Brian Hyer, ‘“Sighing Branches”: Prosopopoeia in Rameau’s Pigmalion’, Musical Analysis, 13 (1994): 7–50 at 36–40.

Ibid., 40–41. Such strong forms of discursive constructionism may be traced back to Michel Foucault; see Giles Hooper, The Discourse of Musicology (Aldershot: Ashgate, 2006), 90–91.

Lawrence Kramer, ‘Odradek Analysis: Reflections on Musical Ontology’, Musical Analysis, 23 (2004): 287–309 at 289 and 290.

Kramer, ‘Odradek Analysis’, 291.


I share Hooper’s critique (after Habermas) of discursive constructionism in its ‘epistemo-ontological’ variant: ‘For if the musical object exists only as a function of the discourse that generates it, then we appear to be confronted with a peculiar “textualized” version of an original Fichtean self-positing; and this form of what Robert Pippin terms “absolute textuality” surely ignores the brute materiality of a music which not only shapes discourse but which must impose limits on the extent to which discourse can shape or construct it.’ (Hooper, The Discourse of Musicology, 91; original emphasis).

For a concise, yet insightful survey of this topic, running through the major music-theoretical strands of Western music, see Nicholas Cook, ‘Epistemologies of Music Theory’, in The Cambridge History of Western Music Theory, ed. Thomas Christensen (Cambridge: Cambridge University Press, 2002), 78–105.

Ian Bent, ‘History of Music Theory: Margin or Center?’, in Theoria, 6 (1992): 1–21 at 9.


See Charles M. Atkinson, ‘Tonos/Tonus’, in Handwörterbuch der musikalischen Terminologie, ed. Albrecht Riethmüller (Stuttgart: Franz Steiner Verlag, 2005), vi. 341–358.

For the bibliographic references to these studies, see Matthew Brown and Douglas J. Dempster, ‘The Scientific Image of Music Theory’, Journal of Music Theory, 33 (1989): 65–106 at 100–101, nn. 2 and 3.

Thomas Christensen, Rameau and Musical Thought in the Enlightenment (Cambridge: Cambridge University Press, 1993); Robert Snarrenberg, Schenker’s Interpretive Practice (Cambridge: Cambridge University Press, 1997); Karl Braunschweig, ‘Enlightenment Aspirations of Progress in Eighteenth-Century German Theory’, Journal of Music Theory 47 (2003): 273–304; Jairo Moreno, Musical Representations, Subjects, and Objects: The Construction of Musical Thought in Zarlino, Descartes, Rameau, and Weber (Bloomington: Indiana University Press, 2004).

Ronald Woodley, ‘Renaissance Music Theory as Literature: On Reading the Proportionale Musices of Iohannes Tinctoris’, Renaissance Studies, 1 (1987): 209–20.

Christopher Page, ‘Reading and Reminiscence: Tinctoris on the Beauty of Music’, Journal of the American Musicological Society, 49 (1996): 1–31.

Susan Fast, ‘Bakhtin and the Discourse of Late Medieval Music Theory’, Plainsong and Medieval Music, 5 (1996): 175–91.

Leofranc Holford-Strevens, ‘Humanism and the Language of Music Treatises’, Renaissance Studies, 15 (2001): 415–49. In the present collection of essays, the theorist’s name, also sometimes given as Franchino Gaffurio, Gafori, Gaffurius, etc., has been harmonized to Franchinus Gaforus.

Cristle Collins Judd, Reading Renaissance Music Theory: Hearing with the Eyes (Cambridge: Cambridge University Press, 2000).

Dorit Tanay, Noting Music, Marking Culture: The Intellectual Context of Rhythmic Notation, 1250–1400 (Holzgerlingen: American Institute of Musicology; Hänssler-Verlag, 1999).

Fast, ‘Bakhtin and Late Medieval Music Theory’, 183.

Ibid., 190 (original emphasis).

Woodley, ‘Renaissance Music Theory as Literature’, 210.


In Woodley’s own words: ‘we must regard Tinctoris’s efforts primarily as a means of enriching his own personal style of writing, and striving through this acquired style to a position of greater authority and influence.’ (Ibid., 217).

For a more nuanced discussion of this vast topic, see the insightful pages on Tinctoris’s humanist models in Reinhard Strohm, ‘Music, Humanism, and the Idea of a “Rebirth” of the Arts’, in Music as Concept and Practice in the Late Middle Ages, The New Oxford History of Music III.1, ed. Reinhard Strohm and Bonnie J. Blackburn (Oxford: Oxford University Press, 2001), 346–88 at 360–68 and the Testimonia in the Appendix, 389–405.

For an overview of this topic, see Patrick McCreless, ‘Music and Rhetoric’, in The Cambridge History of Western Music Theory, ed. Thomas Christensen (Cambridge: Cambridge University Press, 2002), 847–79. A recent contribution on the German tradition of musica poetica is Bettina Varwig, ‘“Mutato semper habitu”: Heinrich Schütz and the Culture of Rhetoric’, Music & Letters, 90 (2009): 215–39.

