• 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

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.

Generalized Musical Intervals and Transformations 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.