**Mathematical World**

Volume: 28;
2009;
161 pp;
Softcover

MSC: Primary 00;

Print ISBN: 978-0-8218-4873-9

Product Code: MAWRLD/28

List Price: $37.00

AMS Member Price: $29.60

MAA member Price: $33.30

**Electronic ISBN: 978-1-4704-1196-1
Product Code: MAWRLD/28.E**

List Price: $37.00

AMS Member Price: $29.60

MAA member Price: $33.30

#### Supplemental Materials

# Mathematics and Music

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*David Wright*

Many people intuitively sense that there is a connection between
mathematics and music. If nothing else, both involve counting. There
is, of course, much more to the association. David Wright's book is an
investigation of the interrelationships between mathematics and music,
reviewing the needed background concepts in each subject as they are
encountered. Along the way, readers will augment their understanding of
both mathematics and music.

The text explores the common foundations of the two subjects, which
are developed side by side. Musical and mathematical notions are
brought together, such as scales and modular arithmetic, intervals and
logarithms, tone and trigonometry, and timbre and harmonic analysis.
When possible, discussions of musical and mathematical notions are
directly interwoven. Occasionally the discourse dwells for a while on
one subject and not the other, but eventually the connection is
established, making this an integrative treatment of the two
subjects.

The book is a text for a freshman level college course suitable for
musically inclined or mathematically inclined students, with the
intent of breaking down any apprehension that either group might have
for the other subject. Exercises are given at the end of each
chapter. The mathematical prerequisites are a high-school level
familiarity with algebra, trigonometry, functions, and graphs.
Musically, the student should have had some exposure to musical
staffs, standard clefs, and key signatures, though all of these are
explained in the text.

#### Readership

Undergraduate students interested in math and/or music.

#### Reviews & Endorsements

This book is written with a different spirit. It reviews some basic concepts in both mathematics and music from the very beginning, presuming no background in either of these fields. ...Wright has packed an ambitious overview into 150 printed pages.

-- Springer Science & Business

All the necessary mathematical and musical theory and notations are introduced as they are needed, and the book is clearly illustrated, easy to read and learn from, and certainly to be recommended. ...the author's treatment of the subject is down to earth and realistic, and I certainly plan to use the book in future courses that I teach on the subject.

-- LMS Newsletter

In classroom use, this polished book gives mathematics students a demystification of music theory's prerequisites and music students a motivated selective review of high school mathematics.

-- CHOICE Magazine

#### Table of Contents

# Table of Contents

## Mathematics and Music

- Cover Cover11 free
- Title page iii5 free
- About the author v7 free
- Contents vii9 free
- Introduction ix11 free
- Basic mathematical and musical concepts 117 free
- Horizontal structure 1733
- Harmony and related numerology 3147
- Ratios and musical intervals 4561
- Logarithms and musical intervals 5369
- Chromatic scales 6177
- Octave identification and modular arithmetic 6985
- Algebraic properties of the integers 85101
- The integers as intervals 95111
- Timbre and periodic functions 103119
- The rational numbers as musical intervals 123139
- Tuning the scale to obtain rational intervals 137153
- Bibliography 147163
- Index 149165 free
- Back Cover Back Cover1178