What is a Musical Scale? Regularity and Convention in the Organization of Pitch

Abstract

Musical scales are near-universal in human music, and most readers will feel they already know what a scale is. On closer inspection, however, the literature lacks a consensus definition: which conditions are necessary and sufficient shifts across disciplines and traditions, and the term turns out to cover several distinct objects. I argue this is less a failure of rigour than a sign that ``scale'' names several related objects: prescriptive abstractions, instrument tunings, statistical regularities in performed pitch, perceptual categories, social conventions. I adopt an empirical definition -- a scale as a statistical regularity in pitch organisation relative to a tonic -- that is portable across traditions and computable from recordings, and situate it alongside the other senses of the term. Even this empirical core is not purely observational, as convention enters in deciding which pitches belong to a scale. And a further step of grouping scales into named categories is a separate convention, which I approach through prototype theory and illustrate with examples from Irish music. Separating these layers provides a basis from which scales can be re-examined empirically and cross-culturally.