NB. I was sent this book as a review copy.

Music by the numbers leads us on a journey, as stated in the title, from Pythagoras to Schoenberg. In many ways the endpoint is stated early on, giving us clues that a revolution in mathematical thinking about musical scales will be encountered in the early twentieth century. Indeed the journey through musical practice, mathematics, physics and the biology of hearing is woven rather beautifully together, giving the account of our step by step explorations of tonal systems and their links to the physics of vibration. The development of calculus and the triumph of Fourier take as from the somewhat numerological and empiric realms of musical experimentation to the age of a true understanding of timbre – the way different instruments express harmonics and their overtones in different admixtures. A lot of emphasis is placed on the development of scales based on subtly different frequency ratios, which were developed over the years (particularly within European music, non-European music being given only very brief comment) to balance the physical, mathematical and aesthetic qualities of the various possible tunings of instruments.

Through the book it feels like the discussion is building up to the revolution in music in the 20th century, and it is taken in parallel with Einstein’s development of general relativity. Einstein and Schoenberg’s lives are compared, as is the public acceptance of their revolutionary ideas. A strong emphasis is placed on the use of ‘relativity’ in the theories which they developed. What I find most interesting is that with this build up comes a clear message that Eli Maor is not a fan of the music of Schoenberg, even if he can appreciate the revolution which he created.

I do very much like the way Maor balances the interplay between mathematics, physics and musical theory, and what I thought might feel contrived, actually creates a compelling picture of the development of an art-form which, while we understand it well mathematically, physically and even physiologically, we are perhaps further from understanding it psychologically.

Though it is not within the scope of the book, and as it is never intended to be encyclopedic, I would definitely like to know more about the other musical scales which have been developed in other cultures. The ubiquity of music in culture, dating back at least 35,000 years is mentioned, and I think that the diversity of musical appreciation which has exploded over this time is something that I would like to explore now.

If I have one contention about the book, it is that in the last section, in looking forward to future developments of physics and music (leading on from Einstein and Schoenberg’s work), there is a brief discussion of string theory, which, while more or less right, has some mistakes which may raise the hackles of other string theorists who happen upon this book. Such criticisms should not however detract from the rest of the work which I found fascinating and very enjoyable to read.

All this being said, I think that anyone with an interest in music and a reasonable memory of high school mathematics should find the book a really interesting exploration of the subtleties in mathematical developments which have driven something which we mostly think of as an experimental, creative pursuit to express emotion through the invisible movement of pressure waves in the air.

I leave you here with the relativistic music of Schoenberg who, as you will discover if you read the book, overturned two millennia of musical theory to create an art form outside of the realms of what was previously thought necessary for beautiful acoustic expression. Let me know in the comments your thoughts on the aesthetic nature of what he produced. I happen to disagree with Maor on this one.

Book reviews – MathemafricaJune 2, 2018 at 11:33 am[…] Music by the Numbers, From Pythagoras to Schoenberg – By Eli Maor, a review […]