1 What is Mathematical Music Theory?
 1.1 Historical and Transdisciplinary Anchors
 1.2 Epistemological and Pragmatic Considerations
2 >Classical< MaMuTh-Achievements
 2.1 Wellformed Tone Systems
 2.2 Structure Theory of Consonance and Dissonance
 2.3 Transformation and Voice Leading Parsimony
3 Metalanguage and Internal Logics
 3.1 Transformational Logics
 3.2 The Logics of Projecting
 3.3 Analytical Example: Scriabin’s Study Op. 65 No. 3
1 Introduction
2 Mozart’s Dice Game.
3 Birkhoff’s Aesthetic Measure.
4 Fibonacci Numbers and Bartók.
5 Mazzola’s Mathematical Music Theory.
6 General Aesthetical and Ethical Considerations on Mathematics and Music.
1 Models
 1.1 What Are Models?
 1.2 Modulation
 1.3 Counterpoint
 1.4 Performance
2 Concepts
 2.1 Generalization of Common Structures
 2.2 Forms
 2.3 Conceptual Galois Theory
 2.4 Denotators
 2.5 The RUBATO Enterprise
3 Local and Global Compositions
 3.1 Categories of Local Compositions
 3.2 Finite Completeness
 3.3 Categories of Global Compositions
 3.4 Grothendieck Topology and Cohomology
4 Classification
 4.1 Enumeration Theory
 4.2 Standard Objects
 4.3 Global Compositions from Coefficient Systems
 4.4 Orbit Spaces and Classifying Schemes
5 Towards Grand Unification
 5.1 An Isomorphism Between Instances of Harmony and Counterpoint
 5.2 Conclusion and Preview
1 Introduction
2 Form Semiotics
3 The Category of Form Semiotics
4 Galois Correspondence of Form Semiotics
1 Introduction
2 >>Encylospace<< and Universal Concept Formats
3 Forms
4 Denotators
5 Local Compositions
6 Morphisms of Local Compositions
7 Examples of Forms, Denotators and Local Compositions
 7.1 Modules in Musicology
 7.2 Examples of Local Compositions
8 The Form Pianoscore and the Denotator
Träumerei
9 Examples for Morphisms of Local Compositions
 9.1 Example: Transposition (Key Change)
 9.2 Example: Inversion with Retrograde
10 Epilogue
1 Introduction
2 Related Work
3 Gesture Spaces
 3.1 Symbolic and Physical Gesture Curves
 3.2 Towards Calculation of Physical Gesture Curves
4 Construction of Symbolic Gesture Curves
 4.1 Fingers Moving at Infinite Speed
 4.2 Curve Subdivision and Construction
 4.3 Freezing a Symbolic Gesture Curve
5 Results
6 Conclusions and Future Work
7 Acknowledgements
1 Introduction
2 Two Basic Requirements
3 Complex Shape Generation
4 Object-Oriented Theory of Geometry
5 Transfer
6 Wreath Products
7 Mathematical Theory of Transfer
8 Theory of Gestalt
9  Shape Generation by Group Extensions
10 Algebraic Theory of Inheritance
11 Theory of Relative Motion
12 Serial-Link Manipulators
13 Musical Modulation
14 Recoverability
15 Theory of Symmetry-Breaking
16 New Foundations to Geometry
17 Rigorous Theory of Aesthetics
18 Inferred Starting States
19 Musical Meter
20 Complex Shape
21 Theory of Musical Composition
1 Introduction
2 Enumeration of Non-Isomorphic Mosaics
3 Enumeration of Non-Isomorphic Canons
4 Enumeration of Rhythmic Tiling Canons
5 Some Results on Regular Complementary Canons of Maximal Category
1 Introductory remarks on the role of group theory in music
2 The Minkowski-Hajós Problem
3 List of Hajós groups
4 Conclusion
5 Aknowledgements
1 What Is this All About ? Paving the Way
 1.1 Rhythmic Canons and Tiling
 1.2 Loops and Lines
 1.3 Aperiodic Canons
2 Older Results
 2.1 Why Infinite Tiles are Less Interesting
 2.2 Repetition
 2.3 Affine Transformation within a Fixed Period
 2.4 Hajós groups and Vuza canons
 2.5 Reduction
 2.6 Equirepartition
3 Recent Results
 3.1 Around Cyclotomic Polynomials
4 Polyrhythmic Canons and Future Results
 4.1 Johnsons’s Question and the Number 15
 4.2 A Tiny Step in an Unexpected Direction
 4.3 Prospects
1 Introduction
2 The >>Rhythmic Oddity Property<<
3 Construction of asymmetric pairs
4 Counting the solutions
5 Results
1 Performance Grammars
2 Analytical Stemmas
3 Consequence for the choice of Statistical Models