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, andStudies 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 hiswork in music theory.

"Generalized Musical Intervals and Transformations, David Lewin's masterpiece, has prompted a twenty-year efflorescence in the field of mathematical and systematic music theory. GMIT leads readers to the head of a series of distinct paths, suggests by example where each path leads, and leaves readers to their own explorations. Many music theorists now spend their careers working out different aspects of the vision presented here; there is plenty and enough to go around."-Richard L. Cohn, Battell Professor of the Theory of Music, Yale University

• by Ed Gollin: Foreword by David Lewin: 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-communicative GIS; Some Timbral GIS models 5: Generalized Set Theory (1): Interval Functions; Canonical Groups and Canonical Equivalence 6: Generalized Set Theory (2): The Interjection 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 11: Appendix A: Melodic and Harmonic GIS Structure; Some Notes on the History of Tonal Theory 12: Appendix B: Non-Communicative 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, andStudies 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 hiswork in music theory.

"Generalized Musical Intervals and Transformations, David Lewin's masterpiece, has prompted a twenty-year efflorescence in the field of mathematical and systematic music theory. GMIT leads readers to the head of a series of distinct paths, suggests by example where each path leads, and leaves readers to their own explorations. Many music theorists now spend their careers working out different aspects of the vision presented here; there is plenty and enough to go around."-Richard L. Cohn, Battell Professor of the Theory of Music, Yale University

• by Ed Gollin: Foreword by David Lewin: 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-communicative GIS; Some Timbral GIS models 5: Generalized Set Theory (1): Interval Functions; Canonical Groups and Canonical Equivalence 6: Generalized Set Theory (2): The Interjection 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 11: Appendix A: Melodic and Harmonic GIS Structure; Some Notes on the History of Tonal Theory 12: Appendix B: Non-Communicative 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, andStudies 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 hiswork in music theory.

"Generalized Musical Intervals and Transformations, David Lewin's masterpiece, has prompted a twenty-year efflorescence in the field of mathematical and systematic music theory. GMIT leads readers to the head of a series of distinct paths, suggests by example where each path leads, and leaves readers to their own explorations. Many music theorists now spend their careers working out different aspects of the vision presented here; there is plenty and enough to go around."-Richard L. Cohn, Battell Professor of the Theory of Music, Yale University

• by Ed Gollin: Foreword by David Lewin: 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-communicative GIS; Some Timbral GIS models 5: Generalized Set Theory (1): Interval Functions; Canonical Groups and Canonical Equivalence 6: Generalized Set Theory (2): The Interjection 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 11: Appendix A: Melodic and Harmonic GIS Structure; Some Notes on the History of Tonal Theory 12: Appendix B: Non-Communicative Octatonic GIS Structures; More on Simply Transitive Groups Index