🎯

Polyrhythm Calculator

Work out any polyrhythm such as 3 against 2, 4:3 or 5:4: note spacing in milliseconds for each rhythm at your tempo, the common grid (LCM) and a pulse-by-pulse chart of where the notes fall.

Rhythm A (notes per cycle)

Rhythm B — the beat (notes per cycle)

Tempo of rhythm B

Loading calculator…

How it works

cycle = B beats × 60 ÷ BPM · rhythm A spacing = cycle ÷ A · rhythm B spacing = cycle ÷ B · grid = LCM(A, B) pulses per cycle · A note on every (grid ÷ A)-th pulse, B note on every (grid ÷ B)-th pulse · rhythm A tempo = BPM × A ÷ B

A polyrhythm plays two evenly spaced pulses over the same span of time — three notes against two, four against three and so on. The trick to learning one is the common grid: the least common multiple of the two numbers. For 3:2 the grid has 6 pulses; rhythm A lands on pulses 1, 3 and 5 and rhythm B on 1 and 4, which you can count as "1-2-3-4-5-6" or say as "pass the gol-den but-ter". Here rhythm B is the beat you tap your foot to, and the calculator gives exact millisecond spacings for programming a sequencer or delay.

Worked example

3 against 2 at 90 BPM: two beats take 1,333.33 ms, so rhythm A plays every 444.44 ms (a tempo of 135 BPM) and rhythm B every 666.67 ms. The 6-pulse grid has a pulse every 222.22 ms.

Sources: Wikipedia — Polyrhythm · Wikipedia — Least common multiple

Frequently asked questions

How do you count a 3 against 2 polyrhythm?

Count six even pulses. Play rhythm A on 1, 3 and 5 and rhythm B on 1 and 4. Together they form the pattern both–A–B–A, often spoken "pass the gol-den but-ter".

What is the difference between a polyrhythm and a polymeter?

A polyrhythm fits different numbers of notes into the same time span (3 notes in the time of 2). A polymeter keeps the same note length but different bar lengths (a 3-beat pattern against a 4-beat one), so the downbeats drift apart.

What is the LCM grid?

The least common multiple of the two numbers — the smallest number of equal pulses that both rhythms land on exactly. 4:3 needs 12 pulses and 5:4 needs 20.

How do I practise a polyrhythm?

Set a metronome to the grid pulse, play the combined pattern slowly with both hands, then speed up and drop the grid click so only the beat remains.

Related calculators

BPM to Milliseconds Calculator

Turn a tempo in BPM into note delay times in milliseconds — quarter, eighth, sixteenth, dotted and triplet values for delay and reverb.

Metronome Subdivision Calculator

See the click interval in milliseconds for any tempo and subdivision (eighths, triplets, sixteenths, quintuplets, sextuplets, septuplets and thirty-seconds), the equivalent subdivided BPM to set on a plain metronome, the bar length, and swung-eighth timings.

BPM to Note Duration Calculator

Convert a tempo in BPM into the length of every note value in milliseconds, with dotted and triplet timings for delays.

Bars & Beats to Time Calculator (BPM)

Convert bars and beats to minutes and seconds at any tempo and time signature, a duration into bars, or bars plus a duration into BPM. Plan a whole arrangement with start times for every section, turn a DAW position like 33.1.1 into a time, and get beat and note lengths (straight, dotted, triplet) in milliseconds, samples per beat and video frames.

Tempo-Synced Delay, Pre-Delay & Reverb Time Calculator

Delay times in milliseconds for every note value at a given BPM (straight, dotted, triplet), reverb pre-delay and decay settings that sit on the grid, compressor attack and release starting points, and LFO rates in Hz for tempo-locked modulation.

This calculator is for educational purposes. Double-check important results before acting on them.