Polyrhythm is the simultaneous sounding of two or more independent rhythms. A simple example of a polyrhythm is 3 evenly-spaced notes against 2, with the 3-beat pattern being faster than the 2-beat pattern, so that they both take the same amount of time. Other simple polyrhythms are 3:4, 4:3, 5:4, 7:4, etc. Another form of polyrhythm, which might also be termed polymeter, would be phrasing to suggest a different meter than the one being played by the rest of the ensemble. A common example of this in jazz would be phrasing quarter notes in groupings of 3 to suggest 3/4 time while the ensemble plays in 4/4. Compare with hemiola (not a polyrhythm). Traditional African music is heavily polyrhythmic, although, unlike below, the downbeats do not usually coincide. Frank Zappa, especially towards the end of his career, experimented a lot with complex polyrhythms, such as 11:17, and even nested polyrhythms. The metal band Meshuggah also have some polyrhythms in their music, although their quirkiness is mostly of a polymetric nature. Much minimalist and totalist music makes extensive use of polyrhythms. Henry Cowell and Conlon Nancarrow created music with yet more complex polytempo and using irrational numbers like pi:e.
Common polyrhythms found in jazz are 3:2, which manifests as the quarter-note triplet; 2:3, usually in the form of dotted-quarter notes against quarter notes; 4:3, played as dotted-eight notes against quarter notes (this one demands a good deal of technical proficiency to pull off, and was not at all common in jazz before Tony Williams used it when playing with Miles Davis); and finally 3/4 time against 4/4, which along with 2:3 was used famously by Elvin Jones and McCoy Tyner playing with John Coltrane.
The following is an example of a 2 against 3 polyrhythm, given in time unit box system (TUBS) notation; each box represents a fixed unit of time; time progresses from the left of the diagram to the right, although this is irrelevant since the pattern is symmetric. Beats are indicated with an X; rests are indicated with a blank.
2 against 3 polyrhythm
|2-beat rhythm ||X || || ||X || || ||X || || ||X || || ||X || || ||X || || ||X || || ||X || || |
|3-beat rhythm ||X || ||X || ||X || ||X || ||X || ||X || ||X || ||X || ||X || ||X || ||X || ||X || |
A common memory aid to help with the 2 against 3 polyrhythm is that it has the same rhythm as the phrase "not difficult"; the simultaneous beats occur on the word "not"; the second and third of the triple beat land on "dif" and "cult", respectively. The second 2-beat lands on the "fi" in "difficult." Try saying "not difficult" over and over in time with the sound file below. Another phrase with the same rhythm is "cold cup of tea":
Similar phrases for the 3 against 4 polyrhythm are "pass the gosh darn butter" and "what atrocious weather"; The 3 against 4 polyrhythm is shown below.
3 against 4 polyrhythm
|3-beat rhythm ||X || || || ||X || || || ||X || || || ||X || || || ||X || || || ||X || || || |
|4-beat rhythm ||X || || ||X || || ||X || || ||X || || ||X || || ||X || || ||X || || ||X || || |
As can be seen from above, the counting for polyrhythms is determined by the lowest common multiple, so if one wishes to count 2 against 3, one needs to count a total of 6 beats, as lcm(2,3) = 6 (123456 and 123456). However this is only useful for very simple or polyrhythms, or for getting a feel for more complex ones, as the total number of beats rises quickly. To count 4 against 5, for example, requires a total of 20 beats, and counting thus slows the tempo considerably. However some players, such as classical Indian musicians, can intuitively play high polyrhythms such as 7 against 8.
Below are some example polyrhythms in MIDI format:
- 2 against 3 polyrhythm in MIDI format
- 3 against 4 polyrhythm in MIDI format