Reconciling Tonal Conflicts: Mod-7 Transformations in Chromatic Music

Robert T. Kelley


Here you will find my paper on mod-7 transformations. The research presented here comes from my dissertation work. The analytical model introduced in this paper is used to investigate enharmonic progressions and directional tonality. Feel free to contact me about my work with enharmonic progressions and directional tonality in chromatic harmony and the use of mod-7 transformations for analyzing post-tonal diatonic music: <>.


Reconciling Tonal Conflicts:
Mod-7 Transformations in Chromatic Music

(PDF format)


Abstract

The study of music as involving 7 step classes in 12 pitch classes has been the basis for a large amount of recent scholarship. While the mod-7 and mod-12 systems need not be related to any tuning system in particular, I will nevertheless show that there is an isomorphism between the diatonic scale system of 5-limit just intonation and the group of pitch/step-classes used by diatonic theorists. That mod-7 diatonic theory shares properties with both 5-limit just intonation and mod-12 set theory has ramifications for the analysis of all music that makes some reference to a mod-7 diatonic collection, regardless of its complexity, tuning system, or tonal context (or lack thereof). Because of the strong connection between the diatonic scale and 5-limit just intonation, tuning principles can provide the basis for a set of strictures governing the appropriate diatonic spelling of chords within chromatic progressions. A specific type of transformational graph, based on models in Lewin's GMIT (1987), will provide a means for studying highly chromatic passages from a tonal and prolongational perspective. I will give examples of specific analytical contexts in which a diatonic reading can provide intriguing insights into chromatic music. The first type of harmony that the analytical method illuminates is enharmonic progressions, exemplified by an excerpt from CÚsar Franck's Symphonic Variations, and the second is directional tonality, as found in Hugo Wolf's "Der Mond hat eine schwere Klag' erhoben" (1890).


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