The Sound of Numbers is a book about the mathematics of music theory—that is, the use of mathematics to describe, analyze, and create musical structures such as rhythms, scales, chords, and melodies. Music theorists have used mathematics to solve musical problems for centuries, and some composers have turned to mathematics for inspiration. Mathematicians, too, have investigated musical questions. However, there has been a significant disconnect between these fields since the eighteenth century. This book aims to interpret the work of music theorists in a manner that is accessible to readers with scientific training and some background in music, and it aims to connect questions familiar to music theorists with problems and techniques that arise in mathematics.