Polyrhythm is the simultaneous sounding of two or more independent
rhythms. Polyrhythms can be distinguished from
irrational rhythms, which can occur within the context of a single
part; polyrhythms require at least two rhythms to be played concurrently, one of which is typically an irrational rhythm.
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 5-2, 5-4, etc. Where one of the parts involves an irrational rhythm, the resulting rhythm could be said to be an "irrational polyrhythm"[citation needed].
Another form of polyrhythm, which might also be termed polymeter[citation needed], 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, particularly that of West Africa, is known for its highly complex polyrhythms and, unlike the examples given below, the downbeats do not usually coincide. Rhythms and counter rhythms evidence the common African cultural tradition of call and response, with different drum lines, other musical instruments, bodies and voices contributing rhythmic elements that complement and communicate with one another. This element of instrumental, as well as vocalized, call and response is also evident in the polyrhythmic quality of jazz, a musical form with its origins in the African American community.
