Polymeter

Polymeter is the use of multiple meters simultaneously within a single piece of music. In this application, polymeter means combining loops of different lengths, so that they slip relative to each other, the way oscillators with different frequencies shift phase relative to each other. Polymeter is more interesting when the loop lengths being combined are relatively prime, meaning they share no common factors except one. Such loop combinations gradually drift apart (diverge) and then drift back together (converge) in a predictable way, producing intricate patterns of interference as they do so. Various tools are provided to work with convergences.

Complex polymeter

Complex polymeter is the simultaneous use of three or more relatively prime meters. For example, a composition that uses the meters 4/4, 5/4, and 7/4 all at the same time is in complex polymeter.

Polymeter versus polyrhythm, odd time, and phasing

• Polyrhythm means combining different rhythms. There's no requirement that the rhythms be different lengths or exhibit phase shift. Polyrhythm is a very general category, of which polymeter is a subset.
• Odd time means using an odd meter (5/4, 7/4, 11/4 etc.), or alternating between several odd meters, one after the other. It's the use of multiple odd meters simultaneously that distinguishes polymeter from odd time.
• Phasing is a more general category than polymeter. Any system that combines oscillations of different frequencies exhibits phasing. Loops of different lengths "slip" in and out of phase relative to each other, i.e. they phase. Polymeter is a specialized subset of phasing. Polymeter adds a constraint that the different loop lengths must share a common unit (e.g. a sixteenth note). In other words, polymeter is quantized phasing. In phasing, the slippage is continuous, whereas in polymeter, the slippage is discrete: it occurs in steps. Phasing is good for ambient music; polymeter is good for rhythmic music.