + + quinque siue dyatesseron + vel + siue + et + dyapente. + Sed + Cumque + vt dictum + est + + , tantum soni qui + fuerint + fuerunt + fluerunt + secundum dyapason + duplici + + + + + consonabunt + consonat + consonant + consonanter + + , alii vero minime, sicut ostensum + est + + + + per + propter + antedictam causam. + + et cetera. + sequitur 42. + problema 19e. particule. + + +

+
+ +
+ + Quadragesimumsecundum + problema + 42m + Quadragesimum secundum: + Quadragesimumsecundum. + Quadragesimum + primum problema. + + +

+ PROPTER QUID SI QUIS + PROPTER QUID SI QUID ALTERA + + PROPTER QUID SI QUIS ALTERA NITEM ACCIPIAT AUT YPATEM ACCIPIAT, YPATE + SOLA UIDETUR SUBSONARE? + AUT QUIA NEATE FINIENS ET DEPERDITA YPATE + FIT? + SIGNUM AUTEM POSSE AB YPATE NEATEN POSSE CANERE. + SICUT ENIM EXISTENTE IPSA CAUSAM NEATE, SIMILITUDINEM ACCIPIUNT AB IPSA. + QUONIAM AUTEM ET ECHO CANTUS QUIDAM EST, TACTUS EST UOCIS NEATIS + FINIENTIS SONUS EXISTENS IDEM SONO + YPATES MOUET CONUENIENTER, SIMILITUDINI YPATEM NITE UIDETUR MOUERE. NEATEN + ENIM SCIMUS UBI MOUETUR ASSUMPTA. YPATEN AUTEM IPSAM UIDENTES + INCOMPREHENSIBILEM EXISTENTEM ET SONUM IPSIUS AUDIENTES, HANC PUTAMUS SONARE. + QUOD IN MULTIS NOBIS ACCIDIT, IN QUIBUS NEQUE RATIONE. NEQUE SENSU POSSUMUS + CERTIFICARE CERTUM. + AMPLIUS SI PERCUSSA NEATE MAXIME TENSA + ACCIDIT IUGUM MOUERI NICHIL UTIQUE ERIT MIRABILE. MOTO AUTEM OMNES CORDAS + PARITER MOUERI ET SONUM FACERE NON IRRATIONABILE. ALIIS QUIDEM IGITUR NEATIS + SONUS ALIENUS EST ET FINIENS ET INCIPIENS, YPATE AUTEM FINIENS IDEM. NON + APPOSITO PROPRIO SUO MOTU, ILLIUS UIDEBITUR OMNIA EORUNDEM ESSE NON EST + INCONUENIENS. ERIT AUTEM MAIOR QUAM RELIQUARUM CORDARUM SONUS, QUOD HEE QUIDEM + A NEATE SICUT IMPULSE MOLLITER SONUERUNT, NEATE AUTEM, TOTA SUI IPSIUS + POTENTIA EXISTENS, IPSARUM FORTISSIMA EST. + QUARE MERITO ET SECULARIUM IPSIUS MAIUS ERIT QUAM + QUOD EST ALIARUM, QUARE BREUES MOUERI, SICUT IPSIS + . + + Quare si quis cantu + aut tactu + aut tacta + aut atactu + + + + altera + altam + + + + suscipiat + + suscipiet + + + nitem + + nitorum + vocem + + siue + extremam, quia multiplex vt + visum + rismis quidem + dictum + + + est + + , aut pro et ypatem accipiat, simul coniungens + alias + alteras + ambas + quidem + alteram + altera + altam + vocem, tunc sola + ypate sentitur ultimo subsonare, + + non + nota + quidem quod minorem sonum reddat, + sed + seu + + + + sonat + at + posterius cum sonus eius finitur, ipsa enim est + illa + ista + + ex qua relinquitur + sonus, ille + ille, sonus + + + faticius + + + + + + diutius resonatio dicta uel neate seu + + tinitus + + + + timitus cantus + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit primo assignans + Primo soluit assignans + Soluit et primo assignat + + + causam + causam et + , .2° confirmat et declarat + ipsam magis + magis ipsam + . + Secunda + ibi secunda + : + AMPLIUS. Primo igitur + + causam dat + dat causam + dat causam causam + , + dicens hoc esse + dicens ideo esse + huius esse dicens + huiusmodi dicens esse + huiusmodi dicens hoc esse + + quoniam cum sonus + nites + + vites + finitur + deperditur + disperditur + de proportione + et + occultatur + + hoc vtatur + propter resonationem + + ypates + + , + ceu + seu + sicut + maior motus depellit minorem, ea + namque + enim + + + sola videtur posterius + videtur posterius sola + videtur sola posterius + videtur posterius + + subsonare.

+

+ + Deinde. + + SIGNUM. + + Declarat 2° + Secundo declarat + per signum, dicens + signum nobis ideo + signum nobis illud + signum nobis id + signum nobis hoc + signum nobis + + + demonstrans est + + demonstrans esse + demorans est + denotans est + esse designans + quoniam neate potest amplius subsonare + + tanta + causata + + cata + causata + + causatam + ab ypate diutius + remanendo + remanente + post tactum corde + quam neate alicuius alterius corde. Vnde cum ipsa + potissime + potissima + sit causa, + vt accidat + + vt accidet + ne accidat + neate, omnes relique corde + in terminatione + iteratione + in + qnacoe + qvando a commune + et + + suorum sonorum + suscipiunt similitudinem ab + ypate + + ypatem + .

+

Nosce quod + neate interdum + + interdum neate + + sumitur + + pro hypate + pro nete + + . Vt visum est + + .13. + + et .39. + 239. + et .19º. + : + est enim quasi corda iuuenilis et inferior accipitur etiam pro resonatione secunda que + sentitur + retinetur + diu post percussionem, + ceu + seu + sicut + + hic. + Ps.Arist. + Prob. + XIX.13, 918b ll. 3–6; and XIX.39, 921a ll. 7–31 + Sicut + enim neate corda est inferior, ita + resonatio etiam + etiam resonatio etiam + resonatio et + etiam resonantia + ypates est debilior sono priori, + sic vt + + sic nunc + + concidant.

+

Quod autem ita sit + ostenditur etiam + etiam ostenditur + ostenditur et + ostenditur + per + echo + + + + + de quo dictum est + + + .11a. + 14 + , + Ps.Arist. + Prob. + XI.23, 901b ll. + 18–19; XI.51, 904b ll. + 29–33 + quod est quidam + cantus + tinitus + et intus + + seu sonus + + + + reflexus. Est enim + hic + huius + + + + echo + + + + + + + cantus + aut + autem + seu + sonus + + vocis siue soni + neatis uel + + + + + + resonationis + + finientis + + finis entis + existens idem cum sono + ypates + + ypate + principaliori, quando fuit + + tactus eius + eius tactus + , + differens + differentiis + , + tamen + tamen a + cum + tam + + priori et + + posteriori + + , fortiori et debiliori. Nam cum + aliquid mouetur ita vt decenter + + adaptetur + + aptetur + similitudini soni + qui + que + quo + fit secundum ypatem, postremo + tunc + autem + + + apparet + + ac si + sicut + + + nite + + vite + + actu tangeretur resonatio siquidem + + ypates + ypate + videtur sono principaliori netes adaptari. + Tam + Vum + Illius + + + enim + causa + + + + immensus est + + est immensus + immersus est + intensus est + + ypates sonus quod deficiens + + equiparatur + + equiparetur + sono netes principaliori. Quod ostenditur quia + + neatem + + neate + alterius + corde + corde alterius + ab ypate scire dicimur + quando + cum + tangitur + presignata + prelibata + + corda et + mouetur ab ea altera. Sed secus accidit circa ypatem quoniam etiam si videmus quod ypates non + comprehendatur + comprehenditur + ita vt manifeste + tangi eam + eam tangi + + + scimus + videmus scimus + sentimus + , sonum + tamen + tamen autem + tantum + audientes in + communi + + communim + + + extimamus + + existimamus + propter + ipsius + ipsam + eius + + + diuturnam + + + + resonationem + fore ipsius. Quod declarat eo quod id non solum + hic accidit + accidit hic + huius accidit + , verum + + et in multis + etiam in multis + multis + aliis rebus de quibus non habemus perfectam rationem neque + sensum + + perspicacem + perspicationem + perspicuitatem + perfectum seu perspicacem + . ex quibus + possumus certificari omnino + possumus omnino certificari + certificari omnino + non possumus omnino certificari + in talibus tunc accipimus inde aliquam opinionem + + estimatione debili + + debili estimatione + existimatione debili + ex terminatione debili + + + constrictam + constructam + coniectiua + . Sic itaque ypate + resonat + sonat + pre aliis. Neate etiam, que ultimo relinquitur, ipsius extat que + aliarum + aliorum + + + occultat + + occidat + et deperdit neatem.

