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A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice

A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice Two interlocking types of discourse develop these ideas. One, substantiating the fourth claim, is theoretical and instrumental: it demonstrates a geometric model through which the other claims may be represented and explored, and which can serve composers seeking ways to organize their own 1 See Hook 2011, Whittall 2011, and Headlam 2012a (as well as the author's response [Tymoczko 2012] and the reviewer's rejoinder [Headlam 2012b]). Journal of Music Theory 57:1, Spring 2013 DOI 10.1215/00222909-2017151 © 2013 by Yale University Journal of Music Theory music. On its own terms, I find this model persuasive and poietically suggestive, as the author intends. The other is specifically historical, asserting that development of Western polyphony can be understood as progressively more elaborate attempts to realize all five features, whose mutual dependency induced composers to find similar solutions. Evidence for this thesis is adduced from analyses of individual passages, references to recent (rarely historical) theory, and statistical characterizations of many related works. Its persuasiveness may be judged by how well the model fits the diverse music, what processes it can explain that other theories do not, whether it makes convincing connections between passages that other theories would treat as distinct, and how http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Music Theory Duke University Press

A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice

Journal of Music Theory , Volume 57 (1) – Mar 20, 2013

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Publisher
Duke University Press
Copyright
Copyright © Duke Univ Press
ISSN
0022-2909
eISSN
1941-7497
DOI
10.1215/00222909-2017151
Publisher site
See Article on Publisher Site

Abstract

Two interlocking types of discourse develop these ideas. One, substantiating the fourth claim, is theoretical and instrumental: it demonstrates a geometric model through which the other claims may be represented and explored, and which can serve composers seeking ways to organize their own 1 See Hook 2011, Whittall 2011, and Headlam 2012a (as well as the author's response [Tymoczko 2012] and the reviewer's rejoinder [Headlam 2012b]). Journal of Music Theory 57:1, Spring 2013 DOI 10.1215/00222909-2017151 © 2013 by Yale University Journal of Music Theory music. On its own terms, I find this model persuasive and poietically suggestive, as the author intends. The other is specifically historical, asserting that development of Western polyphony can be understood as progressively more elaborate attempts to realize all five features, whose mutual dependency induced composers to find similar solutions. Evidence for this thesis is adduced from analyses of individual passages, references to recent (rarely historical) theory, and statistical characterizations of many related works. Its persuasiveness may be judged by how well the model fits the diverse music, what processes it can explain that other theories do not, whether it makes convincing connections between passages that other theories would treat as distinct, and how

Journal

Journal of Music TheoryDuke University Press

Published: Mar 20, 2013

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