Schuller differentiates between thewestern and African understandings of polyrhythmic playing by stating that westernmusicians generally see polyrhythm as two or more rhythmic patterns played simultaneouslybut always resolving or meeting at the start and ending of phrases, bar lines and other centralpoints in the music. In contrast, “African music” reveals a far more intricate, extended,“polymetrically organized” understanding of polyrhythms, in which the individual rhythmicphrases hardly ever, and sometimes never coincide vertically (Schuller 1968, 11). These twointerpretations of polyrhythm are apparent in much U.S.-American jazz and can be seen toshift closer to the African approach in the later styles of jazz through the rhythmiccontributions of musicians such as John Coltrane, Tony Williams and Miles Davis. KeithWaters states that polyrhythm and polymeter, which he terms “metrical conflict”, were a keyfeature of music performed and recorded by the Miles Davis Quintet from 1965 to 1968(Waters 2011, 68).In terms of the use of polyrhythm in Western music from the pre-jazz era, Schuller citesCharles Ives as the only European composer who experimented with polymetric andpolyrhythmic structures, stating as an example Ives’s Fourth Symphony. Gridley deviatesfrom Schuller by suggesting that polyrhythms were used in European folk and concert musicin America for a long time before the jazz era came about but were not as prominent as inAfrican music (Gridley 1999, 45). He acknowledges the African ancestry of polyrhythms asoriginating from combinations of rhythms which can be heard in ragtime music. He definespolyrhythms as “the sounding of some rhythms that have a basis of two pulses while

Polyrhythms and Polymeter