A geometry of music: harmony and counterpoint in the extended common practice

In this groundbreaking book, Tymoczko uses contemporary geometry to provide anew framework for thinking about music, one that emphasizes the commonalitiesamong styles from Medieval polyphony to contemporary jazz. INDICE: 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 Transpositionand 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 leadingbetween 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.; 7.2Voice 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 'Drömmesyn,' (Vision), Op. 62 no. 5 (1895).; B. Debussy's 'Fetes' (1899).

• ISBN: 978-0-19-533667-2
• Editorial: Oxford University
• Encuadernacion: Cartoné
• Páginas: 432
• Fecha Publicación: 01/04/2011
• Nº Volúmenes: 1
• Idioma: Inglés