Compositional Strategies in Mensuration and Proportion Canons, ca. 1400 to ca. 1600 Edward A. Melson Schulich School of Music McGill University, Montreal August, 2008 A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Master of Arts in Musicology. © Edward Andrew Melson 2008 ii Abstract. This thesis presents a detailed list of mensuration and proportion canons written between 1400 and 1600 and an analysis of several of those canons. Proportion canons are a subset of mensuration canons, pieces in which one melody, under different rhythmic interpretations according to the rules of mensuration, appears simultaneously in more than one voice. The type of mensuration and proportion canons discussed in this thesis display simultaneous entry of the voices: all voices begin together and sing through the same music at different speeds. This type of composition is difficult to create, and places extreme demands on composers‘ ingenuity. Existing analysis of such pieces is extremely rare and not particularly revealing of compositional process. This thesis presents a method of analysis that explains proportion and mensuration canons in terms of initial conditions of pitch transposition and mensuration, and explores the contrapuntal options thus made available to the composer. Résumé. Ce mémoire présente une liste détaillée de canons mensurables et de proportion, composés entre 1400 et 1600, et des analyses de plusieurs de ces canons. Canons de proportion comprennent un sous-ensemble de la catégorie de canons mensurables, compositions dans lesquelles une mélodie, suivant au moins deux mensurations simultanés, apparait simultanément dans plusieurs voix. Les canons soumis à l‘analyse par le présent document sont tous du type à faire entrer les voix simultanément : l‘ensemble des voix commence au même moment et chant la même mélodie, chacune à une vitesse différente des autres. Cette méthode de composition est extrêmement difficile à maîtriser, et met à l‘épreuve l‘ingénuité du compositeur. Les quelques analyses qui existent déjà ne sont pas révélatrices du processus de composition. Cette étude dévoile une approche à l‘analyse des canons mensurables et de proportions qui les explique à partir des conditions initiales : transposition et mensuration, et explore les options contrapuntiques qui en résultent. iii Table of Contents. Abstract. ii. Table of Contents. iii. Acknowledgements. iv. List of Examples. v. List of Figures. vi. List of Tables. viii. Introduction. ix. Chapter 1. Terms and Definitions. 1. Chapter 2. Two-voice Proportion Canons. 10. Chapter 3. The Josquin Agnus dei II and Other Three-Voice Proportion 22. Canons. Chapter 4. Pierre de La Rue’s Agnus dei II in Four Voices. 38. Chapter 5. Transmitting Josquin’s Agnus dei II: A Short Reception History. 52. Conclusion. 72. Appendix. 75. Bibliography. 111. iv Acknowledgements. This thesis would not have been possible without help and input from many people. My thanks go first to my advisors, Professors Julie Cumming and Peter Schubert of McGill University. They supported my original idea and read, re-read, and commented at nearly every step of the process. I am also particularly grateful to Olivier Trachier for sharing his insights and teaching materials on proportional canons and their composition: his explanations had a formative influence on my thinking. My thanks go also to Professor Ruth DeFord, Professor Peter Urquhart, and Dr. Virgina Ervin Newes for their advice on where and how to search for canons. My friends and colleagues have been a source of inspiration: Eric Smialek, Maria Francou- Desrochers, and Krissy Keech for her constant enthusiasm. Loren Carle and Mike Ethen helped me out with a memorable brainstorming session on counterpoint during intermission. Asher Yampolsky listened as I talked through several canon problems, and thanks to his initiative, as well as Professor Cumming‘s support, many of us sang Renaissance polyphony regularly during my time at McGill. Thanks to Dan Donnelly for a little help with Latin, and to Lynda Paul, who came through with photocopies and good advice more than once. Special thanks are due to both my parents, for all the help and encouragement they have given me, in this and in other endeavours. My father, John Melson, read through some less than perfect explanations and managed to distil the formulas that I was looking for. And finally, thanks to Shamin for being there while this thesis was in progress, and for sticking around now that it‘s finished. v List of Examples Page Example 1.1. Benedictus, Missa L’homme armé super voces 7 musicales., Josquin des Prez. Example 1.2. Et resurrexit, Missa Prolationum, Johannes 8 Ockeghem. Example 2.1. Score with rhythmic positions labeled in the 12 Benedictus, Missa Sine nomine, Josquin des Prez. Example 2.2. Qui venit, Missa L’homme armé s.v.m., Josquin. 