Polyrhythm Generator — 3:2, 4:3, 5:4, 5:3

A polyrhythm places two rhythmic patterns over the same span: one voice plays three attacks where the other plays two, or four against three. This generator runs two independent click voices from one clock, with exact 3:2, 4:3, 5:4 and 5:3 ratios, per-voice volume, and a cycle the two voices always share.

How to use it

1. The page opens on 3:2 with voice 2 already enabled, so pressing Start gives you the cross-rhythm immediately. Voice 1 is the woodblock; voice 2 is the beep, so the two grids stay distinguishable by ear.
2. Set voice 1’s tempo. In ratio mode voice 1 is the source of truth: its BPM and the ratio together decide voice 2’s tempo, shown next to the ratio buttons as “Voice 2 · N BPM” with a “locked by ratio” tag.
3. Pick a ratio: 3:2, 4:3, 5:4 or 5:3. The ratio buttons change the relationship; the readout updates with the derived voice 2 tempo.
4. Shape each voice. Voice 2 has its own subdivision (off, eighths, triplets, sixteenths), its own volume slider, and a mute button. Voice 1 keeps the main metronome’s controls: meter, subdivisions, kit and speed trainer.
5. Count the cycle, not the clicks. Say the cycle numbers aloud; the voices only agree at the cycle start, and that is the point you are training.

The ratio convention

Read every ratio as voice 1 : voice 2.

• A label of a:b means voice 1 sounds a attacks over one cycle and voice 2 sounds b.
• The cycle spans a of voice 1’s beats, and both voices land together at the start and the end of it.
• Voice 2’s interval is the cycle length divided by b, so the cycle closes exactly on both grids.

At 120 BPM, voice 1 beats are 0.5 seconds apart and the derived voice 2 tempos are:

Ratio	Voice 1 attacks per cycle	Voice 2 attacks per cycle	Cycle length	Voice 2 tempo at 120 BPM
3:2	3	2	1.5 s	80 BPM
4:3	4	3	2.0 s	90 BPM
5:4	5	4	2.5 s	96 BPM
5:3	5	3	2.5 s	72 BPM

Editing voice 2’s tempo manually clears the ratio and switches to Custom: the two BPMs then drive their own grids independently.

Counting the ratios

The reliable method is to count the cycle in equal units and give each voice its positions. The number of units is the point where both voices meet again — six for 3:2, twelve for 4:3, twenty for 5:4, fifteen for 5:3.

Ratio	Count the cycle as	Voice 1 lands on	Voice 2 lands on
3:2	1–6	1, 3, 5	1, 4
4:3	1–12	1, 4, 7, 10	1, 5, 9
5:4	1–20	1, 5, 9, 13, 17	1, 6, 11, 16
5:3	1–15	1, 4, 7, 10, 13	1, 6, 11

For 3:2 the spoken result is “one, two-three, four, five-six” with the two hands meeting on the one. For 4:3, count to twelve and let the three-side stay slow and even while the four-side moves underneath it.

A practice method

1. Hands separately. Tap voice 1’s positions with your right hand only, then voice 2’s with your left hand only. Do not combine them yet; each grid has to be automatic on its own.
2. Add the metronome one voice at a time. Start the tool on the ratio at a slow tempo (60 BPM works well), play voice 1’s part on an instrument with voice 2 muted, then unmute voice 2 and let it play while you hold voice 1.
3. Together at half the speed of your ambition. Count the cycle aloud and tap both parts. If the cycle start does not land together, the tempo is too high; drop it and repeat.
4. One cycle at a time. Stop at the cycle end and restart. Accuracy at the meeting point matters more than playing continuously.
5. Move to the instrument. Play a single pitch on each of one voice’s attacks while the other voice plays from the speakers; then swap.
6. Raise the tempo in small steps. The ratio stays exact at every tempo; only your ability to place the attacks changes.

Musical context

The 3:2 cross-rhythm has a name in Western music: the hemiola, where a passage in triple metre temporarily groups into two, or vice versa. Layered cross-rhythms are also fundamental to many West African drumming traditions, where several parts with different cycle lengths interlock over a shared pulse. In both cases the technique is the same one this page trains: hold one grid steady in your body while another plays against it.

Accuracy and limits

• Ratios are exact while the ratio is selected. Both voices are scheduled from the same audio clock, and voice 2 is re-anchored to voice 1 whenever the ratio or voice 1’s tempo changes, so there is no cumulative drift between them.
• Custom mode is approximate. Setting voice 2’s BPM by hand removes the mathematical lock; the voices run independently from that point.
• Voice 2 has its own timbre. It always plays the beep sound, so the two voices stay separable. There is no per-voice kit picker.
• Voice 1 keeps the main meters. Its accent pattern is the usual one for the selected meter; voice 2 accents the first attack of each cycle and plays the rest plain.
• The speed trainer moves the ratio with the tempo. When a ramp step fires, voice 2 is re-anchored so each tempo segment starts a fresh, aligned cycle.