Mathematics can be used to analyze musical rhythms, to study the sound waves that produce musical notes, to explain why instruments are tuned, and to compose music. This book explores the relationship between mathematics and music through proportions, patterns, Fibonacci numbers or the Golden Ratio, geometric transformations, trigonometric functions, fractals, and other mathematical concepts. The book is organized into eight chapters: (1) "The Essence: Introduction"; (2) "The Beat: Rhythm"; (3) "The Tone: Frequency, Amplitude"; (4) "The Tune: Tuning"; (5) "The Song: Composition"; (6) "The Source: Instruments"; (7) "The People: Human Connections"; and (8) "The Curiosities: An Assortment." An epilogue, end notes, bibliography, and index conclude the book. (MM)