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 article explores the historical development of common-practice musical style and how that development might connect to the cognition of key within the history of Western European tonality. First, musical corpora of 19 composers were divided into three-chord progressions, and these progressions were tallied. The chord tallies were used for a cluster analysis and for measurements of inter-corpus cross entropy. The cluster analysis divided the corpora in ways that conform to historical and stylistic intuitions, and inter-corpus cross entropy was found to correlate with the years separating the corpora. These findings show that the chronological distance between two musical corpora seems to predict compositional similarity and that chord-progression norms are connected to specific historical situations. In order to model how these changes might affect the cognition of musical key, a corpus-sensitive key-finding algorithm was used to decode key within a famous example of musical ambiguity, the opening of Beethoven’s “Eroica” symphony. Each corpus-trained model created a slightly different key interpretation, suggesting that historically situated models of tonal cognition might indeed interpret the same stimulus differently.