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almost twenty years after GMIT's initial publication, this Oxford University Press edition features a previously unpublished preface by David Lewin, as well as a foreword by Edward Gollin contextualizing the work's significance for the current field of music theory.

Table of 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

About the Author :
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.

Review :
"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 "David Lewin's great gift was his ability to connect sophisticated mathematics to musical experience in ways that were deeply compelling, never losing sight of either the music, or the experience. Together these two volumes display both his theoretical brilliance and his sensitivity to the individuality of musical works. Most significantly, they are imbued with his unflagging dedication to and abiding love for the acts of making and understanding music."--Andrew Mead, Professor of Music, University of Michigan "Lewin was a revolutionary thinker, and GMIT is a revolutionary book."--Journal of the American Musicological Society "David Lewin's work is among the most important on music theory in the twentieth century. Through some of the examples of practical applications, Generalized Musical Intervals and Transformations was the inception and theoretical basis of the 'Neo-Riemannian' strand of tonal music theory. In addition, its transformational network analysis paradigm has become part of every music theorist's standard repertory for analysis, and has since been extended by Lewin himself, Klumpenhouwer, Lambert, Stoecker, Headlam, Rahn, and Mazzola among many others. The analytical essays in Musical Form and Transformations illustrate the new analytical paradigm Lewin introduced in Generalized Musical Intervals and Transformations. These seminal works on music theory are essential reading."-John Rahn, Professor of Music, University of Washington "While David Lewin's thought had been animated for decades by some of these books' ideas---the complex significance of interval, the audibility of pitch-class inversional indices, the definition of directed motion more by context than convention---it was their concentrated presentation here that enabled many readers to assimilate them as a 'theory.' The result was a shift in the discipline's conception of its methods, even its goals, to the point where imitation of the books (of their imitable aspects) could become a career path. In a renewed encounter with the originals, we are confronted once more by Lewin's intellectual probity, his intense concern with every construction's relation to hearing (which need not mean anything so simple as that every construction is heard), his fastidious eschewal of hype. With these taken as exemplary, the field would change again."--Joseph Dubiel, Professor of Music, Columbia University "A book that has rightly earned its place as one of the most important and highly esteemed of its kind in the last half century or so...This OUP volume makes what truly is a revolutionary theory on the way music works (and not just contemporary music... Bach and Wagner people the opening pages in no small way) available to us now. Put in the work to understand the admittedly often dense (but always lucidly set out) material which Lewin handles so deftly, and the rewards are huge. The technicalities of the book's production, indexing, footnoting, clarity of reproduction of the examples (musical and mathematical), proofing and so on are all just as one would expect from OUP. Unreservedly recommended." --Classical.net