Linda Page Cummins, Correr 336, Part 4: A New Compendium of Late Medieval Music Theory :: Philomusica on-line :: Rivista di musicologia dell'Università di Pavia


Linda Page Cummins


Correr 336, Part 4: A New Compendium of Late Medieval Music Theory

Saint Bonaventure, on the ways of making books: Someone … writes the materials of others, adding but nothing of his own, and this person is said to be the compiler.

(A. J. Minnis, Medieval Theory of Authorship)


The manuscript Venice, Biblioteca del Museo Correr, Correr 336, part 4, is devoted principally to a compilation of Latin music theory texts dealing with hexachords (including coniunctae) and mutation, intervals, and modal theory, all presented without attribution.[1] The compiler claims to have made the collection for his own use and that of pupils; thus it represents the interests of a musician who was also a teacher and who chose material that he considered practical, organized in a way he intended to be useful. Because I have been able to find concordances for almost all of the texts included in the longer of the compendium’s two main sections, comparison with these sources has made it possible to determine what portions of pre-existing material the compiler included, what he omitted, what he changed, and how he imposed a design on his borrowed material. The comparison thus reveals his attitudes, concerns, and prejudices, as well as his perception of his role as compiler. The work also provides an example of a compendium or compilation that is far more than merely a series of copied sources.

The present MS Correr 336 is a composite volume consisting of four separate manuscripts. At some point after these were bound together, the folios were numbered sequentially 1-456 (with some errors) at the bottom center of the rectos; earlier foliations are evident in the last three manuscripts (this will be explained for part 4 below). According to a table of contents on the second front flyleaf, the first manuscript contains the Tractatus de admirandis et secretioribus philosophiae arcanis by Giovanni Mariano Buri, the second the Opera spirituale of Bartolomeo Mozzi da Seravalle, dedicated to Clement XI. The third manuscript contains a hand-written copy, dated 1502, of the 1496 print of Franchino Gaffurio’s Practica musice, followed by a treatise in Italian on mensuration (Perche in ogni cosa la brevita et expeditione de quella e cosa degna como se dice in Brevitate moderni gaudent …), the latter not mentioned in the table of contents.

The table of contents makes no reference whatever to the fourth manuscript, which contains the music theory compilation; this omission may in part explain why this fourth manuscript was long overlooked. Giuliano di Bacco identified it as a source for Divina auxiliante gratia in his 2001 study of the transmission of the Ars contrapunctus of Johannes de Muris.[2] A description of the manuscript first appeared in RISM’s Theory of Music 6 (2003).[3]

Correr 336, part 4, consists of 32 paper folios (215 x 157 mm) gathered in two fascicles of eight bifolios each; there are two visible watermarks: a crown somewhat similar to Briquet 4752 (Carignola 1453) on ff. 425-441 and three mountains surmounted by a double cross somewhat similar to Briquet 11778 (Padua 1490-1502) on ff. 443-454, both signalled in RISM Theory of Music 6. Though the folios of part 4 are now numbered 425-456, the original numbering of the bifolios (1-8 for the first half of the first fascicle and 9-16 for the first half of the second) is still visible in the lower right corners of the rectos; thus we know that this document was intended as a work, or at least as the opening of a work. The collection of music theory was copied onto the first twenty-three folios (ff. 425-447) in medium brown ink in a not particularly refined cursive humanistic hand; paragraphi and some captions are in red, as is a good deal of underlining of text within the writing block. A collection of Psalm and Magnificat tones (ff. 448-456), copied in a more careful book hand using darker ink, seems to be the work of a different scribe, and I do not consider it in this essay.

The crudeness of the handwriting in the collection of music theory and the sometimes fanciful but rarely carefully drawn paragraphi in red ink lead a reader at first sight to consider this a carelessly produced document—an impression not ameliorated by a crowded writing block (unlined, but with the four margins drawn in pencil) in which the number of lines varies between 32 and 44, initials that appear to have been placed thoughtlessly, a confusing array of captions in both brown and red ink (captions in red sometimes duplicating those in brown, sometimes centered but more often placed in margins or at the ends of lines or squeezed between them), and a repetitious and seemingly haphazard sequence of topics—intervals, for instance, are discussed four times, modal theory five times, hexachords and mutation six times; the various texts offer differing and sometimes contradictory views. This first-sight impression is far from correct, but discerning the compiler’s design depends on both the identification of the sources from which he borrowed and the unraveling of visual cues, particularly initials and captions.

The largest initial in the treatise, and the only one written in red ink and within space left for it in the writing block, marks the source identified by RISM’s Theory of Music 6 (pp. 629-30) as a digest of plainchant (on ff. 434r-444r), drawn "in part" from Marchetto’s Lucidarium; this is, in fact, Divina auxiliante gratia, drawn not in part but entirely from the Lucidarium and known from five other manuscripts.[4] This copy of Divina includes the chapter titles present in four of the five other versions of the text;[5] they are written in the brown ink, given adequate space and often centered, and appear to have been part of the first layer of copying. Though the entire caption (Capitulum de plus the topic) appears in the first entries, the label Capitulum is soon dropped, leaving only de plus the topic. (The only four red captions found within the Correr Divina were squeezed into space underneath examples, and do not appear as captions in the other versions of that text.)[6] Initials that mark subdivisions of the Divina text—much smaller than the opening of Divina but as large or larger than any others in other sections of the Correr text—are also in brown, placed within the writing block, and often decorated with red; this also fits the pattern of other Divina copies. Thus it would appear that the Correr scribe copied the Divina text from an exemplar not very different in layout from most other known sources.

If the Divina text is excluded from consideration of the physical appearance of the Correr document, two things become clear: only two initials of considerable size and only two captions that are centered and in brown ink remain for consideration.

The two large initials, the opening N (Nota quod sunt tres modi cantandi) and the S (Sciendum quod mutatio) on folio 426v—both written in brown ink, in the left margin outside the writing block, and decorated in red—mark the points at which the compiler began to copy from his other two main source texts. As the compiler in neither case began at the beginning of the source texts as they are known from other manuscripts—that is, did not begin with the incipits that usually identify such texts—these initials are the only vestiges that remain to signal the beginning of something new. The RISM Theory 6 entry indicates material corresponding to chapter 8 of Berkeley’s First Treatise ("p. 84 et passim," referring to Ellsworth’s edition), beginning in Correr on f. 429r (De motetis et aliorum cantuum iudicium iudicandi); but Berkeley material actually begins on f. 426v (marked by the initial S just mentioned) and corresponds to the second through the eighth chapters, that is, the bulk, of Berkeley’s First Treatise. This extract includes not only the well-known reference to mode in motets and ballades noted by RISM, but also the discussions of mutation, mode, and very significantly coniunctae (hexachords built on notes other than C, G, and F).[7] RISM does not mention a third substantial concordant source, Rome, Vallicelliana C.105, 119r-123v, from which La Fage published excerpts.[8] The Correr compiler takes material from near the opening of the C.105 treatise as his own opening statement, following that text through the end of the discussion of plainchant, breaking off where C.105 begins a discussion of counterpoint.

Outside Divina, with only two exceptions, all other captions in Correr (excluding labels for musical examples) were written in red in spaces too small for them to have been allocated in advance, and thus were most likely part of a second layer of copying; their inclusion may in fact have been as much an afterthought as their physical appearance suggests. Perhaps the addition of red chapter titles, almost all beginning with de plus the topic in the manner of the Divina captions, occurred to the scribe after he had copied the Divina text.

