1

DE FUNDAMENTO DISCANTI

Ryan Taycher Indiana University

rtaycher@indiana.edu

39th Annual Meeting of the Society for Music Theory Vancouver, BC w November 3-6, 2016

Table 1 Selected treatises stating the tenor is the foundation of discant

Author Title/incipit and date Reference to “fundamentum discanti”

Jacobus Leodiensis Tractatus de consonantiis musicalibus (early 14th c.)

Debet autem quilibet discantus tenorem habere vel aliquem cantum qui loco tenoris ponatur. Dicitur autem tenor a teneo, -nes, quod totum discantum tenet. Est enim fundamentum ipsius et ab ipso totus cantus debet regulari (Waesberghe et al. 1988, 46).

Every discant must have a tenor, or some song that is notated in the place of the tenor. Tenor is called after teneo, tenes [to hold], since it holds the whole discant. For it is the foundation, and on the basis of it the whole song must be ruled (Jacobus 2015a, 14).

Jacobus Leodiensis Speculum musicae, Book VII (ca. 1330)

Vel potest dici discantus a ‘dy’ quod est ‘de’ et cantu, quasi de cantu sumptus, idest de tenore supra quem discantus fundatur sicut aedificium aliquod supra suum fundamentum; unde ille cantus tenor dicitur quia discantum tenet et fundat (Bragard 1973, 9)

Alternatively one may speak of discantus after dy which means from, and cantu as it were derived from chant, that is, from the tenor upon which the discantus part is founded, just as a building upon its foundation. That is why the chant is called tenor [holder], for it holds and provides the foundation for the discantus part (Jacobus 2015b, 14-17).

Anonymous (John of Tewkesbury?)

Quatuor principalia musicae, Quartum principale (1351)

Sciendum est secundum Curiam Romanam et francigenos et omnis musicales cantores, quod tenor, qui discantum tenet, integre et solide pronunciari debet et in mensura, ne supra discantantes dissonanciam incurrunt, et hoc ratio exigit: nam super instabilem fundamentum stabile edificium construi non potest; sic nec supra instabilem tenorem vix sive dissonantia discantus pronunciari potest (Aluas 1996, 523).

It must be known that—according to the Roman Curia, French authors, and all musical singers—the tenor (which holds the discant) ought to be pronounced solidly, and in measure, lest dissonances occur in the voices that discant. And this is required by reason: for a stable edifice cannot be built on an unstable foundation: similarly, the discant cannot be pronounced without dissonance on an unstable tenor (Aluas 1996, 749).

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Table 2 Selected treatises stating counterpoint is the foundation of discant

Author Title/incipit and date Reference to “fundamentum discanti”

Anonymous Inc. “Cum notum sit” (ca. 1350s)

Et prius de contrapuncto sit prima conclusio quod contrapunctus non est nisi punctum contra punctum ponere vel notam contra notam ponere sive facere, et est fundamentum discanti. Et quia sicut quis non potest supra edificare nisi prius faciat fundamentum, sic aliquis non potest bene et firmiter discantare nisi prius addiscat et sciat contrapunctum (Di Bacco 2001, 299).

And first on counterpoint let the first conclusion be that counterpoint is nothing but the placement of point against point or the placement or construction of note against note, and is the foundation of discant. And because just as someone is not able to build above unless a foundation should first be made, thus anyone is not able to discant well and firmly unless he should first learn and understand counterpoint.

Philipoctus de Caserta

Regule contrapuncti (late 14th c.)

Sciendum est quod contrapunctus est fundamentum discanti. Ut sicut hedificium non potest bene se regere sine fundamento, ita et homo non potest bene firmiter discantare nisi prius sciat contrapunctum (Wilkins 1964, 95).

It should be understood that counterpoint is the foundation of discant. Just as one is not able to direct himself without a foundation, so man is not able to discant well and firmly without first understanding counterpoint.

Goscalcus “The Berkeley Manuscript” (inc. “Quoniam in antelapsis temporibus”; 1375)

Cum autem habito fundamento discantus, quid est ipse contrapunctus, utile sit et expediens, ac iocundum, scire voces in partes divider, hoc est loco unius vocis plures in cantu proferre (Ellsworth 1984, 118-120).

