Author: Kuusi, Tuire
Title: Set-Class and Chord: Examining Connection between Theoretical Resemblance and Perceived Closeness
Institution: Sibelius Academy
Completed: November 2001
The study examined connections between set-classes and perceptual estimations of chords derived from them. The study had two aims, the first of which was to compare theoretical resemblance with perceived closeness. Another aim was to analyze both factors relevant for perceptual estimations of chords and factors relevant for theoretical resemblance.
The study analyzed nine similarity measures. Statistical analyses of shares of values produced by these measures were made. Additionally, the datasets produced by the measures were analyzed using multidimensional scaling. The three factors that emerged were interpreted by (near)chromatic property, pentatonic property, and whole-tone property. An additional factor relevant for set-class similarity was the cardinality of the largest mutually embeddable subset-class of the two set-classes of a pair.
In the empirical part of the study closeness between pentachords was rated by subjects. Additionally, pentachords were rated one at a time on nine semantic scales. When the closeness ratings were compared with measured similarities, a rather high connection was found.
The underlying factors guiding perceptual estimations of chords were analyzed. The most important factor was the degree of consonance of the chords, which could also be explained by theoretical consonance models. The other factors were the chords' association with some traditional tonal chord, the chords' associations with the whole-tone collection, and the width and register of the chords. An additional factor guiding closeness ratings was the number of common pitches between two chords. Most of these qualitative chordal characteristics could be explained by quantitative properties of the set-classes. Only the width and register of chords seemed to operate independently from set-classes.
In this study a connection was found between theoretical resemblance and perceived closeness as well as between set-class properties and perception of chords. The results of the study can be interpreted to indicate that the quantitative properties of set-classes had an effect on the qualitative characteristics of chords derived from them, and these qualitative chordal characteristics had effects on the subjects' estimations.
Keywords: similarity measures, closeness estimations, aural perception, multidimensional scaling, factor analysis, hierarchical clustering, semantic differential, statistical analysis, pitch-class set-theory, pentad class, pentachord