The two remaining brown captions signal the large-scale structure of the Correr treatise: first, the title Ars cantandi at the beginning, followed by the later addition of scilicet de modis cantandi in red; second, Manus on folio 444v. These brown captions introduce the two major divisions of the Correr compendium: Ars cantandi is a comprehensive survey of the art of plainchant; Manus is at once a review and an exhortation to pupils to commit the information presented to memory. These sections having been established, it becomes possible to address the seemingly haphazard and repetitious sequence of topics. I will consider the two sections in order.



The discussion of hexachords and mutation in Ars cantandi is drawn principally from unknown sources concordant first with Vallicelliana C.105, then with Berkeley; but the compiler seems to have tailored each to create a more logical sequence of material. He begins (without prologue) with C.105’s discussion of the properties of hexachords ("There are three manners of singing, square square b, nature, and soft or round b"),[9] and continues by identifying the three initial letters, C, F, G ("In every place where G is found, there is the beginning [of the hexachord] of square square b, that is, ut; and [when ut is] C, there [is the hexachord of] nature; and [when] ut is F, there is the beginning [of the hexachord] of round b, that is, soft b.")[10] He omits two short passages on mutation from C.105 (items I/A/1 and I/A/4), as they anticipate material better introduced later. Berkeley will provide the bulk of his discussion of mutation, but as the Berkeley section 1.2 (in Ellsworth’s edition) begins with a definition of disiuncta ("A disjunction is a violent transition from one hexachord to another, without whatever mutation of syllables might be possible there"),[11] the Correr compiler omits it, probably deeming it inappropriate for opening a discussion of mutation. Instead he inserts a straightforward definition of mutation and a discussion of its fundamentals drawn from the tradition of Johannes de Garlandia (I/A/7/a).[12] Only after this does he turn to Berkeley’s exhaustive discussion, encompassing not only the conventional hexachords (item I/A/7/b) but coniuncta hexachords built on EEb, FF, A, Bb, D, Eb, a, bb, d, eb, and aa as well (item I/A/7/b). After a discussion of mode, which the Correr compiler includes (to be discussed below), the Berkeley text returns to examples of hexachords, mutations, and coniunctae (item I/A/9/a-e), which the Correr compiler supplements with examples and a further discussion he either invented himself or drew from unidentified sources (items I/A/9/f-g). Thanks to the compiler’s judicious cutting and pasting, material on mutation from the three sources follows in a logical and progressive manner. (The same is true of the treatment of mode he constructed, as we shall see below.)

Though he omitted Berkeley’s definition of disiuncta, the compiler of Ars cantandi retained its examples of the practice (item I/A/9/c), with a significant modification. He replaced the diminished fifth with the less objectionable minor sixth (by definition a disiuncta since it cannot be negotiated within a single hexachord). He also replaced Berkeley’s caption in which these disiunctae are called "notable" (notabiles), replacing that term with "good" (bone)—the strong implication being that he did not find the diminished fifth "good." And in fact he omits the diminished fifth both from the list of intervals and their definitions (I/A/3)—even though the concordant texts in C.105 include it[13]—and from the examples of intervals he provides in item I/A/9/h; this list, the definitions, and the examples replace Berkeley’s chapter 9, whose discussion of intervals includes the diminished fifth.[14]

The compiler introduces modal theory on f. 425r (item I/A/2), in simple statements drawn from C.105: "Note that there are four letters that are finals, low D, E, F, and G... Note that there are eight tones, four authentic and four plagal."[15] He omits a discussion of the notes of the gamut as well as material on register and mode duplicated in the previous passage, but continues with the classification of mode by species of diatessaron and diapente, the five classes of tones (perfect, imperfect, pluperfect, mixed, intermixed), rules for choosing between b natural and b flat in the first tone, and the doctrine of employing the cord (the note a third above the final) to determine, in ambiguous cases, whether a mode is authentic or plagal. These statements present the fundamentals of the modal theory of Marchetto of Padua, pervasive in Italian music theory treatises of the fourteenth and fifteenth centuries.[16]

At 427v (item I/A/8), Berkeley provides a more conventional, but a more complete, doctrine of plainchant: from Berkeley 1.5 (Ellsworth, 66-75) the definition of mode, the "original four authentic modes of the Greeks" (protus, deuterus, tritus, tetrardus) expanded by the addition of four plagal modes to create eight, the ethnic names of the modes, and ranges of the modes (regular and irregular; the latter with ranges greater than a tenth); from Berkeley 1.6 (74-81), the four finals and the modes that use each, then the initial letters of the various modes; from Berkeley 1.7 (80-85), examples of the psalm tones. Significantly, given his lack of hesitation to omit or change material from his sources, the Correr compiler does retain Berkeley’s doctrine of mode in polyphonic music.

The culmination of the modal theory is the full-blown treatment of Marchetto’s doctrine in Divina auxiliante gratia, ff. 434r-444r (item I/A/10). Divina includes material from treatises 9 and 11 of the Lucidarium nearly complete (that is, the bulk of Marchetto’s modal doctrine, and the preliminary treatment of intervals), treatise 12 on the cord, treatise 13 on rests, and treatise 14 on clefs and registers. Divina developed its own manuscript tradition, appearing in six sources (see Contents, note 32); as only one of them contains the Lucidarium itself (I-PIu, 606), and that one is devoted in large part to Marchetto’s works, one may say that in the other five manuscripts Divina functions as a primary representative of his modal theory, standing in for the longer treatise. Thus the compiler’s discussion of mode progresses from the simple statements of C.105 to more sophisticated treatments, covering both the traditional doctrine of Berkeley and Marchetto’s more radical approach.

Following the Divina text, which does not include Marchetto’s subdivision of the tone, the scribe appends a short passage (f. 444r-v, item I/A/11) dealing with the tone, semitones, and the smaller dieses taken from Martianus Capella’s Nuptiae Philologiae et Mercurii. This may be a nod to one of the most controversial features of Marchetto’s theory, his division of the tone into five dieses. Perhaps the compiler of the Correr manuscript only knew Marchetto’s reputation but did not have a text of the Lucidarium to copy and so used another text in which the word diesis appears (though these dieses are not those Marchetto had described); another Marchettan digest, Sciendum quod antiquitus, mentions Marchetto’s division of the tone at the end of a work otherwise devoted entirely to modal theory.[17]



The second section of the Correr compendium (item I/B) opens with the heading Manus and closes with a diagram of the information so often projected onto the hand: the scale, the letters, hexachords and their syllables, registers, etc. Here the compiler turns to practicality, issuing an exhortation to pupils to learn terms, "since the beginning of all knowledge is to know terms, as the Philosopher [Aristotle] says in the first book of the Posterior Analytics,"[18] and to commit to memory the material here presented [item I/B/1]. He begins appropriately with gamma, the first letter of the hand, and with an explanation of its name; this corresponds to the subject matter he had deleted from the beginning of Vallicelliana C.105, and also from the beginning of Divina auxiliante gratia. (The opening of Manus is similar to, but not a literal repetition of, the Divina opening; see below.) He continues with a review of the Ars cantandi material, repeating the introductory paragraph on mutation literally, several times referring the reader back to information given "previously" (antea); but in this section, information is presented in formats more conducive to memorization.[19]

Mnemonic verses for remembering the finals of modes appear on f. 447r (item I/B/7):[20]



The first and second tone are on D or on A

Est in .d. uel in a / primus tonus atque secundus:

The third and the fourth are on E or stand on square square b

Tercius et quartus est in e uel in square b quadrum statuuntur:

(the fourth sung with soft b)

jdem quartus per b molle locutus:

The fifth and the sixth tones rest on F or on C;

Cun [sic] quinto et sexto tono in F uel in C requiescunt:

The seventh and eighth hold G as their end;

Septimus et octauus in .g. seseneunt [l. sustinent?] sibi finem:

The seventh sometimes comes to rest on high D.

