Music

Escher’s Drum

My aim in this piece was to create a rhythmic tapestry that visits eight different rhythmic tiling canons. A rhythmic tiling canon is a composition in which each player repeats the same pattern, with each player beginning at a different time.  The 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.

This piece visits all eight possible rhythmic tiling canons where the cycle consists of twelve beats and the entrances of the players are equally spaced. Before writing this piece, I created a visualization of these eight possibilities where they were shown in sequence, with gaps in between them. My goal in the current piece was to visit the same eight possibilities in a seamless way, where there would be no gaps. My idea was that in progressing from a tiling canon based on rhythm A to one based on rhythm B, there should be a connecting passage where rhythm A is mixed with rhythm B. And so the current piece consists of the eight tiling canons (in which all three voices play the same rhythm) together with connecting passages where different voices play different rhythms.

My aim was to arrange the canons so that, if canon B follows canon A, the mixture of B and A sounds interesting. In order to do this, I tested all possible mixtures of the eight rhythms to find the ones I liked best. There were more than (8 choose 2) = 28 pairs to consider, because each rhythm consists of twelve beats (three bars in 4/4 time), and when two rhythms are superimposed there can be a skew of 0, 1, or 2 bars.

At first I tried to structure the piece so that no rhythm would ever be revisited, but I abandoned this goal after finding certain rhythms to be “dead ends,” so to speak. That’s to say, I might progress from rhythm A to rhythm B and, in the transition period, might enjoy the mixture of A and B. But then, while playing rhythm B, I might not be able to find any rhythm C that hadn’t already been played, where I could transition from B to C with a good-sounding B/C mixture. In such cases I had to return from rhythm B to another rhythm previously visited, so that I could then step from that previous rhythm to a new one.

In some cases I tried to make transitions from one rhythm to another smoother by a process of subtraction. If moving from A to B, I might gradually strip notes away from A until it began sounding like it might be a stripped-down version of B. These subtracted rhythms notwithstanding, a notable aspect of this piece is that it is based entirely on eight rhythms — no more than eight. Another notable aspect is that throughout the piece, the three players never coincide on the same beat — neither when they are playing a canon nor when they are playing transition material between canons — that is by design.

My experience in writing this piece was one of constant remembrance: thinking of African rhythms I had heard before. It fascinated me that these eight tiling canons and their combinations can be derived mathematically, but they sound so reminiscent of rhythms I’ve heard musics from the African continent, rhythms that I imagine must have evolved through a process of experiment and enjoyment. Incidentally, though I’ve been seeking out good records of African percussion for much of my life as a record enthusiast, the number of albums I return to is fairly small — I’d list these as the main ones: “Olatunji, Drums of Passion,” “Drummers of Dagbon,” “Drummers of Burundi,” and “Yoruba Drums from Benin, West Africa.” Let me know about any others I should listen to!

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