1 Theoretical Foundations

2 Diatonic Space

3 Paths in Pitch Space

4 Tonal Tension and Attraction

5 Prolongationl Functions

6 Chromatic Tonal Spacesm

7 Prolongations in Chromatic Spaces

8 Atonal Structures

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.