See the discussion of this point in the chapter ‘The Quarrel of Philosophy and Rhetoric’ in Nancy Struever, The Language of History in the Renaissance (Princeton, NJ: Princeton University Press, 1970), which explores the rhetorical nature of historical writing. Paraphrasing literary critic Frank Kermode, for instance, Struever describes rhetoric as ‘not so much systematic in a philosophical sense as a mnemotechnical system for making fruitful connections between disparate insights’ (p. 15, emphasis mine).

For an overview of Erasmus’s treatise, based on Cicero’s De oratore and Quintilian’s Institutio oratoria, see Peter Mack, A History of Renaissance Rhetoric, 13801620 (Oxford: Oxford University Press, 2011), 80–87; Thomas Sloane, ‘Schoolbooks and Rhetoric: Erasmus’s De Copia’, Rhetorica: A Journal of the History of Rhetoric, 9 (1991): 113–129. For an English edition of De copia, see Copia [italics in the original]: Foundations of the Abundant Style: De duplici copia verborum ac rerum commentarii duo, trans. and annotated by Betty I. Knott, in The Collected Works of Erasmus, ed. Craig R. Thomson, vol. 24: Literary and Educational Writings 2, De copia / De ratione studii (Toronto: University of Toronto Press, 1978), 279–659.

Sloane, ‘Schoolbooks and Rhetoric’, 116–21.

For an overview of this philosophy of language, and how it may apply to renaissance philosophies of language, see Michael Losonsky, Linguistic Turns in Modern Philosophy (Cambridge: Cambridge University Press, 2006), 38–40. Humanist Lorenzo Valla has at times been interpreted as viewing language as constitutive of reality. For a critique of this line of argument, see John Monfasani, ‘Was Lorenzo Valla an Ordinary Language Philosopher?’, in Journal of the History of Ideas, 50 (1989), 309–23.

Walter Jost describes rhetorical inventio as ‘creative or inventive rather than merely reactive or serendipitous’, because it underscores the evaluative process by which we see certain facts (and their reciprocal connections) as more significant than others (Walter Jost, Rhetorical Investigations: Studies in Ordinary Language Criticism (Charlottesville: University of Virginia Press, 2004), 14–15).

Carl Dahlhaus, Untersuchungen über die Entstehung der harmonischen Tonalität (Kassel: Bärenreiter, 1968); English trans. by Robert O. Gjerdingen, Studies on the Origin of Harmonic Tonality (Princeton: Princeton University Press, 1990), hereafter SOHT. In her review of the Studies, Eva Linfield points out that ‘emergence’ and ‘genesis’ might have provided a more adequate translation of Entstehung in this particular context, as they suggest a slow and nebulous process of formation rather than an event at a particular point in time (Journal of Music Theory, 36 (1992): 389–400).

For a concise assessment of Dahlhaus’s Studies in relation to Riemann, see Michael Heinemann, ‘Im Schatten Riemanns. Zu Dahlhaus’ Entstehung der harmonischen Tonalität’, in Carl Dahlhaus und die Musikwissenschaft: Werk, Wirkung, Aktualität, ed. Hermann Danuser, Peter Gülke, and Norbert Miller, in collaboration with Tobias Plebuch (Schliengen: Argus, 2011), 314–20; on the significance of Dahlhaus’s theory of tonality for American music theory, see Alexander Rehding, ‘Dahlhaus zwischen Tonalität und Tonality’, in the same volume, 321–34.

Notable examples here are Joel Lester, who emphasizes the coexistence of ‘modal’ and ‘tonal’ theories in the eighteenth century in his Between Modes and Keys: German Music Theory, 1592–1802 (Stuyvesant, NY: Pendragon Press, 1989), esp. chaps. 4 and 5; Harold Powers, who did not believe in ‘modality’ to begin with (witness his landmark articles cited below, n. 46; and scholars of the next generation such as Gregory Barnett, who argues that the system of ‘church keys’ mirrored the harmonic practice of seventeenth-century composers more adequately than modal theory (see, for instance his ‘Modal Theory, Church Keys, and the Sonata at the End of the Seventeenth Century’, Journal of the American Musicological Society, 51 (1998): 245–81).

Dahlhaus, SOHT, 67–151. The label ‘harmonic tonality’ is tangible proof that the concepts of ‘harmony’ and ‘tonality’ have become virtual synonyms in current academic discourse, for better or worse (perhaps for that reason the Cambridge History of Western Music Theory includes a chapter on ‘Tonality’, but not one on ‘Harmony’). ‘Harmony’ is of course a much older concept than ‘tonality’, and one might object that the latter hijacks the former only at the risk of distortion. Nevertheless, the discussion that follows, while focused on ‘harmony’, will inevitably spill over to include the notion of ‘tonality’ as well.

