¹ Apel, Willi, The Notation of Polyphonic Music 900–1600, 5th edn (Cambridge, Mass., 1953), 103Google Scholar. For a high-resolution facsimile see https://www.diamm.ac.uk/sources/716/#v=d&z=2&n=5&i=https%3A%2F%2Fwww.diamm.ac.uk%2Fimages%2F26274%2F&y=349&x=513 (accessed 20 Dec. 2018). This source is dated in the Oxford Summary Catalogue to between 1426 and 1436, and thus represents a distinctly earlier tradition than Tinctoris’s late fifteenth-century discussions of theory.

² See The Mellon Chansonnier, ed. L. Perkins and H. Garey (New Haven, 1979). It is possible that Tinctoris was the Mellon scribe, though this seems far less likely than the notion that he had a hand in the compilation. On the acrostic that points towards this, see Ronald Woodley, ‘Minor Coloration Revisited: Okeghem’s Ma bouche rit and Beyond’, in Ceulemans, Anne-Emmanuelle and Blackburn, Bonnie J. (eds.), Theéorie et analyse musicales 1450–1650/Music Theory and Analysis. Actes du colloque international Louvain-la-Neuve, 23–25 septembre 1999 (Musicologica Neolovaniensia, Studia 9; Louvain-la-Neuve, 2001), pp. 39–63Google Scholar, esp. p. 56.

³ See below, n. 13.

⁴ See De Ford, Ruth I., Tactus, Mensuration and Rhythm in Renaissance Music (Cambridge, 2015), pp. 16–18CrossRefGoogle Scholar.

⁵ All references to this text are taken from Anonymous XII, Tractatus et compendium cantus figurati (London, British Library, Add. MS 34200; Regensburg, Proskesche Musikbibliothek, 98 th. 4^o), ed. J. M. Palmer, Corpus Scriptorum de Musica, 35 (Neuhausen-Stuttgart, 1990), pp. 41–93.

⁶ Anon. XII, ch. 10, ibid., p. 64; translation my own. For the full text of the chapter see pp. 63–4.

⁷ This is not to suggest that such points of coincidence do not normally occur at structurally important points, rather that the understanding of the function of this symbol was perhaps more nuanced than our contemporary label would connote.

⁸ ‘Aliquod est signum convenientiae et formatur sic: [signa], quod signum alio vocabulo dicitur signum cadentiae, ubi una vox post pausas cadit supra reliquam’ (my italics). See Palmer, J., ‘A Late Fifteenth-Century Anonymous Mensuration Treatise (Ssp) Salzburg, Erzabtei St. Peter, a VI 44, 1490’, Musica Disciplina, 39 (1985), pp. 87–106Google Scholar, at p. 96. It is available at http://www.chmtl.indiana.edu/tml/15th/ANOCOMP_TEXT.html (accessed 13 Mar. 2019).

⁹ Translation from Bailey, J. A. and Lee-De Amici, B. A., ‘Bridging the Medial Caesura’, in Kirkman, A. and Slavin, D. (eds.), Binchois Studies (New York and Oxford, 2000), pp. 181–98Google ScholarPubMed, at p. 194.

¹⁰ Further reasons to support the attribution of this chapter to another author are discussed below and in A. Whittaker, ‘Musical Exemplarity in the Notational Treatises of Johannes Tinctoris (c. 1435 – 1511)’ (Ph.D. thesis, Birmingham City University, 2016), p. 214.

¹¹ Tinctoris, De punctis, ch. xx (supplementary), ed. and trans. J. J. Dean, Early Music Theory Online, http://earlymusictheory.org/Tinctoris/texts/depunctis/#pane0=Edited&pane1=Translation (accessed 7 July 2017); emphasis my own. The MS is digitized at https://lib.ugent.be/catalog/rug01%3A000991275. See Figure 1 below.

¹² I have taken the phrase ‘those whom rests annoy’ to mean singers uncomfortable with counting extended periods of rests, or who may have benefitted from additional notational support.

¹³ The brief discussion that follows draws upon Epp, M., ‘Reading the Signs: Notation and Performance in the French Polyphonic Song Repertory’, in Power, B. E. and Epp, M. (eds.), The Sounds and Sights of Performance in Early Music: Essays in Honour of Timothy J. McGee (Farnham, 2009), pp. 103–22Google Scholar.

¹⁴ See Bent, M., ‘“Res facta” and “Cantare super Librum”’, Journal of the American Musicological Society, 36 (1983), pp. 371–91CrossRefGoogle Scholar.

¹⁵ I use the term ‘sounded’ here in its most abstract sense. It is most likely that Tinctoris imagined that this type of example would be consulted silently, with the notational characteristics further supporting such a viewpoint. These issues are explored more fully in Whittaker, ‘Musical Exemplarity’.

¹⁶ Tinctoris, , De arte contrapuncti, I.vii, ed. D’Agostino, G. (Florence, 2008), p. 174Google Scholar; trans. A. Seay (Rome, 1961), p. 35. All further quotations from Tinctoris’s counterpoint treatise are taken from D’Agostino’s edition and Seay’s translation.