Since the foundation of discant is now at hand (which is counterpoint itself), it may be useful and expedient—and also pleasant—to know how to divide the syllables into parts, that is, how to extend several syllables in place of one syllable in the cantus (Ellsworth 1984, 119-121)

Anonymous Tractatus de contrapuncto et de musica mensurabilii (inc. “Ad sciendum artem cantus”; ca. 1400)

De contrapuncto autem qui est fundamentum totius biscantus [sic], ulterius sciendum est quod contrapuncti quindecim sunt species, … (Anonymous 1995, 56).

Moreover, concerning counterpoint—which is the foundation of all discant—it should further be known that there are fifteen species [i.e., intervals] of counterpoint, …

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Example 1 Analysis of Examples 1-8 of diminished counterpoint in perfect tempus, major prolation from De diminutione contrapuncti (cf. Di Bacco 2001, 304-8)1

1 “X” noteheads indicate dissonances above the tenor, and open noteheads indicate the note-against-note framework. The labels identify elaborative figurations: upper, lower, double, and incomplete neighbors (UN, LN, DN, IN); upper and lower thirds (U3, L3); passing tones (PT); and anticipations (Ant.).

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Example 2 Suggested interval progressions of simplex discantus (i.e., note against note) from Petrus dictus Palma ociosa’s Compendium de discantu mensurabili

a) 8–6–5 above repeated note in tenor (Wolf 1914, 510)

b) 5–6–5 above repeated note in tenor (Wolf 1914, 511)

c) 8–5–3–1 above ascending stepwise tenor (Wolf 1914, 512)

Example 3 Examples of measurable discant adorned with flowers from Petrus dictus Palma ociosa’s Compendium de discantu mensurabili and structural analysis

a) Excerpt from the first mode, longs 1-4 (cf. Wolf 1914, 519)

b) Excerpt from the fourth mode, longs 1-4 (cf. Wolf 1914, 522)

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(Example 3 cont.)

c) Excerpt from the eighth mode, longs 7-10 (cf. Wolf 1914, 528)

d) Excerpt from the ninth mode, longs 1-4 (cf. Wolf 1914, 528-29)

Table 3 Dissonance treatment in De diminutione contrapuncti

Type of Dissonance Perf./Maj. Impf./Min. Perf./Min. Impf./Min.

Passing Tone 52 19 27 9

(*PT1) 6 — 1 —

(*PT2) 1 — — —

(*PT3) 1 — 1 —

Upper Neighbor 13 — 2 2

Lower Neighbor 7 — 2 —

Double Neighbor 2 — — 2

Incomplete Neighbor 24 14 12 4

Anticipation — 1 — —

6

10

8 5

8 5 3

to

*

8

8 6 5

5 8 8 5 8

6 8 3 5

to

L3 UN

ANT LN

U3U3

L36 5IN

56

UN IN

R

3

œ ¿ ¿ œ œ ¿ ¿ œ œ ¿ œ ∑ ∑ ∑ ∑ ∑9 ∑ ∑ ∑ ∑ ∑ ∑ ∑16 ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑25 ∑ ∑ ∑ ∑ ∑ ∑ ∑

©

Score

IN

*PT1

*PT2 *PT3

IN

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Example 4 Structural analysis of Gloria Apt 28 (F-Apt 16 bis, fols. 17v-18r), breves 1-38 (PMFC 23, 104-107; cf. Ivrea 64 [I-Iv 115, 48v] S-H, 22-23)

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Selected Bibliography

Aluas, Luminita Florea. 1996. “The Quatuor principalia musicae: A Critical Edition and Translation, with Introduction and Commentary.” PhD dissertation, Indiana University.

Anonymous. 1995. Tractatus de contrapuncto et de musica mensurabili: (Mss. Munich, Staatsbibliothek, Clm. 16208 et 24809). Edited by Christian Meyer. Neuhausen-Stuttgart: American Institute of Musicology, Hänssler-verlag.

Busse Berger, Anna Maria. 2005. Medieval Music and the Art of Memory. Berkeley: University of California Press.

——. 2009. “The Problem of Diminished Counterpoint.” In Uno gentile et subtile ingenio: Studies in Renaissance Music, edited by M. Jennifer Bloxam, Gioia Filocamo, and Leofranc Holford-Stevens, 13-27. Turnhout: Brepols.

Di Bacco, Giuliano. 2001. De Muris e gli altri: sulla tradizione di un trattato trecentesco di contrappunto. Lucca: Libreria musicale italiana.

