A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice
- Author: Tymoczko, Dmitri
a tour de force, a rich and suggestive summation of an exciting new perspective, a jumping-off point for further explorations —
Book
$86.75Out of stock at the UK distributor
Contents
- PREFACE
- PART I. Theory
- 1 Five Components of Tonality
- 1.1 The five features.
- 1.2. Perception and the five features.
- 1.3 Four Claims.
- A. Harmony and counterpoint constrain each other.
- B. Scale, macroharmony, and centricity are independent.
- C. Modulation involves voice leading.
- D. Music can be understood geometrically.
- 1.4 Music, magic, and language.
- 1.5 Outline of the book, and a suggestion for impatient readers.
- 2. Harmony and Voice Leading
- 2.1 Linear pitch space.
- 2.2 Circular pitch-class space.
- 2.3 Transposition and inversion as distance-preserving functions.
- 2.4 Musical objects.
- 2.5 Voice leadings and chord progressions.
- 2.6 Comparing voice leadings.
- 2.7 Voice-leading size.
- 2.8 Near identity.
- 2.9 Harmony and counterpoint revisited.
- 2.10 Acoustic consonance and near-evenness
- 3. The Geometry of Chords
- 3.1 Ordered pitch space.
- 3.2 The Parable of the Ant.
- 3.3 Two-note chord space.
- 3.4 Chord progressions and voice leadings in two-note chord space.
- 3.5 Geometry in analysis.
- 3.6 Harmonic consistency and efficient voice leading.
- 3.7 Pure parallel and pure contrary motion.
- 3.8 Three-dimensional chord space.
- 3.9 Higher-dimensional chord spaces.
- 3.10 Voice leading lattices.
- 3.11 Triads are from Mars, seventh chords are from Venus.
- 3.12 Two musical geometries.
- 3.13 Study guide.
- 4. Scales
- 4.1 A scale is a ruler.
- 4.2 Scale degrees, scalar transposition, scalar inversion.
- 4.3 Evenness and scalar transposition.
- 4.4 Constructing common scales.
- 4.5 Modulation and voice leading.
- 4.6 Voice leading between common scales .
- 4.7 Two examples.
- 4.8 Scalar and interscalar transposition.
- 4.9 Interscalar transposition and voice leading.
- 4.10 Combining interscalar and chromatic transpositions.
- 5. Macroharmony and Centricity
- 5.1 Macroharmony.
- 5.2 Small-gap macroharmony.
- 5.3 Pitch-class circulation.
- 5.4 Modulating the rate of pitch-class circulation.
- 5.5 Macroharmonic consistency.
- 5.6 Centricity.
- 5.7 Where does centricity come from?
- 5.8 Beyond tonal and atonal.
- PART II. History and Analysis
- 6. The Extended Common Practice
- 6.1 Disclaimers.
- 6.2 Two-voice medieval counterpoint.
- 6.3 Triads and the Renaissance.
- 6.4 Functional harmony.
- 6.5 Schumann's Chopin.
- 6.6 Chromaticism.
- 6.7 Twentieth-century scalar music.
- 6.8 The extended common practice.
- 7. Functional Harmony
- 7.1 The thirds-based grammar of elementary tonal harmony.
- 7.2 Voice leading in functional harmony.
- 7.3 Sequences.
- 7.4 Modulation and key distance.
- 7.5 The two lattices.
- 7.6 A challenge from Schenker.
- 8. Chromaticism
- 8.1 Decorative chromaticism.
- 8.2 Generalized augmented sixths.
- 8.3 Brahms and Schoenberg.
- 8.4 Schubert and the major-third system.
- 8.5 Chopin's tesseract.
- 8.6 The Tristan Prelude.
- 8.7 Alternative approaches.
- 8.8 Conclusion
- 9. Scales in Twentieth-Century Music
- 9.1 Three scalar techniques.
- 9.2 Chord-first composition.
- A. Grieg's Drommesyn, (Vision), Op. 62 no. 5 (1895).
- B. Debussy's Fetes (1899).
- C. Michael Nyman's The Mood That Passes Through You (1993).
- 9.3 Scale-first composition.
- A. Debussy's Des pas sur la neige (1910).
- B. Janacek's On an Overgrown Path, Series II, no. 1 (1908).
- C. Shostakovich's Fs minor Prelude and Fugue, Op. 87 (1950).
- D. Reich's New York Counterpoint (1985).
- E. Reich's The Desert Music, movement 1 (1984).
- F. The Who's Can't Explain (1965) and Bob Seger's Turn the Page (1973).
- 9.4 The Subset Technique.
- A. Grieg's Klokkeklang, (Bell Ringing), Op. 54 no. 6 (1891).
- B. Petit Airs, from Stravinsky's Histoire du Soldat (1918).
- C. Reich's City Life (1995).
- D. Stravinsky's Dance of the Adolescents (1913).
- E. The Miles Davis Group's Freedom Jazz Dance (1966).
- 9.5 Conclusion.
- 10. Jazz.
- 10.1 Basic jazz voicings.
- 10.2 From thirds to fourths.
- 10.3 Tritone substitution.
- 10.4 Altered chords and scales.
- 10.5 Bass and upper-voice tritone substitutions.
- 10.6 Polytonality, sidestepping, and playing out.
- 10.7 Bill Evans's Oleo.
- 10.8 Jazz as modernist synthesis.
- CONCLUSION
- APPENDIX A. Measuring voice-leading size
- APPENDIX B. Chord geometry: a technical look.
- APPENDIX C. Discrete voice leading lattices.
- APPENDIX D. The interscalar interval matrix.
- APPENDIX E. Scale, macroharmony, and Lerdahl's basic space.
- APPENDIX F. Some study questions, problems, and activities.
- BIBLIOGRAPHY
- INDEX