This encyclopaedic book proposes a sweeping reformulation of the basic concepts of Western music theory, revealing simple structures underlying a wide range of practices from the Renaissance to contemporary pop. Its core innovation is a collection of simple geometrical models describing the implicit knowledge governing a broad range of music-making, much as the theory of grammar describes principles that tacitly guide our speaking and writing. Each of its central chapters re-examines a basic music-theoretical concept such as voice leading, repetition, nonharmonic tones, the origins of tonal harmony, the grammar of tonal harmony, modulation, and melody. These are flanked by two largely analytical chapters on rock harmony and Beethoven. Wide-ranging in scope, and with almost 700 musical examples from the Middle Ages to the present day, An Owner's Manual weaves philosophy, mathematics, statistics, and computational analysis into a new and truly twenty-first century theory of music.
Lots to digest here, full of fascinating music theory ideas, and written very accessibly. I didn't find the spiral diagrams to be particularly helpful though, but I understand they're a bit of a compromise resulting from smooshing a higher-dimensional structure into two dimensions. Still, intriguing book that I will enjoy rereading. (May write a more extensive review later, but too lazy right now.)
This is the best book I've ever found that tries to recreate what algorithms are going on inside of composers' heads as they compose. My only complaint is that the book isn't nearly as constructive as I might hope!