Recursive Structure, Inversional Pitch-Class Relations, and “Monkishness” in Thelonious Monk’s “Ruby, My Dear”

Published in November 16, 2016 issue of Jazz Perspectives

The goal of this study is to elucidate the musical meanings behind some of the more unusual passages in one of Thelonious Monk’s best-known compositions, “Ruby, My Dear.” A five-note scale-degree set is identified that appears on the surface level of the A sections and the bridge, and on a higher structural level as the set of all tonalities established by authentic cadence throughout the piece, including the final tonality at the end of the coda. Pitch-class inversion operations are found to govern the internal structure of three particularly unusual passages, and in two of them, are found to highlight the global dominant in conjunction with the higher-level manifestation of the set described above, helping to prepare the final cadence of the piece. Far from being gratuitously non-conformist, then, Monk’s unusual passages — his “Monkish” moments, as it were — are found to play key roles in the logical unfolding of this piece.

A Geometrical Approach to Two-Voice Transformations

ABSTRACT This paper introduces a simple numerical metric describing two-voice transformations and demonstrates how it can be used to characterize both two-voice, note-against-note counterpoint and relationships between pairs of motive forms. This metric, dubbed “voice-leading class” or “VLC”, is calculated by representing each two-voice transformation as a vector in the Cartesian plane (Tymoczko uses this concept in A Geometry of Music),† and measuring the angle it makes with the horizontal axis. Passages of two-voice, note-against-note counterpoint in works by ten composers comprising more than 9,500 transformations have been analyzed using VLC histograms, and a continuum of structure is found to exist. Some histograms have no discernible structure, some have structure characterized by clustering with or without spikes corresponding to perfect parallel and/or antiparallel motion, and some have quasi-symmetrical distributions centered on VLC values corresponding to perfect parallel and/or antiparallel motion. Due to the high level of structure in some VLC histograms, the hypothesis that VLC is a compositional determinant in some pieces is cautiously advanced. Using VLC as a tool for studying motivic transformation, the Scherzo and Scherzo da Capo from Bartók’s Fifth String Quartet are analyzed. In addition to a high level of histogram structure, VLC is found to illuminate a phenomenon in which successive VLC values trade places within motivic transformations from one motivic transformation to the next, particularly at important formal junctures. Finally, VLC is found to be useful for studying chromatic compression and diatonic expansion.

Work in progress
† Dmitri Tymoczko, A Geometry of Music (New York: Oxford University Press, 2011), 66-67.