Description
Book SynopsisIn this groundbreaking book, Tymoczko uses contemporary geometry to provide a new framework for thinking about music, one that emphasizes the commonalities among styles from Medieval polyphony to contemporary jazz.
Trade Reviewa tour de force, a rich and suggestive summation of an exciting new perspective, a jumping-off point for further explorations. * Peter Pesic, Times Literary Supplement *
Table of ContentsPREFACE; PART I. THEORY; 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; 2.1 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; 3.1 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; 4.1 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; 5.1 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; 6.1 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; 7.1 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; 8.1 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; 9.1 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; 10.1 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