Carl Dahlhaus et al., ‘Harmony’, § 1: ‘Historical Definitions’ in Grove Music Online (, as at December 2018). See also the citation on the Ionian and Aeolian clausulas below at para. 28. By positing harmony as a network of ‘structural principles’ informing both modern and pre-modern music, the citation is somewhat at odds with the thrust of the entry as a whole, which rests on a hard distinction between ‘harmonically based’ (2.iii, fifth paragraph) and (presumably) ‘non-harmonically-based’ compositions and music-historical eras. It is not my intention to offer here an exhaustive account of Dahlhaus’s notion of harmony; I discuss the topic also in my ‘The History of Music Theory after Dahlhaus’s Studies on the Origin of Harmonic Tonality: On the Relationship between Musical Concepts and Musical Phenomena’, Theoria: Historical Aspects of Music Theory, 24 (2017): 157–71.

For instance, the same series of dyads may be regarded either as a self-contained interval progression (i.e. as counterpoint), or as ‘fragments of chord progressions’ (Studies, 69), i.e. as harmony properly, and chap. 2 of the Studies begins with the argument that ‘… terms like “chord” and “basse fondamentale” do not designate objective facts that one can point to in a musical score. Rather, these terms denote cofactors in a particular mode of musical perception, factors that receive their full meaning (Sinn) only in relation to other factors’ (Studies, 67: ‘Ausdrucke wie “Akkord” und “Basse fondamentale” bezeichnen keine Sachveralte, auf die man in den Noten zeigen könnte, sondern Teilmomente einer musikalischen Hörweise, die erst in der Beziehung zu anderen Momenten ihren Sinn erhalten’, Untersuchungen, 57). Whatever ‘full meaning’ might mean here, it should be noted that this is not an argument against the existence of objective musical facts, on which Dahlhaus’s harmonic theory in the end is predicated, but rather a general prescription on how to identify them (holistically rather than individually), leaving aside here the additional problem that the individual components of Dahlhaus’s entelechy, such as ‘chord’ and ‘basse fondamentale’, belong to different categorical domains across the practice/theory divide.

SOHT, chap. 2 (‘Intervallic and Chordal Composition’), esp. 67–70, and 288 (Untersuchungen, 57–60 and 256); the crucial distinction, however, is already stated in the introduction: ‘Tonal harmony rests on [the assumption] that a triad constitutes a primary, direct unity’ (SOHT, 3; Untersuchungen, 7).

The example is also discussed in Thomas Christensen, review of Dahlhaus, Studies on the Origin of Harmonic Tonality, trans. Gjerdingen, and of Lester, Between Modes and Keys, Music Theory Spectrum, 15 (1993): 94–111 at 98–99.

SOHT, 218; Untersuchungen, 197.

It is interesting to observe that Dahlhaus will occasionally use Latin terms (such as clausula, species, or finalis), when discussing authors such as Pietro Aron, who wrote for the most part in the vernacular, and Zarlino, who always did. Intentionally or not, the archaic-sounding labels in the Studies read as a distancing device that in a subtle way colors and bolsters Dahlhaus’s historical narrative. For example, he speaks of ‘mi-clausula’ and ‘la-clausula’ in reference to Pietro Aron’s Toscanello in musica (1523, reprint 1529; see SOHT, 90; Untersuchungen, 82). Ironically, Aron’s Latin term for cadence is cadentia, not clausula (as shown in Book III, chapters 35–51, of his Libri tres de institutione harmonica of 1516). In the same paragraph, Dahlhaus also mentions Zarlino’s discussion of the ‘discant-bass clausula’ in Istitutioni harmoniche, Book III, chap. 53 (p. 221), overlooking the fact that a musical cadence for Zarlino is a cadenza, while the term clausula designates textual closure (‘la Cadenza … non è però da usarla, se non quando si ariva alla Clausula, overo al Periodo, contenuto nella Prosa, o nel Verso’, ibid.).

Robert Gjerdingen, Music in the Galant Style (Oxford: Oxford University Press, 2007), 177.

Ibid., 178.

Ludwig Holtmeier, ‘Heinichen, Rameau, and the Italian Thoroughbass Tradition: Concepts of Tonality and Chord in the Rule of the Octave’, Journal of Music Theory, 51 (2007): 5–49 at 11. On the partimenti, see in particular Giorgio Sanguinetti, The Art of Partimento: History, Theory, and Practice (Oxford: Oxford University Press, 2012). The author describes this performing/notational tradition, which provided keyboard players the essential information for improvising a composition on their instrument, as a strand of ‘non-verbal theory’ (pp. 9–10), implicitly claiming that the partimenti contributed a great deal to shaping eighteenth-century ‘harmonic tonality’ without trying to capture it in words. The wide success of a tradition of music making distinctly uninterested in conceptualizing the age-old melodic-harmonic patterns that constituted its core calls out the shortsightedness of the modern bias towards understanding the musical choices and conventions of the past in light of the concepts attached to them at any given time.