¹⁷ I have placed ‘bad’ and ‘correct’ in quote marks, as the criticisms that Tinctoris makes of other composers must be viewed from the perspective of his theoretical persona, seemingly uncompromising and highly conservative. Tinctoris is much more measured in his criticisms in the treatise on counterpoint than he is in his earlier Proportionale musices, where he describes errors of similar magnitude as ‘inexcusabilis’ [inexcusable]. A quite different view of his musical attitudes can be gained if his standalone musical compositions are consulted in detail. On this issue see Rothfarb, L., ‘Tinctoris vs. Tinctoris: Theory and Practice of Dissonance in Counterpoint’, In Theory Only: Journal of the Michigan Music Theory Society, 9 (1986), pp. 3–31Google Scholar.

¹⁸ This is somewhat analogous to the use of solmisation syllable labels in Tinctoris’s Expositio manus, with these markings being presented in red ink across the three main sources of his works: V, BU and Br1. Indeed, signa congruentiae are used in examples containing solmisation syllables in Heyden’s, Sebald De arte canendi (Nuremberg, 1540)Google Scholar for a similar purpose: see p. 40.

¹⁹ Tinctoris, De arte contrapuncti, II.xxix, ed. D’Agostino, p. 352; trans. Seay, p. 126 (translation adjusted).

²⁰ It should be noted here that Tinctoris does concede that many composers make use of dissonances that last for a longer duration than he would like, and that his criticisms stem from a desire to educate young composers in the correct way to compose, discouraging them from imitating the practices shown in his two citations.

²¹ Tinctoris also uses a passage from Domarto’s Missa Spiritus almus in his Proportionale musices as an example of the incorrect manner of indicating proportional relationships.

²² The need to have fully understood a theoretical text in order to pick out the relevant part of the musical example is particularly apparent in Tinctoris’s De imperfectione notarum musicalium. The models of exemplification associated with the treatise on imperfection are curious, given that they seem to be less ‘user-friendly’ than some of Tinctoris’s earlier works. For example, there are multiple instances in the imperfection treatise where Tinctoris demands understanding of precepts he has yet to cover, and theorises well beyond the realms of normal notational practice. For a more detailed discussion, see Whittaker, ‘Musical Exemplarity’, pp. 141–9 and 158–66.

²³ The complexity is also slightly increased by the placement of the dissonance as part of a syncopated cadential unit, requiring a slightly more careful consultation of the mensural context.

²⁴ There are, of course, notable exceptions. On Tinctoris’s activities as a composer see W. E. Melin, ‘The Music of Johannes Tinctoris (ca. 1435–1511): A Comparative Study of Theory and Practice’ (Ph.D. diss., University of Ohio, 1973); Dean, J. J., ‘Towards a Restoration of Tinctoris’s L’homme armé Mass: Coherence, Mensuration, Varietas’, Journal of the Alamire Foundation, 5 ‘Johannes Tinctoris I’ (2013), pp. 11–40CrossRefGoogle Scholar; Blackburn, B. J., ‘A Lost Guide to Tinctoris’s Teachings Recovered’, Early Music History, 1 (1981), pp. 29–116CrossRefGoogle Scholar. The majority of Tinctoris’s musical compositions, excluding his polyphonic miniatures, are edited in Johannes Tinctoris, Opera Omnia, ed. W. E. Melin, Corpus mensurabilis musicae, 18 (n.d., 1976).

²⁵ This type of example accounts for the majority of examples in Books II and III of the counterpoint treatise.

²⁶ See Woodley, R., ‘Sharp Practice in the Later Middle Ages: Exploring the Chromatic Semitone and its Implications’, Music Theory Online, 12/2 (2006)CrossRefGoogle Scholar; M. Bent, ‘On False Concords in Late Fifteenth-Century Music’, in Ceulemans and Blackburn (eds.), Théorie et analyse musicales 1450–1650, pp. 65–118.

²⁷ Tinctoris, De arte contrapuncti, II.xxxiv, ed. D’Agostino, p. 362; trans. from Woodley, ‘Sharp Practice in the Later Middle Ages’, p. 27.

²⁸ It is unusual to find an example of Tinctoris’s own composition that demonstrates a practice that he instructs his readers to avoid. There is an argument to suggest that a small part of the reason that signa congruentiae have been deployed is to show the reader that he is aware of the points where his composition appears to commit a theoretical error.

²⁹ The complexities of this term are discussed below.

³⁰ Given that the first cadential passage demonstrates the flattening of a perfect concord to make it imperfect, it follows Tinctoris’s usual pedagogical logic for the next instance to demonstrate the second of his theoretical points.

³¹ Woodley suggests that the symbol for the chromatic semitone had tuning implications, and thus the ‘sound’ of this chromatic alteration might have been quite different to our hearing through modern ears and tuning systems. See Woodley, ‘Sharp Practice in the Later Middle Ages’.

