The Topos of Music: Geometric Logic of Concepts, Theory, and Performance, Volume 1

Front Cover
Guerino Mazzola
Springer Science & Business Media, Sep 23, 2002 - Mathematics - 1335 pages
2 Reviews
Man kann einen jeden BegrifJ, einen jeden Titel, darunter viele Erkenntnisse gehoren, einen logischen Ort nennen. Immanuel Kant [258, p. B 324] This book's title subject, The Topos of Music, has been chosen to communicate a double message: First, the Greek word "topos" (r01rex; = location, site) alludes to the logical and transcendental location of the concept of music in the sense of Aristotle's [20, 592] and Kant's [258, p. B 324] topic. This view deals with the question of where music is situated as a concept and hence with the underlying ontological problem: What is the type of being and existence of music? The second message is a more technical understanding insofar as the system of musical signs can be associated with the mathematical theory of topoi, which realizes a powerful synthesis of geometric and logical theories. It laid the foundation of a thorough geometrization of logic and has been successful in central issues of algebraic geometry (Grothendieck, Deligne), independence proofs and intuitionistic logic (Cohen, Lawvere, Kripke). But this second message is intimately entwined with the first since the present concept framework of the musical sign system is technically based on topos theory, so the topos of music receives its top os-theoretic foundation. In this perspective, the double message of the book's title in fact condenses to a unified intention: to unite philosophical insight with mathematical explicitness.
  

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User Review  - ztutz - LibraryThing

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 ... Read full review

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A beautiful book. Mazzola has generated a majestic work on the theory of music. Music which stills the savage beast is a resonant phenomenon throughout human history. Why? Because music is much closer to cognition than the author recognizes. This book is more properly a first step to a physically accurate model of cognition.
Res ipsa loquitur
 

Contents

What is Music About?
3
Topography
9
Musical Ontology
23
Models and Experiments in Musicology
29
programs
35
Navigation
39
Denotators
47
Local Compositions
105
Taxonomy of Expressive Performance 733
736
Performance Grammars
747
Stemma Theory
755
Operator Theory
773
Architecture
807
The RUBETTE Family
813
contrapunctus_III
817
Performance Experiments
833

Symmetries and Morphisms
135
Yoneda Perspectives
175
Paradigmatic Classification
191
Orbits
203
sources
258
Topological Specialization
275
Global Compositions
299
Global Perspectives
333
Global Classification
349
Classifying Interpretations
369
Esthetics and Classification
387
Predicates
397
Topoi of Music
427
Visualization Principles
439
Topologies for Rhythm and Motives
453
Motif Gestalts
465
Critical Preliminaries
501
Harmonic Semantics
529
1 rubato
546
Cadence
551
Modulation
563
program
573
Applications
593
Melodic Variation by Arrows
617
Interval Dichotomies as a Contrast
630
Modeling Counterpoint by Local Symmetries
645
Local and Global Performance Transformations
663
performances
665
Performance Fields
681
Initial Sets and Initial Performances
695
Hierarchies and Performance Scores
711
Statistics of Analysis and Performance
853
Differential Operators and Regression
871
Principles of Music Critique
905
Critical Fibers
911
Unfolding Geometry and Logic in Time
933
Local and Global Strategies in Composition
939
The Paradigmatic Discourse on presto
945
Synthesis by Guerino Mazzola
955
ObjectOriented Programming in OpenMusic
967
kuriose_geschichte
972
Historical and Theoretical Prerequisites
993
Estimation of Resolution Parameters
999
The Case of Counterpoint and Harmony
1007
A Common Parameter Spaces
1013
B Auditory Physiology and Psychology
1035
Sets Relations Monoids Groups
1057
Rings and Algebras
1075
E Modules Linear and AffineTransformations
1083
F Algebraic Geometry
1107
G Categories Topoi and Logic
1115
H Complements on General and Algebraic Topology
1145
Complements on Calculus
1153
J Eulers Gradus Function
1165
Two Three and Four Tone Motif Classes
1183
N WellTempered and Just Modulation Steps
1197
O Counterpoint Steps
1211
Bibliography
1221
Leitfaden
1227
Index
1253
Copyright

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