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Open Access Thesis
Master of Music (M.M.)
Year Degree Awarded
Month Degree Awarded
A new analytical tool called “voice-leading class” is introduced that can quantify on an angular scale any transformation mapping one pitch dyad onto another. This method (based on a concept put forth by Dmitri Tymoczko) can be applied to two-voice, first-species counterpoint or to single-voice motivic transformations. The music of Béla Bartók is used to demonstrate the metric because of his frequent use of inversional symmetry, which is important if the full range of the metric’s values is to be tested. Voice-leading class (VLC) analysis applied to first-species counterpoint reveals highly structured VLC frequency histograms in certain works. It also reveals pairs of VLC values corresponding to motion in opposite directions along lines passing through the origin in pitch space. VLC analysis of motivic transformations, on the other hand, provides an efficient way of characterizing the phenomenon of chromatic compression and diatonic expansion. A hybrid methodology is demonstrated using Segall’s gravitational balance method that provides one way of analyzing textures with more than two voices. A second way is demonstrated using a passage from Bartók’s Concerto for Orchestra. Finally, the third movement of the String Quartet #5 is analyzed. Families of geometrically related VLC values are identified, and two are found to be particularly salient because of their relationship to major and minor thirds, intervals which play an important role in the movement. VLC values in this movement are linked to contour, form, motivic structure, pitch-class sets and pitch centricity, and are thus demonstrated to be useful for understanding Bartók’s music and the music of other composers as well.
Abrams, Douglas R., "A Geometrical Approach to Two-Voice Transformations in the Music of Bela Bartok" (2014). Masters Theses. 1.