Название:The Topos of Music: Geometric Logic of Concepts, Theory, and Performance
Страниц: 1363 pages
Размер: 16,3 MB
The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Tone. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Tone 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.