A Simple Mathematics of Musical Pitch and Time

How the mathematics of pitch and time shed light on how music is made, performed, and heard.

Music is composed of patterns of sound in patterns of time. In A Simple Mathematics of Musical Pitch and Time, renowned music theorist Richard Cohn explores how the mathematics that govern these patterns in pitch and time—from scales to melodies and harmonies to rhythms—can offer readers new insights into the ways that music is composed, performed, and experienced by musicians and audiences.

Designed to be accessible to readers who may be new to mathematics or to music theory, Cohn uses concepts from set theory and graph theory to introduce a simple, yet analytically powerful, mathematical model rooted in the physical properties of pitch and time and what we know about how the human brain processes them. He then introduces readers to a series of cyclic universes, which can be interpreted either as units of time that combine to form cycled rhythms or as pitches that combine to form scales or chords.

In each chapter, he reveals how these cyclic universes can be applied to a wide range of music, from the historical repertoire of the European classical tradition to the music of West Africa. He also explores tuning theory, harmony, and voice leading and shows how his mathematical model offers a unique set of tools for understanding these crucial topics.