Tonal Pitch Space
Building on the foundation of Lerdahl and Jackendoff's influential A Generative Theory of Tonal Music, this volume presents a multidimensional model of diatonic and chromatic spaces that quantifies listeners' intuitions of the relative distances of pitches, chords, and keys from a given tonic. The model is employed to assign prolongational structure, represent paths through the space, and compute patterns of tension and attraction as musical events unfold, thereby providing a partial basis for understanding musical narration, expectation, and expression. Conceived as both a music-theoretic treatise and a contribution to the cognitive science of music, this book will be of interest to music theorists, musicologists, composers, computer musicians, and cognitive psychologists.
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PATHS IN PITCH SPACE
TONAL TENSION AND ATTRACTION
CHROMATIC TONAL SPACES
PROLONGATIONS IN CHROMATIC SPACES
adjacent atonal attraction rule basic space bass beat branching cadence cadential chapter chord distance rule chordal level chordal space chordal/regional space chromatic circle of fifths cognitive context cycle diatonic collection diatonic space dissonance dominant downbeat of bar fifth function global GTTM GTTM's harmonic attraction hexatonic hexatonic scale hierarchical tension interpretation intervals leading tones leading-tone listeners major major second melodic attraction metrical attractions minor triad minor-third motion motive move musical surface neighboring nonharmonic tones notation octatonic collection octatonic scale octave parallel Parsifal pattern pitch pitch-space pivot pivot-region preferred Prelude progression prolongational analysis prolongational level prolongational structure psychoacoustic realized regional space representation root salience scale degree schema Schoenberg semitone sequence seventh shortest path shown in Figure soprano spatial stable step stepwise strong prolongation superordinate third phrase time-span level time-span reduction tonal music tonic Tonnetz transpositional Tristan chord voice leading voice-leading weak prolongation whole-tone