Polyrhythm Calculator
Calculate polyrhythm beat timing relationships — find when two rhythms realign and the ms timing for each beat at a given BPM.
Polyrhythm Analysis
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.