+

+ + Deinde. + + AMPLIUS. Secundo + confirmat + confirmat confirmat + declarat + causam predictam uel alteram subiungit, dicens quod non est mirabile + aliquod + aliquid + si + contingat + contingit + + + iugum + iustum + istam + moueri + subito + cito + + + a + situ suo cum ypate + + fuerit + fuerint + fuit + maxime tensa. Si accidat quod + premissum est + premissum + premisit + , + neque etiam + + neque + est mirum. Si omnes + tunc corde + corde tunc + cum corde + + + alie + + + + pariter moueantur + pariter moueatur + moueantur pariter + moueantur + + + et + in + et in + sonum reddant + + cum iugum + coniugum + coniunctum + cui + innituntur + + immittuntur + + a + sua mox + mouetur + mouentur + mouerunt + moueantur + positione, licet tamen sic accidat sonus + neates + qui fit ab aliis cordis + + preterquam + + ab ypate + extraneus + extraneus etiam + extremus + + est et + debilis in principio ac etiam in fine, + cum + cum primo + cum in + + + ypates + + ypate + + + concidat sonum. Sed + huius + huiusmodi + + sonus incipiens et finiens idem + permanet, non enim sono + apponitur seu adiungitur + adiungitur seu apponitur + apponitur ceu adiungitur + adiungitur seu opponitur + + concidat sonum sed huius sonus + incipiens + dat sonum sed huius + sonus incipiens et finiens + sonus incipiens + et finiens idem permanet + et finiens idem + permanet non enim sono adiungitur + permanet non enim sono adiungitur seu apponitur. + aliarum, + seu + ceu + econtra, ipsa + namque + enim + + proportio + + concitata + + + concita + + motu videbitur quod omnes soni sint + + earundem + + + + cordarum aliarum + + eius, cum + ei, cum + cuius + + in eam + concidant + concidunt + non concidant + + + + occultati + + . Quod + + etiam, cum + cum etiam + est, cum + + + sit + sint + fit + + soni ceteris fortioris, id non + reputatur + reparatur + inconueniens, quare tunc sonus ipsius + + est + erit + + maior quam sonus aliarum cordarum. Nam alie + quidem impulse mollem + reddunt + reddiderunt + sonum et paruum, ac si esset quedam neate ypates. Cuius + equidem + eadem + eidem + quidam + + + est neate + est neates + tota, cum + extet + extat + existat + fortissima virtute ceterarum cordarum. + + Quod + Quod sicut + Quod sit + Quid + principalior ostendit + eius + ipsius + sonus, per iugum siquidem audio scabellum super quod + substentantur + + corde aut + illud + + vniversaliter super quod + innixe + in nixeto + in nixeto + nixeto + inuise + in mese + + + + + extenduntur + coextenduntur + coextenditur + . Vel per iugum + intelligit + intelligitur + + + sinzeusim siue + + + + + + + sinzeus in siue + Initeus in sui + + + coniunctionem + coniunctioni + coniunctione + coniectionem + + + duorum + duarum + duo + + + tetracordarum + + cetera cordarum + retrocordorum + + in mese, vt videbitur + .44 + in + .44. + innixe + coexuntur + .

+

+ + Deinde. + + + MERITO. + QUARE MERITO. + QUINTO. + + Concludit + tertio intentum, dicens + quare non immerito secularium + + ipsius ypates + ypates ipsius + + unus ypates + ipsius compates + + vel + + condeterminatio + cum determinatio + conterminatio + confirmatio + + + seu + vel + siue + finis, solent enim musici, et + maxime + + + + psallentes + + + psallentis + , in diuinis + in fine + + dicere + + seculorum amen. Est maius + et diutius + in diuinis + perdurans + quam + + + + secularium + secularum + seculorum + secularus + reliquarum cordarum, + quapropter + quam propter + per + + + reliquis sicut + sicut reliquis + reliquas sicut + reliquis sic + + + ipsis + ipsius + + existentibus breuis motus + in + + ypate + longi + longum + longa + longe + longius + + + neatem + neate + neatem diutius permanet + + omnium + + conterminatur + conterminantur + in + ipsam + ipsa + . Et ideo + eam solam + solam eam + in eam solam + accidit subsonare, + vt componatur + huius + huiusmodi + sermo. + Ipsa + + illa + ista + ita + corda videtur + sola subsonare + subsonare sola + + subsonare + + + + + + seu + siue + + post alias + resonare + cordas sonare + sonare + + + , cuius neate diutius + permanet + permaneat + post cessationem aliarum neates, + talis quidem + quidem talis + tales quidem + talis quod + , + vt declaratum est, ypate + vt declaratum est est, ypate + ypate sonum, vt declaratum est + vt declaratum est, ypate est + vt declaratum, etiam in ypate + .

+

Nosce quod potest + causa huius + causa huiusmodi + causa eius + hoc causa + eam huius + + + breuitatis + breuiter + + + assignari + talis assignari + asignari talis + signari + , quia + ypate + + sonum reddit + reddit sonum + sonum reddat + grauem, + qui + que + + extenditur secundum longum + latum et profundum, + reliqua + relique + vero ad ipsam acutum, qui secundum longum + + , + vt + ceu + seu + sicut + + + visum est + visum e + visum + + + xia. + Ps.Arist. + Prob. + XI.16, 900b ll. 17–25 + Tardius + autem + aut + + + + quietatur + quietatus + comoratur + commutatur + + sonus aeris secundum plures moti dimensiones + quam secundum + unam + unum + cum + dictum etiam sit + etiam dictum sit + dictum etiam sit quod + etiam sit + dictum est etiam + + graue tarde et multum moueri + acutum + acuta + acutum vero + + + econtra + + , + vt + + + + visum est sepius antea + visum sepius antea + + . + + et cetera. + sequitur 43. + problema 19e. particule. +

+
+ +
+ + Quadragesimumtertium + problema + 43m + quadragesimum tertium. + Quadragesimumtertium. + 42m. + problema. + + +

+ PROPTER QUID DELECTABILE + + PROPTER QUID DELECTABILE UNIUS CANTUS EST SI AD LYRAM ET FISTULAM + CANTANT? + AUT QUIA OMNE DELECTABILE MIXTUM DELECTABILI UNUM + EST? + FISTULA ENIM DELECTABILIUS EST LYRA, QUARE ET CANTUS HOC MIXTO LYRA DELECTABILIUS + UTIQUE ERIT, QUONIAM MIXTUM IMMIXTO DELECTABILIUS EST, SI UTRORUNQUE SENSUM + ALIQUIS SIMUL ACCIPIAT. + UINUM ENIM DELECTABILIUS EST OXIMELLE. PROPTER ID + QUOD MIXTA SUNT MAGIS IPSIS QUE A NATURA MIXTA QUAM QUE A NOBIS, EST ENIM ET + UINUM QUOD EST MIXTUM EX ACUTO ET DULCI HUMORE. MANIFESTANT AUTEM ET GRANATA + UOCATA MUZA. + CANTUS QUIDEM IGITUR ET FISTULA MISCENTUR SIBI + IPSIS PROPTER SIMILITUDINEM, SPIRITU ENIM UTRAQUE FIUNT. SONUS AUTEM LYRE, + QUONIAM AUTEM NON SPIRITU FIT. + AUT MINUS SENSIBILE QUAM QUI EST FISTULE + INCOMMIXTIBILIS EST UOCE? FACIENS AUTEM DIFFERENTIAM SENSUI MINUS DELECTAT, + QUEMADMODUM IN SAPORIBUS DICTUM EST. + AMPLIUS FISTULA QUIDEM MULTA SUO SONO ET + SIMILITUDINE OCCULTAT PECCATORUM QUE SUNT CANTUS. LYRE AUTEM SONI, EXISTENTES + TENUES ET INCOMMIXTIBILES UOCI SECUNDUM SE CONSIDERATI ET EXISTENTES SIBI + IPSIS MANIFESTUM FACIUNT CANTUS PECCATUM, QUEMADMODUM REGULE EXISTENTES + IPSORUM. INIUSTIS AUTEM IN CANTU CULPATIS, COMMUNE EX UTRISQUE NECESSARIE PEIUS + FIERI + . + + Quare cantus vnius cum altero + mixtus + + vel cantus vnicus + vel cantus unius + vel cantus uel + vel cantus + + + + delectabilis + delectabilius + laudabilis + + + et suauis existit + existit et suauis + vel suauis existit + , puta, si + fuerit aliquis + aliquis fuerit + + + cantans + cantus + + in sono lyre uel fistule? + Et + + adhuc delectabilior est + cantus fistule + quam lyre, + et + + per + se + et + + + + + + coniectus + coniunctus + + cantui, ita vt triplex fiat comparatio: puta, cantus simplicis ad + + compositum, et simplicis ad simplicem + compositum, et simplicitatem + simplicem + , + vt + et + non + + + fistule ad lyram, et compositi ad compositum, + sicut + vt + non + ac + + + + fistule et cantus ad lyram + et cantum.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit et primo assignat + causam quare + causam et quare + quia + cantus + vnius + vnus + cum sono alterius vel cantus + vnicus + + musicus + + + sit + fit + delectabilis, + dicens prius + prius dicens + dicens primo + causam esse quoniam delectabile + omne + esse + etiam + + + commixtum est + + + quod mixtum est + , et + vnitum + vnicum + mixtum + ex diuersis, vt declaratum + est + + + + .38 + .18 + prius + . Quod autem + sit + sic + + + delectabile vnum existit, + cum tunc + tamen tunc + cum tamen + cum causa + cum + + + vniformius + + uniformis + + sensum moueat.

+

+ + Deinde. + + + FISTULA ENIM. + FISTULA. + Comparat 2° fistulam + ad lyram penes + + delectationem + delectationem et + . Secundo assignat causam quare sonus fistule + est + sit + + delectabilior + eo qui + eo quod + est quod + quam + lyre. + Secunda + Secunda + ibi + Ibi secunda + Ibi + : + AUT. + + autem + āt + + + Dicit + + ergo + igitur + enim + + + primo + quod fistula est + delectabilius instrumentum auditu quam lyra. + Vnde etiam cantus commixtus + + ex + cum + voce et fistula + + est + erit + + iocundior + + commixto ex + + cum mixto et + voce et lyra + + + + . Et hoc quia illud + quod + + + + est mixtum + mixtum est + mixtum + + est conmixtum + + + delectabilius + delectabilius est + + + eo quod + eo quod est + simplex et + + immixtum + + + , dummodo mixtura vtrorumque + mixtibilium + + sensibilium mixtibilium + sentiatur + vtcunque + vtrumque + vtique + existens tamen in quadam + conmixtione + coniunctione + soni notione + .