Ibid., 6.

Wye J. Allanbrook, ‘Theorizing the Comic Surface’, in Music in the Mirror: Reflections on the History of Music Theory and Literature for the Twenty-First Century, ed. Andreas Giger and Thomas J. Mathiesen (Lincoln: University of Nebraska Press, 2002), 195–216. Allanbrook traces the modern interest in the ‘objectification of the deep’ (p. 199) to the Romantic view of music as a privileged means for capturing ‘the inner nature and the in-itself’ of things, below the phainomena on the surface (pp. 195–6).

For instance, in the opening paragraph of his landmark article on tonal types, Harold Powers observes that ‘The sonic surface [of renaissance polyphony] is sometimes faintly exotic, often charmingly vague and undirected to our ears, but hardly alien’, in ‘Tonal Types and Modal Categories in Renaissance Polyphony’, Journal of the American Musicological Society, 34 (1981): 428–70 at 428; over a decade later, he still maintained that ‘The surface manifestations of 16th-century polyphonic tonalities … are much like those of 18th-century polyphonic tonalities’, in ‘Is Mode Real? Pietro Aron, the Octenary System, and Polyphony’, Basler Jahrbuch für historische Musikpraxis, 16 (1992): 9–52, at 13–14. For her part, Margaret Bent has emphatically argued that ‘Superficial similarities between medieval and later phenomena (things that sound like triads and V–I cadences) have placed us in danger of ignoring major differences in the grammar and syntax which govern their use’, in ‘The Grammar of Early Music: Preconditions for Analysis’, in Tonal Structures of Early Music, ed. Cristle Collins Judd (New York: Garland, 1998), 15–59 at 30–31.

My discussion of this topic is indebted to Bonnie J. Blackburn, ‘Leonardo and Gaffurio on Harmony and the Pulse of Music’, in Essays on Music and Culture in Honor of Herbert Kellman, ed. Barbara Haggh (Paris: Minerve, 2001), 128–49.

‘Quinta autem quam diapente integra … mediam obtinet concordem chordam cum extremis. Componitur enim ex duabus primis simplicibus scilicet tertia minore atque tertia maiore concordi medietate servata. Inde suaviorem ducit extremitatum concordiam quasi quae certa imitatione harmonicae adhaereat medietati’ (Practica musicae, Bk 3, chap. 5 (Milan: Guilermus le Signerre, 1496), fol. cc vijv), ‘A diapente or perfect fifth … has an intermediate tone concordant with the outer tones, for it is composed of the first two single intervals a minor third and a major third meeting in the middle on a common tone. Thus its outer tones produce a more pleasant concord, as if the concord were related to the middle division in a certain harmonious imitation [read: as if imitating the harmonic mean of the octave]’ (Franchinus Gaffurius [Gaforus], Practica musicae, trans. Clement A. Miller, Musicological Studies and Documents, 20 (n.p.: American Institute of Musicology, 1968), 120).

‘Ea enim [i.e. harmonia] est extremarum contrariarumque vocum communi medio consonantias complectentium suavis et congrua sonoritas. quam iccirco a consonantia differe constat. Haec namque sola proportione: duabus saltem illa producitur. Hinc falso sunt arbitrati qui consonantiam et harmoniam idem esse posuerunt. nam quamquam harmonia consonantia est: omnis tamen consonantia non facit harmoniam. Consonantia namque ex acuto et gravi generatur sono: Harmoniam vero ex acuto et gravi conficiunt atque medio,’ Franchinus Gafurius [Gaforus], De harmonia musicorum instrumentorum opus (Milan: Gotardus Pontanus, 1518), fol. 80v. (‘For harmony is a pleasant and concordant sonority of outer opposing tones embracing consonances through a common medial tone, and for this reason it is firmly determined that it differs from a consonance. For the latter is produced by a single proportion and the former from at least two. Thus those who have posited that consonance and harmony are the same have judged falsely. For although a harmony is a consonance, nevertheless not every consonance makes a harmony, for a consonance is formed from a high and a low sound, but a harmony is produced from a high, low, and medial sound.’ Franchinus Gaffurius [Gaforus], De harmonia musicorum instrumentorum opus, trans. with introd. Clement A. Miller, Musicological Studies and Documents, 33 (Neuhausen–Stuttgart: American Institute of Musicology; Hänssler Verlag, 1977), 173, with slight adjustments to Miller’s wording). These excerpts are discussed in Blackburn, ‘Leonardo and Gaffurio’, 131–32.

Hugo Riemann, History of Music Theory, Books I and II: Polyphonic Theory to the Sixteenth Century, trans. with preface, commentary, and notes Raymond H. Haggh (Lincoln: University of Nebraska Press, 1962): 284 (n. 6).

SOHT, 19–20 (Untersuchungen, 19–20). I have not been able to locate in Gaforus the precise passage(s) that occasioned Dahlhaus’s critique.