Septimus in .d. quandoque quiessit acuto:


A note introducing the verses calls them "a certain rule for recognizing the tones, briefly presented—the rule placed at the beginning notwithstanding";[21] the discrepancy signalled by "notwithstanding" (non obstante) is surely between the verses given here—easily memorized in that all the cofinals lie a fifth above the corresponding finals even though the high D, often cited as cofinal of the seventh and eighth modes, is really unsuitable for them, as the third above it is minor—and the more accurate listing at the beginning of Ars cantandi, where the cofinals are given as A, square B, round square b, and high C.[22]

An exhaustive list (item I/B/5) of the notes of the gamut with their letter names, syllables, hexachords, and mutations fully spelled out is, thanks to its repetitions and formulaic presentation, also in a form conducive to memorization. The following are typical of the entries, which extend from Gamma-ut all the way up to E-la:[23]



Cfaut. C is a low letter; fa and ut are two syllables and two mutations, fa to ut ascending and ut to fa descending. Fa is sung through square square b and is governed by the ut of Gamma ut; ut is sung through nature in the low register, and is governed by itself.

C.faut / C est litera grauis. fa et ut sunt due note et due mutatione<s> scilicet fa in ut ascendendo ut in fa descendendo: fa cantatur per square b quadrum et regitur ab ut de gamaut: et ut cantatur per naturam et regitur a se ipso /

Alamire. A is a high letter; la, mi, and re are three syllables and six mutations, la to mi and vice versa, mi to re and vice versa, la to re and vice versa. La is sung through nature and is governed by the ut of Cfaut; mi is sung through soft b and is governed by the ut of Ffaut; re is sung through square square b and is governed by the ut of Gsolreut.

Alamire. a est litera acuta. la my re sunt tres note et sex mutationes scilicet la in my et e conuerso / my in re et e conuerso / la in re et e conuerso: la cantatur per naturam et regitur ab ut de Cefaut: my cantatur per /b/ molle et regitur ab ut de ffaut / re cantatur per square b quadrum et regitur ab ut de gsolreut:



After this list, the compiler cautions: "And all these you are to commit to your memory,"[24] then he advises readers to turn back to examples of mutation "notated on folio 5 and following"[25] (i.e., ff. 429r-430v of the current numbering), where such examples do, in fact, appear. I shall return to this last point.



Many of the compiler’s text manipulations have been noted; one more remains. In every other copy of Divina auxiliante gratia, the preface reads (minor variations aside):



With the aid of divine grace, I intend to compile a short treatise on the art of plainchant, first for my own edification, and second for the profit of pupils. [It is] extracted for the most part from the books of Boethius and the most excellent teacher, the music theorist Master Marchetto the Paduan.

Diuina auxiliante gratia breuem tractatum compilare intendo de arte musicali plana. et hoc primo ad eruditionem mei secundo ad proficuum adiscentium tamen pro maiori parte ex libris boetij ac excellentissimi doctoris musici videlicet Magistri marcheti paduani extractum.



In place of this, the Correr compiler introduced Divina only with the phrase "Divina auxiliante gratia, etc." Did he do this because he regarded the opening as too well-known to bother copying? Because he intended to use the remainder of that first sentence later (which he did)? Because he deliberately wished to suppress the attribution? Though he relocates the words that in other manuscripts follow his "etc." to the opening of Manus (and it is this relocation that proves his copy of Divina included the full preface), he never names Boethius or Marchetto. There is, in fact, nothing from Boethius in Divina; Boethius seems to have been mentioned only auctoritatis causa by its compiler. The compiler of the Correr compendium seems to have felt little need of auctoritatis causa or indeed of auctoritas, whether real or invented. Of the three major texts he chose, only Divina includes an attribution in the extant sources; the concordant sources for his shorter excerpts (Martianus Capella, for example) may include an attribution, but it is not present in the passages he selected.[26] Whether by choice or by chance, the Correr compiler needed only the deliberate omission of the Divina attribution to create a text that lacks any attribution at all. In fact, the Correr text lacks any appeal to authority other than to God and Aristotle. The following excerpt gives the opening of Manus.



Desiring to treat of the rules of song, first for my own edification, second for the profit of pupils, not in my own words but in those of others almost completely—plucking flowers—with the Lord providing inspiration, I compiled this short little work; and since the beginning of all knowledge is to know terms, as the Philosopher says in the first book of the Posterior Analytics, in those same [words of the others] we shall consider, first, what gamma is ...

Cupiens de rationibus cantus tractare. primo ad erudicionem mei / secundo / ad profectum adissencium / non meis sed aliorum dictis quasi expleto flores decerpens[27] / domino Inspirante hoc breue opusculum compilauj: Et quia principium alicuius scientie est scire terminos ut ait philosophus in primo posteriorum / in eisdem videbimus primo quid sit gama...



The reference to Aristotle is not an appeal to authority to lend credibility to the information presented; rather it is an appeal to students, urging them to learn, to memorize. Words from the opening of Divina have been relocated and refocused to serve what may very well have been the compiler’s primary purpose—though, as taken from Divina, it occupies second place: "for the profit of pupils."

The deliberate excision of material from a source drawn on for Ars cantandi and the relocation of it into Manus suggests that whoever compiled the two thought of them as a unit; but can Correr 336, part 4, be seen as the original version of the compilation? That is, did the creator of Correr 336, part 4, compile his text from separate documents, or simply copy a text that already existed as a unit in some other manuscript? Consider the treatment of initials in Ars cantandi. In the part of the text that corresponds to material in Vallicelliana C.105 there is only one large initial; it is placed in the margin and decorated with red tracery. In the part that corresponds to material in the Berkeley treatise, the initials are smaller and undecorated but still placed in the margins. In the part that presents Divina auxiliante gratia and the text from Martianus Capella, initials are relatively large and placed within the writing block; the first of them, a D that begins the Divina text and is the largest initial in the manuscript, is uniquely in red ink. The first initial of Manus is again in the margin. These variations in style strongly suggest that the scribe of Correr took not only the words he copied but their visual style from various exemplars. If so, both the relocation of text from Divina to Manus and the folio-number reference in Manus back to a passage in Ars cantandi represent efforts of the compiler of Correr 336, part 4, to unify the disparate texts he had borrowed from various sources and arranged in a feasible order.

In the first sentences of the opening of Manus (above), the Correr compiler echoes St. Bonaventure’s definition of the compiler: he has written "not in my own words but in those of others," but with one caveat: "almost completely"—and he echoes this definition using the words of another (the Divina compiler)—"almost completely." As Parkes and Minnis have shown, much of the contribution of compilers in the later Middle Ages consisted of imposing order on the material they copied, often by dividing a large work into sections, providing new headings, making tables of contents, even reorganizing material—all to make the information more accessible to the reader.[28] The Correr compiler, working with multiple sources, has performed this same function. He has made the material of music theory accessible by ordering from simple to more complex, by omitting material (and perhaps by adding headings) to make smoother and more logical transitions from one topic to another, and by dividing his material into two units: knowledge on the one hand, and on the other the practical methods of absorbing that knowledge.

The Correr compiler has also described his working method; he chose his sources as though "plucking flowers"; but it is clear that he has not created this bouquet willy-nilly. It is a meticulously crafted arrangement of carefully chosen flowers that the compiler has pruned, selected, separated, and rearranged to create a bouquet whose design is logical, practical, and beautiful.

