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Generalized musical intervals and transformations
David Lewin
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Frontmatter
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Foreword by Edward Gollin (page ix)
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Preface (page xiii)
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Acknowledgments (page xxvii)
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Introduction (page xxix)
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1. Mathematical Preliminaries (page 1)
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2. Generalized Interval Systems (1): Preliminary Examples and Definition (page 16)
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3. Generalized Interval Systems (2): Formal Features (page 31)
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4. Generalized Interval Systems (3): A Non-Commutative GIS; Some Timbral GIS models (page 60)
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5. Generalized Set Theory (1): Interval Functions; Canonical Groups and Canonical Equivalence; Embedding Functions (page 88)
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6. Generalized Set Theory (2): The Injection Function (page 123)
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7. Transformation Graphs and Networks (1): Intervals and Transpositions (page 157)
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8. Transformation Graphs and Networks (2): Non-Intervallic Transformations (page 175)
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9. Transformation Graphs and Networks (3): Formalities (page 193)
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10. Transformation Graphs and Networks (4): Some Further Analyses (page 220)
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11. Appendix A: Melodic and Harmonic GIS Structures; Some Notes on the History of Tonal Theory (page 245)
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12. Appendix B: Non-Commutative Octatonic GIS Structures; More on Simply Transitive Groups (page 251)
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Index (page 255)
Journal Abbreviation | Label | URL |
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JMT | 50.1 (Spring 2006): 111-127 | http://www.jstor.org/stable/27639416 |
INT | 21 (2007): 155-190 | http://www.jstor.org/stable/40214038 |
JAMS | 62.1 (Spring 2009): 205-222 | http://www.jstor.org/stable/10.1525/jams.2009.62.1.205 |
Citable Link
Published: 2007
Publisher: Oxford University Press
- 9780199890194 (ebook)
- 9780195317138 (hardcover)
- 9780199759941 (paper)