Number Study: a few pieces written for a Music Theory class and inspired by numbers in some way. I had not yet reached the fruition of my love for math, but this was when I first realized there were deeper connections between math and music than were immediately obvious. The cover art has a collection of four prime numbers surrounding a composite number that has been struck out. The assignment was to write one piece of music to demonstrate a straightforward association between numbers and music, and as was usual for me, I wrote several and turned in my favorite. “Timelessness” was performed at a student recital in the spring of 1988.
“One/Eight” revolves around a sequence of time signatures repeating the pattern {1/8, 2/8, …, 7/8, 8/8; 8/8, 7/8, …, 2/8, 1/8 }. The pitches are less important than the patterns. In this example, the numeric association is strictly the counting of the time — but listen for the one instrument that ignores the time signature specified by the measures.
“Timelessness” is the opposite: a series of chords explicitly not to be played in time, and written out as instructions to the performer involving statements like “when one performer wishes to move to the next chord…” and the like. The score is very efficient — one page contains three minutes of music for a sextet, and each performance of it should vary widely. For this piece, the numeric aspect was in the absence of indications of duration or tempo.
Last, “Primes” uses a series of pitch classes the components of which multiplied together define tempi. Pitch classes are interesting objects: since western music is based on a 12-note scale, arithmetic mod 12 is very useful. The pitch class theory involves reducing a set of notes to a particular form, with the notes clustered as best as possible at the “bottom” of the scale presumably to make it easier to compare pitch classes and do some of the other (more interesting) analyses. I used a series of pitch classes involving only prime numbers (2,3,5,7,11), and took those values into meaning tempo as well as pitch. Notice that when the tempo changes, so does the character of the implied harmony.