+

+ + Deinde. + + + UINUM. + UNUM. + VNDE. + Declarat + secundo id in + id .2°. + in + 2° illud in + 2° + in + + mixtione + + nature et artis + nature id est artis + nature naturis + , dicens quod + vinum quod + unum quod + vnumquodque + illud quod + est simplex arte, conmixtum + + tamen + cum + + natura, + est delectabilius + delectabilius est + + + oximelle + exmilleus + ex melle + + seu + + acetimelle + + + aceto melle + accetimellis + aceti + aceti et melle + , quod + est + est in + arte + constructum + constrictum + constructionem + conmixtum + ex + melle + melle et + + aceto et aqua. Propter quod + vino + vinum + + modo + ipsi sunt amplius + mixta + + conmixta + ea que sunt + nature + natura + vere + + quam in + mixtione + + commixtione + artificiali per nos constructa, sicut illa que + oximellis + oximelle + ex mellis + . In priori causa + + vera extat + extat uera + extat natura + existat vera + + mixtio in + oximelle + + oximello + exmellere + , + vero + nature + vero secundum + + + sensualis + sensibilis + sensum + + tantum. Nam + vinum, quod + vnumquodque + est + mixtum quoddam + + quoddam mixtum + + nature, + componitur + compositum + compositio + ex humore acuto et dulci + mixtione + commixtione + + sufficienter. + Circa + Certa + Causata + quod manifestant + + granata + grauata + generata + nominata + musa seu + + muza se + muca seu + + + + messa + + musa + , id est media, sunt enim + tria specie: dulcia, + acida, et + acida + acuta, et + media ( + conmixta + + commixti + + ex dulci et acetoso sapore). Et ideo magis delectant quando in vno tertio + facta sunt natura talia quam si miscerentur + + arte + aere + dulcia + cum + + + + acidis. + Quidam + Quidem + quoque + habet + habent + + + + ex melle + oximelle + + loco eius quod + + expositum + expositum est + est expositum + + + ex melle + eximelle + oximelle + melle + , quod non + sic + sit + + + approbo, + quamuis id + quam id + quamuis sic + quamuis + licet + + + + + exposuerim + exposueram + exposuerint + expositum sit + + + quandoque + quoniam + .

+

+ + Deinde. + + CANTUS. Applicat ad propositum concludendo, dicens + itaque + itaque quod + ita + + cantus + in + et + fistula + commiscetur + commiscentur + + sibi ipsis propter similitudinem quam + habent + habent in + ad inuicem. Quod ostenditur + quia + quoniam + quando + ex + vtrique, vt cantus et fistule, soni perficiuntur flatu ex ore, + namque + enim + prodeunt. + Sed + Quod + + sonus lyre non, sed + potius tactu + perficitur + construitur + instruitur + rotatio. Que autem similia sunt ad inuicem delectant amplius, cum + delitia + delitie + delectatio + + + causentur + causetur + causantur + tenetur + ex coniunctione conuenientis cum + conueniente + conuenienti + conueniente vt + + + 4° + de <app> + <lem wit="#γ #κ #Ea">accidenti</lem> + <rdg wit="#π #Py #m #v" ana="#morphological">accidente</rdg> + </app>. + Gal. + De morbo et acc. + IV.6 (The Greek original which d'Abano is here paraphrasing occurs in + bk. I of the treatise called De symptomatum causis) +

+

+ Nosce + Notandum + + quod mixtio + vini + + proportionatur sono + sono proportionatur + composito + + et + + + facto ex fistula et voce, que autem + ex oximellis + + + oximellis + oximell + oximelli + oximel + ex melle + + simplici + + aut + autem + + composito + + ex voce et lyra, respectu alterius + qui + que + + ex fistula.

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit + assignans + assignando + et assignat + + + causam + aliam causam + causam duplicem + quare sonus lyre non + vt qui fistule est + vt qui fistule + est vt qui fistule + vt que fistule est + delectabilis. + Secunda: AMPLIUS. + Secunda + ibi: AMPLIUS. + Ibi secunda: + AMPLIUS. + + + + Dicit + Dicens + + + + primo + prius + + id + id prius + esse quoniam sonus lyre minus est + sensibilis quam sonus fistule, + quam minus + quare minus + quamuis + , + enim + eius + ein + + + componibilis + ponibilis + comparabilis + possibilis + est cum voce, + habet + hec + enim + differentiam + differentia + dicta + , vt iam visum est ad ipsam. + + Ex illo autem + Ex isto autem + Ex illo + Et ideo + quod differentiam + et diuersitatem ad sensum habet + et diuersitatem habet ad sensum + habet et diuersitatem ad sensum + diuersitatem + minor sentitur delectatio, sicut + apparuit + apparet + + in saporibus arte + et natura mixtis + et natura in mixtis + et natura compositis + commixtis et natura + .

+

+ + Deinde. + + + AMPLIUS. + AMPLIUS. Amplius + Assignat + causam secundam + secundam causam + causam dicens + secundam. + causam duplam + , dicens quod fistula propter suum sonum et eius similitudinem, quia sua fortitudine soni + extollit + + excellit + excedit + vocem cantantis, obtegit multa peccata in cantu contingentia. Sed soni + lyre + lyres + lyri + , + quia + + subtiles sunt et parui et + incommiscibiles + + + + + voci, cum + secundum + per + se + considerantur + consideratur + considerentur + , + prout + cum + + + in seipsis + + + + extant + extent + + et non in aliis, + quibus + in quibus + qui hiis + + + occultentur + occultantur + , + manifestum est quod + manifestum quod + manifestum + aliam quam + Minor quia + circa ipsos peccatum + accidit in cantu, + nam + non + in ipso, sicut in aliis + scientiis + sonis + sunt + canones + canonem + quidam per quos armonice canitur, a quibus + cum + receditur contingit in cantu peccare. Quare subditur quod + + accidit + acutum + + + iniustis + + in musicis + in instrumentis + in tristis + in istis + non recte predictos canones + obseruantes + obseruantibus + + alia littera + multis ac + multis hac + multis autem + + melior, vt peccent et + culpentur + culpent + cohientur + in cantu. Quod enim commune + existit + ex istis + , + vt ex + ex + + + vtrisque + + confectum + cum factum + , puta voce et instrumento sicut lyra, + necessarie + necesse est + necessa est + vocem + deterius perfici eorum + consonantia + dissonantia + discordantia + distantia + , + contra + circa + + regulas + + armonicas + armonice + canonicas + factum. + + et cetera + sequitur 44m. + problema 19e. particule. +

+
+ +
+ + Quadragesimumquartum + problema + 44m + Quadragesimumquartum. + quadragesimumquartum. + 43m. + problema. + + +

+ PROPTER QUID SEPTEM + + PROPTER QUID SEPTEM QUIDEM MEDIA + UOCATUR, OCTO AUTEM NON EST MEDIUM? + AUT QUIA SEPTEM CORDARUM FUERUNT ANTIQUITUS CONSONANTIE, SEPTEM AUTEM HABET MEDIUM? + AMPLIUS EORUM QUE SUNT IN MEDIO EXTREMITATUM, + MEDIUM SOLUM PRINCIPIUM QUODDAM EST, EST ENIM ALTERA EXTREMITATUM DECLINANTIUM IN ALIQUA DISTANTIA PER MEDIUM + QUOD PRINCIPIUM EST: HOC EST MEDIUM. QUONIAM AUTEM ULTIMA MEDIUM EST + CONSONANTIE NEATE ET YPATE, HORUM AUTEM IN MEDIO RELIQUI SONI, QUORUM MEDIA + UOCATA SOLA PRINCIPIUM EST ALTERIUS TETRACORDI, IUSTE MEDIA APPELLATUR. + EORUM AUTEM QUE SUNT IN MEDIO QUARUNDAM + EXTREMITATUM MEDIUM ERAT PRINCIPIUM SOLUM + . + + Repetit + 25° + et + + vtcunque + vtrunque + + + 33m., + dicens + + + quare + .7. dicitur habere medium et cetera.

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + Soluit + + et primo assignat causam, + et iam + et inde + que iam + unde + + apparuit + 2°. + Quia + mentionem fecerat + + fecerat mentionem + de medio, ostendit + quomodo + + accipiatur medium + medium accipitur + accipitur medium + accipiuntur medium + + + cum dicitur + .7. habere medium + + cuius gratia problema + + repetiit + repetit + .

+

+ Secunda + Secunda ibi + Ibi secunda + Ibi + + AMPLIUS. + Dicit + + igitur + igitur primo + + quod vno modo + dicitur medium + medium dicitur + + quoddam principium + + existens medium + inter duo extrema nam + illud principium per quamdam distantiam equaliter declinat ab vtroque + extremorum dicitur medium + + inter duo extrema, nam illud principium + quod + + per quandam distantiam equaliter + declinat + determinat + + ab vtroque extremorum dicitur + medium, + sicut in aliqua consonantia est dare + sicut aliqua consonantia est dare + sicut in alia consonantia est dare + sicut in alico sonantia est dare + inter + + duo + + ultima + extrema sicut in alia distantiam est dare .2. extrema + + vt vnus sit sonus + + cantus + + causatus + ab ypate fortis existens, + secundus + secundo + alius + a neate siue + nete, inter quos est dare plures sonos medios + distantes ab extremis + ab extremis distantes + secundum + maius + magis + et minus, + ceu + seu + + inter vnum et septem + + que intermedia + + inter que ueniunt media + que alias inter inde cum media + 5. + intermedia + quia inde cum media + + + vt + et + + + .5. reliqua + dicantur + dicatur + dicuntur + + + media + mediam + .

