Interval-Class Content in Equally Tempered Pitch-Class Sets: Common Scales Exhibit Optimum Tonal Consonance

Abstract

Pitch-class sets (such as scales) can be characterized according to the inventory of possible intervals that can be formed by pairing all pitches in the set. The frequency of occurrence of various interval classes in a given pitch-class set can be correlated with corresponding measures of perceived consonance for each interval class. If a goal of music-making is to promote a euphonious effect, then those sets that exhibit a plethora of consonant intervals and a paucity of dissonant intervals might be of particular interest to musicians. In this paper, it is shown that the pitch-class sets that provide the most consonant interval-class inventories are the major diatonic scale, the harmonic and melodic minor scales, and equally tempered equivalents of the Japanese Ritsu mode, the common pentatonic scale, and the common "blues" scale. Consonant harmonic intervals are more readily available in these sets than in other possible sets that can be drawn from the 12 equally tempered pitch chromas.