Mathematics and music

178 Pages·2009·3.53 MB·English

by  Wright, David

Mathematics and Music

http://dx.doi.org/10.1090/mawrld/028
MATHEMATICAL WORLD VOLUME 28
Mathematics and Music
David Wright

Providence, Rhode Island
2000 Mathematics Subject Classification. Primary 00–01, 00A06.
For additional informationand updates on this book, visit
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Library of Congress Cataloging-in-Publication Data
Wright,David,1949–
Mathematicsandmusic/DavidWright.
p.cm. —(Mathematicalworld;v.28)
Includesbibliographicalreferencesandindex.
ISBN978-0-8218-4873-9(alk.paper)
1.Musicalintervalsandscales. 2.Musictheory—Mathematics. I.Title.
ML3809.W85 2009
781.01′51—dc22
2009014813
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About the Author
David Wright is professor of mathematics at Washington University in
St. Louis, where he currently serves as Chair of the Mathematics Depart-
ment. HereceivedhisPh.D.inMathematicsfromColumbiaUniversity,New
YorkCity. Aleadingresearcherinthefieldsofaffinealgebraicgeometryand
polynomialautomorphisms,hehasproducedlandmarkpublicationsinthese
areas and has been an invitedspeakerat numerous internationalmathemat-
icsconferences. He designedand teachesa universitycourseinMathematics
and Music, the notes from which formed the beginnings of this book.
As a musician, David is an arranger and composer of vocal music, where
hisworkoftenintegratesthecloseharmonystylecalledbarbershopharmony
with jazz, blues, gospel, country, doo-wop, and contemporary a cappella.
He is Associate Director of the St. Charles Ambassadors of Harmony, an
award winning male chorus of 160 singers. He also serves as a musical
consultant and arranger for numerous other vocal ensembles. He is active in
the Barbershop Harmony Society and was inducted into its Hall of Fame in
2008. As arranger and music historian David has been featured in national
radio and TV broadcasts at home and abroad and has authored several
articles on vocal harmony.

Contents
Introduction ix
1 Basic Mathematical and Musical Concepts 1
2 Horizontal Structure 17
3 Harmony and Related Numerology 31
4 Ratios and Musical Intervals 45
5 Logarithms and Musical Intervals 53
6 Chromatic Scales 61
7 Octave Identification and Modular Arithmetic 69
8 Algebraic Properties of the Integers 85
9 The Integers as Intervals 95
10 Timbre and Periodic Functions 103
11 The Rational Numbers as Musical Intervals 123
12 Tuning the Scale to Obtain Rational Intervals 137
Bibliography 147
Index 149
vii