+

+ Notandum + Nota + quod + huius + huiusmodi + + + medium dicitur principium + medium dicitur + principium medium dicitur principium + eo quod est + habitus quidam virtutis qui principium extat + actuum + actium + acutiuum + acutum + , cum sit diuisibile habens quantitatem. + Est et + Est etiam + aliud medium vere + indiuisibile; quale medium + dicitur + dicuntur + + + solum illa habere + solum habere illa + solum illi habere + illa + sola habere + quorum + medium est principium alterius + tetracordi + + + + + tetracorda + . Quod non appellatur uere principium, sed + + medium magis, + sicut + sic + positis .7. cordis, quarta, + quidem + quidam + vt mese, repetita cum tribus + + superioribus et inferioribus + etiam + tribus + inferioribus et tribus superioribus + , + constituuntur + constituitur + constituetur + constituunt + + duo + + tetracorda + + + + + tunc mese vtrobique vere medium extat. + + verbi gratia + verbi gratia si ordinantur + + + + Ypate. + + + + Parypate. + primum tetracordum. + + + Lychanos. + + + + Mese. + + + + Paramese. + + + + Paranete. + secundum + + tetracordum. + retracordium + + + + + Nete. + + +
+ + + Et + + huius + huiusmodi + + + duo quidem + quidem duo + secundo quidem + duo + .20. + quidem + illius quidem + + + tetracorda + + + + secundum + sinzeusim ordinantur + + + sinzeusim + , + + + + cum autem + + fuerint + fuerit + + .8. corde secundum + dyazeusim + + + + + + + + computantur. + + + +

+

+ + Deinde. + + EORUM. + + Tunc + Nunc + repetit medium prius horum, et apparet sic igitur medium est duplex: vnum quidem geometricum siue quo ad nos + aut + autem + aliud + + + per abnegationem + + paranegomon + extremorum, aliud vero + arismetricum seu + + rei + rei uel + uel + in uel secundum + + + per + pre + + indiuisibilem + equidistantiam + + ab extremis.

+

Apparet denique quod secundum primum + + medium + modum + potest dici + dyaocto + + + + . Vnde + primo + musice: + in + octocordo + + + sexto + corde + + + due semper + duo + semper + + medie reperiuntur, et + + non + + vna media potest inueniri. + Boeth. + De inst. mus. + Ι.20 (Friedlein p. 208, ll. 8–10) + + + et cetera. + sequitur 45. + problema. +

+
+ +
+ + Quadragesimumquintum + problema + 45m + quadragesimumquintum. + Quadragesimumquintum. + 44m. + problema. + + +

+ PROPTER QUID MULTI + PROPTER QUID MULTIPLICANTES + + PROPTER QUID MULTI CANTANTES SALUANT MAGIS RITHIMUM QUAM PAUCI? + AUT QUIA MAGIS AD UNUM, AUT ET RECTOREM, INTENDUNT + ET TARDIUS INCIPIUNT, QUARE FACILIUS IPSUM ADIPISCUNTUR? IN UELOCI QUIDEM + IGITUR MAGIS FIT PECCATUM. + ACCIDIT AUTEM DUCI INTENDERE MULTOS. APPROPRIATUS + AUTEM NULLUS UTIQUE IPSORUM ILLUSTRABITUR, ELEUANS MULTITUDINEM. IN PAUCIS + AUTEM MAGIS ILLUSTRANTUR, PROPTER QUΟD SECUNDUM SE IN SE IPSIS MAGIS + EXERCITANTUR QUAM APUD DUCEM + . + Repetit + .22m + .22m. + problema + 21m + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit et primo assignat causam + et iam visum est + vt iam visum + + . Secundo + declarat + assignando + differentiam + inter habentes ducem in cantu + et + et inter + + non + habentes + habentem + . Cuius + causa + causam + + reiterauit sermonem: + 2a + 2a ibi + ibi + + ACCIDIT. + Dicit + Dicens + + 2° contingere quod + multi ad ducem attendant vt eorum cantus + saluetur + saluentur + per amplius, quoniam cum fuerint + + multi + + , nullus + ipsorum + eorum + determinatur, vt + eleuando vocem suam propter multitudinem, non paruam poterit + illustrari + et super aliorum + + voces + vocem + vocens + + + suam extollere + suas extollere + suam vocem extollere + suam attollere + suam excellere + , cum plurimi magis valeant quam vnus appropriatus. Sed in paucis cantantibus + id + illud + + + + poterit + potest + sufficienter contingere, quare pauci cantantes plus + secundum + + semet ipsos exercitantur et + singulariter + similliter + vniformiter + + + apparent + apparet + in cantu suo + illustrari + illustrati + quam + qui + que + + + apud ducem plures cantantes + existunt + existent + + , + + non enim + enim + + + + singulatim + sigillatim + sed ad ducem exercitantur. + + + et cetera + amen + dooo . + + +

+
+ +
+ + Quadragesimumsextum + problema + 46m + quadragesimum.sextum. + Quadragesimumsextum. + 44m. + problema. + + +

+ PROPTER QUID IN ACUTUM + PROPTER QUID IN ACUTIS + + + PROPTER QUID IN ACUTUM DISSONANT PLURIMI? + AUT QUIA FACILIUS ACUTUM DIMITTERE + QUAM GRAUE? + CANTANT IGITUR ACUTE MAGIS, ET IN QUO CANTANT + PECCANT + . + + + Huius + Huiusmodi + Cuius + Huius problematis + + precessit + expositio + .26°.. Et ueritas + illic iam + iam illic + illic + hic iam + + apparuit + cuiusdam + apparentis contrarietatis inter + .37m + .27m. + , et + istud + + illud + + + cum + tamen + dictum sit ibidem difficilius esse acute cantare quam grauiter. Hic autem videtur contrarium dici. + + et cetera + +

+
+ +
+ + Quadragesimumseptimum + problema + 47m + quadragesimum septimum + Quadragesimumseptimum. + 45m. + problema. + + +

+ PROPTER QUID ANTIQUI + + PROPTER QUID ANTIQUI, SEPTEM + CORDARUM FACIENTES CONSONANTIAS, RELIQUERUNT YPATEM, SED NON NITEM + RELINQUERUNT? + AUT NON YPATEM, SED NUNC PARAMESEN APPELLATAM, + ABSTULERUNT ET TONILEM DISTANTIAM. UTEBANTUR AUTEM ULTIMA MEDIA DENSI IN + ACUTUM, PROPTER QUOD ET MEDIAM IPSAM APPELLAUERUNT. + AUT QUIA ERAT SUPERIORIS TETRACORDI FINIS, + INFERIORIS AUTEM PRINCIPIUM, ET MEDIAM HABEBAT PROPORTIONEM TONO + EXTREMITATUM + ? + + Repetit + + 7m, et + apparuit iam + iam apparuit + apparet iam + + + eius + + + + expositio + propositio + expositio propositio + + et apparuit iam ex ipso 7 + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + + + + Soluit + Soluit assignans + + + dupliciter + causam dupliciter + , + aliter tamen + aliter causam + et aliter + quam prius, dicens primo quod non abstulerunt + + de 7 cordo + de 7º + corde + de 7 + cordis + de a cordo + decacordo + + ypatem, sed non pro neque cordam + appellatam + dictam + + + paramese + paramesem + seu + tritem + + trite + cetere + . Sed abstulerunt + + + , vt propositum est, + nitem + + nitem uel netem + et per consequens + toni + tonum + thonum + communi + + distantiam, que + attenditur ab vna corda in aliam siue + ab vna voce in + alteram + aliam + , + ceu + seu + sicut + + vt re. + Constituunt + enim due + voces tonum ita quod vna corda + cassata + causata + cessata + + + tollitur vox vna + tollitur vna vox + tolleri vox vna + + coller + coll'. + mox una + , et per consequens + tonus + + totius + , cum ex duabus + constet vocibus. + Auferentes + + + autem + nete + nete quia + nete qua + netem + , ne + armonie + + destruerentur + destruentur + , cum media corda paramese, + puta + + primo + modo medii + modo media + + + dicto + dicta + dicte + + + .44., + supplebant + supplebunt + supplebantur + + defectum + nete + sublate + + . Vtebantur + + enim + enim cum + + media, + scilicet paramese + + paramese scilicet + , loco + ultime + ultimo + , + scilicet nete + videlicet nete + paranete scilicet + , quod erat + + cum + quod + + extendebant + + eam + eum + + + in tantum + tantum + + vt sonum + redderet + reddent + rediret + + + acutum + + + , ad modum nete, ita quod cum + ypate + + constituerent + constituerunt + construerent + dyapason, sicut cum nete preexistente. Et merito quoniam corda + + extensior acutiorem reddit sonum + extensior reddit sonum acutiorem + exterior acutiorem reddit sonum + extentiora tuciorem reddit sonum + , grauior + autem tardiorem, quare + mediam + + medium + appellauere, eo quod medium + habet virtutem + virtutem habet + tenet virtutem + + extremi + + ad ipsum comparatum + + comparatum ad ipsum + . + Si + Scilicet + + + namque + enim + autem + + minus + extensa plus tenet locum medii, amplius vero extremi, aut + erat + erit + + + + policordum + + pollicordum dum + policordium uel policorniam + + + diegeugeneum + + + + + + + + + + + + , id est + disiunctum + + + disiectum + districtum + , ubi cordarum + + reiterantur alique + alique + alique reiterantur + uel duplantur, vt + apparuit + apparebit + apparebat + apparente + + + 3° + problemate 3º + 30 + .13 + .

+

+ + Deinde. + + AUT. Assignat aliam causam, dicens + quia media + corda + cordarum + , + vt + vel + paramese virtute quidem + et non distantia, vt tactum , erat + finis tetracordi superioris et principium + alterius + + + finis + inferius + + + tetracordi + + + tetracordandi + tractandi + + inferioris, vt + visum + + dictum est uel visum + + + est + + . Que, secundum quod + existit media + media existit + existit mediam + ex illic media + est media + , habet proportionem ad extremitates ambas suo tono, secundum quod + fuerit + fuerint + + + + isti + viri + + extremorum comparata uel + alteri + alter + alterius + . Nam medium comparatum ad + + extrema + extremum + vnum extremorum + + videtur alterum, .5. + + phisicorum + + , aut + ordinabatur + ordinabitur + ordinabam + paramese + ante mese + ante mesem + quoniam mese + aut in mese + , vt + distantia + destructa + + + etiam + + fere + sit + fit + sic + media. + Sic + Sicut + + igitur quia paramese habet + vicem + nitem + vocem + extremorum vt medium, et quia + per eam + per eum + postea + ambo constituuntur + + tetracordi + + + + tetracorda + + virtute + saltem. + Siue + Sine + Seu + + nete dubitatur, quia dictum est in septimo quod non abstulerunt + + nitem + + nete + + , + sed + secundum + scilicet + + tertiam + + id est tritem + + id est trite + vt tritem + id est netem + siue paramese.