³² Interestingly, Br1, fols. 96^vb–97^ra presents this example without signa, a practice which I discuss later in this article. Indeed, Br1 omits signa from all of the examples in Books II and III.

³³ Bent, ‘On False Concords in Late Fifteenth-Century Music’.

³⁴ Woodley, ‘Sharp Practice in the Later Middle Ages’, pp. 3–6.

³⁵ For a detailed discussion of this topic see Luko, A., ‘Tinctoris on Varietas’, Early Music History, 27 (2008), pp. 99–136CrossRefGoogle Scholar; S. Gallagher, ‘Models of Varietas: Studies in Style and Attribution in the Motets of Johannes Regis and his Contemporaries’ (Ph.D. diss., Harvard University, 1998). See also A. Luko, ‘Unification and varietas in the sine nomine Mass from Dufay to Tinctoris’ (Ph.D. diss., McGill University, 2008).

³⁶ Tinctoris, De contr., III.vi, ed. D’Agostino, pp. 374–6; trans. Seay, p. 137, with small modification. If ‘redicta’ is taken to be translated as ‘reduplication’, then it is possible to link it to the notion of ‘conduplicatio’, as discussed in the Rhetorica ad Herennium. I am grateful to Jeffrey Dean for drawing my attention to this.

³⁷ It is interesting to note that this example is approximately the same length as O Deus princeps …, the example demonstrating chromatically altered concords. A number of Tinctoris’s examples from this passage follow a similar formula, and thus may constitute something of a model of composition. This structure normally consists of three or four musical phrases, each of which is articulated with clear cadences. Examples of this style usually fit within the span of a single opening, or require only a small extension onto the second side of an opening. The one exception to this rule is that with the text ‘Salve martyr virgoque Barbara’ found in De contr. II.xxiii.

³⁸ The signum on the the sixth note of the Tenor, clearly visible in Figure 5 and present in BU, is erroneously omitted from Seay’s edition. See Johannes Tinctoris, Liber de arte contrapuncti, ed. Albert Seay, Opera theoretica, ii, Corpus Scriptorum de Musica, 22 (n.p., 1975), pp. 152–3. D’Agostino records this signum correctly in his edition: see D’Agostino, pp. 374–5.

³⁹ Although using slightly different pitches, the rhythmic characteristics are retained, addressing the ‘one or more’ melodic intervals of a restated figure described in the text.

⁴⁰ One could argue that this is a rather ‘clumsy’ compositional moment on Tinctoris’s part, though this does not diminish its pedagogical usefulness. In musical terms, however, it does disrupt the pleasant, if rather predictable, polyphonic shape of the rest of the example. The repeated Cs, in analytical terms, create the sense of a brief moment of rest across the voice parts.

⁴¹ Tinctoris’s contemporaries would not have conceived this as a C major triad. The triadic figure, however, was common for natural trumpets given the pitch constraints of the overtone series. This is a seemingly rare instance where the example content does not follow the order of the text strictly, though this does not affect the text–example relationship significantly.

⁴² See Whittaker, Adam, ‘Signposting Mutation in some Fourteenth- and Fifteenth-Century Music Theory Treatises’, Plainsong & Medieval Music, 26 (2017), pp. 37–61CrossRefGoogle Scholar.

⁴³ See ‘Rubrication’, in Suarez, M. F., , S.J., and Woudhuysen, H. R. (eds.), The Oxford Companion to the Book (Oxford, 2010)CrossRefGoogle Scholar, http://www.oxfordreference.com/view/10.1093/acref/9780198606536.001.0001/acref-9780198606536-e-4231 (accessed 21 Aug. 2016).

⁴⁴ See Huot, S., From Song to Book: The Poetics of Writing in Old French Lyric and Lyrical Narrative Poetry (Ithaca, NY and London, 1987), esp. pp. 36–9Google Scholar, pp. 46–82, pp. 99–105.

⁴⁵ Ibid., p. 99.

⁴⁶ The most recent contribution to this debate is Woodley, ‘The Dating and Provenance of Valencia 835: A Suggested Revision’, Early Music Theory Online, http://earlymusictheory.org/Tinctoris/Articles/DatingAndProvenanceOfValencia835/# (accessed 13 May 2017). Woodley’s article also summarises other earlier contributions to this debate.

⁴⁷ See Perkins, ‘Introduction’, in The Mellon Chansonnier, pp. 1–32. Some other manuscripts copied by Crispus make use of similar symbols as rubrication marks.

⁴⁸ I am grateful to Jeffrey Dean for discussing this with me at some length. This practice applies throughout the manuscripts and is being included in updated editions on http://earlymusictheory.org/Tinctoris/. See C. Goursaud, ‘The Neapolitan Presentation Manuscripts of Tinctoris’s Music Theory: Valencia 835 and Bologna 2573’ (Ph.D. thesis, Birmingham City University, 2016).