Hierarchizability as a Predictor of Scale Candidacy

Abstract

Scales from divergent musical cultures tend to have both intuitive structural similarities and one common functional property: within a given scale, each note takes on a unique shade of meaning in the context of the scale as a whole. It may be that certain structural traits facilitate this functional property—in other words, that scales with particular structural characteristics are more globally integrated and capable of being processed in a top-down manner. Representing pitch collections as bit strings, the current work shows that in Western European, Northern Indian, and Japanese traditional musics, collections that are more densely packed with recursively nested non-overlapping, uniquely identifiable repeated substrings (more hierarchizable) are more likely to appear as scales (p = .002).

Interpreting the tonal hierarchy through corpus analysis.

“…Previous research indicates that one of the measures considered here, duration, may be most effective as a cue for recovering the tonal hierarchy when it is used to emphasize particular intervallic patterns (Lantz, et al, 2014). In addition, it has been suggested that listeners rely on rare intervals to infer tonality (Browne, 1981; Butler, 1990a; Butler & Brown, 1984) and that scales with certain intervallic patterns are more capable of holding hierarchical information (Verosky, 2017). Future work might shed light on how the measures of tonal emphasis explored here interact with intervallic structure and other measures of tonal emphasis to give rise to an overarching tonal hierarchy.…”

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

“…Theories of scale selection are commonly based on cognitive biases, of which we will give a brief summary: liking harmonicity [166,167], disliking sensory dissonance [168,169] (or liking sensory dissonance [114]), tonal fusion [30], neurodynamic theory [170], transmissibility PLOS ONE [12,132,160,171,172], memory [173], and theories based on mathematical properties of scales [174][175][176][177][178][179].…”