Polyrhythm Calculator
A polyrhythm occurs when two distinct rhythmic groupings are played simultaneously at the same overall tempo. The key mathematical property is that both rhythms coincide again after a number of pulses equal to the least common multiple (LCM) of the two groupings. For example, 3 against 4 creates a cycle of LCM(3,4) = 12 pulses. This calculator finds the LCM cycle length, the pulse positions of each rhythm within the cycle, and the interval between beats for each group at a given BPM.
Polyrhythm formula
Cycle length = LCM(grouping_A, grouping_B)
LCM(a, b) = a * b / GCD(a, b)
Cycle duration (ms) = (LCM / grouping_A) * quarter_note_ms
Interval A (ms) = cycle_ms / grouping_A
Interval B (ms) = cycle_ms / grouping_B
The quarter note duration is 60,000 / BPM milliseconds. The cycle takes exactly LCM / grouping_A quarter notes (since each full bar of grouping A takes LCM / grouping_A beats). Both rhythms restart together at the end of the cycle.
Common polyrhythm cycles
- 2:3 (hemiola basic) - LCM = 6 pulses. Found in Afro-Cuban clave, jazz ballads.
- 3:4 - LCM = 12 pulses. Most common polyrhythm, found across many musical traditions.
- 4:5 - LCM = 20 pulses. Common in contemporary classical music.
- 3:5 - LCM = 15 pulses. Found in Indian classical music (tala patterns).
- 5:7 - LCM = 35 pulses. Complex polyrhythm used in avant-garde jazz.
Polyrhythm: frequently asked questions
What is a polyrhythm?
A polyrhythm is two or more rhythmic patterns with different groupings played simultaneously. The most common is 3 against 4 (triplets against straight eighth notes), where three evenly-spaced notes fit in the same time as four. The patterns coincide again after LCM(3,4) = 12 pulses.
How do you calculate when two rhythms coincide?
The two rhythms realign at the least common multiple (LCM) of their beat groupings. LCM(3,4) = 12 pulses. LCM(2,3) = 6 pulses. LCM(4,5) = 20 pulses. The LCM tells you how many of the smallest subdivision pulses pass before both patterns restart together.
What is the difference between polyrhythm and polymeter?
Polyrhythm means different numbers of beats fit in the same time span (3 against 4). Polymeter means different bar lengths but the same beat rate (3/4 against 4/4). In polyrhythm the beat speeds differ; in polymeter the bar lengths differ.
What is the interval between beats in a 3:4 polyrhythm?
If the total cycle is 12 pulses, the pattern-of-3 places beats at pulses 0, 4, 8. The pattern-of-4 places beats at pulses 0, 3, 6, 9. Each group divides the LCM equally by its number.
What are common polyrhythms in music?
3:4 is the most common (hemiola). 2:3 appears in Cuban clave rhythms. 4:5 and 5:6 appear in complex jazz and contemporary classical music. West African and Indian classical music extensively use complex polyrhythmic structures. The LCM grows rapidly for large coprime numbers.
Official sources
- Audio Engineering Society (AES): aes.org - music theory and rhythm standards.
- MIDI Association: midi.org - timing and beat specifications.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.