isochronal chrysalides (2024)

8′; violin, cello, piano

I became intrigued by fractal sequences, which are number sequences that contain infinite copies of themselves. One such sequence is a periodic sequence, where a subsequence repeats indefinitely. For example, the sequence 123123123… contains the repeating subsequence 123. A particular fractal sequence that interested me transforms the Fibonacci sequence, an infinite non-repeating sequence, into a periodic sequence by applying a modulo. In this process, each number is divided by a modulo number, and the remainder becomes the new number in the sequence. For example, 6 mod 4 = 2, because 6 ÷ 4 = 1 with a remainder of 2.

I aimed to compose a piece using these repeating sequences, known as Pisano periods, by turning them into rhythms with associated numerical harmonies in just intonation. The word “isochronal” means equal duration or recurring at equal intervals, and “chrysalides” (the plural of chrysalis) typically refers to the transitional state of insects, though it can also describe any transitional phase. Thus, the musical material in isochronal chrysalides emerges as ever-changing cycles: unfolding, developing, yet recurrent.

[score is available upon request]