A fundamental assumption of distributional key-finding methods is that the frequency distributions of pitch classes in all keys are transpositionally equivalent. We tested this assumption with three experiments. First, using data from the openings of 995 major-key pieces and 596 minor-key pieces in the Yale-Classical Archives Corpus, we found that scale-degree distributions differ significantly from one key to another, and further analysis revealed that pieces keys with signatures having relatively more accidentals exhibit significantly more chromaticism than keys with fewer accidentals. Second, we examined whether these data might be accounted for by different keys’ varying modulation tendencies, and found this to be the case: keys with more accidentals modulate more frequently to more distant keys. Finally, we attempted to exclude modulatory passages from our data using a key profile analysis to identify key and mode within our dataset; however, the results of Experiment 1 still held. In sum, even when using a method that assumes transpositional equivalence, we found a difference between key profiles of different keys.

This essay begins by reviewing issues in psychological measurement that motivated some of the research summarized in Cognitive Foundations of Musical Pitch (Krumhansl, 1990). These were challenges to geometrical models of similarity, asymmetrical measures of similarity, and contextual effects. It then considers the impact that statistical learning has had on research and theory about music cognition, suggesting this emphasis may have underestimated the importance of other psychological processes contributing to the experience of music. Finally, it discusses three problems with traditional analyses using unidimensional, sequential statistics. The first is that music is hierarchical, with important relationships between non-adjacent events. The second is that the dimensions of music, specifically, pitch and time, interact. The third is the assumption that probabilities remain constant throughout a composition. Rather, music contains artful deviations from normative probabilities contributing to the experience of tension and release.