Charting Enharmonicism on the Just-Intonation Tonnetz

Robert T. Kelley

Welcome to Robert Kelley's Just-Intonation Webpage. Here you will find the paper I delivered at the 2003 Annual Meeting of Music Theory Southeast. The paper has been completely revised and now forms parts of chapters 2, 3, and 5 of my dissertation.

Charting Enharmonicism on the Just-Intonation Tonnetz:
A Practical Approach to Neo-Riemannian Analysis

(PDF format)


In this study, I propose a theory of voice leading for use with the tonal space of the just-intonation Tonnetz. The theory is based largely upon established theories of diatonic voice leading and chromatic harmony, and also draws upon the principles of just intonation within the tonal system. The unambiguous expression of intervals as untempered ratios is dependent upon an established seven-step diatonic scale in which the intervals can function. Tuning corrections must be made at specified junctures within the just-intonation diatonic system in order to show its stability in comparison with chromatic harmony in just intonation. Only then can the various types of enharmonic progressions be unambiguously charted spatially as directed motion on the Tonnetz. In addition to providing a diatonic context for parsimonious voice leading between any two tertian sonorities, the just-intonation Tonnetz model allows for seventh chords, non-chord tones, augmented-sixth chords, other chromatically inflected chords, and extended tertian chords to be expressed on the tonal network along with the traditional triadic transformations. Examples of the analytic method are given here through the graphing of several typical enharmonic progressions drawn from the two Rhapsodies, Op. 79, of Johannes Brahms. Finally, a case-by-case method for treating atypical resolutions of normally functional chords is suggested through a just-intonation analysis of the opening of the Prelude to Wagner's Tristan und Isolde.



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