Polymeter vs polyrhythm

They are easily mistaken for each other

As I continue to build groove pedagogy resources, I want to clear up some persistent confusion about polymeter and polyrhythm. If you don't feel like reading the whole post, it can be summed up in this image:

The most concisely I can put this into words:

• In polymeter, the grid lines are aligned, but the downbeats aren't.

• In polyrhythm, the downbeats are aligned, but the grid lines aren't.

Imagine a metronome ticking along. You can group the ticks together to make a meter. Most Anglo-American popular music organizes the ticks into units of four or eight or sixteen; this is called duple or quadruple meter. It is also pretty common to group the ticks into units of three or six or twelve; this is called triple meter. Occasionally, a piece of music will group the ticks into units of five or seven or some larger prime number. This is called odd or complex meter, and it is frequently confused with polymeter and polyrhythm. They are not the same thing! Even if the grouping uses an odd or prime number larger than three, it's still only a single grouping, so it's just a single meter.

Polymeter is the combination of two different groupings of metronome ticks at the same tempo. For example, one instrumental part might play a repeated pattern that is four ticks long. Meanwhile, another instrumental part might play a repeated pattern that is three ticks long. These patterns will align every twelve ticks. Three against two or three against four polymeter is an extremely common musical technique; you hear it every time you turn on pop radio.

Now imagine two metronomes ticking at different tempos, one faster, one slower. Every so often, however, they happen to line up. This is called polyrhythm. For example, one metronome might do four ticks in the same amount of time that the other metronome does three ticks. We could have saved a lot of confusion by calling this "polytempo" or "polysubdivision" rather than "polyrhythm".

You can think of tuplets as short bursts of polyrhythm. Triplets are by far the most common polyrhythm in Anglo-American music, and you hear them across every style and era. Polyrhythms involving bigger odd numbers like five or seven are rare in Western pop music, but you hear them in jazz and classical, and they are more common in music from other parts of the world.

It is not always easy to find crisp, clear real-world examples of polymeter and polyrhythm, especially if you want to compare them side by side. To help your aural intuition (and my own), I wrote this song. It presents 3:4, 5:4, 6:4 and 7:4 polymeters and polyrhythms. It includes samples of "New East St Louis Toodle-oo" by Duke Ellington, because who doesn't love Duke Ellington? Here's a chart.

Three against two

The more common name for 3:2 polymeter is hemiola. The classic example is "Carol of the Bells", two beats of 6/8 superimposed on three beats of 3/4.

You also hear this rhythm in Bach a lot, for example in the Menuet from his Partita No. 5 in G major. It's especially clear at 1:07.

For 3:2 polyrhythm, listen to "Afro Blue" by Mongo Santamaría. It's really a 6:4 polyrhythm, but you can think of it as a pair of 3:2 cells.

I wanted to hear how the Bach minuet would sound with the beat from "Afro Blue." Turns out it sounds really cool.

There's also some sweet 2:3 polyrhythm in Brad Mehldau's recording of the Beatles' "Baby's In Black". Listen starting at 4:05 in the album version (4:11 in the video below), where he plays clear groups of two against the underlying three (halfspeed four against three). He plays a steady quarter note pulse in his left hand, three to the bar, which helpfully anchors you in the meter.

Three against four

Three vs four polymeter might be the single most commonly used rhythmic device in Black American music. Richard Cohn calls it "the Platonic model of funky rhythms." It is absolutely everywhere in drum patterns, guitar strumming patterns, basslines, vocal melodies, and so on. For example, the ubiquitous tresillo pattern is a three vs four polymeter that gets interrupted after two and a third cycles. 

Triplets against a 4/4 background are also extremely common in Anglo-American pop. Listen to any Migos song:

Common though they are, triplets are not quite as common as you might think. There is a widespread misconception that swing is a triplet feel, and it isn't. When people talk about swing in terms of triplets, they are really describing a feel called 12/8 shuffle, so named because you could notate it in 12/8 time rather than triplets in 4/4. It's commonly used in the blues, country, and early rock. The Grateful Dead's "Truckin'" uses this feel.

You might call the "Truckin'" triplet groove a variety of swing, but it is not the same thing you hear in a Miles Davis or John Coltrane recording.

You sometimes also encounter four vs three, that is, triple meter with groupings of four overlaid.

There is not much 4:3 polymeter out there. Déaglin Ó Faoláin pointed me to the left hand part in this one Chopin mazurka.

You can hear 4:3 polyrhythm in "Fake Empire" by The National. You can hear that "eat your goddamn spinach" rhythm most clearly at 1:45 when the full drum beat enters.

Five against four

The two best-known examples of five against four polymeter are "Touch and Go" by the Cars and "Let Go" by Radiohead. Five against four polyrhythm is actually a bit more common, because quintuplets have become a trope in hip-hop and jazz. You can hear them in several places in "DUCKWORTH" by Kendrick Lamar, and throughout "Sequence Start" by Sungazer.

Six against four

Six against four is a more finely subdivided version of three against four.

"Kashmir" by Led Zeppelin is the archetypal example of six against four polymeter in popular music. 

Six against four polyrhythm is not so common in Anglo-American music, but it is everywhere in Sub-Saharan Africa. In the video below, wait a few seconds for the second mbira to enter.

Seven against four

To find examples of seven vs four, you have to leave pop music behind entirely.

I could not find a single example of seven vs four polymeter. Surely one exists? Put it in the comments.

Sarah Jeffery recommended on Twitter that I check out "Miserere, a duo: Mr Giles" or "A lesson of descant of thirtie-eight proportions of sundry kinds made by Mr Giles, Mr of the Children of Windsor, then and now Mr of the Children of the Chappell also" by Nathaniel Giles from 1594. You can hear 7:4 polyrhythm starting in measure 29, among many other polyrhythms. It's wild!

There are lots of septuplets in the third movement of Samuel Barber's Excursions Op. 20. The piece also has quintuplets, sextuplets and nonuplets.

Most of the examples of polyrhythm and (larger units of) polymeter that I could find out there are instructional videos on YouTube. People seem to be a lot more eager to teach you about these things than to use them in actual music. Here's a whole YouTube channel that just demonstrates polyrhythms! It's fun, but if you are looking for examples in a "real world" context, you have to dig a bit more. Signals Music Studio has more examples of polymeter here:

David Bruce has collected lots of examples of polyrhythm from Chopin and Ligeti, though in many Chopin pieces the rubato gives it more of a free-flowing feel than strict polyrhythm:

David Bennett has some more examples from pop:

There is lots of polyrhythm and polymeter in the past hundred years of experimental and avant-garde music. I... do not know enough about any of it to give examples. If folks want to leave them in the comments, please do!