For the profit of modern scholars, the Correr compiler offers another glimpse into the concerns of the medieval musician, concerns that center around the selection of appropriate material and the dissemination and teaching of useful and practical information; the Correr treatise also illustrates the liberties a compiler may feel free to take with his source texts, presents a compilation that exhibits a unity that simple collections often lack, and thus offers an expanded view of the variety of forms a compilation may take; and the manuscript itself should alert scholars to the possibility that physical appearance may veil, rather than reveal, a logical underlying plan.


Appendix – Contents of Venice, Biblioteca del Museo Correr, Correr 336, part 4:















in marg.

in margin




in red




I. Texts on music theory. Ff. 425r-447v.


A. Ars cantandi: Compilation of texts on plainchant. Cap. med.: Ars cantandi [rub.: scilicet de modis cantandi]. Ff. 425r-445v.


1. On hexachords, their initial letters and properties; on the three registers. Inc. Nota quod sunt tres modi cantandi, scilicet square b quadro, natura, et b mole... Cont. [cap. rub.: de natura cantus] Nota quod sunt tres nature cantus scilicet graves, acute, et superacute... [cap. rub.: de literis principalibus] Nota quod litere principales sunt tres scilicet C.F.G... Exp. ... et in g per square b quadrum. F. 425r.


~ Rome, Biblioteca Vallicelliana, MS C.105,[29] f. 119r-v (excerpt in La Fage, 423). C.105 continues with a note on mutation: "ut re mi ascendit, fa sol <la> quoque descendit."


2. On mode.


a) Inc. [cap. rub.: de tonis] Nota quod toni sunt 8. primus ascendit quintam re la... Exp. ... Octauus ascendit quartam: ut fa. F. 425r.


~ C.105, f. 119v. C.105 continues with a discussion of the twenty notes of the gamut, their registers, and a list of the eight modes (the latter two items duplicating material previously presented).


b) Inc. [cap. rub.: de finalibus literis] Nota quod litere finales sunt quatuor... Cont. littere confinales sunt quatuor... Nota quod primus tonus atque secundus finitur in d graue... [cap. rub.: de natura tonorum] Nota quod toni sunt octo. quatuor autentici et quatuor plagales... [cap. rub.: de perfectione tonorum] Nota quod tonorum alius perfectus, alius imperfectus, alius plusquamperfectus, alius mixtus, alius commixtus... [cap. rub.: de partibus musice] Nota quod partes musice sunt due species principales scilicet diatesseron et diapente... [cap. rub.: de formatione tonorum] Nota quod primus tonus formatur ex prima specie dyapente et ex prima dyatessaron superius... [cap. rub.: quomodo cantari (sic) debemus tonos perfectos] Nota quod si primus tonus sit perfectus cantari debet per square b quadrum... Exp. ... si per square b cantaretur tunc in eo reperiatur tritonus qui omnino est euitandus in omni cantu. Ff. 425r-v.


~ C.105, 119v-121v (excerpts in La Fage, 423-24).


3. On intervals. Inc. [cap. rub.: de speciebus cantuum] Nota quod species cantus sunt 16, scilicet unisonus. tonus. semitonus... Exp. Bis dyapason est dispositio 16 [sic] vocum et coherentia 11. [sic] tonorum cum quatuor semitonis sicut ad [sic] C grauj ad C superacuto. et in omni loco ubi talis coniuntio invenitur. Ff. 425v-426r.


~ C.105, 121v-123r, which presents a slightly different array of intervals (omitting the unison but including the diminished fifth, omitted from the list in Correr 336) with different definitions (excerpts in La Fage, 424); texts of both C.105 and Correr 336 make similar mistakes in counting the numbers of tones and semitones in the eleventh, twelfth, and double octave.


4. On clefs. Inc. [cap. rub.: de clavibus] Nota quod clavis est reseratio omnium notarum ... Exp. secunda [fig.] sic formatur et ponitur in C acuto. F. 426r.


~ C.105, 123r (excerpt in La Fage, 424-25). C.105 continues with a note on mutation: "Nota quod mutatio est uariatio uocis seu note in eodem spatio uel linea eodem sono. Et nota quod ut mutatio fiat op [sic] oportet ut uoces sint equales."


5. On the invention of B flat. Inc. [cap. rub.: de invencione b mollis] Nota quod b rotundum b [sic] inventum fuit tribus de causis ... Exp. ... tertio causa essentie in quinto et sexto tono. F. 426r.


~ C.105, 123r (printed in La Fage, 424-25).


6. On judgment of mode by the cord. Inc. [cap. rub.: de corda] Nota quod sunt aliqui cantus qui ultra dyapente non ascendunt et sub suo fine nisi discendunt ... Exp. corda septimi et octaui toni est square b quadrum acutum. F. 426r.


~ C.105, 123r-v. C.105 continues with a Graduslehre table and accompanying treatise.


7. On mutation and coniunctae.


a) Introduction. Inc. [cap. rub.: de mutationibus] Mutatio sic difinitur. mutatio est unius vocis dimissio propter aliam in eodem spacio vel linea ac in eodem sono: ... Cont. [cap. rub.: propter quid sit mutatio] Nota quod mutatio aliquando fit causa signi sequentis scilicet b rotundi et square b quadri: ... Exp. ... Nota quod ubi sunt due voces tantum ibi sunt due mutationes. vbi autem sunt tres ibi sunt 6 mutationes. Nota quod in bfa.square bmi non fit mutatio quia .bfa.bmi. habet duas diuierssas voces et duas diuerssas litteras et mutatio oportet fieri eadem voce et sono. quia square b quadrum habet signifficare duricies. et b.rotundum molicies. et in duo sunt contraria ergo de mi in fa non fit mutatio. F. 426r-v.


~ Ars musice plane optima et perfecta, I-Ls, 359, 107rb-108rb (ed. Nigel Gwee, "De plana musica and Introductio musice," 348-49; and, less closely, Introductio musice secundum magistrum de Garlandia, CS 1:160a-b, 161b (reedited on the basis of all sources by Gwee, 264-67, 277-78, and on the basis of four sources by Meyer, Musica plana Johannis de Garlandia, 72, 75).[30]


b) Doctrine of mutation, presented as a continuation of the preceding. Inc. Sciendum quod mutatio prout hic sumitur nichil aliud est quam unius vocis propter aliam ad minus a se tono differente dimissio in eodem loco omnino... Cont. [cap. rub.: de ratione mutationis] Racione vocis quando ut est infima. la vero suprema ... [cap. rub.: de coniunctionibus vocum que patent in mutationibus] Pro his sciendum quod in manu secundum usum sunt loca 14 in quibus sunt coniuntiones vel compositiones duarum vel plurium vocum... Exp. ... que omnia supradicta prout manum usualiter concernunt inferius per exempla declarabo. Ff. 426v.


~ Berkeley 1.2 (Ellsworth, 48-50)


c) On coniunctae. Inc. His igitur una cum infrascriptis exemplis diligenter consideratis. potest unusquisque voces cuiusque cantus discernere easque secundum rationem debite iudicare: nisi forte intervenerit aliquis inusitatus cantus. quem aliqui sed male falssam musicam appelauerunt. alij perfectam musicam: alij per coniunctam vel coniunctas connominaverunt. et bene: [cap. rub.: de coniunctionibus cantuum] Est enim coniuncta quedam aquisita canendi actualis attributio in qua licet facere de tono semitonum et e converso... Cont. Amplius autem diversi cantores diversum numerum coniunctarum posuerunt. nan [sic] allij 7. allij 8 allij vero plures dixerunt esse coniunctas: [cap. rub.: de proprietatibus cantuum et coniunctis] Dico autem ego quod 10 posunt esse coniuncte:... Exp. ... quibus omnibus ut supra scripta sunt cum infrascriptis exemplis. cum intellectis plenarie atque satis non deberet quis de cognicione vocum et earum discrecione indicantia in cantu quocunque aliquatenus dubitare. Ff. 426v-427v.


