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

Guerino Mazzola (Author)

Book Description

Publication Date: January 17, 2003 | ISBN-10: 3764357312 | ISBN-13: 978-3764357313 | Edition: 1

The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Töne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Töne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory of musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples.

Editorial Reviews

Review

Topos of Music is an extensive and elaborate body of mathematical investigations into music and involves several and ontologically different levels of musical description. Albeit the author Guerino Mazzola lists 17 contributors and 2 collaborators, the book should be characterized as a monograph. Large portions of the content represent original research of Mazzola himself, and the material from other work is exposed from Mazzola's point of view and is well referenced. The preface preintimates an intended double meaning of the term topos in the title. On the one hand, it provides a mathematical anchor, which is programmatic for the entire approach: the concept of a cartesian closed category with a subobject classifier. (...) Zentralblatt MATH

Product Details

• Hardcover: 1335 pages
• Publisher: Birkhäuser Basel; 1 edition (January 17, 2003)
• Language: English
• ISBN-10: 3764357312
• ISBN-13: 978-3764357313
• Product Dimensions: 10 x 7.2 x 2.4 inches
• Shipping Weight: 6.3 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,923,710 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

4 of 5 people found the following review helpful:

5.0 out of 5 stars A massive and massively impressive work, February 16, 2010

By 

Michael A. Duvernois (Minneapolis, MN United States) - See all my reviews
(TOP 500 REVIEWER)    (REAL NAME)   

This review is from: The Topos of Music: Geometric Logic of Concepts, Theory, and Performance (Hardcover)

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.

0 of 1 people found the following review helpful:

5.0 out of 5 stars Will it make composers compose better?, April 14, 2011

By 

Andrew J Young - See all my reviews

This review is from: The Topos of Music: Geometric Logic of Concepts, Theory, and Performance (Hardcover)

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.

8 of 21 people found the following review helpful:

2.0 out of 5 stars The shotgun approach to deep musical structure, June 24, 2008

By 

David Stutz (Seattle, WA USA) - See all my reviews
(REAL NAME)   

This review is from: The Topos of Music: Geometric Logic of Concepts, Theory, and Performance (Hardcover)

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.