Author: Gosman, Alan R.
Title: Compositional Approaches to Canons from Ockeghem to Brahms
Institution: Harvard University
Begun: April 1997
Completed: August 2000
This dissertation examines methods of large-scale organization within a span of European canonic writing extending from Ockeghem through Brahms. The organizational methods discussed serve a wide variety of ends, from assuring that consonances and chords sound between parts, to providing musical demonstrations of contrapuntal and harmonic theoretical systems. The first part of the dissertation focuses on patterns involving intervals between notes in the dux; the second part focuses on intervallic patterns involving both dux and comes voices.
Chapter One examines four Renaissance canons. The analyses show that there are strong patterns involving intervals between dux notes separated by the time interval of the canon. These dux patterns free the composer to focus on large-scale melodic considerations, rather than constantly verifying that a melodic choice is harmonically viable. Chapter Two considers how the canonic notes separated by the time interval of the canon can be organized in support of contrasting music-theoretical explanations. Two canons by Zarlino, found as the culminating compositional examples in Part III of the Istitutioni harmoniche, are compared with two canons by Rameau, found as the culminating examples in Book III of the Traité de l’harmonie. The differences between the pieces are considered in the context of the ways each composer organizes his treatise as a whole and his ideas about harmony in particular.
Chapter Three shows a number of Baroque and Classical canons that depend on very similar patterns of intervals between dux notes. These dux patterns limit the harmonic progressions from which a composer may choose. Chapter Four considers canons whose dux notes are best understood as being organized by harmonic, rather than intervallic patterns. Burmeister’s account of how to compose this type of piece by what he calls a harmoniola is discussed. This chapter also extends the harmoniola’s function from that of a compositional tool to that of an analytical tool.
Part Two of the dissertation finds multiple examples of what I call "canonic threads"—patterns made of alternating dux and comes TIC notes at the time interval of the canon. The concept of canonic threads is developed using as focus pieces Bach’s Goldberg Variations, and Brahms’s Variations on a theme by Schumann, Op. 9. Threads are shown to be a powerful method of integrating a theme’s harmonic and phrase-structural constraints into a variation with strict canonic form.
Keywords: canon, counterpoint, Ockeghem, Zarlino, Rameau, Bach, Brahms
Part I - Dux Patterns
1. Stacked Canons
2. Rameau and Zarlino: Polemics in the Traité de l’harmonie
3. Dux Patterns and Harmonic Progressions
4. The Harmoniola
Part II - Canonic Threads
5. Canonic Threads: Formal Features
6. Repeated-Note Threads
7. Stepwise Threads
8. Threads at Intervals Larger than a Second
9. Arpeggiated Threads
Cambridge, MA 02138