~ Berkeley 1.3-4 (Ellsworth, 50-66).


8. On mode.


a) Definitions and basic theory. Inc. [cap. rub.: quid sit tonus] Ad propositum igitur redeundo videre restat quid sit tonus prout hic sumitur: ... Cont. [cap. rub.: de ordine cantuum] Omnis vero cantus regularis debet in 10 vocibus contineri... [cap. rub.: de modo constituendi cantuum (sic)] Insuper volentes facere cantum aliquem toni autentici specialiter ecclesiasticum potest sepe hilariter ascendere et descendere per quinque voces aut sex et aliquando per 7 vel 8... [cap. rub.: de motetis et alliis cantibus] De cantibus vero aliis puta motetis baladis et huiusmodi sciendum quod in placalibus eque bene possunt ascendi et descendi [sic] per plures voces sicut in autenticis... [cap. rub.: de locis finiendi cantus] Sciendum est primo quod quatuor sunt litere principales in quarum alica cantus ecclesiasticus debet regulariter facere suum finem... [cap. rub.: de literis principalibus vel inicialibus incipere debet cantus] Primus autem tonus finiens in d graue: habet sex litteras principales seu iniciales... Exp. ... si uero non ascendat in d acutam nisi bina vice erit octaui toni: Ff. 427v-428v.


~ Berkeley 1.5-6 (Ellsworth, 66-80).


b) On Psalm tones. Inc. [cap. rub.: de Euouae] Preterea cum in finibus antifonarum ponatur comuniter Euouae. ... [cap. rub.: versus] Unde versus: Nota primus ad quintam. secundus ad tertiam. tertius ad sextam. quartus ad quartam. quintus ad quintam. sextus ad tertiam. septimus ad quintam. octauus ad quartam. et sic etiam recordor [cap. rub.: de inceptione spalmorum (sic.) secundum tonos] De inceptionibus autem spalmorum secundum tonos versus: Primus cum sexto fa sol la semper abeto... [cap. rub.: de inceptione tonorum] Nota quod secundus et octauus tonus soleniter incipi debent per ut re ut fa...[cap. rub.: de mediacionibus spalmorum (sic)] De mediationibus quidem ipsorum psalmorum reperio hos versus: Septimus et sextus dant fa mi re mi ... [cap. rub.: de fine spalmorum per euouae] Fines autem ipsorum spalmorum senper dicendi sunt pro ut Euouae demonstrant: Et hoc Euouae debet sic regulariter terminari ut post eorum finem congrua fieri possit inceptio antiphonarum. F. 428v.


~ Berkeley 1.7 (Ellsworth, 80-84).


c) On mode in motets and ballades (further), diagram of gamut. Inc. [cap. rub. med.: De motetis et aliorum cantuum Iudicium iudicandi] Restat quidem nunc de cantibus aliis puta motetis. baladis et huiusmodi de quibus [del.] tonis seu modis iudicandi fuerint aliqua declaracione: ... (examples) Exp. Opus duorum graduum ex quinque coniunctim et diuisim in prima deductione et sic potest fieri in aliis deductionibus istorum duorum graduum et aliorum trium per ordinem: (Ex.). F. 429r.


~ Berkeley 1.8 (Ellsworth, 84-86, 88 Exx. 8 ["Primus gradus"] and 9 ["Secundus gradus," truncated]).[31]


9) Material on hexachords, mutations, coniunctae, intervals.


a) [cap. med. rub.: De deductionibus] Prima deductio cuius omnes uoces cantantur per square b quadrum. ... (Exx.). F. 429r-v.


~ Berkeley, 88, Exx. 1-7.


b) [cap. rub.: De locis 14 que sunt in manu.] sequntur 14 loca in quibus possunt fieri mutationes de voce in vocem ... Ff. 429v-430v.


~ Berkeley, 92, Exx. 26-39.


c) [cap. rub.: Iste sunt quedam bone disiuncte.] Iste sunt quedam bone disiuncte. Ff. 430v-431r.


~ Berkeley, 94, Ex. 40.


d) [cap. rub.: deductiones coniunctarum]. F. 431r.


~ Berkeley, 94, Exx. 45, 46, 43.


e) [cap. rub.: gradus] F. 431r.


~ Berkeley, 88, Exx. 1 (again), 9-12 condensed; 90, Exx. 13-25 highly condensed.


f) Examples of mutation. [cap. rub.: de mutationibus] De mutationibus. Mutatio est dimissio unius vocis propter alteram propinquam (Exx.). F. 431r-v.


g) On letters, hexachords, and mutations. Inc. [cap. rub.: de literis musicalibus] In principio sunt septem litere musicales videlicet a.b.c.d.e.f.g ... Cont. [cap. rub.: de deducionibus quod sunt] Deduciones sunt tres videlicet naturam. b molle seu rotundum. et square b quadrum ... [cap. rub.: quid est deducio] Deducio est discursus sex vocum videlicet ut re my fa sol la ... [cap. rub.: versus] Versus. ut re my scandunt: fa sol la quoque desendunt: (Exx. of mutations: per square b quadro grave ... mutationes ascendendo et descendendo a b molle supra acuto in square b supra acuto ut hic) Ff. 431v-433v.


h) On intervals, with examples: Unisonus. Tonus. Semitonus. Ditonus. Dyapente. Tonus cum diapente. Semitonus cum dyapente. Dyatesseron. Tritonus. Diapason. Exadem. Eptadem. Bisdyapason. Ff. 433v-434r.


10. On mode: Divina auxiliante gratia.[32]


a) Preface, presented as a continuation of the preceding discussion of intervals. Inc. [cap. rub. med.: De duobus genera (sic) specierum] Divina auxiliante gratia etc. et brevitatis causa ... Exp. ... accedo ad duo genera specierum, videlicet dyatesseron et dyapente / ad hoc ut istis cognitis faciliter omnes toni possent cognosci. F. 434r


b) On the species of diatessaron and diapente. Inc. Pro cuius declaratione sciendum est quod licet nos primo dicamus in manu gamaut ... Cont. ars ibi non incipit. sed solum in a re. et incipit prima species dyatesseron que formatur a tono semitono et tono:... De istis autem qualiter omnes autentici et placales toni formantur inferius clare patebit: Ff. 434r-435r.


~ Marchetto, Lucidarium 9.1.70, 77-114 (Herlinger, 340-60).


c) On the modes. Inc. [cap.: Capitulum de tonis; cap. rub.: Capitulum de tonis] Accedendo ad declaracionem tonorum videndum est quod quatuor sunt toni scilicet primus tertius quintus septimus ... Cont. [cap. rub.: de perfectione et imperfectione tonorum autenticorum; cap.: Capitulum de perfeccione et inperfeccione tonorum] Visis et tonis autenticis et placalibus nunc uidendum est de ipsorum perfeccionibus... [cap. rub.: De perfectione tonorum placalium] In placalibus uero scilicet perfectus ascensus est cuiuslibet a suo finali sextam ascendere et quartam a suo finali descendere et non vltra... [cap. rub.: De imperfectione tonorum] Tonus autem imperfectus siue sit autenticus siue sit placalis ... Exp. ... uel cum alio quam cum suo autentico si sit placalis videtur conmisceri. Ff. 435r-436r.


