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VOICE LEADING IN SET-CLASS SPACE

VOICE LEADING IN SET-CLASS SPACE Figure 1. Transformational voice leading via transposition and fuzzy transposition in pitch and pitch-class space in this case, deviates from the others by a semitone. That amount of deviation, defined as the offset number, is given in parentheses below the transposition number.2 The voice leading thus involves minimal offset. As in Figure 1a, the transformational voice leading (i.e., the mappings induced by a transformation) and the registral lines coincide. In Figure 1c, the second chord in the pair (Y3) is transposed up two semitones from its position in the previous progression (Y2). As a result, p the voice leading from X to Y3 is *T+2. The offset number remains 1, because the soprano still deviates by only one semitone from the prevailing transformation. This voice leading is no longer smooth, because all of the voices are moving by two or three semitones, but it still involves minimal offset. The progression does not involve actual, crisp transposition, but it is maximally uniform; that is, it comes as close as possible to being an actual transposition, deviating by only one semitone of offset.3 In this sense, the transformation in Figure 1b is also maximally uniform (as well as smooth). Once http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Music Theory Duke University Press

VOICE LEADING IN SET-CLASS SPACE

Journal of Music Theory , Volume 49 (1) – Jan 1, 2005

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Publisher
Duke University Press
Copyright
Copyright 2005 by Yale University
ISSN
0022-2909
eISSN
1941-7497
DOI
10.1215/00222909-2007-002
Publisher site
See Article on Publisher Site

Abstract

Figure 1. Transformational voice leading via transposition and fuzzy transposition in pitch and pitch-class space in this case, deviates from the others by a semitone. That amount of deviation, defined as the offset number, is given in parentheses below the transposition number.2 The voice leading thus involves minimal offset. As in Figure 1a, the transformational voice leading (i.e., the mappings induced by a transformation) and the registral lines coincide. In Figure 1c, the second chord in the pair (Y3) is transposed up two semitones from its position in the previous progression (Y2). As a result, p the voice leading from X to Y3 is *T+2. The offset number remains 1, because the soprano still deviates by only one semitone from the prevailing transformation. This voice leading is no longer smooth, because all of the voices are moving by two or three semitones, but it still involves minimal offset. The progression does not involve actual, crisp transposition, but it is maximally uniform; that is, it comes as close as possible to being an actual transposition, deviating by only one semitone of offset.3 In this sense, the transformation in Figure 1b is also maximally uniform (as well as smooth). Once

Journal

Journal of Music TheoryDuke University Press

Published: Jan 1, 2005

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