Polyrhythms explained: 3 against 2, 4 against 3, polymeter, and how to program them in a DAW

A polyrhythm is "the simultaneous use of two or more rhythms that are not readily perceived as deriving from one another" (Wikipedia). In practice: two evenly spaced pulses that divide the same span of time differently, and only meet on the downbeat. A polymeter is a different thing that people often mix up with it, and the difference matters when you sit down at a DAW.

3 against 2

The simplest case is three evenly spaced notes against two, written 3:2 and also called a hemiola. You can notate it as three quarter notes over two dotted quarters in 6/8, or as quarter-note triplets over two quarters in 2/4 (Wikipedia).

To feel it, divide the cycle into six equal steps (six is the smallest number both 2 and 3 divide into):

The usual spoken mnemonic, "nice cup of tea", traces the combined pattern: steps 1, 3, 4 and 5.

3:2 is not an exotic effect. In much non-Saharan African music, cross-rhythm is the generating principle, and 3:2 is treated as its basic form (Wikipedia).

4 against 3

4:3 is the same idea with a 12-step grid: one part hits every 3 steps, the other every 4. Written out, it is four dotted eighths over three quarter notes in a bar of 3/4 (Wikipedia). It is harder to hold, and in jazz it was uncommon until Tony Williams played it with Miles Davis (Wikipedia).

Polymeter is not the same thing

In a polyrhythm the two parts share one cycle and divide it differently. In polymeter, "the bar sizes differ, but the beat remains constant", so the parts drift apart and eventually agree: four bars of 7/4 equal seven bars of 4/4 (Wikipedia). The same source notes that even 3/4 against 6/8, which sounds like two meters, usually works as one meter with primary and secondary beats (Wikipedia).

A quick test: if both parts share the same bar line and land together every bar, it is a polyrhythm. If one loop is a different length and only realigns after several bars, it is polymeter.

How to program them in a DAW

Polyrhythm: change the grid, not the tempo. Set the clip or pattern length to one bar, then give each part its own subdivision. For 3:2 in 4/4, put the "2" part on half notes and the "3" part on half-note triplets; most DAWs have a triplet grid toggle for this; in Ableton Live it is Ctrl+3 (Win) / Cmd+3 (Mac) (Ableton). For 4:3, set the bar to 3/4, put the "3" on quarter notes and the "4" on dotted eighths. When the grid can't do it, use the least common multiple: a 12-step sequencer pattern handles both 3:2 and 4:3.

Polymeter: change the loop length. In a step sequencer or drum machine, set one track to 16 steps and another to, say, 12 or 7, keeping the same step size. Clip-launching DAWs do the same with loops of different lengths that keep playing until they realign. Count the realignment: 16 against 12 meets every 48 steps; 16 against 7 only every 112.

Make it audible. Put each pulse on a sound with its own register and timbre (a low tom against a high rim, say). Polyrhythms collapse into mush when both parts share a sample.

Where you've heard them

• The National, "Fake Empire": 4 over 3 (Wikipedia).
• Britney Spears, "Till the World Ends": a 4:3 hook (Wikipedia).
• Mongo Santamaría, "Afro Blue" (1959): described as the first jazz standard built on a 6:4 cross-rhythm; John Coltrane's 1963 recording recast it as 3/4 swing (Wikipedia).
• Chopin, Étude Op. 10 No. 10, and Rachmaninoff, Piano Concerto No. 2: both cited for cross-rhythm (Wikipedia).
• Mozart, Don Giovanni: two orchestras in 3/4 and 2/4, later joined by a band in 3/8 (Wikipedia).
• The Cars, "Touch and Go" (polymeter): drums and bass in 5/4, guitar, synth and vocals in 4/4 (Wikipedia).
• Meshuggah (polymeter): riffs in unusual lengths cycling over a 4/4 base (Wikipedia).

What we think

Most producers already own the tools for this and never use them, because a DAW's default is one tempo, one time signature and one loop length for everything. The cheapest way out is polymeter, not polyrhythm: shorten one drum track to 7 or 12 steps and let it run against a 16-step groove. It sounds composed rather than random because the step size never changes, and it gives a four-bar loop a much longer real cycle without writing a single extra note. Save true polyrhythms like 4:3 for a single moment, a hook or a fill, where the tension is the point; across a whole track they tire the listener out. And learn 3:2 by ear first. It is the one that underlies a huge share of the world's music, and once you hear it you'll notice it everywhere.

FAQ

What is the difference between a polyrhythm and a polymeter? A polyrhythm divides one shared cycle two ways. A polymeter keeps the beat the same but uses different bar or loop lengths, which realign only after several bars.

What is a hemiola? Another name for 3 against 2.

How do I play 3 against 2 with two hands? Count six steps; one hand plays 1, 3, 5 and the other 1 and 4.

Do I need a special plugin? No. A triplet grid, a 12-step pattern or loops of different lengths cover almost every case.