+

Dicendum quod antiquitus + fuit primitus + fuit inuentus + fuit prius + + paramese quam nete + inuenta + inuentam + , + ceu + seu + sicut + + pretactum + + est + est in + + + 13°. + deinde + Demum + + + superueniens + superuenientis + preueniens + perueniens + veniens + + + tripandius + + + , extrahens tertiam + cordam vt + paramese + paramesem + paramesen + paramese est + + a cordarum ordine, + netem + nete + vel netem + neque + loco illius adiunxit ita vt primitus non + fuerit + fuit + nete, postea vero adinuenta extiterit. Et sic + vtrunque + + vtraque + + verificabitur + + particula + problema + . + + et cetera + sequitur 48. + problema 19e. particule. + +

+
+ +
+ + Quadragesimumoctauum + problema + 48m + Quadragesimumoctauum + Quadragesimumoctauum. + 46m. + problema. + + +

+ PROPTER QUID IN TRAGEDIA + PROPTER QUID IN TRAGEDIA CHORI + + PROPTER QUID IN TRAGEDIA CHORI NON YPODORISTIUM NEQUE YPOFRIDISTIE + CANTANT? + AUT QUIA CANTUM MINIME HABENT HEE CONSONANTIE, QUO + INDIGENT MAGIS CHORO? + CONSUETUDINEM AUTEM CONSONANTIAM QUE QUIDEM EST + YPOFRIDISTIUM OPERATIUUM, PROPTER QUOD ET IN GERIONEM + EXITUS ET DEARMATIO IN HAC FACIEBANT. + YPODORISTIUM AUTEM MAGNIFICUM ET STABILE, PROPTER + QUOD ET CITHARISTISSIMA EST CONSONANTIARUM. + HEC AUTEM UTRAQUE CHORO QUIDEM IN CONSONANTIA, EIS + AUTEM QUE SUNT A SCENA MAGIS PROPRIA. ILLI ENIM HEROUM MUTATIUI, HII AUTEM + DUCES ANTIQUORUM SOLI FUERUNT. + PROPRII AUTEM HOMINES QUORUM EST CHORUS. PROPTER + QUOD ET CONUENIT IPSI LAMENTABILIS ET QUIETUS MOS ET MELOS, HUMANA ENIM. + + HEC AUTEM HABENT ALIE CONSONANTIE, MINUS AUTEM + ILLIS QUE EST YPOFRIGISTIUM, DIUINA UEL FURIOSA AUTEM ET BACHICHA. SECUNDUM + HANC QUIDEM PATIMUR ALIQUID, PASSIUI AUTEM IMBECILLES MAGIS FORTIBUS SUNT, + PROPTER QUOD ET IPSA CONUENIT CHORIS. SECUNDUM AUTEM EAM QUE EST YPODORISTIUM + ET YPOFRIDISTIUM OPERAMUR QUOD NON EST PROPRIUM CHORO. + EST AUTEM CHORUS CURATOR INOPERABILIS, + BENIUOLENTIAM ENIM SOLUM PREBET QUIBUS ADEST + . + Repetit + 30m + 30. + problema + .3°. + + + vt amplius + exponat + apponat + + + + dicens + quare chori + secundum tragediam + secundum tragedia + sicut tragedia + secundum trocordia + non cantant cantum + + ypodoristium + + + + + + + et multo minus + et multo minus et + et multo minus et multo + minus + + + + ypofrigium + + + ypostigium + upotragium + ? Que autem ista + exposita sunt + exposita + expositum est + + + .30°. + .3°. + + + antea + antea sunt + + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit et primo in communi + dicens + + dicit + causam esse quia + huius + huiusmodi + consonantie, puta + ypodoristie + + + + + + + + + ac + et + + + ypofrigie + + ypofrigistice + + + , non habent modum cantandi quo amplius indigent cantantes cantu chorico. + + Alie + Alia + + + namque + enim + consonantie proportione indigent + chori, et + alie + alia + + leges + + comedice + + comete + , sub quibus + ypofrigius + + + + + + continetur + continentur + continet + continere + + cantus et + + ypodoricus + + + , vt apparuit .15.

+

+ + Deinde. + + CONSUETUDINEM. + + Solutionem declarat secundo + Secundo declarat solutionem + solutionem declarat + 2° declarat + in + speciali + + + speciali + spali + et + spirituali + , + postea + + primo + notificat quid sit chorus. + Secunda + Secunda ibi + ibi Secunda + + EST AUTEM. + + Adhuc + Ad hoc + + + ostendit + .2°. + ostendit + primo + ostendit + + quales + sint cantus + ypodoristii + + + ypodoristum + ypodorium + yporistii + et + ypofrigii + + + + + , et + quorum + chorum + + + + secundo + 2a + + + chorici + chorico + qui chorici + . + Secunda + Secunda + ibi + Ibi secunda + Ibi + + + PROPRII AUTEM. + + Dicit + dicens + primo quod ex consuetudine longa est + consonantiam + consonantia + quandam percipere in cantu ab infantia, enim mox audiuntur. + Et ideo leges cantus + quidam fuerunt + quidem fuerunt + appellati, vt visum + est + + + 28. Que quidem consonantia + consuetudinaria secundum cantum + ypodoristium + + + ypodoristi + et + ypofrigium + + + + + + attenditur + + + artem dicitur + + + maxime + maxima + , cum + operatiuus + operatiuis + operatiuum + existat. + + Ipso + Ipsi + enim laborantes + incitantur + exitantur + excitantur + exercitantur + ad opus, vt + apparet + patet + in sono quem emittunt + antennas + + + + + anthoras + ante nos + in malos + eleuantes + + + . Et ideo cantus + qui + + fuere + fuerunt + + antiquitus apud + gerionem + + genortem + et gentem + darmaticam + + + + + + + + + faciebant + fatiebant + exitus tandem et + + terminationes + terminantes + terminationem + + + in consonantia + in consonantiam + consonantiam in + + + ypofrigiam + + + + + , sicut et + ditirambi + + + + + + dyterambus + dyachitambum + dicti rambi. + + + demum + + deinde + + concidunt + + in ipsam + ipsam + in ipsa + , vt visum + est + + + + 30° + 3° + .

+

+ + Deinde. + + + YPODORISTIUM. + YPODORISTI + YPODORISTUS. + Ostendit secundo qualis sit cantus + + ypodoristium. Dicit quod + + + ypodoricis. Dicit quod + ypodoristus, dicens quod + ypodorisi, dicens quod + dicens ypodoristium + + ypodorum + + + cantus + + ypodoristius + + + + ypodoristicum + ypodoristium + + + + + + est + est est + fit + + + magnificus laudabilis virilis stabilis + laudabilis magnificus virilis stabilis + magnificus virilis laudabilis stabilis + magnificus laudabilis et virilis + laudabilis magnificus stabilis et + virilis + . Vnde inter ceteras consonantias est forte + citaricissimus + + + + + cicurrissimus + ticurrissimus + acutissimus + . + Existit + + quod propter + propter quod + quam propter + lidium dictum sit vt + visum est + visum + apparet + + + 30° + 3° + , et in hiis + indicatur + + sue rationis maior + rationis sue maior + rationis sui maior + sue rationis maius + sue + .

+

+ + Deinde. + + + HEC AUTEM. + + HIC AUTEM. + HUC AUTEM. + HOC AUTEM. + HUIC AUT. + CUM AUTEM. + NON AUTEM. + Ostendit qualis sit cantus choricus subdens minorem, dicens quod hec vtraque consonantia, puta + + ypofrigium + + + ypophrygius + ypofrigia + ypophigia + ypofrigii + ypofori + ypoforis + et + ypodoristium + + ypodoristia + ypodoristica + ypodorius + ypodoris + ypodotis + , relatione cantus chorici + est + + + + velut + valde + ultima + universaliter + verus + + + + in + + + + consonantia + consonantiam + consonantias velud consonantia + + . Vnde est + + illis + istis + ipsis + extranea, sed magis + propria + pro + + + duobus predictis + duabus predictis + predictis duobus + duobus + primis + + + cantandi modis + modis cantandi + est consonantia + ascema dicta, existens + + + dicta ascema, existens + + vt visum + est + + prius + mutatiua + mutata + mutatam + mutam + . Et + huius + huiusmodi + quidem + consonantia + consonantie + consonant + modi appellati + commutatiui + + comutatum + + erant in + vsu + vsi + visu + + + apud + + amplius + + + hereos + + + + , ipsi enim + soli + solum + fuerunt duces et gubernatores antiquorum, + + incitantes + incitando + excitantes + ipsos in actus + huius + huiusmodi + cantibus, vt in bellum uel aliud. + Et proprie + Et proprie in + Et proprium + + + + ypofrigium + + + ypophrygius + ypifrigis + ypofrigii + + ypofri + , + operatiui + operatim + + + enim + enim sunt + est + magis.

+

+ + Deinde. + + + PROPRII. + PROPRII AUTEM. + + + Ostendit + dicit + + qualis et quorum sit cantus choricus, dicens primo quod homines + singulares et priuati sunt illi quorum cantus est choricus, et + propterea + + propter hoc + propter + + + fruuntur + finitur + formatur + fortiter + + + hiis + iis + illis + + que ipsius. + Sibi namque + Si enim + + + conuenit + competit + vt + sit + + + + lamentabilis + + lemdabilis + , + inducens + + vt ducens + + + + in pietatem + in pietates + impietatem + homines, + etiam + et et + + + agrestes, et quietus more + in + + + et + + + + honestus + honesti + omestus + et + melodiosus + + + melodiosos + maxime, hec enim humana sunt et mansueta. Et + ideo + + + + amatores tali + amatores tale + amatorabtali + admonitores tali + + genere cantandi vtuntur + in demulciendo + + + + et demulciendo + inde multitudo + + + dominarum primitus animos suarum + agrestes + primitus agrestes animos suarum dominarum + primitus dominarum animos suarum agrestes + primitus dominarum animos agrestes suarum + primitus dominarum animos suos + agrestes + dominarum primitus animas suarum agrestes + .

