Interpreting the tonal hierarchy through corpus analysis.

Abstract

Research in tonality perception commonly references the correlation between scale-degree occurrence frequencies and probe-tone ratings of tonal stability. This corpus study compares frequency of occurrence with 3 other statistical cues of tonal emphasis: average scale-egree duration, percentage of scale-degree instances appearing on downbeats, and percentage of scale-degree instances appearing in phrase-final positions. Using a mixed linear model that accounts for membership in the diatonic scale and random effects at the melody level, Experiment 1 finds that all frequency-and non-frequencybased measures of tonal emphasis except duration are highly significant predictors of the tonal hierarchy, with scale membership explaining the most unique variance, followed by phrase-final position and frequency of occurrence, then metric placement. Experiment 2 demonstrates that controlling for scale membership greatly attenuates the relationship between occurrence frequencies and probe-tone ratings, with frequencies explaining only 7% of variance in the tonal hierarchy beyond scale membership. Experiment 3 shows that phrase-final position, metric placement, and frequency best differentiate the tonic from other scale degrees, with all other predictors failing to reach significance. Together, these results suggest that higher frequency counts correspond to a more general tendency for tonally stable scale degrees to be emphasized across multiple musical dimensions and that frequency of occurrence is not a uniquely informative cue of tonal emphasis.

Essen as a Corpus of Early Musical Experience

“…Correlations in corpus profiles were then computed between Essen and the children's song corpus as well as between Essen and the two comparison corpora. [2] Correlations were reported both for profiles of the total chromatic and for profiles of diatonic scale degrees since correlations for the total chromatic can disproportionately reflect the difference between in-scale and out-of-scale tones, leading to high values of r not necessarily representative of diatonic scale degrees (Verosky, 2021). Finally, permutation tests were performed (Good, 2005) to determine whether the correlation between Essen and the children's song corpus was significantly stronger than the correlations between Essen and the comparison corpora.…”

“…Huron (2006) found that frequency profiles from Essen have a correlation of r = .92 with frequency profiles from Bach fugues while Arden (2003) reports a correlation of r = .99 with frequency profiles from common-practice art-song melodies compiled by Knopoff and Hutchinson (1983). Beyond common-practice music, Verosky (2021) found correlations of r = .96 for the total chromatic and r = .85 for diatonic scale degrees with major diatonic melodies from the de Clercq and Temperley (2011) rock corpus.…”

Convergent evolution in a large cross-cultural database of musical scales

“…Another statistical regularity in musical pitch is tonality-i.e., the distribution of notes, how they are played (duration, ornamentation), and their transition probabilities [109,110]. Of the various aspects of tonality, tonal hierarchies (probability distribution of notes) [111] have been best documented across cultures [73,[112][113][114][115].…”