The Topos of Music: Geometric Logic of Concepts, Theory, and Performance, Band 1Springer Science & Business Media, 23.09.2002 - 1335 Seiten 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. |
Inhalt
What is Music About? | 3 |
Topography | 9 |
Musical Ontology | 27 |
Applications | 28 |
Navigation | 39 |
Denotators | 47 |
Local Compositions | 105 |
Symmetries and Morphisms | 135 |
Operator Theory | 773 |
Architecture | 807 |
The RUBETTE Family | 813 |
alptraeumerei | 829 |
Performance Experiments | 833 |
Statistics of Analysis and Performance | 853 |
Differential Operators and Regression | 871 |
Principles of Music Critique | 905 |
Yoneda Perspectives | 175 |
Paradigmatic Classification | 191 |
Orbits | 203 |
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 |
rubato | 457 |
Motif Gestalts | 465 |
Critical Preliminaries | 501 |
source | 505 |
Harmonic Semantics | 529 |
Cadence | 551 |
Modulation | 563 |
Local and Global Performance Transformations | 663 |
Performance Fields | 681 |
Initial Sets and Initial Performances | 695 |
nextrubato | 696 |
Hierarchies and Performance Scores | 711 |
Taxonomy of Expressive Performance | 733 |
performances | 736 |
Performance Grammars | 747 |
audio_files | 752 |
Stemma Theory | 755 |
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 |
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 |
A Conceptual Field | 1053 |
Sets Relations Monoids Groups | 1057 |
Rings and Algebras | 1075 |
E Modules Linear and Affine Transformations | 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 |
Index | 1253 |
1267 | |
1288 | |
1303 | |
1042 | 1313 |
Andere Ausgaben - Alle anzeigen
The Topos of Music: Geometric Logic of Concepts, Theory, and Performance Guerino Mazzola Eingeschränkte Leseprobe - 2012 |
The Topos of Music: Geometric Logic of Concepts, Theory, and Performance, Band 1 Guerino Mazzola Keine Leseprobe verfügbar - 2002 |
The Topos of Music: Geometric Logic of Concepts, Theory, and Performance Guerino Mazzola Keine Leseprobe verfügbar - 2013 |
Häufige Begriffe und Wortgruppen
A-addressed A@RR abstract address change affine functions algebraic ambient space analysis appendix approach arrows automorphism basic bijection canonical chapter charts chords classification colimit commutative commutative diagram concept construction coordinates corresponding defined definition denotators diagram discussion dodecaphonic dominance elements endomorphisms Euler example fact fiber product figure finite functor geometric germ gestalt given global compositions Grothendieck topology group action harmonic identifier integer interpretation inversion isomorphism classes lemma linear mathematical means melody metrical module complex monoid morphism motif motives musicological naive natural transformation navigation nerve notation objective local compositions onset ontology orbit paradigm paradigmatic parameters perspective pitch classes pitch space poetical precise predicates projection recursive relation rhythms scale semantic semiosis semiotic sequence simplex sound structure subfunctor Summary surjective symmetry symmetry group theorem tonality topology transformation values Yoneda's lemma zero-addressed