Blackburn, ‘Leonardo and Gaffurio’, 131–2.

In similar fashion, Alexandre Koyré argued that Galileo’s mathematical account of a physical object in free fall implies that he had the concept of inertial mass, even though it was labeled as such only at a later time. See Branko Mitrović, ‘Attribution of Concepts and Problems with Anachronism’, History and Theory, 50 (2011): 303–27 at 310.

Gaforus, Practica musice, Bk. 3, chap. 2, fol. cc viiir.

Gaforus, De harmonia, Bk 3, chap. 10, fol. lxxxv.

Blackburn, ‘Leonardo and Gaffurio’, 132.

See Bonnie Blackburn, ‘The Dispute about Harmony c.1500 and the Creation of a New Style’, in Théorie et analyse musicales/Music Theory and Analysis: 1450–1650, Proceedings of the International Conference Louvain-la-Neuve, 23–25 September 1999, ed. Anne-Emmanuelle Ceulemans and Bonnie J. Blackburn (Louvain-la-Neuve: Départment d’histoire de l’art et d’archéologie, Collège Érasme, 2001), 1–37.

For instance, a compelling argument has been made that the rhetorical principle of varietas informs the eight rules of counterpoint laid out by Tinctoris in the last book of his counterpoint treatise. See Alexis Luko, ‘Tinctoris on Varietas’, Early Music History, 27 (2008): 99–136. In similar fashion, Rob Wegman has argued that Tinctoris’s counterpoint treatise goes beyond the traditional task of regulating the use of consonances and dissonances in polyphony. Rather, Tinctoris ‘sought to promote a sensitive appreciation of the musical quality that contemporary composers … had brought to consummate perfection—consonant sweetness (suavitas, dulcedo).’ (Rob C. Wegman, ‘Johannes Tinctoris and the “New Art”’, Music & Letters, 84 (2003): 171–88 at 172. In short, counterpoint in Tinctoris is more a rhetorical than a grammatical tool.

The original text and English translation of the Expositio are currently available in the Stoa Consortium legacy version of the online Tinctoris edition, The Theoretical Works of Johannes Tinctoris, ed. Ronald Woodley (; also edited in Johannis Tinctoris Opera theoretica, ed. Albertus Seay, 2 vols. plus iia in 3, Corpus scriptorum de musica, 22 (n.p.: American Institute of Musicology, 1975–8), i. 31–57. Seay points to the relative insularity and ‘old-fashioned’ character of the Expositio when he observes that the treatise ‘contains few references to contemporary practice’ and avoids comparisons between ‘past and present’. See Albert Seay, ‘The Expositio manus of Johannes Tinctoris’, Journal of Music Theory, 9 (1965): 194–232 at 195.

For a review of the nuts and bolts of the solmization system, see Albert Seay’s introduction to his translation of the treatise (‘The Expositio manus of Johannes Tinctoris’, 194–99); Carol Berger, ‘The Hand and the Art of Memory’, Musica disciplina, 35 (1981): 87–120; and Andrew Hughes and Edith Gerson-Kiwi, ‘Solmization’, § I: ‘European medieval and Renaissance systems’ in Grove Music Online ( In chap. 3 of my own monograph on Guidonian solmization, The Renaissance Reform of Medieval Music Theory: Guido of Arezzo Between Myth and History (Cambridge: Cambridge University Press, 2010), I have attempted to compile a catalogue of the hands found in extant manuscripts of music theory up to c.1500, many of which are also reproduced in Joseph Smits van Waesberghe, Musikerziehung: Lehre und Theorie der Musik im Mittelalter, Musikgeschichte in Bildern, 3.iii (Leipzig: VEB Deutscher Verlag für Musik, 1969), figs. 61–84. The historical background of the terminology of the Expositio manus is now easily accessible by consulting the Lexicon musicum Latinum medii aevi published by the Bavarian Academy of Sciences (in progress). The glossary is currently available at the Academy’s website ( while the more detailed thesaurus, which documents the use of the terms in specific treatises, is also available online (

Needless to say, this has been the accepted view by the scholarly community on the subject in recent decades. However, as the following discussion will show, it is possible to argue that the foundational view of the hand overstates the significance of the six syllables in the musical theory and practice of the Middle Ages and Renaissance. See my ‘Virtual Segments: The Hexachordal System in the Late Middle Ages’, The Journal of Musicology, 23 (2006): 426–67, and ‘The Heptachordal Basis of Hexachordal Theory: On the Semiotics of Musical Notation in the Middle Ages’, Plainsong and Medieval Music, 22 (2013): 169–94; also my monograph cited in the previous footnote.

In similar fashion, Frieder Rempp has stressed the ahistorical mode of presentation of the Expositio manus; see his ‘Elementar- und Satzlehre von Tinctoris bis Zarlino’, in Geschichte der Musiktheorie, ed. Frieder Zaminer, vol. 7: ‘Italienische Musiktheorie im 16. und 17. Jahrhundert: Antikenrezeption und Satzlehre’ (Darmstadt: Wissenschaftliche Buchgesellschaft, 1989), 41–220 at 57.

