Jana Kubitza Millar
University of North Texas, PhD Dissertation, 1984.
Allen Forte's theory of pitch-class set structure has provided useful tools for discovering structural relationships in atonal music. As valuable as set-theoretic procedures are for composers and analysts, the extent to which set relationships are perceptible by the listener largely remains to be investigated. This study addresses the need for aural-perceptual considerations in analysis, reviews related research in music perception, and poses questions concerning the aural perceptibility of set relationships. Specifically, it describes and presents the results of a computer-assisted experiment in testing the perceptibility of set-equivalency relationships. The experiment consisted of three phases for participation by subjects: a perception ability test in which subjects were screened for absolute-pitch and interval recognition, an interactive tutorial on the fundamentals of set theory to provide subjects with some criteria for making judgments about set equivalency, and a perception test on recognizing equivalency relationships. All training and testing was administered using Apple microcomputers. The perception test was designed to measure how recognition of set equivalency may be affected by the perceptual ability of the listener, the set types used and the particular set manipulation involved in the equivalency relationship. The test paradigm consisted of the presentation of an original set followed by three comparison sets, one of which was transpositionally or inversionally equivalent to the original, the other two being non-equivalent lures in an Rp, R1 or R2 similarity relation with the original. Five set equivalency relationships were used: ordered transposition, ordered inversion, ordered transposition with octave displacement, reordered transposition and reordered inversion. Statistical tests of subject-response data showed that: subjects with absolute-pitch recognition performed with more accuracy; ordered transformations were more recognizable than reordered transformations; transpositional equivalencies were more discernable than inversional equivalencies; octave displacement disguised set equivalency; and non-equivalent sets with similarity through contour or successive interval invariance were easily confused with equivalent sets.