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UNIFORM TRIADIC TRANSFORMATIONS

UNIFORM TRIADIC TRANSFORMATIONS A number of other objections to the neo-Riemannian approach have also been raised. Its application to standard diatonic progressions is awkward. This observation perhaps relates to the uncomfortable and incomplete integration of the fundamentally diatonic transformations D and M discussed above, and undoubtedly bears some responsibility for the fact that satisfactory applications of neo-Riemannian methodology, even in highly chromatic music, have generally been confined to isolated short passages. The theory is said to disregard the concept of chord roots, which has long been fundamental to tonal theory and is surely relevant even in the repertoire favored by neo-Riemannian theorists. The theory is said to be insufficiently attentive to the distinction between chord and key area, and to hierarchical distinctions in general. Most of the problematic issues just raised are addressed, directly or indirectly, by the simple algebraic framework proposed on the following pages for the study of triadic transformations. A uniform triadic transformation, or UTT, is described in componentwise fashion, through a root-interval approach. Each UTT consists of a sign (+ or , indicating whether the transformation preserves or reverses mode) and two transposition levels (integers mod 12: one for major triads, the other for minor, indicating the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Music Theory Duke University Press

UNIFORM TRIADIC TRANSFORMATIONS

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
10.1215/00222909-46-1-2-57
Publisher site
See Article on Publisher Site

Abstract

A number of other objections to the neo-Riemannian approach have also been raised. Its application to standard diatonic progressions is awkward. This observation perhaps relates to the uncomfortable and incomplete integration of the fundamentally diatonic transformations D and M discussed above, and undoubtedly bears some responsibility for the fact that satisfactory applications of neo-Riemannian methodology, even in highly chromatic music, have generally been confined to isolated short passages. The theory is said to disregard the concept of chord roots, which has long been fundamental to tonal theory and is surely relevant even in the repertoire favored by neo-Riemannian theorists. The theory is said to be insufficiently attentive to the distinction between chord and key area, and to hierarchical distinctions in general. Most of the problematic issues just raised are addressed, directly or indirectly, by the simple algebraic framework proposed on the following pages for the study of triadic transformations. A uniform triadic transformation, or UTT, is described in componentwise fashion, through a root-interval approach. Each UTT consists of a sign (+ or , indicating whether the transformation preserves or reverses mode) and two transposition levels (integers mod 12: one for major triads, the other for minor, indicating the

Journal

Journal of Music TheoryDuke University Press

Published: Jan 1, 2002

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