+

+ + Deinde. + + + HIC + HEC + HOC + + + AUTEM. + ETIAM. + Ostendit 2° quod talia minus insunt + ceteris + + aliis + + consonantiis + + achorica + + a chorico + , dicens quod relique consonantie + prefate + prefacte + pretacte + minus participant + cum + + predictis, nam + ypofrigia + + + + est diuina + seu + et + legalis, vt apparuit .15. + + et + + vel + + + .28. + .24. + .18º. + .26. + , vel + furiosa + + furiosam + furioso + incitans homines + in tumultum + et + + furiam + + . + Est autem + Aut est + + aut + + + bachica + + + + + brachia + + + praua + puta + biana + + + solida + solido + stolida + solitu + + , iuxta illud + + noni + + 30e, + 30e + 4º, + .34e, + regule, + + + propter quod + propter quid + + + bachici + + + + + arthici + artifices vt + frequenter + frequentetur + sunt mali. + Ps.Arist. + Prob. + XXX.10, 956b ll. 11–12 + Iuxta siquidem + huius + huiusmodi + consonantiarum + imperfectarum + dictarum + frigiarum + factarum + fictarum + + + modum + modo + modos + + patimur + aliquid, cum autem patimur + + imbecilliores + + + imbecilles + , amplius fortibus + reddimur + + redduntur + . + Et + ideo non possumus + cantum tenere + tenere cantum + tantum cantum tenere + choricum, sed leges facimus + + et + vt + aut + + ascema, vt tactum + est + + + .15°. Sed quia hiis opposite + sumus dispositi + dispositi sumus + sumus disposite + + cum + cantus est lamentabilis + + et cetera + + , + tunc + tunc .3. + tamen + competit dispositio nostra + et + potentia cantibus + predicta cantantibus + procantibus + + choricis. Potest enim ipsos seruare, + quamuis + quam + licet + cum + + + + extent + extant + existunt + exterit + sint + laboriosi, non autem + conuenit + + vt + sicut + + + dictum + + + est + + ypofrigiam + ypofrigia + + proprie ipsis, + operatiua + operatam + operatiam + operava + temperatera + + namque, sicut expositum + est + + .

+

+ + Deinde. + + EST AUTEM. Ultimo + manifestat + monstrat + quid + sit + est + + + + + chorus + choris + , dicens quod + + + chorus est + velut quidam + velut quod + uniuersaliter quidam + sicut quidam + quidam valde + + + curator + curat + , + studet enim remouere curas et + sollicitudines + + solicitudinem + ab audientibus. Est + et + etiam + + + inoperabilis, non + enim + enim non enim + eos + eam + + + incitat + excitat + ad actus + vt + + ypofrigium + + + ypofrigius + ypofrigii + ypofrigia + , + sed + licet + + + solum + + sonum + actum + + + beniuolentiam et complacentiam + benuolentiam + inducit quibus auditu + incurrit + + occurrit + occurat + . + Nihil + + enim post factum + relinquit + reliquid + cum + solum + sono + + animos demulcere + laboret + laborat + labores + . + + et cetera + sequitur 49m. + problema 19e. particule. +

+
+ +
+ + Quadragesimumnonum + problema + 49m + xl. Nonum. doooo + Quadragesimumnonum. + 47m. + problema. + + +

+ PROPTER QUID SONORUM + + PROPTER QUID, SONORUM FACIENTIUM CONSONANTIAM, IN GRAUIORI EST + MOLLIOR? + AUT QUIA IN MELODIA SUA UOCE MOLLIS EST ET QUIETA, EA AUTEM QUE EST RITHIMI MISTIONE + ASPERA ET MOTIUA? + QUONIAM AUTEM GRAUIS QUIDEM SONUS MOLLIS ET + QUIETUS EST, ACUTUS AUTEM MOTIUUS, ET HABENTIBUS IDEM MELOS, ERIT UTIQUE + MOLLIOR GRAUIOR IN EODEM MELOS MAGIS. ERAT AUTEM MELOS IPSI MOLLE + . + + Quare consonantia ex grauibus causata + + sonis + sonus + est + mollior + melior + + + et delectabilior + + ac delectabior + + + + quam ex acutis + + + acutis + + + constructa + constituta + ?

+

+ + Deinde. + + AUT QUIA. Soluit, + primo ostendens + primo ostendit + et primo ostendit + + + quare + quod + consonantia + vocis + vocum + + + grauioris + grauiori + grauiore + grauior + est + mollior + + melior + . 2° adaptat + ad eam que sonorum + eam que sonorum + que sonorum ad ea + + + illic + ibi + . QUONIAM AUTEM. + + Dicit causam + + Dicit primo causam + Dicens causam + Assignat causam dicens + + + esse quoniam huius + huius esse quoniam + esse huius quoniam + esse quoniam huiusmodi + esse quia huiusmodi + + consonantia + in + + melodia + + melius + propter + suam vocem + vocem suam + suam + + + delectabilem + delectationem + laudabilem + + + ex qua + ex qui + in qua + + + construitur + constituitur + astruitur + mollis + est et + et + est + quieta, iuxta illud quod + prius dictum est + dictum est prius + dictum est + dictum prius + de cantu chorico. Sed fere per oppositum consonantia + + rithimica ob suam mixtionem minus + consonam + consona + + + + + aspera existit + asperexerit + aspera + , pungens auditum + + et immutans + + et mutans + + + mox + subiecta + subiuncta + subita + , quasi alteratione + nature + + preliatiua + + preliata + preliatam + .

+

+ + Deinde. + + + QUONIAM. + QUONIAM AUTEM. + QUANDO AUTEM. + Applicat ad sonum, dicens similiter + + esse + est + omne + + in sono + quoniam grauis, vt dictum + est + + de voce mollis, est + + quietus et + et quietus + quietus est et + et quietus et + amenus, sed acutus + asper est + asper + et + conmotiuus + commotus + commutiuus + comonens + . Vnde posito quod + extat vtrobique eadem + vtrobique extat eadem + extet vtrobique eadem + melodia illa que + est grauior + grauior est + erit grauior + erat grauior + + + mollior et + et mollior + melior est et + + + delectabilior + delectabilior erit + in + eadem + eodem + melodia magis, nam + melos + + ipsius est + ipsi est + ipsius + + + molle + melle + + + quasi + id est + dulce.

+

+ Nota + Notandum + quod + cetera + certa + omnis + ita + circa + et altera + + consonantia debet constare ex acuto et graui. + Mollior tamen est + amenior + et amenior + et suauior + amor + et amor + et a motu + cum in graue tendit + + quam + quem + antea + + + quando + cum + in acutum. + + et cetera + sequitur 50m. + problema 19e. particule. +

+
+ +
+ + Quinquagesimum problema + Ultimum problema + 50m + Quinquagesimum. + Quinquagesimum. + 48m. + problema. + + +

+ PROPTER QUID EQUALIUM + + PROPTER QUID EQUALIUM DOLIORUM ET SIMILIUM SIQUIDEM ALTERUM UACUUM FUERIT, + ALTERUM UERO AD MEDIUM PLENUM, DYAPASON CONSONAT ECHO? + AUT QUIA DUPLEX FIT ET QUE EST EX MEDIO EIUS QUE + EST EX UACUO? + QUID ENIM DIFFERT HOC QUAM IN FISTULIS? UIDETUR + ENIM UELOCIOR MOTUS ACUTIOR ESSE, IN MAIORIBUS AUTEM TARDIUS AER OBUIAT. ET IN + DUPLICIBUS TANTUM, ET IN ALIIS PROPORTIONALE. CONSONAT AUTEM DYAPASON ET + DUPLEX ITER AD MEDIUM + . + + Quare + + si + cum + aliquis accipiat duo dolia eiusdem + + mensure + materie + + + quantitatis + + et + + + figure et + et + + vniuersaliter similitudinis omnis, in omnibus + enim + + + sit equalitas nisi + in hiis in + in iis in + in + in hiis nisi in hiis in + + quibus + fit + sit + comparatio, + vt visum est + vt visum + + + .5°. + 25°, + .5°. + et 5º, + + Pietro expresses this idea in his commentary on + problem 10 of particula 15. His reference to 5/25 is + obscure. + + puta quod + vnum sit + sit vnum + vnum est + + omnino + corpore + + solido + + solito + vt liquore + aliquo + acuto + + + + vacuum + + plenum, tamen aere + aere tamen plenum + plenum, tamen aer + + + , + + idem + namque + enim + tamen + + + apud vulgus est + est apud vulgum + amplius vulgus est + + + vacuum + et plenum aere + et aere plenum + plenum tamen aere + + , + .7°. + topicorum, + Arist. + Top. + VII.1, 152b, l. 20 + + et alterum sit semiplenum, et + percutiantur + percutiatur + etiam equaliter + quocunque + modo + ambo, vel + clametur in ipsis; tunc + echo + + + resultans + ex + in + + + hiis + ipsis + + + per refractionem + per fractionem + prefatis + ad parietes reddit + simphoniam + + + + dyapasonicam + + + dyapason sonicam + dyapason solidam + dyapason eam + dyapason causa + dyapason + .

+

+ + Deinde. + + + AUT. + AUT QUIA. + Soluit et + + dicit primo causam + + primo dicit causam + id primo causam + primo dicens causam + esse quia sonus causatus ex vacuo vase + + se habet + habet se + + + + ad sonum causatum + ex + a + semipleno in + dupla proportione + in proportione dupla ad sonum causatum a semipleno + , continet enim bis eius + totum + + quod + quidem + vacuum + omne + esse + id quod + semiuacuum + + semimatium + semiatiuum + soni vacuum + . Dictum est + autem + enim + + + + .13° + 30. + .20. + quod dyapason ex numero duplici nascitur.

