The Ultimate Polyrhythm
I first began to investigate this idea in 2009, when I was practising long polyrhythms at the piano. I wanted to make "multi" polyrhythms and soon realised that the key to cumulative complexity was prime numbers. These can be stacked without any of the patterns "fitting inside" any of the others. I also realised that composing in this fashion quickly generates very long forms. In each case, the total length of the polyrhythm, in terms of quaver units, is found by multiplying the values of its components, and of course the effect is exponential.
Since any piece constructed on these principles by definition cannot be in a time signature, I write the structure in 4-4 time for ease of reading (the duration of "bars" in the diagram above is 8 quavers). The problem for the conductor is that what he or she conducts bears no rhythmic relation to what they hear, except in terms of overall dynamics.
The mini-structure I show above, including the start of only five cycles, has a total period (U) of 7x11x13x17x19x23, which is 7,436,429 quaver units. If we set the tempo at 120 crotchets a minute, or two quavers a second, then it would take over 6 weeks to play the whole thing. I have made several pieces using 14 prime polyrhythms, and this concept I call the Big Bang, because after about 25 billion years, there would come a final, apocalyptic unison which would shake the foundations of the universe. But it might be too late to pick up the cheque from the composing society.
I think this is terribly exciting, not just because it gives rise to some interesting music, but also because it is hard to visualise how such short periods take such a long time to align themselves - reminding me of the story about the grains of rice and the chessboard.
The Big Bang
First, here is an extract from a literal representation of the mathematical idea, where the beginning of each period is marked by a percussion sound. This version is MIDI.
Here's an extract from the structure, performed by four percussionists, where voices switch on and off.
The Wrong Door
I wrote this piece because Griegakademiet had an agreement with FMKV, giving us composition students the chance to write for this top professional ensemble. The structure of the piece is strictly polyrhythmic primes, but I added a four-four pulse in the percussion to make it groove. The title comes from my experiment with "cutting out" a section of the structure and replacing it with something surreal, as if walking into the wrong room in a building, and coming across something unexpected.
Taking this concept as a starting-point, I've also written a piece for strings, a piece for speaking choir, and FMKV will play another piece I am writing in the same "style" in March 2012.More info coming...