Polyrhythm Cycle Length Calculator
In a polyrhythm, two rhythms with different counts ride over the same span of time and realign only at the end of a full cycle. The smallest grid on which both land is the lowest common multiple of the two pulse counts. Enter the two counts (for example 3 and 4), the tempo of the main pulse, and how many main-pulse beats make up one cycle. This calculator returns the cycle length in common subdivisions and the cycle duration in seconds and milliseconds.
Polyrhythm cycle formula
gcd = greatest common divisor of a and b
lcm = a * b / gcd
cycle seconds = beats per cycle * (60 / BPM)
subdivision ms = (cycle seconds / lcm) * 1000
The lowest common multiple is the number of evenly spaced subdivisions in the cycle. Dividing the cycle time by that count gives the duration of one subdivision, the grid spacing for programming the rhythm.
Common polyrhythms
- 3 against 2: cycle of 6 subdivisions.
- 3 against 4: cycle of 12 subdivisions.
- 4 against 5: cycle of 20 subdivisions.
- 5 against 7: cycle of 35 subdivisions.
- 6 against 4: cycle of 12 subdivisions (they share a factor of 2).
Polyrhythms: frequently asked questions
What is a polyrhythm cycle?
A polyrhythm layers two pulses with different counts, such as 3 against 4. They start together, drift apart, and only line up again after a whole cycle. The cycle length in common subdivisions is the lowest common multiple of the two counts; for 3 against 4 that is 12 subdivisions.
How do you find the lowest common multiple?
Multiply the two numbers together and divide by their greatest common divisor. For 3 and 4, the greatest common divisor is 1, so the lowest common multiple is 12. For 6 against 4, the greatest common divisor is 2, so the lowest common multiple is 12, not 24.
How long is the cycle in seconds?
Enter the tempo of the main pulse and how many of those main-pulse beats fill one cycle. The cycle time is that beat count times the seconds per beat (60 divided by BPM). For a 3 against 4 polyrhythm spanning one bar of 4 beats at 120 BPM, the cycle is 2 seconds.
What does the subdivision count tell me?
It tells you the smallest grid on which both rhythms land. Programming the polyrhythm at that resolution (for example, twelfth notes for 3 against 4) lets you place every note exactly on the grid in a sequencer.
Sources and definitions
- The cycle of a polyrhythm is the lowest common multiple of the two pulse counts; LCM = a * b / GCD is a standard result of number theory.
- National Institute of Standards and Technology: SI units reference (time in seconds).
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.