Polyrhythm Cycle Calculator - When 3 Against 2 Lines Up Again

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What a polyrhythm is

A polyrhythm is two rhythms played at the same time, with different numbers of beats in the same span of time. The most famous is 3 against 2: one musician plays three evenly spaced notes while another plays two evenly spaced notes, and both finish at the same moment. It sounds complicated, but it is built from simple arithmetic. The same idea scales up: 4 against 3, 5 against 4, 7 against 5, and any other pair you care to try. This calculator finds the moment when both rhythms meet again, and how long each step lasts.

Polyrhythms appear everywhere once you listen for them. West African drumming is built on them. Jazz drummers play 3 against 2 over a walking bass line. Rock drummers sneak them into fills. Electronic producers layer a three-note pattern over a four-beat bar and call it groove. The rhythms sound rich because your ear hears two pulses at once, and the tension between them is part of the music.

How to use the calculator

Enter the first rhythm, for example 3.
Enter the second rhythm, for example 2.
Enter the tempo in beats per minute.
Read the cycle length in steps, the cycle time in milliseconds, and each rhythm’s step length.

A worked example

Take 3 against 2 at 60 beats per minute. A beat lasts 1,000 milliseconds. The two rhythms meet again after the least common multiple of 3 and 2, which is 6 steps. The full cycle therefore lasts 6,000 milliseconds, or six seconds. The three-rhythm plays one note every 2,000 milliseconds, because 6,000 divided by 3 is 2,000. The two-rhythm plays one note every 3,000 milliseconds, because 6,000 divided by 2 is 3,000. Both start together, both end together, and in between they never land on the same step except at the start and the end.

Now take 4 against 3 at 120 beats per minute. A beat lasts 500 milliseconds. The least common multiple of 4 and 3 is 12, so the cycle lasts 12 times 500, or 6,000 milliseconds. The four-rhythm plays every 1,500 milliseconds, and the three-rhythm plays every 2,000 milliseconds. The diagram in the tool shows the pattern: dots for hits and marks for silence, so you can see the two rhythms weaving past each other until they meet again.

Why the least common multiple matters

The least common multiple is the smallest number that both rhythm numbers divide evenly. It is the first step count where both rhythms have played a whole number of notes and land together. Before that point, at least one rhythm is always mid-cycle. That is why polyrhythms feel like they are pulling apart and coming back together: they literally are. The cycle length tells you how long you must listen before the pattern repeats, and that length grows fast. 5 against 4 repeats after 20 steps, and 7 against 5 repeats after 35 steps, which is why complex polyrhythms sound so long and winding.

Knowing the cycle length helps you practise. If you play 3 against 2, count six small steps, not three or two. Tap the three-rhythm with one hand on steps 1, 3 and 5, and the two-rhythm with the other hand on steps 1 and 4. Once your hands can do that, speed it up. Counting the full cycle, instead of each rhythm separately, is the trick that makes polyrhythms learnable.

Tips for practising polyrhythms

Start with 3 against 2. It is the foundation, and every other polyrhythm builds on the same idea.
Count the full cycle out loud before you play it. Say the step numbers, then add the hands.
Practise slowly. At 60 beats per minute, you have time to hear each hand separately.
Use the calculator’s step lengths to set a metronome or a drum machine to each rhythm on its own, then combine them.

Common mistakes

The most common mistake is counting only one rhythm and hoping the other falls into place. It will not. Both rhythms need the shared cycle as their frame. Another mistake is speeding up too soon: a polyrhythm played fast but unevenly sounds like a mistake, while the same polyrhythm played slowly and evenly sounds like music. A third mistake is thinking the rhythms must start together every bar. They only need to meet at the end of the cycle, and the space between meetings is where the music happens.

Use this calculator to plan any polyrhythm before you practise it. When you know the cycle length and the step times, the rhythm stops being a mystery and becomes a pattern you can count, play and enjoy.

Who uses polyrhythms

Drummers use them to build fills, jazz players use them to stretch time, classical composers from Brahms to Steve Reich have built whole pieces on them, and producers use them to make electronic grooves feel alive. If your rhythms sound flat, a polyrhythm is often the missing ingredient.

Polyrhythm Cycle Calculator – When 3 Against 2 Lines Up Again