Lecture: 'A Geometrical Approach to Two-Voice Transformations'
December 1, 2017
Fine Arts Center
UMass Amherst Campus
The department of music and dance presents a talk by Doug Abrams, a PhD student in music theory, entitled "A Geometrical Approach to Two-Voice Transformations."
This talk introduces a simple numerical metric describing two-voice transformations and demonstrating how it can be used to characterize both two-voice, note-against-note counterpoint and relationships between pairs of motive forms. This metric, called “voice-leading class” or “VLC”, is calculated by representing each two-voice transformation as a vector in the Cartesian plane, 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 - apart from histograms that reveal patterns unique to specific pieces - a continuum of structure is found to exist. 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 Trio from Bartok’s Fifth String Quartet is analyzed, and VLC is found to illuminate contour, form, motivic structure, pitch-class set structure, and pitch centricity. Finally, VLC is found to be a useful tool for studying the phenomenon of chromatic compression and diatonic expansion.