Item description for The Topos of Music: Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola, Stefan Goller & Stefan Muller...
The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Tne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Tne 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.
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Est. Packaging Dimensions: Length: 2.25" Width: 7" Height: 9.5" Weight: 6.2 lbs.
Release Date Jan 17, 2003
Publisher Birkhäuser Basel
ISBN 3764357312 ISBN13 9783764357313
Availability 0 units.
More About Guerino Mazzola, Stefan Goller & Stefan Muller
Reviews - What do customers think about The Topos of Music: Geometric Logic of Concepts, Theory, and Performance?
The shotgun approach to deep musical structure Jun 24, 2008
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.