Ellsworth, Oliver B., ed. and trans. 1984. The Berkeley Manuscript: University of California Music Library, MS. 744 (olim Phillipps 4450). Lincoln: University of Nebraska Press.

Fuller, Sarah. 1986. “On Sonority in Fourteenth-Century Polyphony: Some Preliminary Reflections.” Journal of Music Theory 30 (1): 35-70.

——. 1987. “Line, Contrapunctus and Structure in a Machaut Song.” Music Analysis 6 (1-2): 37-58.

——. 2002. “Organum–discantus–contrapunctus in the Middle Ages.” In The Cambridge History of Western Music Theory, edited by Thomas Christensen, 477-502. New York: Cambridge University Press.

——. 2013. “Contrapunctus, Dissonance Regulation, and French Polyphony of the Fourteenth Century.” In Medieval Music in Practice: Studies in Honor of Richard Crocker, edited by Judith A. Peraino, 113-52. Middleton, WI: American Institute of Musicology.

Jackson, Roland. 1957. “Musical Interrelations between Fourteenth-Century Mass Movements: A Preliminary Study.” Acta Musicologica 29: 54-64.

Jacobus. 1973. Speculum Musicae. Vol. 7. Corpus Scriptorum de Musica 3. Edited by Roger Bragard. Rome: American Institute of Musicology.

——. 2015a. “[?Jacobus], Tractatus de consonantiis musicalibus, with relevant passages from the Speculum musicae by Jacobus.” Translated by Rob C. Wegman (working paper). Accessed 25 July 2015. https://www.academia.edu/14377922/Jacobus_Tractatus_de_consonantiis_musicalibus_c._1300_

——. 2015b. “Jacobus: Speculum musicae Book VII.” Translated by Rob C. Wegman (working paper). Accessed 8 September 2015. https://www.academia.edu/15520575/Jacobus_The_Mirror_of_Music_Book_VII_complete_for_double-sided_printing

Leach, Elizabeth Eva. 2000. “Counterpoint and Analysis in Fourteenth-Century Song.” Journal of Music Theory 44 (1): 45-79.

Leech-Wilkinson, Daniel. 1993. “Written and Improvised Polyphony.” In Polyphonies de tradition orale: Histoire et Traditions Vivantes: Actes du Colloque de Royaumont 1990, edited by Michel Huglo, Marcel Pérès, and Christian Meyer, 171-182. Paris: Creaphis.

Leitmeir, Christian Thomas. 2007. “Arguing with Spirituality against Spirituality. A Cistercian Apologia for Mensural Music by Petrus dictus Palma ociosa (1336).” Archa Verbi 4: 155-199.

Sachs, Klaus-Jürgen. 1974. Der Contrapunctus im 14. und 15. Jahrhundert: Untersuchungen zum Terminus, zur Lehre und zu den Quellen. Wiesbaden: Franz Steiner Verlag.

——. 2005. “‘…artem istam cum gaudio perficies’—zum Traktat des Petrus dictus Palma ociosa (1336).” In Mittelalter und Mittelalterrezeption: Festschrift für Wolf Frobenius, edited by Herbert Schneider, 54-75. Hildesheim: Georg Olms.

Waesberghe, Joseph Smits van, Eddie Vetter, and Erik Visser, eds. 1988. Jacobi Leodiensis Tractatus de consonantiis musicalibus, Tractatus de intonatione tonorum, Compendium de musica. Buren: Knuf.

Wegman, Rob C. 2014. “What is Counterpoint?” In Improvising Early Music: The History of Musical Improvisation from the Late Middle Ages to the Early Baroque, edited by Dirk Moelants, 9-68. Leuven: Leuven University Press.

Wilkins, Nigel. 1964. “Some Notes on Philipoctus de Caserta (c. 1360?–c. 1435).” Nottingham Medieval Studies 8: 82-99.

Wolf, Johannes, ed. “Ein Beitrag zur Diskantlehre des 14. Jahrhunderts.” Sammelbände der Internationalen Musikgesellschaft 15: 505-34.

PMFC Cattin, Giulio and Francesco Facchin, eds. 1989/1991. French

Sacred Music. Polyphonic Music of the Fourteenth Century 23. Les Ramparts, Monaco: L’Oiseau-Lyre.

S-H Stäblein-Harder, Hanna. 1962. Fourteenth-Century Mass Music in France. Corpus Mensurabilis Musicae 29. N.p.: American Institute of Musicology.