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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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Paths in Pitch Space

Paths in Pitch Space

Chapter:
(p.89) 3 Paths in Pitch Space
Source:
Tonal Pitch Space
Author(s):

Fred Lerdahl

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195178296.003.0003

Using geometrical projections from the distance algorithms in the previous chapter, this chapter develops the notion of pitch-space paths in sequences of events at multiple prolongational levels. Pitch-space paths are traced in two Chopin preludes through contrasting spatial representations, including regional, chordal/regional, scale-degree, and pitch-class/chordal spaces. The exposition moves to the treatment of regional prolongations and to parallel mixture, the latter causing a collapse in regional space, with examples taken from Schubert and Wagner. An extended discussion ensues of narrative paths in Wagner's Parsifal. The chapter concludes with historical references to pitch-space paths in the music of Schubert and Schumann, and to an analogy to semantic paths in linguistic theory.

Keywords:   prolongational level, parallel mixture, chordal space, pitch-class, scale-degree, regional space, regional prolongations, Parsifal, semantic paths

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