+

+ + Deinde. + + + QUID + QUOD + + ENIM. + Secundo remouet + dubitationem + dubium alias dubitationem + dubium + , quia crederet aliquis + quod ex sonis talium non resultaret + + simphonia + + + sicut ex sonis aliorum. Et ideo subdit quod non est aliqua differentia + + quin + quando + quare + quasi + ex sonis + + istorum + istarum + istis + istorum non + + constituatur + + dyapason consonantia + dyapason secundum + consonantiam + , + ceu + seu + sicut + + ex sono fistularum et + huius + huiusmodi + instrumentorum motorum spiritu + seu + ceu + tactu. Quod ostendit + inuentio + inuentor + inuentorum + musice + malleorum + + + soni proportione, vt dictum + est + est in + + + primo, quod siquidem + contingere bene + potest + contingere potest bene + bene contingere potest + considero vnde ponit + + cum + + ubique + + in talibus ratio + semper proportionis duplicis + proportionis duplicis semper + semper proportionis dupliciter + + + obseruetur + bene obseruetur + . Quod ostenditur + quia + quia a + quod + dyapason causatur + ex + + acuto et graui + graui et acuto + acuto + quod + hic + huius + huic + accidit, + nam + est iam + motus uelocior factus in + semipleno + angustia loci percipitur + + esse + + acutior, in maiori autem tardius mouetur et obuiat + aer + aeri + + resistenti, propter + + plurimam + plurima + multam + + + quantitatem ipsius + ipsius quantitatem + + + motam + motum + et per longam distantiam vt visum + est xia + xia est + xia + est + 41 + , ita quod in + hiis que sunt dupla + + ad inuicem + in ad inuicem + et + in + + + + + + etiam + aliis + aliis etiam + + que aliquam proportionem + numeralem habent + habent numeralem + habent + numeralem + inter se consonat et efficitur + penes + + duplicia + + duplaria + dyapason. Cadit enim duplex + iter + inter + + + + et + est + + + + distantia + distantiam + + extremi ad medium, + vt in pleno, + vnum autem + vni autem + vini aut + verum autem + autem numeri + + + in + + + + semiuacuo + + + , cum alterum + contineat + continet + + + pleni medietatem. Secundum vero + epitrica + + epitricam + + dyatesseron et + emiola + + + + emioligi + dyapente + et cetera + et illic + , vt + monstratum + + + manifestum + + est + .13°.

+

+ Ex + Et + hiis vtique + quam + + breuius + breuiter + vermis + + + prodierunt + prodierint + producunt + in lucem + + vtcunque + vtrunque + circa liberales artes, et + maxime circa + maxime + + + + + mathematica + + mathematicam + mathematicas + methaphysica + + + problemata + probabilis + proposita + + problemata mathematica + , grandi + textuali + + + caligine cum eius + corruptione + corrupta + + + inuoluta quandoque + quandoque inuoluta + inuoluta quando + . + In quibus etiam + In pluribus etiam + In quibusdam etiam + quia plurimis extranea non + grandis + grandi + + + vtilitas + vtilitatis + subtilitas + que hodie + appetitur + + summe reperitur + reperitur + + , quare + ipsa + in ipsa + ea + + + + celerius + + + + percurri + precucurri + precurri + precurrari + precucari + procurari + . + Nunc + Non + + autem + + deinceps + + circa + reliquas + + aliquas + + + partes + partes cum + partes si + + + physice + + , + naturalemque + naturalisque + naturalesque + naturaleque + naturaliaque + maxime, problemata tam circa + composita + quam + quam circa + simplicia + existentia + + + tractabuntur. + + et cetera. + + + + sequitur + amen. Deo gratias amen + Explicit decimanona particula. + Explicit particula 19a deo gratias + Explicit particula xixa. sequitur .xx.ma +

