Generalized Musical Intervals and Transformations [Paperback]

David Lewin'sGeneralized Musical Intervals and Transformationsis recognized as the seminal work paving the way for current studies in mathematical and systematic approaches to music analysis. Lewin, one of the 20th century's most prominent figures in music theory, pushes the boundaries of the study of pitch-structure beyond its conception as a static system for classifying and inter-relating chords and sets. Known by most music theorists as GMIT , the book is by far the most significant contribution to the field of systematic music theory in the last half-century, generating the framework for the transformational theory movement. Appearing almost twenty years after GMIT's initial publication, this Oxford University Press edition features a previously unpublished preface by David Lewin, as well as a foreword by Edward Gollin contextualizing the work's significance for the current field of music theory.

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

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