Using Interval Cycles to Model Krumhansl's Tonal Hierarchies

Abstract

The analyses presented in this paper use interval-cycle profiles to show that there is a statistical link between interval cycles and Krumhansl and Kessler's (1982) major- and minor-key tonal hierarchies. An interval cycle is the minimum number of additive iterations of an interval that are required for the original pitch classes to be restated—a formal property that we hypothesize leads to perceptual grouping referred to as interval-cycle proximity. The interval cycles that best explain the extent to which any chord's interval-cycle profile correlates with the tonal hierarchies are found to be those belonging to dominant harmonies, particularly the dominant seventh. The results of the analyses and the interval-cycle proximity hypothesis are discussed with respect to Browne's (1981) rare-interval hypothesis and Brower's (2000) musical pattern mapping schema.