Tuire Kuusi Set - Class and Chord : Examining Connection between Theoretical Resemblance and Perceived Closeness Studia Musica 12 Sibelius Academy Helsinki

This study examined connections between pitch-class set-theoretical abstract concepts, set-classes, and perceptual estimations of chords derived from the set-classes. The study had two aims, the first of which was to compare theoretical resemblance with perceived closeness. Another aim was to illuminate and analyze both factors relevant for perceptual estimations of chords and factors relevant for theoretical resemblance. The study also analyzed a selection of theoretical resemblance models. The models were socalled similarity measures. Statistical analyses of distributions of values produced by these measures were made. It turned out that the values produced by different measures could not be compared with one another because the distributions of values differed so much from one measure to another. Hence, the values were modified into percentiles. In the empirical part of the study, pentachords derived from pentad classes were used. Closeness between pentachords was rated by subjects. The subjects also rated the pentachords one at a time on nine semantic scales. The subjects’ closeness ratings were compared with similarity values as percentiles calculated by nine pitch-class set-theoretical similarity measures. A rather high connection was found between theoretical set-class similarity and aurally estimated chordal closeness. The underlying factors guiding perceptual estimations of chords were examined. The methods used were multidimensional scaling, hierarchical clustering, and factor analysis. The first (and the most important) factor guiding perception of both chord pairs and single chords was the degree of consonance of the test chords, which could also be explained by theoretical consonance models. Another factor was the chords’ association with some traditional tonal chord. The chords’ association with the whole-tone collection was the third factor guiding closeness ratings, while the combination of the width and register of the chords was the third factor guiding single-chord ratings. An additional factor guiding closeness ratings was the number of common pitches between two chords.