Music by the Numbers

How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century Music is filled with mathematical elements, the works of Bach are often said to possess a math-like logic, and Igor Stravinsky said "musical form is close to mathematics," while Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen went further, writing music explicitly based on mathematical principles. Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century development: the nearly simultaneous emergence of Einstein's theory of relativity and Schoenberg's twelve-tone system. Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.

Eli Maor

Preface ix
1 Prologue: A World in Crisis 1
2 String Theory, 500 BCE 13
SIDEBAR A It's All about Nomenclature 22
3 Enlightenment 24
4 The Great String Debate, 1730-1780 38
SIDEBAR B The Slinky 52
5 A Most Precious Gift 55
6 Musical Temperament 70
SIDEBAR C Music for the Record Books: The Lowest, the Longest, the Oldest, and the Weirdest 78
7 Musical Gadgets: The Tuning Fork and the Metronome 82
8 Rhythm, Meter, and Metric 91
9 Frames of Reference: Where Am I? 99
SIDEBAR D Musical Hierarchies 116
10 Relativistic Music 120
11 Aftermath 130
SIDEBAR E The Bernoulli 138
12 The Last Pythagoreans 142
Bibliography 147
Illustration Credits 149
Index 151