~ Marchetto, Lucidarium 11.2.1-34 (Herlinger, 372-88).


d) On judgment of the modes. Inc. [cap.: Capitulum quod non solum toni sunt iudicandi propter ascensum et descensum:] Sunt non nulli qui absque specierum lege cantus diiudicant cuius toni sunt ... Exp. ... Nos autem posumus ostendere quomodo cantus per suas distinctiones et species cognoscantur. F. 436r-v.


~ Marchetto, Lucidarium 11.3.1-11 (Herlinger, 390-94).


e) On formation of the first mode. Inc. [cap.: Capitulum qualiter primus tonus formetur.] Primus tonus formatur ex prima specie dyapente: que est a d graue ad a acuto et ex prima specie dyatesseron superius ... Exp. ... Et talis tonus dicitur aquisitus eo quod eius species aquiruntur per uariationem signorum b rotundi et square b quadri et etiam quia inproprie terminatur: F. 436v-438r.


~ Marchetto, Lucidarium 11.4.1-48 (Herlinger, 394-416).


f) On initial notes of the first mode. Inc. [cap. med.: De principiis primi tonj.] Primus tonus habet principia sex videlicet C. D. E. F. G gravia et a acutum:... Cont. Item in c grauj... Item in E graui et hoc Et hoc [sic] commiste ... Exp. ... Possunt autem species proprie in principiis propriis terminare et in C et in D acutis: Mixte autem in mixtis: et commixte in commistis. sed rarissime in E graui terminare: F. 438r-v.


~ Marchetto, Lucidarium 11.4.49-59. 73-74, 81-86 (Herlinger, 416-20, 428, 430-32).


g) On the second mode. [Inc. cap. med.: De secundo tono:] Secundus tonus formatur ex prima species dyapente sicut primus: et ex prima dyatesseron: comuni et inferius... Cont. Secundus autem tonus habet quinque principia propria videlicet: A.C.D.F graue et vnum plusquamperfectum: scilicet: gamaut... Exp. ... Possunt autem eius species terminare in suis principiis propriis. Et in g graue / et in a acuto: F. 438v.


~ Marchetto, Lucidarium 11.4.87-105 (Herlinger, 432-40).


h) On the third mode. Inc. [cap. De tercio tono.] Tercius tonus formatur ex secunda specie dyapente et secunda dyatesseron superius ... Cont. Tercius tonus habet principia propria quatuor scilicet E.F.g graue et C acutum:... Exp. ... ad euitandum tritonum qui caderet uel cadere posset cum ab b secundo acuto descensum faceret / a d graue uel ab ipsa E ascensum faceret ad b secundum acutum. Ff. 438v-439r.


~ Marchetto, Lucidarium 11.4.106-22 (Herlinger, 440-46).


i) On the fourth mode. Inc. [cap. med.: De quarto tono.] Quartus tonus formatur a secunda specie dyapente et secunda dyatesseron. comuni et inferius:... Cont. Quartus autem tonus habet sex principia scilicet C.d.E.F.G grauia et a acutum:... Exp. ... Possunt et eius species terminare in omnibus suis principiis et in square b quadrum acutum. F. 439r-v.


~ Marchetto, Lucidarium 11.4.123-36 (Herlinger, 446-52).


j) On the fifth mode. Inc. [cap. med.: De quinto tono.] Quintus tonus formatur in suo ascensu ex tercia specie dyapente: et tercia diatesseron: superius... Cont. Quintus tonus habet principia propria quatuor. scilicet F et g graue: a et C acutum: et vnum plusquamperfectum scilicet d graue... Exp. ... si vero ad ipsum d atingat et ultra dyapason ascendat a fine dicetur plusquamperfectus supra / et mixtus infra: F. 439v-440v.


~ Marchetto, Lucidarium 11.4.137-72 (Herlinger, 454-70).


k) On the sixth mode. Inc. [cap. med.: De sexto tono]. Sextus tonus formatur in suo asensu ex tercia specie dyapente: et tercia dyatesseron: ... Cont. Sextus tonus habet tria principia vsitata scilicet c.d et f graue... Exp. ... Possunt autem eius species terminare in omnibus suis principiis et in g graue: F. 440v.


~ Marchetto, Lucidarium 11.4.173-83 (Herlinger, 472-76).


l) On the seventh mode. Inc. [cap. med.: De septimo tono] Septimus tonus formatur ex quarta specie dyapente: que sursum est tendens... Cont. Septimus tonus habet principia sex scilicet F et G graue a et square b quadrum acutum. c et d acutum... Exp. ... Possunt autem eius species terminare in omnibus suis principiis et in C.E. et g acutis: Ff. 440v-441r.


~ Marchetto, Lucidarium 11.4.184-96 (Herlinger, 476-82).


m) On the eighth mode. Inc. [cap. med.: De octauo tono] Octaus tonus formatur ex quarta specie dyapente: que incipitur in g graue: et ex tercia specie dyatesseron:... Cont. Octauus tonus habet propria principia quinque scilicet d.f.g. grauia a et C acutum: et unum plusquamperfectum scilicet C graue... Exp. ... Possunt autem eius species terminare in omnibus suis principiis et in secundo square b quadro: et d acutum. F. 441r.


~ Marchetto, Lucidarium 11.4.197-211 (Herlinger, 482-88).


n) On the naming of the species of diatessaron and diapente. Inc. [cap. De speciebus dyatesseron: et dyapente quomodo in tonis posite nominentur:] Viso et declarato de tonis qualiter per species formentur uidere oportet de ipsis speciebus qualiter nominentur:... Exp. Remissa dicitur illa que fit per tesim id est per descenssum ut hic patet per exemplum [ex.]. F. 441r-442r.


~ Marchetto, Lucidarium 11.4.212-30 (Herlinger, 488-508).


o) On intermediations of the first species of diapente. Inc. [cap. rub. med.: De interrupcionibus; cap. De interrupcionibus dyapente et dyatesseron: et quomodo in quolibet tono interrumpantur:] Et prima interruptio dyapente: fit ex omnibus suis tonis siue per arsim siue tesim ut patet hic per exemplum [ex.] ... Sed notandum est quod species dyapente que fit ex vno interuallo quecunque sit illa: in vno cantu bis uel ter repercussa fuerit quantumcunque talis cantus descendat. etiam si non ascendat ultra suum dyapente: a fine talis cantus dicitur autenticus: ut R. Sint lumbi uestri precinti. F 442r-v.


~ Marchetto, Lucidarium 11.4.231-48 (Herlinger, 508-16).


p) On judgment of modes in ambiguous cases. Inc. [cap. De cantibus qui propter eorum asensum non sunt autentici et propter eorum descensum non sunt placales:] Sunt non nullj cantus qui a fine eorum ad dyapente et non vltra procedunt... Cont. [cap. rub. med.: De Judicio tonorum per cordam:] Corda namque primi et eius placalis est F graue... Exp. ... tria semitonia enarmonica sex dieses faciunt inclusiue: Unus autem tonus continet solum quinque et sic de omnibus cantibus sunt aduertende regule supradicte: F. 442v-443v.


~ Marchetto, Lucidarium 12.1.14-44 (Herlinger, 522-32).


q) On rests. Inc. [cap. De pausis quomodo debeant figurari in cantu:] Sunt non nulli qui proprio suo libito voluntatis absque distincionum specierum ratione ipsas in cantibus figurant ... Exp. ...Neume dicuntur ille que in vnoquoque tonorum diuersse existunt: que quidem ponuntur tan circha principium quam circa medium / et circa finem: que senper terminantur in finali vbi terminari debet cantus in quo posite sunt. F. 443v.


