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The above is the 3-2 clave, the 2-3 clave is the same but with the measures reversed.
Another type is rumba clave. It also can be in the 3-2 direction, as may be shown below, and in the 2-3 direction.
The origins of the rhythms are in polyrhythms of African music, which give more examples of clave rhythm.
There is also a percussion instrument called claves, consisting of a pair of short, thick wooden dowels. When struck they produce a bright clicking noise. Claves are sometimes hollow and carved in the middle to amplify the sound. Claves are often used to beat out clave rhythm, hence the name of the rhythm.
Steve Reich's Music for Pieces of Wood is written for five pairs of claves.