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  2. Generalized musical intervals and transformations

Generalized musical intervals and transformations

David Lewin 2007 © Oxford University Press
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ISBN(s)
  • 9780195317138 (hardcover)
  • 9780199759941 (paper)
  • 9780199890194 (ebook)
Subject
  • Music & Musicology
Citable Link

  • Table of Contents

  • Reviews

  • Stats

  • Frontmatter
  • Foreword by Edward Gollin (page ix)
  • Preface (page xiii)
  • Acknowledgments (page xxvii)
  • Introduction (page xxix)
  • 1. Mathematical Preliminaries (page 1)
  • 2. Generalized Interval Systems (1): Preliminary Examples and Definition (page 16)
  • 3. Generalized Interval Systems (2): Formal Features (page 31)
  • 4. Generalized Interval Systems (3): A Non-Commutative GIS; Some Timbral GIS models (page 60)
  • 5. Generalized Set Theory (1): Interval Functions; Canonical Groups and Canonical Equivalence; Embedding Functions (page 88)
  • 6. Generalized Set Theory (2): The Injection Function (page 123)
  • 7. Transformation Graphs and Networks (1): Intervals and Transpositions (page 157)
  • 8. Transformation Graphs and Networks (2): Non-Intervallic Transformations (page 175)
  • 9. Transformation Graphs and Networks (3): Formalities (page 193)
  • 10. Transformation Graphs and Networks (4): Some Further Analyses (page 220)
  • 11. Appendix A: Melodic and Harmonic GIS Structures; Some Notes on the History of Tonal Theory (page 245)
  • 12. Appendix B: Non-Commutative Octatonic GIS Structures; More on Simply Transitive Groups (page 251)
  • Index (page 255)
Reviews
Journal AbbreviationLabelURL
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
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