Mengozzi, ‘The Heptachordal Basis’, 191–3.

See the modern edition of the treatise, Johannes Gallicus, Ritus canendi vetustissimus et novus, ed. Albert Seay, 2 vols. (Colorado Springs: Colorado College Music Press, 1981); the citations of Gallicus’s text below emend Seay’s transcription, following the reading of GB-Lbl Add. 22315. I discuss Gallicus’s critique of solmization in chap. 6 of The Renaissance Reform of Medieval Music Theory.

‘Quare Guido sex sillabas elegerit ad cantandum, nec plus nec minus, et quare litteras … dictis sillabis miscuerit …’ (Ritus canendi, ed. Seay, ii. 51).

‘et sex illas … propter infantulos fabricare sillabas, quibus nempe tonos magis faciliter aut elevarent aut deponerent ac semitonia, velut quodam adminiculandi baculo sufulti.’ (ibid., 48).

‘[Guido] musicus erat et non cantor purus, non nesciens omne quod canitur, quatuor tantum cuncludi [sic] vocibus ac duobus cum semitonio minori tonis, quod totum aut prima consonantia dyatessaron ab antiquis philosophis appellatur aut tetracordum, hoc est, quatuor cordarum. Quid enim ultra primam dyatessaron agis quod non sit unum et idem…. Nimirum necesse fuit Guidonem, cuius propositum erat quam breviter totum exprimere cantum, has sex nec plus nec minus aut alias huiusmodi totidem fabricare sillabas.’ (ibid., 51; punctuation slightly modified).

‘Ex quo patet illum non sex illas excogitasse sillabas pro rei veritatis quae tonus est cum reliquis abolitione, sed pro parva puerorum ac rudium velut quodam baculo sustentanda capacitate.’ (ibid., 6).

See the section from Book II of the Ritus titled ‘Modus canendi per ut, re, mi, fa, sol, la facilis, verus atque brevissimus’ (ibid., 53–63). The term guidonistae is from Johannes Ciconia’s Nova musica.

Tinctoris wrote both Prop. mus. and the original version of Diff. (the same one eventually printed in Treviso in 1494) within the first two years of his arrival in Naples, or c.1472–74. Cecilia Panti ascribes Exp. manus to a slightly later period (c.1475) by virtue of the identical readings linking some of its definitions – namely, ‘semitonium’, ‘coniunctio’, ‘linea’, and ‘manus’ – to the revised version of Diff. as transmitted in the Brussels manuscript (see Iohannes Tinctoris, Diffinitorium musice: Un dizionario di musica per Beatrice d’Aragona, ed. and trans. Cecilia Panti (Florence: Edizioni del Galluzzo, 2005), xxxvi–xxxix). Ronald Woodley, however, downplays the significance of these textual relationships to the issue of the chronology of the treatises, suggesting that Exp. manus may even have preceded Prop. mus. (see his review of Panti’s edition in Early Music, 34 (2006): 479–81, esp. at 480).

See, for instance, the earlier treatises (or portions of treatises) on musica speculativa by Johannes Ciconia (in Nova musica), Prosdocimus de Beldemandis (Musica speculativa), Ugolino of Orvieto, and, in Tinctoris’s own time, the Carthusian Anonymous (often mistakenly identified as Dionysius the Carthusian), John Hothby, Bonaventura da Brescia, Adam of Fulda, and Faber Stapulensis, to cite only a few 15th-cent. authors. Gaffurio’s discussion of the proportions adopts the traditional model in Book III of his Theorica musice (1492), but follows Tinctoris’s new teaching, applied to issues of musical notation, in Book IV of his Practica musicae (1496).

‘Sub hoc autem genere, velut intuenti perspicaciter apparet, comprehenditur sesquioctava, quae est proportio qua maior numerus ad minorem relatus illum in se totum continet et insuper eius octavam partem aliquotam, ut 9 ad 8, 18 ad 16, etc., sicut hic [Example 2.2]. Ex hac autem proportione Pythagoras dum malleos, quorum primus 8, secundus 9 ponderum erat, compulsare iussit, tonum causari didicit. Quo fit ut hec proportio a Pythagoricis eam sepius “epygdoum” nominantibus, interdum “tonus” et, e converso, tonus ipse “sesquioctava” vel “epygdous” vocetur.’ (Johannes Tinctoris, Proportionale musices; Liber de arte contrapuncti, ed. Gianluca D’Agostino (Florence: Edizioni del Galluzzo, 2008), 50).

