The most recognizable features of the jazz phrasing style known as “swing” is the articulation of tactus beat subdivisions into long-short patterns (known as “swing eighths”). The subdivisions are traditionally assumed to form a 2:1 beat-upbeat ratio (BUR); however, several smaller case studies have suggested that the 2:1 BUR is a gross oversimplification. Here we offer a more conclusive approach to the issue, offering a corpus analysis of 456 jazz solos using the Weimar Jazz Database. Results indicate that most jazz soloists tend to play with only slightly uneven swing eighths (BUR = 1.3:1), while BURs approaching 2:1 and higher are only used occasionally. High BURs are more likely to be used systematically at slow and moderate tempi and in Postbop and Hardbop styles. Overall, the data suggests that a stable 2:1 swing BUR for solos is a conceptual myth, which may be based on various perceptual effects. We suggest that higher BURs are likely saved for specific effect, since higher BURs may maximize entrainment and the sense of groove at the tactus beat level among listeners and performers. Consequently our results contribute with insights relevant to jazz, groove, and microrhythm studies, practical and historical jazz research, and music perception.

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.