Music by the Numbers: From Pythagoras to Schoenberg

by Eli Maor

Overview

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.

Product Details

ISBN-13:	9780691176901
Publisher:	Princeton University Press
Publication date:	05/01/2018
Pages:	176
Sales rank:	545,748
Product dimensions:	5.60(w) x 8.60(h) x 1.00(d)

About the Author

Eli Maor is a former professor of the history of mathematics at Loyola University Chicago. He is the author of seven previous books, including the internationally acclaimed To Infinity and Beyond, e: The Story of a Number, Trigonometric Delights, and The Pythagorean Theorem: A 4,000-Year History (all Princeton).

Table of Contents

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

What People are Saying About This

From the Publisher

"[An] intriguing study."—Barbara Kiser, Nature

"A fascinating investigation of the relationship between math and music—what they have in common, how they differ, and how each has informed the other. A delightful examination of how math and culture interact."—Ian Stewart, author of Significant Figures

"Writing beautifully as he explores the relationship between mathematics and classical music, Eli Maor makes mathematics sing like a violin."—Jerry King, author of The Art of Mathematics

"[A] very readable and enjoyable book."—Karl-Dieter Crisman, MAA Reviews

Editorial Reviews

"In this intriguing study, maths historian Eli Maor traces those echoes, along with the trajectories of the ‘scientists, inventors, composers, and occasional eccentrics’ behind them."—-Barbara Kiser, Nature

"The prolific author Eli Maor has released yet another very readable and enjoyable book on the history of mathematics from Princeton University Press. . . . As with all of Maor’s books, this one belongs in your library so that leading students can learn about unknowns like Joseph Sauveur in the fascinating story of how mathematics and music intersect."—-Karl-Dieter Crisman, MAA Reviews

"Maor is an experienced storyteller. His mixture of musical, mathematical, and physical history, enriched with personal experiences and some unexpected links and bridges are nice reading for anybody with a slight interest in music and science. No mathematical training required."—-Adhemar Bultheel, European Mathematical Society

"This is a fascinating study of the reciprocal relationship between music and mathematics in the West."—-David Lorimer, Paradigm Explorer

"For anyone who ponders the role mathematics has in music, this short and delightful book is a joy to read from cover to cover. It is full of anecdotes and interesting facts and, being by Eli Maor is intensely readable."—-Phil Dyke, Leonardo Reviews

"[Music by the Numbers] is enjoyable and readable"—-Owen Toller, Mathematical Gazette

From the Publisher