Polyrhythm Calculator

See how two cross-rhythms line up. Enter an x-against-y polyrhythm (like 3:4) and a tempo to get each voice's timing in milliseconds, the combined grid, and a visual of where the hits fall.

The green row is voice A, the purple row voice B; a cycle is one full repeat of the pattern.

How it works

A polyrhythm plays two different subdivisions over the same span of time. The cycle repeats when both line up again, which is the lowest common multiple of the two numbers.

cycle length = LCM(a, b) subdivisions

a-side plays every  LCM / a  subdivisions
b-side plays every  LCM / b  subdivisions

If the two numbers share no factors, the cycle is simply a × b.

Worked example

A 3:4 polyrhythm — three against four:

• LCM(3, 4) = 12 subdivisions per cycle
• The 3-side hits every 4 subdivisions; the 4-side every 3
• They coincide only on subdivision 1, then repeat

5:4 gives a 20-subdivision cycle. 6:4 reduces to 3:2, because 6 and 4 share a factor — LCM is 12, but the pattern is the simpler one.

In practice

• Count the composite. To play 3:4, count twelve and place both parts inside it. Counting each hand separately rarely works.
• Polyrhythm is not polymeter. A polyrhythm fits different subdivisions into the same bar; polymeter runs different bar lengths side by side. 3:4 is a polyrhythm; 7/8 against 4/4 is polymeter.
• 3:2 is the gateway. It is the hemiola that underpins a great deal of African, Latin and jazz rhythm, and it is much easier to internalise than it looks.
• In code the LCM is all you need — generate a grid that long and place both parts on it.

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