This book explores the temporal and rhythmic relationships between sounds and the structure of music, between perceptual aspects of the human auditory system and the sound machines (such as musical synthesizers, effects units, drum machines, and musical computer software). People identify the rhythmic structure of music as they tap their feet. Underlying such ordinary motions is an act of cognition that is not easily reproduced in a computer program or automated by machine. The first part of this book discusses the following question: How can we build a device that can “tap its foot” along with the music? The result is a tool for detecting and measuring the temporal aspects of a musical performance: the periodicities, the regularities, and the beat. The second part of the book describes the impact of such a “beat finder” on music theory and on the design of sound processing electronics. The “beat finder” provides a concrete basis for a discussion of the relationship between the cognitive processing of temporal information and the mathematical techniques used to describe regularities in data. These ideas are illustrated in an enclosed CD by numerous sound examples. This book is useful for engineers and musicians interested in the design of audio devices.