Prosdocimus de Beldemandis’s Tractatus practice de cantus mensurabilis (1408) appears to be the first treatise to explicitly link rhythmic proportions to their numerical equivalents. Another theorist active in Padua, Johannes Ciconia, followed suit about three years later in the revised version of Book III of Nova musica, which also circulated as an independent tract (De proportionibus; see Johannes Ciconia, Nova musica and De proportionibus: New Critical Texts and Translations, ed. Oliver B. Ellsworth (Lincoln, NE: University of Nebraska Press, 1993), 440–43). The added section on proportion signs in Ciconia’s treatise may indicate recent exposure to Prosdocimus’s teaching. Later sources highlighting the relation between numerical and rhythmic proportions are discussed in Anna Maria Busse Berger, Mensuration and Proportion Signs: Origins and Evolution (Oxford: Clarendon Press, 1993), 164–68, and Ruth I. DeFord, Tactus, Mensuration, and Rhythm in Renaissance Music (Cambridge: Cambridge University Press, 2015), 14–20.

See, for instance, Book III, chap. 2 (‘Qualiter proportiones signande sunt’), where Tinctoris endorses the strategies for indicating metrical changes adopted in works by Binchois, De Domarto, Faugues, and Du Fay, while singling out for disapproval those by Le Rouge [Guillaume Ruby], [Jean] Puyllois, and Barbingant. This chapter of Prop. mus. is referenced in Reinhard Strohm, The Rise of European Music, 1380–1500 (Cambridge: Cambridge University Press, 1993), 425. However, Ronald Woodley has pointed out that the Mellon Chansonnier, copied in Naples around 1475 under Tinctoris’s direct supervision, occasionally contravenes the precepts guiding the indication of mensura and dissonance treatment found in Tinctoris’s own treatises (see Ronald Woodley, ‘Did Tinctoris Listen to Okeghem? Questions of Textuality and Authority in the Late Fifteenth Century’, presented at the International Congress of Medieval Studies in Kalamazoo (Michigan) in 2006, and currently available at the ‘legacy’ Tinctoris website ( As an editor, Woodley argues, Tinctoris at least at times honors the authority of his musical texts even when they flatly contradict his own authority as a theorist, implicitly admitting that the ‘rhetorical registers’ of music theory (by which the elements of music are parsed, described, explained, and argued about) are not necessarily attuned to the pragmatic choices that often govern musical behaviors. Tinctoris’s own pragmatic attitude about the applicability of his precepts, one may add, points to his awareness of the rhetorical nature of music theory. For an enlightening discussion of Tinctoris’s remarks on Ockeghem’s notational practices, see also Bonnie J. Blackburn, ‘Did Ockeghem Listen to Tinctoris?’, in Johannes Ockeghem: Actes du XLe Colloque international d’études humanistes, Tours, 2–8 février 1997, ed. Philippe Vendrix, Épitome musical, 1 (Paris: Klincksieck, 1998), 597–640.

For a thorough discussion of Tinctoris’s theory of dissonance in connection with the musical practice of his time (including his own), see Lee Rothfarb, ‘Tinctoris vs. Tinctoris: Theory and Practice of Dissonance in Counterpoint’, In Theory Only, 9 (1986): 3–32, and Eunice Schroeder, ‘Dissonance Placement and Stylistic Change in the Fifteenth Century: Tinctoris’s Rules and Dufay’s Practice’, The Journal of Musicology, 7 (1989): 366–89; Frieder Rempp, ‘Elementar- und Satzlehre von Tinctoris bis Zarlino’, 152–6, places Tinctoris’s Dissonanzlehre in broader historical perspective. On the figure of the composer-theorist in the Renaissance, see Emily Zazulia, ‘Composing in Theory: Busnoys, Tinctoris, and the L’homme armé Tradition, Journal of the American Musicological Society, 71 (2018), 1–73.

Capitulum XXIII. Quod in simplici contrapuncto discordantie non sunt admittende, sed in diminuto; et primo qualiter circa partes minime in utraque prolatione ac circa partes semibrevis in minori. In ipso autem simplici contrapuncto discordantie simpliciter et absolute prohibentur, sed in diminuto cum ratione moderata interdum permittuntur. Unde sciendum est – ut veterum musicorum compositiones transeam, in quibus plures erant discordantie quam concordantie – quod fere omnes recentiores non solum compositores verum etiam super librum canentes, tam in prolatione maiori quam in minori, supra primam vel aliam partem minime, et in minori ultra hoc supra primam vel aliam etiam partem semibrevis, posita concordantia, discordantiam eiusdem aut minoris note supra sequentem immediate collocant. E contra vero, tam in prolatione maiori quam in minori, supra primam partem prime duarum minimarum in eodem loco existentium unitarum aut separatarum, vel minime solius, et ultra hoc in prolatione minori supra primam partem duarum semibrevium in eodem etiam loco unitarum aut separatarum, perfectionem aliquam immediate precedentium, discordantia fere semper assumitur.’ (Proportionale musices, ed. D’Agostino, 328–30).

