Customer Reviews

The Topos of Music: Geometric Logic of Concepts, Theory, and Performance

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Category theory meets music meets cognitive theory. There's a huge conceit here, that the most powerful tools of mathematics can bring out further understanding of music. And I was unsure of it to start. But there's a payout here. The math illuminates musical structures in an elegant and deep manner. Along the way there's nearly as much to say about brain function and cognition as music. (Though they're clearly closely related.)

I'd say that the book's audience is necessarily limited, but that for those who can safely approach the book, it's nothing less than a remarkable achievement. I liken it to when, as a physics graduate student, I first encountered Arnold's Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics). Mathematical elegance applied to the world.

I admit, I am a mathematician first and a musician second. I am deeply distrustful of mathematics being applied in places where it is not appropriate, and I am also distrustful of musical theorists who do not compose or perform. But Guerino Mazzola has tested his theories by writing computer programs that write compositions based on his theories. I was pleasantly surprised. I could not tell that what I was listening to was written by a computer. But my judgements are unrefined. I would like to hear other people's opinions, particularly composers. If you don't know the math, is the music good? I'll answer my own question "Will it make composers better?" by saying of course not. I would never encourage an aspiring composer to learn this, unless he or she was truly interested in it. But for those composers who wish to use these techniques, and are technically capapable of utilizing them, how useful will they be? I would like to know the future.

A pompous and confused application of category theory to music.

The math is advanced, and so is the obscurity of the encyclopedic and voluminous prose. This is a pity, since Mazzola makes a number of fascinating and deep observations. Fighting through the dense, barely edited, text to find these gems, however, is an activity best left to the most masochistic of PhD candidates in music theory, especially given the heft and price of the book.