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Table of Contents
Intro
Preface
Contents
Part I Initial Orientation
1 The Basic Problem of Classification
1.1 Structures
1.2 Relationships
1.3 The Overall Challenge
Part II General Formal Concepts
2 Ontology, Oniontology, and Creativity
2.1 Ontology and Oniontology
2.2 Ontology: Where, Why, and How
2.3 Oniontology: Facts, Processes, and Gestures
2.4 A Short Characterization
2.5 Oniontology for Classification
2.6 Creativity
3 Formal Representation of Musical Structures
3.1 Scientific vs. Creative Value of Classification
3.2 Software-oriented Perspectives
4 Denotators over General Categories
4.1 Formal Definition of Forms
4.2 Formal Definition of Denotators
4.3 The Category of Denotators
4.4 First Examples of Denotators in Theory and Practice
4.4.1 First Examples of Denotators
4.4.1.1 Denotators over the Category Mod
4.4.1.2 Denotators over the Category Digraph
4.4.2 Hyperdenotators
4.4.2.1 Hyperdenotators over the Category Mod
4.4.2.2 Hyperdenotators over the Category Digraph
4.4.3 Gestures over Topological Categories
5 Composition Denotators and Classification
5.1 Some Classical Composition Denotators
5.2 The Role of Classification in Tonal Modulation Theory
5.3 Modulations in Beethoven's op. 106
6 Gestural Denotators: A First Overview
6.1 The Symmetric Concept Architecture between Compositions and Gestures
6.2 The Role of Yoneda's Lemma
6.3 Software Perspectives
7 The Escher Theorem for Compositions and Gestures
7.1 The Escher Theorem and Escher Categories
7.1.1 First Examples
Part III Local Classification
8 Local Composition and Gesture Classification
8.1 Classification of Local Compositions
8.1.1 Compositions as Sequences of Module Elements
8.1.2 Eliminating Diagonal Elements
8.1.3 Transforming Sequences to Linear Maps
8.1.4 The Grassmann Scheme for Local Compositions
8.2 Classification Problems for Local Gestures
9 Classification of Chords
10 Motif Classes
10.1 Three Element Motives in Analysis
10.1.1 An Example from Classical Music
10.2 Three Element Motives and an Example of a Melody from this Repertory in the Jazz Composition Synthesis
10.3 A General Algorithm for the Construction of Generic Melodies Composed by Motives of n Elements Each
10.4 Calculation of the Classes of n-element Motives in Z2 12
11 Third Chain Classes
12 Harmony through Third Chains
13 Counterpoint Worlds
14 Strong Interval Dichotomies
15 Microtonal Contrapuntal Theories
15.1 The Category of Strong Dichotomies
15.2 Towers of Strong Dichotomies
16 Dodecaphonic Rows
Part IV Global Classification
17 Global Composition and Gesture Classification
17.1 Why Global Compositions and Gestures
17.1.1 Global Compositions
17.1.1.1 Boulez and Webern
17.1.1.2 Uhde/Wieland and Marek
17.1.1.3 Hoffmann and Kaiser
17.1.1.4 Graeser, Ruwet, and Nattiez
17.1.1.5 Jackendoff and Lerdahl
Preface
Contents
Part I Initial Orientation
1 The Basic Problem of Classification
1.1 Structures
1.2 Relationships
1.3 The Overall Challenge
Part II General Formal Concepts
2 Ontology, Oniontology, and Creativity
2.1 Ontology and Oniontology
2.2 Ontology: Where, Why, and How
2.3 Oniontology: Facts, Processes, and Gestures
2.4 A Short Characterization
2.5 Oniontology for Classification
2.6 Creativity
3 Formal Representation of Musical Structures
3.1 Scientific vs. Creative Value of Classification
3.2 Software-oriented Perspectives
4 Denotators over General Categories
4.1 Formal Definition of Forms
4.2 Formal Definition of Denotators
4.3 The Category of Denotators
4.4 First Examples of Denotators in Theory and Practice
4.4.1 First Examples of Denotators
4.4.1.1 Denotators over the Category Mod
4.4.1.2 Denotators over the Category Digraph
4.4.2 Hyperdenotators
4.4.2.1 Hyperdenotators over the Category Mod
4.4.2.2 Hyperdenotators over the Category Digraph
4.4.3 Gestures over Topological Categories
5 Composition Denotators and Classification
5.1 Some Classical Composition Denotators
5.2 The Role of Classification in Tonal Modulation Theory
5.3 Modulations in Beethoven's op. 106
6 Gestural Denotators: A First Overview
6.1 The Symmetric Concept Architecture between Compositions and Gestures
6.2 The Role of Yoneda's Lemma
6.3 Software Perspectives
7 The Escher Theorem for Compositions and Gestures
7.1 The Escher Theorem and Escher Categories
7.1.1 First Examples
Part III Local Classification
8 Local Composition and Gesture Classification
8.1 Classification of Local Compositions
8.1.1 Compositions as Sequences of Module Elements
8.1.2 Eliminating Diagonal Elements
8.1.3 Transforming Sequences to Linear Maps
8.1.4 The Grassmann Scheme for Local Compositions
8.2 Classification Problems for Local Gestures
9 Classification of Chords
10 Motif Classes
10.1 Three Element Motives in Analysis
10.1.1 An Example from Classical Music
10.2 Three Element Motives and an Example of a Melody from this Repertory in the Jazz Composition Synthesis
10.3 A General Algorithm for the Construction of Generic Melodies Composed by Motives of n Elements Each
10.4 Calculation of the Classes of n-element Motives in Z2 12
11 Third Chain Classes
12 Harmony through Third Chains
13 Counterpoint Worlds
14 Strong Interval Dichotomies
15 Microtonal Contrapuntal Theories
15.1 The Category of Strong Dichotomies
15.2 Towers of Strong Dichotomies
16 Dodecaphonic Rows
Part IV Global Classification
17 Global Composition and Gesture Classification
17.1 Why Global Compositions and Gestures
17.1.1 Global Compositions
17.1.1.1 Boulez and Webern
17.1.1.2 Uhde/Wieland and Marek
17.1.1.3 Hoffmann and Kaiser
17.1.1.4 Graeser, Ruwet, and Nattiez
17.1.1.5 Jackendoff and Lerdahl