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COMPOSITE INTERVAL CYCLE SETS, THEIR RELATIONS, AND APPLICATIONS

COMPOSITE INTERVAL CYCLE SETS, THEIR RELATIONS, AND APPLICATIONS similarity between pitch-class sets, while we will be concerned with other types of relations. In Example 1 we find a brief excerpt from Act III of Alban Berg’s Wozzeck which serves as a preliminary illustration of the issues detailed in the present study. We find two Z-related hexachords, members of SCs 6-17 and 6-43, respectively.5 The ic-vector for both these collections is [322332]. However, as Figure 1 shows, they do not generate equivalent ic-matrices.6 Accordingly, no permutation of pcs in either set exists which generates a matrix equivalent to the other. Further examination of the ic-matrices in Figure 1 reveals important differences in the intervallic content of these pcsets, specifically as regards the cycles on which their intervals lie. For example, each member of ic4 in {0,1,2,4,7,8} exists between adjacencies in the (048) interval cycle. In contrast, the ic4s of {3,5,6,9,a,b} lie on the (159), (26a), and (37b) cycles. This information is conveyed in Michael Buchler’s ic-cycle vector (ICCycV), which shows the number of adjacencies in various cycles, including wrap-around adjacencies. Each of the ICCycV’s six coordinates (subvectors, contained between angle brackets) represents the interval cycles under through .7 Multiple entries in the subvectors (separated by commas) refer http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Music Theory Duke University Press

COMPOSITE INTERVAL CYCLE SETS, THEIR RELATIONS, AND APPLICATIONS

Journal of Music Theory , Volume 46 (1-2) – Jan 1, 2002

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Publisher
Duke University Press
Copyright
Copyright 2002 by Yale University
ISSN
0022-2909
eISSN
1941-7497
DOI
10.1215/00222909-46-1-2-153
Publisher site
See Article on Publisher Site

Abstract

similarity between pitch-class sets, while we will be concerned with other types of relations. In Example 1 we find a brief excerpt from Act III of Alban Berg’s Wozzeck which serves as a preliminary illustration of the issues detailed in the present study. We find two Z-related hexachords, members of SCs 6-17 and 6-43, respectively.5 The ic-vector for both these collections is [322332]. However, as Figure 1 shows, they do not generate equivalent ic-matrices.6 Accordingly, no permutation of pcs in either set exists which generates a matrix equivalent to the other. Further examination of the ic-matrices in Figure 1 reveals important differences in the intervallic content of these pcsets, specifically as regards the cycles on which their intervals lie. For example, each member of ic4 in {0,1,2,4,7,8} exists between adjacencies in the (048) interval cycle. In contrast, the ic4s of {3,5,6,9,a,b} lie on the (159), (26a), and (37b) cycles. This information is conveyed in Michael Buchler’s ic-cycle vector (ICCycV), which shows the number of adjacencies in various cycles, including wrap-around adjacencies. Each of the ICCycV’s six coordinates (subvectors, contained between angle brackets) represents the interval cycles under through .7 Multiple entries in the subvectors (separated by commas) refer

Journal

Journal of Music TheoryDuke University Press

Published: Jan 1, 2002

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