Generalized Musical Intervals and Transformations

Contents

• Foreword by Edward Gollin
• Preface
• Acknowledgments
• Introduction
• 1. Mathematical Preliminaries
• 2. Generalized Interval Systems (1): Preliminary Examples and Definition
• 3. Generalized Interval Systems (2): Formal Features
• 4. Generalized Interval Systems (3): A Non-Commutative GIS
• Some Timbral GIS Models
• 5. Generalized Set Theory (1): Interval Functions
• Canonical Groups and Canonical Equivalence
• Embedding Functions
• 6. Generalized Set Theory (2): The Injection Function
• 7. Transformation Graphs and Networks (1): Intervals and Transpositions
• 8. Transformation Graphs and Networks (2): Non-Intervallic Transformations
• 9. Transformation Graphs and Networks (3): Formalities
• 10. Transformation Graphs and Networks (4): Some Further Analyses
• Appendix A: Melodic and Harmonic GIS Structures
• Some Notes on the History of Tonal Theory
• Appendix B: Non-Commutative Octatonic GIS Structures
• More on Simply Transitive Groups
• Index