Thinkin’ bout medium-range polyrhythms.

(DURHAM) Starting to outline a new piece for trio and computer, I find myself once again in front of some nearly-blank A4 sheets on my clipboard, trying to ask the hard questions. What’s the big idea? What’s the global structure, or at least an initial conception of it? Ensemble roles? Texture? Temporal characteristics? What should the computer do?

Of course, these kinds of questions are on my mind all the time. I’ve been preoccupied by the use of medium-range polyrhythms for a couple of years now, first creating them between two pulses in low-integer ratios with a shared pulse unit, most often the quaver. A bit of background: I made a few pieces over several years using shared-quaver pulses of 3:5:7:9 as a local structural determinant (Safety In Numbers, Immortal Witness, Mare Insularum, Mare Orientale), with interesting results. More recently I’ve moved on to experimenting with higher-integer ratios such as 21:25, creating polyrhythms that don’t share a common pulse unit. Mare Marginis, written last summer for the Ives Ensemble, was my most elaborate exploration of this approach, using a polyrhythm of 21:25 which cycled in 35-bar units. This is what I mean by the term “medium-range polyrhythm” – a juxtaposition of two pulse streams which are mutually prime and complete their cycle in some period, usually 30 and 90 seconds of music, which is substantially less than the total duration of the piece.

Working with higher-integer ratios which must be notated for performers brings up several issues, first and foremost the question of beat division and how that will be achieved in a practical way. If one is making music strictly for computer then this is, of course, not an issue at all; the computer can happily perform any polyrhythmic ratios you can imagine, with no thought for irrational values. If you want to divide one beat by 14.35, then you just tell the computer to do it. For human performers, we need to think quite a bit more conservatively, and here is where the interesting challenge comes in: how to coordinate the computer (which can perform complex rhythmic ratios at all temporal levels), with the ensemble, who are pretty much limited to beat divisions (depending on the tempo) of 2, 3, 5 (and their multiples), and 7?

On a totally different note: here is a nice little game which I somehow managed to win after getting myself two pawns down. I was playing against Deep HIARCS 14, when I should have been paying attention to some undergraduate workshops, but never mind:

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