Chord span and other chordal characteristics affecting connections between perceived closeness and set-class similarity

Abstract

The importance of chord span for estimations of closeness (similarity or resemblance) was examined. The subjects (musically trained and less-trained) were asked to rate closeness between pentachords with spans varying from 6 to 22 semitones. Closeness estimations were found to be only weakly correlated with theoretical similarities calculated by eleven similarity measures. The factors that did guide closeness estimations were analysed using regression analysis and multidimensional scaling. Chord span, common pitches and set-class identity were found to be factors guiding estimations in both subject subgroups. Additional factors guiding the estimations of the trained group were the degree of dissonance, chord voicing and common pitch classes.

Notes

¹Pitch-class set theory was originally developed to provide a theoretical framework for describing pitch organisation of post-tonal music. The reader interested in the basic concepts, objectives and background of the theory can find a general discussion in, e.g., Forte (1973), Rahn (1980), Morris (1987) and Straus (1990).

²The cardinality of the largest mutually embeddable subset-class of set-classes X and Y indicates the number of elements of the largest subset-class that is embeddable in both set-classes X and Y. With cardinality n, an instance of set-class X can have at most n pitch-classes in common with an instance of set-class Y.