Aspects of Well-Formed Scales

Abstract

Pentatonic, diatonic, and chromatic scales share the same underlying structure, that of the well-formed scale. Well-formedness is defined in terms of a relationship between the order in which a single interval generates the elements of a pitch-class set and the order in which those elements appear in a scale. Another characterization provides a recursive procedure for organizing all well-formed scales into hierarchies. Finally, well-formed scales are defined in terms of scale-step measure, and aspects of the diatonic set are examined.