This video provides a visualization of the some of the rhythmic tiling canons described in the paper “Asymmetric Rhythms and Tiling Canons” by Rachel W. Hall and Paul Klingsberg. A rhythmic tiling canon is a composition in which each player repeats the same rhythmic pattern, with each player beginning at a different time. The rhythmic pattern and entry points are crafted so that once all the players have begun to play, there will be exactly one player striking every beat. That’s to say, every beat is covered by one of the players but no two players ever coincide on the same beat. The video illustrates all possible tiling canons where the rhythmic cycle consists of twelve beats and the entrances of the players are equally spaced.
It fascinates me that these rhythms can be derived through a purely mathematical process and yet they sound so good — some of them remind me of various rhythms I’ve heard in musics from the African continent but I’m not well-versed enough to be able to pinpoint a specific region or style. I should add that the rhythms don’t sound good in all contexts: they seem to work best when played on three percussion instruments with distinct timbres. If each voice were played using C in a different octave on a piano, for example, the distinction between voices becomes less clear as the ear tends to hear melodic patterns formed between voices. If the universe is willing, I’ll be posting a follow-up with some original compositions built using these canons as a rhythmic foundation.