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Zusatztext a tour de force, a rich and suggestive summation of an exciting new perspective, a jumping-off point for further explorations. Informationen zum Autor Dmitri Tymoczko is a composer and music theorist who teaches at Princeton University. His 2006 article "The Geometry of Musical Chords" was the first music theory article published in the 127-year history of Science magazine, and was widely covered in the popular press. His music has been performed by ensembles throughout the country, and he has received a Rhodes scholarship, a Guggenheim fellowship, and numerous other awards. Klappentext In 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. Zusammenfassung In 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. Inhaltsverzeichnis 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 a...