~ Marchetto, Lucidarium 13.1.1-11 (Herlinger, 534-36).


r) On the clef. Inc. [cap. med.: De clauibus et que sint] Clauis est reseracio notarum in quolibet cantu signatarum:... Cont. Sed dicet aliquis quid est vox grauis et acuta... Exp. ... et nota quod vnaqueque vox humana quantumcunque ascendere posit et descendere: uel quantumcunque ascensus et descensus est semper penuriam patitur. Ff. 443v-444r.


~ Marchetto, Lucidarium 14.1.1-21 (Herlinger, 538-42).


11. On the tone and smaller intervals. Inc. Dico quidquid rite sonuerit aut tonum esse aut semitonium aut quartam toni que diesis appellatur:... Exp. Acumine uero quod in in [in bis] aciem terminatam gracilis et erecte modulationis extenditur: Ff. 444r-v.


~ Martianus Capella, De nuptiis (Dick, 494-96).[33]


B. Manus: Compilation of texts on plainchant for review and memorization. Cap. med.: Manus. Ff. 444v-447v.


1. Preface, in part employing words retrofitted from Divina auxiliante gratia, item I/A/10/a above: Cupiens de rationibus cantus tractare. primo ad erudicionem mei. secundo ad profectum adissencium. non meis sed aliorum dictis. quasi expleto. flores decerpens. domino inspirante hoc breue opusculum compilavi: F. 444v.


2. On the letters Γ and A, in part employing words retrofitted from Divina. Inc. et quia principium alicuius scientie est scire terminos. ut ait philosophus ... Cont. Dico primo quod gama est nomen grecum ... Expl. Conclusum est igitur quod prima litera artis nostre est / a / ubi dicitur / are / et ibi incipiendum est. F. 444v


3. On letters and registers. Inc. His visis siendum est quod septem sunt litere in quibus omnis cantus dinositur ... Exp. ... Sed dicet aliquis quid est vox gravis. responsum est antea in predicta carta. F. 444v.


4. On mutation. Inc. Et quia contingit per sepe ob necessitatis causam mutationes fieri in huiusmodi scilicet gravi et acuto et e contra. ideo convenienter de ipsis mutationibus nec non a quibus unaqueque illarum sillabarum positarum in manu regatur nunc videndum est. Sed primo quid sit mutatio: Mutatio sic diffinitur. Mutatio est unius vocis dimissio propter aliam in eodem spacio vel linea et eodem sono... Exp. ... quia in gamaut et in are: et in +my et ela tantum vna sola vox reperitur ideo in ipsis nulla fit mutatio quia vna sola vox mutari non potest. F. 444v-445r.


Concordance from "Mutatio sic diffinitur ...": see note to item I.A.7.a, above.


5. On the letters and their syllables, hexachords, and mutations. Inc. Sed gama ut supra dictum est est grecum. g [sic; l. Γ] est litera gravis et ut est nota et cantatur per square b quadrum et regitur per se sola. Are... Exp. E la: e est litera superacutissima la est nota et cantatur per square b quadrum et regitur ab ut de Gsolreut. Que omnia ista reducantur ad tui memoriam. Hec de mutationibus dicta sufficiant. Exempla dictarum mutationum sunt antea scripta et notata. scilicet in carta quinta et sucessive notata respice. Ff. 445r-446r.


~ Nicolaus de Capua, Compendium musicale, Venice, Biblioteca Nazionale Marciana, MS Lat. VIII.82, ff. 6r-9r.


6. On intervals. [cap. rub.: De coniunctione vocum] Inc. Unisonus est duarum uel plurium vocum coniuncio equalem sonum redencium... Tonus est coniuncio duarum vocum plenam elevationem redens sine aliquo intervallo... Semitonus... Exp. ... Semiditonus cum diapason est coniuncio duarum vocum et dispositio sex tonorum cum tribus semitonis: Et inuenitur de g [sic; l. Γ] graue in b molle acuto / de a graue in c acuto / de square b quadro graue in d acuto / de d graue in f acuto / de e graue in g superacuto [sic; l. acuto] / de g acuto in b molle superacuto / de a acuto in c superacuto / de square b acuto in d superacuto: Et exempla posita sunt antea et hec dicta sufficiant: Ff. 446r-447r.


7. Mnemonic verses on modes. [cap. rub.: Regula] Inc. Est quedam Regula ad agnoscendum tonos: breuiter posita non obstante Regula posita in principio ut patet: Est in .d. uel in a / primus tonus atque secundus:... Exp. ... Septimus in .d. quandoque quiessit acuto: F. 447r.


~ Muris, Ars discantus [CS 3:100]; Nicolaus, Compendium [La Fage, 308]; Guilielmus Monachus, Precepta [CSM 11, 15]; etc.[34]


8. The gamut. Diagram of hexachords in the gamut. F. 447v.

II. Psalm and Magnificat tones. Ff. 448r-456v.



[Bio] Linda Cummins, Coordinator of Musicology at the University of Alabama (USA), is the author of Debussy and the Fragment (2006) and is preparing critical editions of the Compendium of Nicolaus de Capua and Divina auxiliante gratia.

[1] This paper stems from research for a larger project, an edition and translation of Divina auxiliante gratia, a fifteenth-century digest of modal theory from the Lucidarium of Marchetto of Padua, which Jan Herlinger and I are preparing. Research was carried out with the assistance of a Research Advisory Committee grant from the University of Alabama. Thanks are due to the staff of the Biblioteca del Museo Correr for their courtesy and assistance. Earlier versions were read at the American Musicological Society, Annual Meeting, Washington, DC, October 2005; Third Annual Conference, Louisiana Consortium of Medieval and Renaissance Scholars, Northwestern Louisiana State University, October 2005; Medieval and Renaissance Music Conference, Tours, France, July 2005.

[2] Giuliano di Bacco, De Muris e gli altri: sulla tradizione di un trattato trecentesco di contrappunto (Lucca: LIM, 2001), 48. With thanks to Di Bacco, who kindly shared this information before the publication of his book and whose input has been invaluable.

[3] Christian Meyer, Giuliano Di Bacco, Pia Ernstbrunner, Alexander Rausch, and Cesarino Ruini, eds., The Theory of Music: Manuscripts from the Carolingian Era Up to c. 1500: Addenda, Corrigenda: Descriptive Catalogue, Répertoire international des sources musicales B III6 (München: G. Henle, 2003), 627-30.

[4] See Appendix, note 32. The Correr manuscript has been particularly helpful in establishing the text of Divina as it is one of only two that transmit the complete text of the treatise, and the pages of the other complete version, I-Fl Ashburnham 1119, have been so badly corroded by ink that the text is sometimes illegible.

[5] In all the others except I-BGc MAB 21.

[6] One exception: De interrupcionibus, Correr 336, f. 443r, has a coordinate in Bergamo MAB 21, f. 84r: De interuptionibus dyapenthe et dyatexaron Capitulum xxxj.

[7] The Correr manuscript thus provides an important further witness to the dissemination of this doctrine in Italy, along with two other Berkeley sources, Catania D.39 (copied in southern Italy or Sicily in 1473) and Bergamo MAB 21 (copied in Bergamo in 1487), the latter described but not collated by Ellsworth.

[8] Adrien de la Fage, Essais de diptherographie musicale (Paris: Legouix, 1864), 423-28.

[9] Nota quod sunt tres modj cantandj: scilicet .square b.quadro. natura. et .b. mole uel rotundum.