+
+
+
+ + + +
+ Back Matter + +
+ List of persons mentioned by Pietro + + Historical figures + + AlAlexander + Aphrodisiensis + + + ArAristoteles + + + AxAristoxenus + Tarentinus + + + AvAvicenna + + + BoBoethius, + Anicius + Manlius + Severinus + + + CoHestiaeus + Colophonius + + + DamJohannes + Damascenus + + + GaGalenus, + Claudius + + + GArGuido + Aretinus + + + HipHippocrates + + + HorHoratius Flaccus, + Quintus + + + IsIsidorus + Hispalensis + + + MacMacrobius + Ambrosius + Theodosius + + + MuMusaeus + Atheniensis + + + NiNicomachus + Gerasenus + + + OvOvidius Naso, + Publius + + + PhilPhiloxenus + Cytherius + + + PhrPhrynichus (tragicus) + + + PlPlato + + + PtPtolemaeus, + Claudius + + + PythPythagoras + + + TerTerpander + Antissenis + + + ThTheophilus + Antiochenus + + + TiTimaeus + Locrus + + + TyTimotheus + Milesius + + + + Mythical figures + + CayCain + + + JuJupiter + + + MemMemoria + + + MerMercurius + + + MosMoses + + + OrOrpheus + + + TorTorebus, filius + Atys + + + TubTubal Cain + + +
+ + + + + +
+ List of titles cited by Pietro, with editions supplied + + d'Abano 1504 + d'Abano, Pietro. Conciliator differentiarum + philosophorum. Venetiis: n.p., + 1504. URL: + AlPr + Pseudo-Alexander of Aphrodisias. + Problemata. Ed. Robert W. Sharples and Sophia + Kapetanaki as Pseudo-Aristoteles (Pseudo-Alexander), Supplementa + Problematorum: A new edition of the Greek text with introduction and annotated + translation. Berlin: De Gruyter, + 2006; trans. Pietro d'Abano in + Vatican Biblioteca Apostolica reg. lat. 747, ff. 62r–104r, URL: + Arist. De an. + Aristotle. De anima. Ed. J. Decorte + and J. Brams as De Anima. Aristoteles Latinus Database + XII.1 URL: + Arist. Cael. + Aristotle. De caelo Ed. + F. Bossier as De caelo et mundo. Aristoteles Latinus Database + VIII URL: + Arist. Eth. Nic. + Aristotle. Liber ethicorum ad Nicomachum. Ed. + R.A. Gauthier as Analytica posteriora (Iacobi + Venetici translationis recensio). Aristoteles + Latinus + XXVI.1–3. Leiden and + Bruxelles: Brill and Desclée De Brouwer, + 1972–1974, URL: + Arist. Metaph. + Aristotle. Metaphysica. Ed. G. + Vuillemin-Diem as Metaphysica, lib. I-XIV. Recensio et + Translatio Guillelmi de Moerbeka. Aristoteles + Latinus + XXV.3. Leiden, New York, and + Köln: E.J. Brill, 1995, URL: + An. Post. + Aristotle. Analytica posteriora. Ed. L. + Minio-Paluello and B. G. Dod as Analytica + posteriora (Iacobi Venetici translationis recensio). Aristoteles Latinus + IV.1–4. Bruges and + Paris: Desclée De Brouwer, 1968, URL: + + Arist. Int. + Aristotle. Peri hermeneias. Ed. L. + Minio-Paluello and G. Verbeke as Periermenias (Peri hermeneias) (uel De Interpretatione). Aristoteles Latinus + II.2. Bruges and + Paris: Desclée De Brouwer, 1965, URL: + + Arist. Ph. + Aristotle. Physica. Ed. F. Bossier + and J. Brams as Physica (translatio + 'uetus'). Aristoteles Latinus + VII. Leiden and New + York: E.J. Brill, 1990, URL: + Arist. Pol. + Aristotle. De politicorum. Ed. Franciscus + Susemihl as Aristotelis Politicorum libri octo cum vetusta + translatione Guilelmi de Moerbeka. Leipzig: + Teubner, 1872. + Arist. Top.Aristotle. + Topica. Ed. L. Minio-Paluello as Topica. Translatio Boethii, Fragmentum Recensionis Alterius et Translatio + Anonyma. Aristoteles Latinus + V.1–3. Bruges and + Paris: Desclée De Brouwer, 1969, URL: + + ArPr + Pseudo-Aristotle. Problemata physica. Ed. + Carolus Ruelle, Hermannus Knoellinger and + Iosephus Klek as Aristotelis quae feruntur + Problemata physica. Leipzig: + Teubner, 1922. + AvCa + Avicenna. Canon medicinae. Trans. Gerardus Cremonensis as Avicennae Arabum + medicorum principis, Canon medicinae. Venice: + Iuntas, 1608. + BoAr + Anicius Manlius Severinus Boethius. De institutione + arithmetica. Ed. Godofredus Friedlein in Anicii Manlii Torquati Severini Boetii De institutione arithmetica libri duo, De + institutione musica libri quinque, 1–173. Leipzig: Teubner, + 1868. + BoMu + Anicius Manlius Severinus Boethius. De institutione + musica. Ed. Godofredus Friedlein in Anicii + Manlii Torquati Severini Boetii De institutione arithmetica libri duo, De + institutione musica libri quinque, 175–371. Leipzig: + Teubner, 1868. + GaAc + Galen. De morbo et accidenti. Ed. C. G. + Kühn as De symptomatum causis libri iii in Claudii Galeni opera omnia, vol. + 7, 83–272. + Leipzig: Knobloch, + 1824. + GaPu + Galen. De differentia pulsuum libri iv. Ed. C. + G. Kühn in Claudii Galeni opera omnia, vol. 8, 493–765. Leipzig: Knobloch, + 1824. + GaSa + Galen. De sanitate tuenda libri vi. Ed. K. + Koch in Corpus medicorum Graecorum + 5.4.2, 3–198. Leipzig: + Teubner, 1923. + HipAph + Hippocrates. Aphorismi. Ed. É. Littré + in Oeuvres complètes d'Hippocrate, vol. 4, 458–608. Paris: Baillière, + 1844. + IsEt + Isidore of Seville. Etymologiae. Ed. W. M. + Lindsay in Isidori Hispalensis Episcopi Etymologiarum sive + originum libri xx, vol. 1. + Oxford: Clarendon Press, + 1911. + MacSS + Macrobius Ambrosius Theodosius. Commentarium in somnium + Scipionis. Ed. Franciscus Eyssenhardt in Macrobius, 465–570. + Leipzig: Teubner, + 1868. + MasAph + Yuḥannā ibn Māsawaiyh. Aphorismorum libri. Ed. + Danielle Jacquart and Gérard Troupeau as Yuhannà ibn Màsawayh (Jean Mésué), Le livre des Axiomes médicaux + (Aphorismi), édition du texte arabe et des versions latines avec traduction + française et lexique. Geneva: + Droz, 1980. See also Biblioteca Apostolica vat. + lat. 2460, f. 39r–42r, URL: + + NiGer + Nichomachus (Dramatist). Geryones. Concerning this lost play, see URL: + Psalm + Liber psalmorum. Ed. Robertus Weber in Biblia sacra iuxta vulgatam versionem, 767–955. Stuttgart: + Deutsche Bibelgesellschaft, 1994. + PtHar + Claudius Ptolemy. Harmonica. Ed. I. + Düring as Die Harmonielehre des Klaudios + Ptolemaios in Göteborgs Högskolas Arsskrift + 36, 2–111. Göteborg: + Elanders, 1930. + SePr + Pseudo-Hermes Trismegistus. De sex rerum principiis. + Ed. Paolo Lucentini and Mark D. Delp in Corpus Christianorum, Continuatio Mediaeualis + 142. Turnhout: + Brepols, 2006. Sometimes + attributed to Gilbert of Poitiers. + +
+ +
+ + + + \ No newline at end of file From 52f689ab339d9070a076bd4b8f41b51036bf7d65 Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Fri, 16 Aug 2024 16:42:33 -0500 Subject: [PATCH 22/25] update: further revision to usage of in --- edition.xml | 183 ++++++++++++++++++++++++++-------------------------- 1 file changed, 90 insertions(+), 93 deletions(-) diff --git a/edition.xml b/edition.xml index 38ad409..afb095c 100644 --- a/edition.xml +++ b/edition.xml @@ -1669,22 +1669,22 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> et ex consuetudine - + quos quod quo quorum - aristotelem impugnat - celi et mundi + aristotelem impugnat + celi et mundi et - 2°. - aristotelem impugnat + 2°. + aristotelem impugnat in @@ -1697,11 +1697,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> celi et mundi celi et mondi celi - . - aristotelem + . + aristotelem in 2° - celi et mundi inpungnat. - + celi et mundi inpungnat. + Arist. De caelo, II.9, consistentiam esse . Vnde - - datum in afforismis + + datum in afforismis datum dam - in aforismis - dictum est in <app> + </choice> in <title ref="#MasAph">aforismis + dictum est in <app> <lem wit="#Vb #Vm #Vz #m #v">afforismis</lem> <rdg wit="#Va" ana="#orthographical">amforismis</rdg> <rdg wit="#Ma #Mb" ana="#orthographical"><gap reason="lost"/></rdg> - </app> - + + damascenus damacenus in <app> <lem wit="#Pp #Pu #Pz #Vo" ana="#J">afforismis</lem> <rdg wit="#Gu" ana="#orthographical #J">amforismis</rdg> - </app> - + + colligatio coligatio @@ -3302,23 +3302,20 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> partini enim - - .xie. vt visum particule - .xie. vt visum est particule - .xie. particule, vt visum est + + .xie. vt visum particule + .xie. vt visum est particule + .xie. particule, vt visum est particule - vt visum est particule - .xie. vt visum est - .5e. particule, vt visum est - + vt visum est particule + .xie. vt visum est + .5e. particule, vt visum est + Ps.-Arist. Prob. XI @@ -5169,15 +5166,15 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> medicinarum mediarum - - prius in tegni, + + prius in tegni, prius in tegi in tegni , prius integri, - + Avic. Can. med. I, fen aquirimus requiritur - + apparens vt apparet - + ethycorum secundo <lem wit="#α #λ #m #v">infirmis</lem> <rdg wit="#Px" ana="#lexical">interimus</rdg> </app></quote> - <app> + <ref><app> <lem wit="#β #γ #κ #m #v">secundum <ref><name ref="#Al"><app> <lem wit="#Ma #Nu #Px #Va #Vm #Vz #m #v">alexander</lem> <rdg wit="#Py #Vb" ana="#orthographical">allexander</rdg> @@ -5870,7 +5867,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> <rdg wit="#Py" ana="#additive">tympana et cetera</rdg> </app>.</quote></lem> <rdg wit="#Ea" ana="#subtractive">secundum</rdg> - </app> + </app></ref> <bibl corresp="#AlPr"><author>Ps.-Alex. Aph.</author> <title ref="#AlPr">Prob. I. delectant delectentur , - + ostensum est ostensum ostensum ostensum ostensum est in - + sexto 18e. @@ -7387,7 +7384,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> enrichimus - + sicut de huius sicut huius de sicut de huiusmodi @@ -7397,7 +7394,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> pulsi scribitur cantu scribitur - + de differentiis pulsuum secundum boecium primo - musice + musice quod - + consonantia consonantiam @@ -20931,27 +20928,27 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> denotat - aristoteles, + aristoteles, - quia singulariter de + <lem wit="#α #Ma #Px #Vm #m #v">quia singulariter <title ref="#ArAn">de anima - 2° - quia singulariter 2° + quia singulariter 2° - de anima + de anima - quia quia 2°. - de anima - quia simul de anima + quia simul 2º - de anima - 2°. - de anima ubi + de anima + 2°. + de anima ubi quia similiter de alia sermo - + determinauit determinant @@ -22008,11 +22005,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> VIII, 1324b l. 12 - + - unde .48. + unde .48. unde .40. unde omnium - + Ps.-Arist. Prob. XIX. eleuatur elleuatur , - + vt visum est vt visum vt insum - + .15 in 5º @@ -25128,15 +25125,15 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> uelocitas causatur, sicut ex multitudine tarditas, - - vt visum est .xia - vt visum .xia - vt visum est 11a particula. + + vt visum est .xia + vt visum .xia + vt visum est 11a particula. - + Ps.Arist. Prob. XI. sensus sensum , - - vt apparet de + <ref><app> + <lem wit="#β #Ea #Ma #Px #Vb #Vm">vt apparet <title ref="#ArAn">de anima - 3°., - vt apparet 3°., + vt apparet 3º - de anima, - vt patet de anima, + vt patet 3° - de anima, - + de anima, + Arist. De an. III. comensurationes eos custodiunt, - + vt sicut @@ -26035,7 +26032,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> tactum tactus est - in principio + in principio huius huiusmodi @@ -26163,13 +26160,13 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> existat est , - + vt apparet per vt patet per vt per - + damascenus damascenus @@ -26593,11 +26590,11 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> ac ordinate, - + vt precipit precipit - regimen + regimen galeni .34e, regule, - + propter quod propter quid - + bachici bachichi @@ -35840,7 +35837,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> quibus fit sit - comparatio, + comparatio, vt visum est vt visum @@ -35850,7 +35847,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> .5°. et 5º, - Pietro expresses this idea in his commentary on + Pietro expresses this idea in his commentary on problem 10 of particula 15. His reference to 5/25 is obscure. From 8d74609477280091390dd9ec207e6be480600c76 Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Fri, 16 Aug 2024 16:50:16 -0500 Subject: [PATCH 23/25] update: complete overhaul of templates for flattening some XML --- mutch.xsl | 62 ++++++++++++++++++++++++++----------------------------- 1 file changed, 29 insertions(+), 33 deletions(-) diff --git a/mutch.xsl b/mutch.xsl index f7b2472..e54a075 100644 --- a/mutch.xsl +++ b/mutch.xsl @@ -5,44 +5,40 @@ exclude-result-prefixes="a rng tei teix xsl" version="2.0"> - - - - - - + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + - + - + - + \ No newline at end of file From 2f0a15b58a2a8976ff056a554fcecd08d0c3edfd Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Sun, 18 Aug 2024 17:45:07 -0500 Subject: [PATCH 24/25] update: add 'blockquote' to some --- edition.xml | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/edition.xml b/edition.xml index afb095c..1b3c018 100644 --- a/edition.xml +++ b/edition.xml @@ -1992,7 +1992,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> isidorum isidorium - + diuiditur diuidetur dicitur @@ -3637,7 +3637,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> ayt boecius - + nichomacum nicomacum @@ -4709,6 +4709,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> nete yperboleon. + "Of the 'moveable' notes whose positions varied in different genera, Lychanos was treated as especially diagnostic of genus, and as a note-name it is sometimes augmented or replaced by enharmonios, chrōmatikē, or diatonos, @@ -10449,7 +10450,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> numeri - quinque + quinque sumpte sumptis @@ -12964,7 +12965,7 @@ type="application/xml" schematypens="http://purl.oclc.org/dsdl/schematron"?> musice - quod + quod ptholomeus quod - + consonantia consonantiam est acuti soni From fc6efb31108a5373a0869c71be280bc1e3867dd4 Mon Sep 17 00:00:00 2001 From: "Samuel J. Huskey" Date: Sun, 18 Aug 2024 17:47:26 -0500 Subject: [PATCH 25/25] update: add individual processing to flatten data --- mutch.xsl | 18 +++++++++++++----- 1 file changed, 13 insertions(+), 5 deletions(-) diff --git a/mutch.xsl b/mutch.xsl index e54a075..5401913 100644 --- a/mutch.xsl +++ b/mutch.xsl @@ -12,16 +12,24 @@ + + + + + - + - + --> +