Generalized Musical Intervals and Transformations

David Lewin's Generalized Musical Intervals and Transformations is 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 an...

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David Lewin's Generalized Musical Intervals and Transformations is 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almost twenty years after GMIT's initial publication, this Oxford University Press edition features a previously unpublished preface by David Lewin, as well as a foreword by Edward Gollin contextualizing the work's significance for the current field of music theory.

Over his 42-year teaching career, David Lewin (1933-2003) taught composition, with an increasing focus on music theory, at the University of California at Berkeley, the State University of New York at Stony Brook, Yale University, and finally at Harvard University. Among his music-theoretic writings are many articles and books, including Musical Form and Transformation (Yale, 1...

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Over his 42-year teaching career, David Lewin (1933-2003) taught composition, with an increasing focus on music theory, at the University of California at Berkeley, the State University of New York at Stony Brook, Yale University, and finally at Harvard University. Among his music-theoretic writings are many articles and books, including Musical Form and Transformation (Yale, 1993), which received an ASCAP Deems Taylor Award, and Studies in Music with Text (posthumous, Oxford 2006). He was the recipient of honorary doctoral degrees from the University of Chicago, the New England Conservatory of Music, and the Marc Bloch University, Strasbourg, France, for his work in music theory.

Foreword by Edward Gollin
Preface
Acknowledgments
Introduction
1. Mathematical Preliminaries
2. Generalized Interval Systems (1): Preliminary Examples and Definition
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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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