The Mathematics of Steve Reich's "Clapping Music"

Joel K. Haack
Bridges: Mathematical Connections in Art, Music, and Science (1998)
Pages 87–92


Mathematics and music have been associated for millennia. Among the musical connections are symmetries and patterns used in composition, such as canons and fugues, the use or appearance of the golden mean in the compositions of Dufay [14 land others [10], the appearance of Fibonnaci numbers in the compositions of Bartok [1, 8], tone rows in serial music, the stochastic music of Xenakis, and the recent appearance of fractal music [3]. Mathematics provides insight into the overtone series, a basis for systems of tuning and the timbre of instruments. A deeper, more profound connection is explored in Rothstein's Emblems of Mind [13; also see reviews 2, 15], which suggests that mathematics and music may each be approaches to Platonic ideals of truth and beauty. At a foundational level of music, pitch and rhythm are also two mathematical connections to music. Usually both of these constituents appear in a piece. Here, however, we will examine in some detail the mathematics suggested by Steve Reich's Clapping Music, a piece based on rhythm alone. (Recordings include Steve Reich: Early Works, ElektraiNonesuch P 79169, 1987 and An American Collection, Harry Christophers, The Sixteen, Collins Classics 12872, 1992.)