17 Example 2.3. In nomine, Missa L’homme armé s.v.m., Josquin. 18 Example 2.4. Agnus dei, Missa a 3 voce, Heinrich Finck. 19 Example 2.5. Continuation of the previous example. 20 Example 3.1. Omne trinum perfectum, Ludwig Senfl. 23 Example 3.2. Agnus dei II, Missa L’homme armé super voces 32 musicales, Josquin des Prez. Example 4.1. Agnus dei II, Missa L’homme armé, Pierre de la 41 Rue. Example 4.2. Continuation of the previous example. 42 Example 4.3. Numbered rhythmic positions in La Rue, 43 Agnus dei II. Example 5.1. Agnus dei II, Missa L’homme armé super voces 52 musicales, Josquin des Prez. From the Petrucci print of 1503. Example 5.2. Glarean‘s resolution of the Josquin Agnus dei 56 II. Example 5.3. A standard resolution of the Josquin Agnus dei 57 II. Example 5.4. Resolution of the Agnus dei II from Berlin Ms. 59 Theor. 1175. Example 5.5. Josquin Agnus Dei II From Pedro Cerone, El 62 melopeo y maestro (1613). vi Example 5.6. Josquin Agnus Dei II From Pedro Cerone, El 63 melopeo y maestro, overleaf of the original. Example 5.7. Gombosi‘s transcription of Josquin‘s Agnus dei 66 II (1954). Example 5.8. A four voice resolution of the Agnus dei II with 68 my annotations. List of Figures. Figure 2.1. Duple mensuration, two-voices, 2:1 proportion, 12 unison, fastest voice in semibreves. Figure 2.2. Duple mensuration, two-voices, 2:1 proportion, 13 comes at the fifth above. Figure 2.3. Duple mensuration, two-voices, 2:1 proportion, 13 comes at the fifth below. Figure 2.4. Duple mensuration, two-voices, 2:1 proportion, 13 comes at the octave above. Figure 2.5. Duple mensuration, two-voices, 2:1 proportion, 13 comes at the octave below. Figure 2.6. Initial conditions for a sample two-voice canon. 16 Figure 2.7. First melodic motion in the dux, rhythmic positions 16 labeled. Figure 2.8. First melodic motion in both dux and comes. 16 Figure 2.9. Second melodic motion in the dux. Comes rhythmic 16 positions labeled. Figure 2.10. Cadence in dux and comes. 17 Figure 2.11. Canon with comes cadence transferred to dux. 17 Figure 2.12. Filling in RP4. 17 Figure 2.13. Filling in the final dux notes. 18 Figure 3.1. Omne trinum perfectum, Ludwig Senfl. 22 Figure 3.2. Three-voices, 1:2:4 proportion, unison. 24 Figure 3.3. Three-voices, 1:2:4 proportion, P4+P5 24 Figure 3.4. 2:1:4 proportion. 25 vii Figure 3.5. 2:4:1 proportion. 25 Figure 3.6. 4 :2 :1 proportion. 26 Figure 3.7. 4:1:2 proportion. 26 Figure 3.8. 1:4:2 proportion. 27 Figure 3.9. 1:2:4 proportions with two upper voices at the 28 unison and the lower voice an octave below. Figure 3.10. Invertible counterpoint in a three voice 30 proportion canon using 2:1 proportion. Figure 3.11. Rhythmic positions in a three-voice proportion 31 canon using 1:4:2 proportion. Figure 3.12. Agnus dei II, Josquin. Rhythmic positioning of 32 consonance and dissonance in simultaneous triple and duple minims. Figure 3.13. 3 :2 :1 proportion, dux motion on rhythmic 33 position 4. Figure 3.14. 1 :3 :2 proportion, dux motion on rhythmic 34 position 4. Figure 3.15. 3 :2 :1 proportion, dux motion on rhythmic 34 position 4. Figure 3.16. 2 :3 :1 proportion, dux motion on rhythmic 35 position 4. Figure 3.17. 2 :1 :3 proportion, dux motion on rhythmic 36 position 4. Figure 3.18. 1 :2 :3 proportion, dux motion on rhythmic 36 position 4. Figure 4.1. La Rue Agnus: Altus, Tenor, and Bassus 39 relationships according to Bizzi. Figure 4.2. Chart of rhythmic values in La Rue, Agnus dei II. 40 From Bizzi, Miroirs, page 119. Figure 4.3. Agnus dei II, Pierre de La Rue. Diagram of note 44 names and rhythms as represented by Bizzi. viii Figure 4.4. Opening phrase of the Agnus dei II, Pierre de la 46 Rue. Figure 4.5. La Rue Agnus dei II. Parallel octaves between bassus 47 and altus as a result of imperfecting ternary values. Figure 4.6. Possible first melodic motions in the dux given La 48 Rue‘s initial conditions and rhythmic profile. Figure 4.7. Limitation or rhythmic placement of melodic 49 motion in ¢ and ¢3. List of Tables. Table 2.1. Dux options for two-voice 2:1 proportion canons. 14 Table 2.2. Initial dux motion in extant two-voice 2:1 15 proportion canons. Table 3.1. Initial motions in 1:2:4 proportion, P5+P4 canons. 27 Table 3.2. Initial motions in 1:2:4 canons at the octave. 29 Table 3.3.