Polyrhythm Calculator
Calculate polyrhythm beat timing relationships — find when two rhythms realign and the ms timing for each beat at a given BPM.
Understanding Polyrhythms
A polyrhythm occurs when two or more rhythmic patterns with different pulse divisions play simultaneously. The most common example is 3 against 2 (3:2) — three evenly spaced notes against two evenly spaced notes in the same time span.
How to Think About It
For a polyrhythm of M against N:
- Both patterns start together and reunite after a number of beats equal to the LCM (least common multiple) of M and N.
- Pattern A subdivides this span into M equal parts.
- Pattern B subdivides this span into N equal parts.
Common Polyrhythms
| Ratio | Description | Found In |
|---|---|---|
| 2:3 | Two against three | Classical, African, Latin |
| 3:4 | Three against four | Jazz, contemporary |
| 3:5 | Three against five | Progressive rock, Indian classical |
| 4:5 | Four against five | Jazz, 20th century classical |
| 2:3:4 | Cross-rhythm | African drumming |
Calculating Beat Spacing
At a given BPM (beats per minute), one beat lasts:
Beat duration = 60,000 ms / BPM
For a polyrhythm of M:N over one beat:
- Pattern A beat spacing = Beat duration / M
- Pattern B beat spacing = Beat duration / N
The Cycle Length
Both patterns return to unison after:
Cycle = LCM(M, N) beats
At 120 BPM with a 3:2 polyrhythm:
- One beat = 500 ms
- Pattern 3 beat spacing = 500 / 3 ≈ 166.7 ms
- Pattern 2 beat spacing = 500 / 2 = 250 ms
- They realign every LCM(3,2) = 6 subdivisions = one full bar
The “In 3 / In 2” Mnemonic
A classic way to feel 3:2:
- Pattern of 3: “Not dif-fi-cult” (3 syllables)
- Pattern of 2: “Nice” (spoken once, landing on beats 1 and 3 of the triplet)
Playing polyrhythms requires internalizing both patterns independently and letting them layer naturally.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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