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Tonal Pitch Space$
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Fred Lerdahl

Print publication date: 2005

Print ISBN-13: 9780195178296

Published to Oxford Scholarship Online: May 2008

DOI: 10.1093/acprof:oso/9780195178296.001.0001

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Diatonic Space

Diatonic Space

(p.41) 2 Diatonic Space
Tonal Pitch Space

Fred Lerdahl

Oxford University Press

This chapter introduces and develops the concept of pitch space, beginning with a distinction between tonal and event hierarchies. After a consideration of previous approaches, the fundamental construct of the basic space is proposed. From this construct an algebraic and geometrical model is developed that calculates the cognitive distance in diatonic space of any pitch, chord, or region (key) to any other pitch, chord, or region. The principle of the shortest path is introduced as a means for deriving time-span and prolongational structures. Empirical issues are engaged, including details of quantification, experimental support for the computed distances, connections of the model to psychoacoustics, related problems in neo-Riemannian theory, and the representation of these structures in the brain.

Keywords:   pitch space, tonal hierarchy, basic space, chord, region, cognitive distance, shortest path, psychoacoustics, neo-Riemannian theory

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