Structural properties of multi-octave scales
Year: 2022
Type: article
Abstract: Whilst not widely extended, non-octave-repeating scales are present in a variety of musical settings, yet have received scarce attention in the existing literature. This paper provides a brief general historical contextualization before focusing on a specific group of two-octave scales based on properties in common with the most widely used scales in Western music. After characterizing them in mathematical terms, an exhaustive list of such scales is provided, being the first exhaustive list of non-octave-repeating scales of any given characteristics. A scale endowed with structural properties attributed to the diatonic collection in the field of diatonic theory – such as well-formed, Myhill property, maximally even or diatonic – is singled out for the first time in this paper.
Source: Journal of Mathematics and Music
Authors: Emmet Crowley, Francisco Gómez-Martín
Institution: Universidad Politécnica de Madrid
Language: English
Subfield: Music
Field: Arts and Humanities
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4308588635