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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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Chromatic Tonal Spacesm

Chromatic Tonal Spacesm

Chapter:
(p.249) 6 Chromatic Tonal Spacesm
Source:
Tonal Pitch Space
Author(s):

Fred Lerdahl

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195178296.003.0006

This chapter extends the diatonic model of Chapter 2 to chromatic spaces that are relevant to the music of the late 19th and early 20th centuries. First, the evolution of pitch space is demonstrated through the collapse of tonal regions to create octatonic and hexatonic structures. The chord distance rule generalizes by means of minor modifications to derive related spaces, such as triadic/octatonic, triadic/hexatonic, whole-tone, and mystic spaces. Further developments include constraints on the form of basic spaces, attractions in chromatic spaces, a procedure for establishing the preferred space in a given context, and a method for measuring interspatial distances. The shape of preferred spaces leads to a metrical analogy, including metrical attractions, as illustrated by a passage in Mozart.

Keywords:   octatonic, hexatonic, chromatic space, mystic spaces, whole-tone, constraints, interspatial distance, metrical attraction

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