Steve Reich's Clapping Music and the Yoruba Bell Timeline

Justin Collannino, Francisco Gómez and Godfried T. Toussaint
Bridges London: Mathematics, Music, Art, Architecture, Culture (2006)
Pages 49–58


Steve Reich’s Clapping Music consists of a rhythmic pattern played by two performers each clapping the rhythm with their hands. One performer repeats the pattern unchangingly throughout the piece, while the other shifts the pattern by one unit of time after a certain fixed number of repetitions. This shifting continues until the performers are once again playing in unison, which signals the end of the piece. Two intriguing questions in the past have been: how did Steve Reich select his pattern in the first place, and what kinds of explanations can be given for its success in what it does. Here we compare the Clapping Music rhythmic pattern to an almost identical Yoruba bell timeline of West Africa, which strongly influenced Reich. Reich added only one note to the Yoruba pattern. The two patterns are compared using two mathematical measures as a function of time as the piece is performed. One measure is a dissimilarity measure between the two patterns as they are being played, and the other is a measure of syncopation computed on both patterns, also as they are played. The analysis reveals that the pattern selected by Reich has greater rhythmic changes and a larger variety of changes as the piece progresses. Furthermore, a phylogenetic graph computed with the dissimilarity matrix yields additional insights into the salience of the pattern selected by Reich.