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ASPECTS OF DEPTH IN K-NET ANALYSIS WITH SPECIAL REFERENCE TO WEBERN'S OPUS 16/4

ASPECTS OF DEPTH IN K-NET ANALYSIS WITH SPECIAL REFERENCE TO WEBERN'S OPUS 16/4 network repeats structural features of the networks it contains in its nodes, taking advantage of the relationship between the group of pitch-class operations (Tn\In), henceforth symbolized as f, and what have been called its outer automorphisms (Tn\In), henceforth symbolized as f. This terminology varies from its appearance in group theory. Pace Klumpenhouwer 1998, here I shall refer to the automorphisms f as the “iconic automorphisms” of f, since they are the automorphisms of f with images in f.1 In any event, the logic of depth invoked here emerges primarily by means of the theory of automorphisms. However, we can invoke different senses of structural depth in the context of K-net analysis, senses that do not primarily engage the theory of iconic automorphisms. In such cases, the sense of structural depth emerges more generally from the theory of networks. The property of recursive structuring between levels may be extended in new ways or may be absent altogether. An analysis of Webern’s op. 16/4 provides the context for addressing the issues raised when we contemplate both old and new senses of depth in K-net theory. As I shall discuss below, exploration along these lines will lead to new technical resources, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Music Theory Duke University Press

ASPECTS OF DEPTH IN K-NET ANALYSIS WITH SPECIAL REFERENCE TO WEBERN'S OPUS 16/4

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
10.1215/00222909-2007-001
Publisher site
See Article on Publisher Site

Abstract

network repeats structural features of the networks it contains in its nodes, taking advantage of the relationship between the group of pitch-class operations (Tn\In), henceforth symbolized as f, and what have been called its outer automorphisms (Tn\In), henceforth symbolized as f. This terminology varies from its appearance in group theory. Pace Klumpenhouwer 1998, here I shall refer to the automorphisms f as the “iconic automorphisms” of f, since they are the automorphisms of f with images in f.1 In any event, the logic of depth invoked here emerges primarily by means of the theory of automorphisms. However, we can invoke different senses of structural depth in the context of K-net analysis, senses that do not primarily engage the theory of iconic automorphisms. In such cases, the sense of structural depth emerges more generally from the theory of networks. The property of recursive structuring between levels may be extended in new ways or may be absent altogether. An analysis of Webern’s op. 16/4 provides the context for addressing the issues raised when we contemplate both old and new senses of depth in K-net theory. As I shall discuss below, exploration along these lines will lead to new technical resources,

Journal

Journal of Music TheoryDuke University Press

Published: Jan 1, 2005

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