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UW-Eau Claire faculty members release mathematics and music book

April 15, 2013
Dr. James Walker
Dr. Gary Don
EAU CLAIRE — Two University of Wisconsin-Eau Claire faculty members recently released a book titled "Mathematics and Music: Composition, Perception, and Performance."

The book is the result of a five-year interdisciplinary collaboration between Dr. Gary Don, associate professor of music and theatre arts, and Dr. James Walker, professor of mathematics.

Throughout the book, Walker and Don show the connection between two seemingly unrelated fields: mathematics and music. This relationship dates back to the fifth century B.C., when Pythagoras, a mathematician and music theorist, used mathematics to describe fundamental musical patterns. By exploring the links between these areas of study, the book aims to help students deepen their understanding of music through mathematics.

"Music is an area that almost everyone loves and it provides an inherently interesting area to look for abstract patterning," Walker said. "In fact, the mathematical techniques that I study (harmonic analysis) correspond very well to what our ears and brains do when we listen to music. I have found that these mathematical techniques are a great aid in analyzing and appreciating the musical sounds that we hear."

Don added that the connection is important for mathematicians, as it is a clear demonstration of the relevance of their field.

According to Walker, the book covers five key areas: the mathematics of musical scales; how pitches and overtones can be displayed graphically and how this aids interpretation of musical performance; how rhythm sequences can be displayed graphically and how this relates to rhythms used throughout the world's music; how typical chord changes can be related to each other in a geometric way (which shows the underlying musical logic behind classical and popular music); and how mathematics is used in audio synthesis for creating new music.

The book will be used as the official textbook for the UW-Eau Claire course "Math 307: Mathematics and Music." The three-credit, online summer class was created as a result of Don's and Walker's collaborative research, and follows closely the topics in the book. The course helps students analyze the techniques behind their own favorites in music. A supplementary website can help students access even more content, including videos, audio tracks and software.

The research that initiated the development of the book was featured in the January 2010 issue of the prestigious mathematics journal Notices of the American Mathematical Society. More information on their paper, "Music: Broken Symmetry, Geometry, and Complexity," can be found in a related UW-Eau Claire news release from 2010. Visit Walker's "Mathematics and Music" YouTube page to view spectrogram videos of a variety of musical pieces.

Don said that he has been interested in both of these disciplines since he was an undergraduate student. An opportunity early in his career at UW-Eau Claire allowed him to pursue these interests through student-faculty collaboration and later through his work with Walker.

"A student-faculty collaborative research project in my first year here allowed me to continue this work with a student with interests and abilities in both mathematics and music," Don said. "This project led to the collaborative work with Jim Walker, and it has been very rewarding to see the additional possibilities inherent in this subject."

Walker said they are excited for the book to be released to the public.

"We are both looking forward to seeing how the book is received," he said.

For more information on the Math 307 class, visit the course website. For general inquiries, contact Dr. James Walker at 715-836-4835 or



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