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Book Review

Music by the Numbers, From Pythagoras to Schoenberg

Eli Maor


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Music by the Numbers, From Pythagoras to Schoenberg
Author: Eli Maor
Publisher: Princeton University Press
Published: 2014
ISBN: 978-0-691-17690-1 (hbk); 978-1-400-88989-1 (ebk)
Pages: 176

The First Chapter of this book is available as a pdf document, from: http://assets.press.princeton.edu/chapters/s11250.pdf

In this relatively short book, the author draws a parallel between the history of mathematics and the history of music theory. Besides the obvious and obligatory topics, and a personal selection of the historical periods, there are also a number of side tracks added as curious anecdotes.

Music by the Numbers should interest mathematicians who enjoy classical music (European) as well as musicians who are curious about the mathematics behind music.
Click here for the home page of this book

This remarkable book by Eli Maor presents a detailed report on the connection between music and mathematics. Eli Maor argues that music has influenced maths, at least as much as maths has influenced music.

Maor gives a selection of historical parallels that can be drawn between the evolution of mathematics and music theory. He builds a bridge between Pythagoras, the creator of the mystical concept of Musica universalis, and the mysterious musical tradition of Schoenberg. His main message is that at some point mathematics and physics have abandoned an overall reference system and accepted local reference frames (think of relativity theory and geometry). At about the same time something similar happened in music theory when keys were no longer maintained over a long time but they became local which has resulted in atonality and Schoenberg's twelve-tone theory.

This is my second book from the same publisher. I now understand why Princeton is considered to be such a great University. Only the luckiest and blessed persons happen to visit this place.

I thank my nephew Suchethan, who gifted me this jewel, which I will treasure forever in my library.


  1. An elaborate account of the relationship between music and mathematics is available in Euler's book on music:

    It is well known that Euler was a prolific writer and the greatest mathematician of our times.

  2. An interesting and simpler overview of the relationship between music and mathematics is available from:

  3. You must understand the mathematical model of vibration of a string to appreciate this book (as well as the graphics on its cover).
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