[10] In omni loco ubi inuenitur .g. ibi est principium .square b. quadrj scilicet ut. et .C. ibi natura. et ut .f. ibi est principium .b. rotundj. scilicet b mole.

[11] The Berkeley Manuscript, ed. and trans. Oliver B. Ellsworth, Greek and Latin Music Theory 2 (Lincoln: University of Nebraska Press, 1984), 48-49. The complete statement: “Quia ab una deduccione sepe sit transitus ad aliam in cantu, quod absque mutacione vocum bono modo fieri non potest, licet aliquando fiat per disiunctas. Est enim disiuncta vehemens transitus ab una deduccione in aliam, absque quacumque vocum mutacione ibi fieri possibile. [Although there may often be a transition from one hexadhord to another in song (which cannot be accomplished in a good manner without the mutation of syllables), it may take place sometimes by disjunctions. A disjunction is a violent transition from one hexachord to another, without whatever mutation of syllables might be possible there.]”

[12] Perhaps the compiler omitted the C.105 definition of mutation because he preferred the term dimissio used both in the Garlandia tradition (“mutatio est vnius uocis dimissio propter aliam in eodem spacio uel linea ac in eodem sono”] and in Berkeley (“Racione vocis … de quacumque voce nemo potest nisi ea dimissa et locus eius inferiori pro ascensu aut superiori pro descensu assumpta”) over the term variatio in C.105 (“Nota quod mutatio est uariatio uocis sue note in eodem spatio uel linea eodem sono”).

[13] Despite this difference and Correr’s inclusion of the unison not present in C.105, the concordance of Correr with C.105 is underlined by their common mistakes in counting the numbers of tones and semitones in the eleventh, twelfth, and double-octave.

[14] Curiously, the diminished fifth appears in a list of intervals in Manus, not under its own name but as a type of tritone: “Tritonus est coniuntio duarum vocum et dispositio trium tonorum sine aliquo semitono et figuratur vno modo scilicet fa my: et inuenitur de f in square b / et de b in e: ¶Item aliter tritonus est coniuncio duarum vocum et dispositio duorum [duorum ex trium corr.] tonorum cum additione duorum semitonorum / et figuratur vno modo scilicet my fa / et inuenitur de square b in f / et de e in b: [The tritone is an interval of two syllables and the arrangement of three tones without any semitone, and it is written in one way, fa-mi; it is found from F to square b and from round b to e. The other tritone is an interval of two syllables and the arrangement of two tones with the addition of two semitones, and it is written in one way, mi-fa; it is found from square b to f and from e to round b.]”

[15] “Nota quod litere finales sunt quatuor scilicet d. e. f. g graves... Nota quod toni sunt 8. 4 autentici. et 4 placales.”

[16] Jan Herlinger, “Marchetto's Influence: The Manuscript Evidence,” in Music Theory and its Sources: Antiquity and the Middle Ages, ed. André Barbera, Notre Dame Conferences in Medieval Studies, no. 1 (Notre Dame, IN: University of Notre Dame Press, 1990), 235-58.

[17] Edited by Raffaello Monterosso, “Un compendio inedito del Lucidarium di Marchetto da Padova,” Studi medievali, 3rd series, 7 (1966): 914-31, on the basis of Pavia, Biblioteca Universitaria, MS Aldini 361; the compendium is transmitted also in that library's MS Aldini 450 and in Sevilla, Biblioteca Capitular y Colombina, MS 5.2.25.

[18] “... quia principium alicuius scientie est scire terminos ut ait philosophus in primo posteriorum.”

[19] On this topic, see Anna-Maria Busse Berger, Medieval Music and the Art of Memory (Berkeley: University of California Press, 2005).

[20] The RISM Theory 6 entry notes the comparison (cfr.) of a “Regula” given on folio 447r with a similar one in the treatise published by Coussemaker as Tractatus de musica plana et organica: Scriptorum de musica medii aevi nova series a Gerbertina altera, 4 vols., ed. Edmond de Coussemaker (Paris: Durand, 1864-76; reprint ed., Hildesheim: Olms, 1963), 2:484-98.

[21] Et quedam regula ad agnoscendum tonos breuiter posita non obstante Regula posita in principio ut patet.

[22] The cofinals given in Berkeley 1.6 (pp. 76-77) are A for modes 1 and 2, square b for mode 3, A for mode 4 (sung with round b), C for modes 5 and 6, D for modes 7 and 8.

[23] A similar list appears in the version of the Compendium musicale of Nicolaus of Capua transmitted in Venice, Marciana, Latini VIII.82.

[24] Que omnia ista reducantur ad tui memoriam.

[25] Exempla dictarum mutationum sunt antea scripta et notata: scilicet in carta quinta et sucessiue notata respice:

[26] C.105, unlike some other lists of short statements about music, is not littered with attributions and misattributions to the great authorities of music, to Boethius and Guido and Bernardus, “etc.”; there is no evidence to suggest that the Correr compiler had access to the third treatise of Berkeley, where the only attribution (to Doctor Gostaltus francigena) is found (Ellsworth, 182-83)—and that only in the Catania manuscript.

[27] Cf., e.g., “quasi quosdam ex prato flores carperes (as if you were plucking flowers out of a meadow),” in Fabian Lochner, “Un Évêque musicien au Xme siècle: Radbod d’Utrecht (917),” Tijdschrift van de Vereniging voor Nederlandse Muziekgeschiedenis 1988, 15; but for ex prato Correr has expleto very clearly.

[28] A. J. Minnis, Medieval Theory of Authorship: Scholastic Literary Attitudes in the Later Middle Ages (London: Scolar Press, 1984), passim. Malcolm Parkes, “The Influence of the Concepts of Ordinatio and Compilatio on the Development of the Book,” in Medieval Learning and Literature, ed. J. J. G. Alexander and M. T. Gibson, 115-141 (Oxford: Clarendon Press, 1976), passim.

[29] Vallicelliana C.105 is an Italian collection of music theory texts from the fourteenth or fifteenth century; see RISM B III2,6.

[30] Nigel Gwee, “De plana musica and Introductio musice: A Critical Edition and Translation, with Commentary, of Two Treatises Attributed to Johannes de Garlandia,” Ph.D. diss., Louisiana State University, 1996; Christian Meyer, ed., Musica plana Johannis de Garlandia, Collection d'Études Musicologiques, 91 (Baden-Baden and Bouxwiller: Valentin Koerner, 1998).

[31] RISM, Theory of Music 6 (p. 629) identifies only the material begining with item I.A.8.c as concordant with Berkeley: “Ellsworth, [Berkeley] Manuscript, p. 84 et passim.”

[32] Divina auxiliante gratia, like other material in the manuscript presented without identification, is a digest of the modal theory presented in the Lucidarium of Marchetto of Padua. It has five concordant sources, all Italian and evidently from the fifteenth century: I-BGc MAB 21 (olim S.IV.37), 67r-86v; I-Fl Ashburnham 1119, 36r-46r; I-Fl Pluteus 29.48, 93r-97v; I-PIu 606, 58r-65r; I-Rv B.83, 18r-29v. Jan Herlinger and I are completing a critical edition and English translation of Divina.

[33] Martianus Capella, De nuptiis Philologiae et Mercurii, ed. Adolfus Dick (Leipzig: B. G. Teubner, 1925), 469-535.

[34] Though RISM, Theory of Music 6 (p. 630) gives the anonymous Musica plana et organica as a concordant reading (CS 2:497: “Est in D vel in A primus tonus atque secundus / Tertius et quartus in square b vel E collocantur / Cum quinto sextus in C vel in F religatur / Septimus, octavus in G sola requiescunt”), this text differs more from Correr’s than those I list above.

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