In a well-known passage from his Complexus effectuum musices, Tinctoris describes musical understanding as a two-stage process whereby perception through the external sense of hearing (sensus extrinsecus) leads to musical knowledge (perfecta cognitio musicae) through the inner faculty of the intellect, and in turn to the ability to judge music correctly (recte/vere iudicare). On this point, see Christopher Page, ‘Reading and Reminiscence’, esp. 7–10, and Rob C. Wegman, ‘“Musical understanding” in the 15th century’, Early Music, 30 (2002): 46–66, at 51–2.

Erasmus in particular considered rhetoric as the art of reconciling opposite arguments. See Jost, Rhetorical Investigations, 16.

‘Der Mangel der antiken Theorie … war vielleicht der, daß die alten Musici immer nur auf das unveränderlich Wesen, auf die Natur der Musik aus waren (und als die Natur der Musik wurde das Phänomen der Konsonanz angesehen, die ein rationales Tonsystem möglich macht), über der Natur aber die Kunst vernachlässigten, die das Tonsystem als ihr Material benutzt’, Michael Zimmermann, ‘Johannes Tinctoris und der Beginn der Neuzeit’, in Europäische Musikgeschichte, ed. Sabine Ehrmann-Herfort, Ludwig Finscher, and Giselher Schubert, vol. 1 (Kassel: Bärenreiter and Stuttgart: Metzler, 2002), 205–237 at 229.

‘Verumtamen sepissime apud infinitos compositores etiam celeberrimos oppositum comperi’ (Liber de arte contrapuncti, ed. D’Agostino, 358). See the extensive analyses of this passage in Karol Berger, Musica Ficta: Theories of Accidental Inflections in Vocal Polyphony from Marchetto da Padova to Gioseffo Zarlino (Cambridge: Cambridge University Press, 1987), 93–115; Peter Urquhart, ‘Cross-Relations by Franco-Flemish Composers after Josquin’, Tijdschrift van de Vereniging voor Nederlandse Muziekgeschiedenis, 43 (1993), 3–41 at 27–31; Margaret Bent, ‘On False Concords in Late Fifteenth-Century Music: Yet Another Look at Tinctoris’, in Théorie et analyse musicales/Music Theory and Analysis: 1450–1650, 65–118, esp. 88–118. A transcription of the three examples by Faugues, Busnoys, and Caron may also be found in The Art of Counterpoint, trans. and ed. Albert Seay, Musicological Studies and Documents, 5 (n.p.: American Institute of Musicology, 1961), 130.

The excerpt may also exemplify the use of an augmented octave between the two upper parts in measure 6, since a cadential g# in the Discantus appears plausible. For a detailed discussion of this point, see Ronald Woodley, ‘Sharp Practice in the Later Middle Ages: Exploring the Chromatic Semitone and Its Implications’, Music Theory Online, 12 (2006), 1–48 at 26–9 and 33–5.

Berger, Musica Ficta, 93–115, and Urquhart, ‘Cross-Relations by Franco-Flemish Composers’, 3–41, esp. 14, where the author argues that composers such as Johannes Lupi, Nicolas Gombert and others may have occasionally designed their polyphonic works to explore or ‘exploit’ cross-relations.

Bent, ‘On False Concords’, 91–118.

Ibid., 99–102. However, in the Busnoys example the ‘fixing’ of the false concord is likely to produce a horizontal tritone (see Urquhart, ‘False Concords’, 367–8).

As pointed out by Urquhart (‘False Concords’, 366; ‘Cross-Relations’, 29) and Berger (Musica ficta, 97).

Thus, Tinctoris is no Artusi, who lambasted Monteverdi for his use of dissonance without even mentioning his name.

See Ronald Woodley’s passing comments on Tinctoris’s attitude to the compositional avant garde of his time in ‘Renaissance Music Theory as Literature’, 219, as well as his remarks on this topic in ‘Did Tinctoris Listen to Okeghem?’.

Likewise, by distinguishing the practice of older musicians from that of more recent ones at the beginning of chap. 23, Tinctoris is implicitly envisioning the possibility that future musicians will find new ways to stretch the boundaries of what he deems grammatically acceptable in his time. Woodley reads such a possibility as a source of anxiety for Tinctoris, aware that the pace of innovation in the polyphonic art of his time threatened the merit and utility of the music-theoretical edifice he had so painstakingly constructed (Woodley, ‘Renaissance Music Theory as Literature’, 219–20).

As suggested, for instance, by Thomas Christensen, ‘Music Theory and its Histories’, in Music Theory and the Exploration of the Past, ed. Christopher Hatch and David W. Bernstein (Chicago: University of Chicago Press, 1993), 9–39, and Peter Schubert, ‘Authentic Analysis’, The Journal of Musicology, 12 (1994): 3–18.

In Emily Zazulia’s words, ‘Pieces of music could function [in the fifteenth-century as much as in later times, one might observe] as theoretical texts, and theoretical texts could inform pieces.’ (‘Composing in Theory’, 66).