A polymetre (Am. Engl.: polymeter) takes place between two (or more) rhythmic phrases when they share the same ‘resolution’, however one’s bar length is shorter or longer than the other, thus causing them to come out of metric sync and return to a common reference point (i.e., the ‘1’) after a number of bars.
An example of a polymetric structure would have one phrase in 4/4, with another one playing in 3/8:
A: 1 . 2 . 3 . 4 . 1 . 2 . 3 . 4 . 1 . 2 . 3 . 4 . 1 B: 1 2 3 1 . . 1 . . 1 . . 1 . . 1 . . 1 . . 1 . . 1
In the above example, notice that it takes 3 bars of 4/4 for voice A and 8 bars of 3/8 for voice B so that they come back to sync.
As a concept, polymetres can often be confused with polyrhythms and vice versa; it’s true that these terms are interchangeable depending on how one looks into it. Strictly speaking, what distinguishes them is that
* in polyrhythms, voices have the same length (usually they are 1 bar long) but different ‘resolution’ (e.g., one would play in triplets, another one in quintuplets)
* in polymetres, phrases have the same resolution but different bar lengths.
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