My compositional fascination with musical canons began in the early 1970s with study (at the University of Michigan) of Ockeghem’s 15th-century polyphony, the 10 canons in Bach’s 18th-century The Musical Offering, and Webern’s 20th-century Symphonie Op.21. As a young professor in the 1980s teaching 16th-century counterpoint at what was then North Texas State University (now UNT), I used canon as a challenging contrapuntal writing assignment. In 1985, a wind ensemble piece, Parallel Horizons (Homage to Schoenberg), was my first formal composition constructed by canon. In Dark Matter, other contrapuntal writing surrounds an extended canon. Now canon pervades much of my 21st-century writing, a challenging yet stimulating and gratifying approach to texture and continuity of material.
Below, for pedagogical demonstration purposes, are collected excerpts from these works. The subject is shown, with indications for when and at what pitch level each answer will occur.
KEY
“P1” = start answer when subject reaches here, at same (unison) pitch level as subject
“+P5” = start answer when subject reaches here, transposed up from subject by P5 (7 semitones)
“-P4” = start answer when subject reaches here, transposed down from subject by P4 (5 st)
“-M9” = start answer when subject reaches here, transposed down from subject by M9 (14 st)
“+P8” = up an octave (12 st); “+P15” = up two octaves; “-P12” = down octave & P5 (19 st)
In the synthesized audios below, each is scored in three voices for a string trio.
Analyzing can be an interesting investigation, but only after listening to each one’s musical character via the synthesized audio clip. Then by writing out a few measures of the suggested answer solutions, you may discover how each answer to the subject 1) interacts rhythmically with the lead voice, 2) at what number of beats time delay, and 3) how the pitch transpositions of the answers affect the contrapuntal intervals (“harmony”).
MAPPING MUSIC 