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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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Prolongationl Functions

Prolongationl Functions

(p.193) 5 Prolongationl Functions
Tonal Pitch Space

Fred Lerdahl

Oxford University Press

This chapter elaborates a new approach to tonal and harmonic function. To do this, it establishes a frame of reference; so it first develops a tonic-finding method, based on the principle of the shortest path. The method is illustrated by examples from Beethoven and Wagner. A theory of function as prolongational position is then proposed and illustrated by excerpts from Bach, Schumann, and Wagner. Issues of functionality are considered, including the notion of functional prolongations. With these analytic tools in hand, the discussion moves to the characterization of standard voice-leading and harmonic schemas in the galant and Classical styles. An analysis of a piece by Mendelssohn illustrates the concept of schematic tension.

Keywords:   tonal function, harmonic function, tonic finding, shortest path, prolongation, voice-leading schema, harmonic schemas, schematic tension

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