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.
Agmon, Eytan. 1991. "Linear Transformations Between Cyclically Generated Chords." Musikometrika 3: 15-40.
. 1997. "The Bridges that Never Were: Schenker on the Contrapuntal Origin of the Triad and Seventh Chord." Music Theory Online 3/1. <http://societymusictheory.org/mto/issues/mto.97.3.1/mto.97.3.1.agmon.html>.
Atlas, Raphael. 1988. "Enharmonic Trompe-l'oreille: Reprise and the Disguised Seam in Nineteenth-Century Music." In Theory Only 10/6: 15-36.
Barbour, James Murray. 1951. Tuning and Temperament, A Historical Survey. East Lansing: Michigan State College Press.
Benjamin, William E. 1981. "Pitch-Class Counterpoint in Tonal Music." In Richmond Browne, ed., Music Theory: Special Topics (New York: Academic Press), 1-32.
. 1982. "Models of Underlying Tonal Structure: How Can They Be Abstract, and How Should They Be Abstract?" Music Theory Spectrum 4: 28-50.
Brown, Matthew. 1986. "The Diatonic and the Chromatic in Schenker's Theory of Harmonic Relations." Journal of Music Theory 30: 1-34.
Brown, Matthew, Douglas Dempster, and David Headlam. 1997. "The #IV(bV) hypothesis: Testing the limits of Schenker's theory of tonality." Music Theory Spectrum 19/2: 155-183.
Childs, Adrian P. 1998. "Moving Beyond Neo-Riemannian Triads: Exploring a Transformational Model for Seventh Chords" Journal of Music Theory 42/2: 181-193.
Clark, William. 1982. "Heinrich Schenker on the Nature of the Seventh Chord." Journal of Music Theory 26/2: 221-59.
Cohn, Richard. 1996. "Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions. Music Analysis 15/1 (March): 9-40.
. 1997. "Neo-Riemannian Operations, Parsimonious Trichords, and their Tonnetz Representations." Journal of Music Theory 41/1: 1-66.
Douthett, Jack and Peter Steinbach. 1998. "Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition." Journal of Music Theory 42/2: 241-263.
Dubiel, Joseph. 1990. "'When You Are a Beethoven': Kinds of Rules in Schenker's Counterpoint." Journal of Music Theory 34/2: 291-340.
Gollin Edward. 1998. "Some Aspects of Three-Dimensional Tonnetze." Journal of Music Theory 42/2: 195-206.
Greenberg, Beth. 1976. "Brahms' rhapsody in G minor, Op. 79, No. 2" A Study of Analyses by Schenker, Schoenberg, and Jonas." In Theory Only I/9-10: 21-29. "Comment on Greenberg" by Charles J. Smith: 31-32.
Hanford, Lisa. 1987. "A New Model for Pitch Motion in Tonal Music." Music Analysis 6/1-2: 133-167.
Harrison, Daniel. 1994. Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents. Chicago and London: University of Chicago Press.
. 2000. "Nonconformist Notions of Nineteenth-Century Enharmonicism." Music Analysis (forthcoming).
Hyer, Brian. 1989. "Tonal Intuitions in 'Tristan und Isolde'." Ph.D. diss., Yale University.
. 1995. "Reimag(in)ing Riemann." Journal of Music Theory 39/1: 101-138.
Isacoff, Stuart. 2001. Temperament: The Idea that Solved Music's Greatest Riddle. New York: Knopf.
Jones, Evan. 2002. "Pervasive Fluency: A Contrapuntal Definition of Stability and Transience in Tonal Music." Ph.D. diss., University of Rochester.
Klumpenhouwer, Henry. 1994. "Some Remarks on the Use of Riemann Transformations." Music Theory Online 0/9. <http://societymusictheory.org/mto/issues/mto.94.0.9/mto.94.0.9.klumpenhouwer.art>.
Lerdahl, Fred. 1994. "Tonal and Narrative Paths in Parsifal." In Raphael Atlas and Michael Cherlin, eds., Musical Transformation and Musical Intuition (Dedham, MA: Ovenbird Press), 121-146.
Lewin, David. 1996. "Cohn Functions." Journal of Music Theory 40/2: 181-216.
Mathieu, W. A. 1997. Harmonic Experience. Rochester, Vermont: Inner Traditions. Reviewed by Norman Carey in Music Theory Spectrum 24/1 (2002): 121-134.
McCreless, Patrick. 1983. "Ernst Kurth and the Analysis of the Chromatic Music of the Late Nineteenth Century." Music Theory Spectrum 5: 56-75.
Mooney, Michael Kevin. 1996. "The 'Table of Relations' and Music Psychology in Hugo Riemann's Harmonic Theory." Ph.D. diss., Columbia University.
Morgan, Robert. 1976. "Dissonant Prolongation: Theoretical and Compositional Precedents." Journal of Music Theory 20: 49-91.
Morris, Robert. 1998. "Voice-Leading Spaces." Music Theory Spectrum 20/2: 176-208.
Proctor, Gregory. 1978. "Technical Bases of Nineteenth-Century Chromatic Tonality: A Study in Chromaticism." Ph.D. diss., Princeton University.
Regener, Eric. 1975. "The Number Seven in the Theory of Intonation." Jounal of Music Theory 19/1: 140-153.
Riemann, Hugo. [1877] 1971. Musikalische Sytnaxis: Grundriss einer harmonischen Satzbildungslehre. [Leipzig: Breitkopf & Hδrtel.] Wiesbaden: Martin Sδndig.
. [1914-15] 1992. "Ideas for a Study 'On the Imagination of Tone,'" trans. Robert Wason and Elizabeth West Marvin. Journal of Music Theory 36/1: 81-117.
Roeder, John. 1994. "Voice Leading as Transformation." In Atlas and Cherlin, eds., Musical Transformation and Musical Intuition, 41-58.
Rothstein, William. 1991. "On Implied Tones." Music Analysis 10/3: 289-328.
Schenker, Heinrich. [1906] 1954. Harmony. Edited by Oswald Jonas, translated by Elisabeth Mann Borgese. Cambridge: M.I.T. Press.
Schoenberg, Arnold. 1954. Structural Functions of Harmony. Edited by Humphrey Searle. New York: Norton.
Smith, Charles J. 1986. "The Functional Extravagance of Chromatic Chords." Music Theory Spectrum 8: 94-139.
Straus, Joseph N. 1987. "The Problem of Prolongation in Post-Tonal Music." Journal of Music Theory 31/1: 1-21.
Walker, Jonathan. 1996. "Intonational Injustice: A Defense of Just Intonation in the Performance of Renaissance Polyphony." Music Theory Online 2/6. <http://societymusictheory.org/mto/issues/mto.96.2.6/mto.96.2.6.walker.html>.
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