Name: Mathematics and music
ISBN: 9780821848739

Mathematics and music

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.

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RochusDec 2024

There are many with various mathematical depth:

- Fauvel et al., Music and Mathematics - From Pythagoras to Fractals, 2003, Oxford UP

- Loy, Musimatics Volume 1, 2006 MIT Press

- Tymoczko, A Geometry of Music, 2011, Oxford UP

- Walker, Mathematics and Music, 2013, CRC Press

- Toussaint, The Geometry of Musical Rhythm, 2013, CRC Press

- Chew, Mathematical and Computational Modeling of Tonality, 2014, Springer

- Hook, Exploring Musical Spaces, 2023, Oxford UP

From my point of view, all titles can be appreciated by non-musicians with mathematical background (though I'm an engineer, not a mathematician, and very much involved with non-classical music). But for your specific requirement, maybe Loy is suited, but personally I consider the later books more interesting, especially Tymoczko and Hook. Book recommendations are always very subjective.

Also note that the music theory commonly taught at high schools and universities is barely able to describe music, or only a small fraction of it. And only a fraction of this theory has a mathematical fundament. Most of it is just a heuristic projection of existing music, only useful for recognizing and classifying elements, and not for deriving new music. In recent years, however, new theories have emerged that allow for both a more formal and a more practical approach.

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RochusFeb 2022

> Are the people good at one also good at other? do mathematicians understand musical theory better than those that have no background in math

Music and music theory are two different things. A person who is an expert in music theory is not necessarily a good musician and vice versa. There are approaches to music theory based on mathematics (see book list below); here at the latest, your assumption is likely to be correct, but hardly in general.

Book list:

Mathematics and Music - Composition, Perception, and Performance

Musimathics Volume 1 and 2

Music and Mathematics - From Pythagoras to Fractals

Mathematical and Computational Modeling of Tonality - Theory and Applications

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ngneerSep 2016

The interested reader is referred to "Mathematics and Music" by David Wright, published by the American Mathematical Society. The realization that the circle of fifths is really there because 5 and 7 (aka -5) are co-prime to 12 was worth the entire thing! Together with 1 and 11 (aka -1) they generate the group Z_{n} for n = 12...

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RodMar 2009

These books are also interesting (and require no more than elementary math):

Mathematics and Music (by David Wright) http://www.math.wustl.edu/~wright/Math109/00Book

Theory and Techniques of Electronic Music http://crca.ucsd.edu/~msp/techniques.htm

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kmillJan 2020

I know you've been in the music business for a few hundred years, Josquin, but there's no need to be so harsh about this undergrad poster! From what I could figure, it's something like a final project for a class on Mathematics and Music at UW Eau Claire. The background material on transformations of sets of pitch classes is in the course textbook. (This doesn't take away from all the citations you helpfully provided, though.)

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