Polyrhythm Generator
Three against four is the classic, and the arithmetic behind it is exact: the two voices realign after twelve subdivisions — their lowest common multiple — and coincide exactly once, because three and four share no factor. Change to four against six and they meet twice, because they share a factor of two, and the whole thing feels tighter and easier to hold. The grid shows both voices against the same subdivisions with the coinciding beats marked.
What this generator does
Places both voices evenly across a shared cycle whose length is the lowest common multiple of the two beat counts, and marks every subdivision where they coincide — a count that always equals their greatest common divisor.
How to use this tool
- Choose how many beats each voice plays.
- Read where the two lines up and where they do not.
- Note the cycle length — that is when the pattern repeats.
- Try a coprime pair against one sharing a factor to hear the difference.
Understanding the controls
- First voice beats
- Between 2 and 12 evenly spaced beats across the cycle.
- Second voice beats
- Between 2 and 12 in the same span. Pairs sharing no factor feel the most independent.
Common use cases
- Practising a cross-rhythm against a visible grid
- Understanding why some polyrhythms are harder to hold than others
- Programming two independent voices in a sequencer
- Teaching lowest common multiple through something audible
- Comparing coprime pairs against ones sharing a factor
How this generator works
The cycle length is the lowest common multiple and each voice is spaced evenly across it. The check confirms both voices are evenly spaced, that the coincidence count equals the greatest common divisor, and that the two at least share the downbeat — which they always must.
Randomness and fairness
Nothing here is random. The two beat counts determine the whole grid, which is why there is no seed.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Two voices only; three-way polyrhythms need a different display entirely.
- No audio playback, so this shows the structure rather than sounding it.
- Both voices are assumed to start together on the downbeat.
- Beat counts stop at twelve, above which the cycle grid becomes too wide to read.
- The grid is recomputed from the two beat counts each time rather than stored.
Privacy and your data
The grid is computed in your browser from the two numbers you choose. Nothing is transmitted or kept.
Related generators
- Euclidean Rhythm GeneratorHits spread as evenly as a cycle allows, using the algorithm that reproduces traditional rhythms from a dozen musical cultures.
- Random Time Signature GeneratorDraws a time signature and explains what it actually means — how many beats, how they group, and what to count out loud.
- Tempo Ladder GeneratorThe metronome marks to work a passage up to speed, spaced so every step is the same amount harder — with the seconds per beat for each.
- GCD and LCM Question GeneratorHighest common factor and lowest common multiple questions with Euclid's algorithm written out and the product identity checked.