The Complex of Non-Chromatic Scales

TL;DR

This paper aims to systematically organize the entire space of musical scales by identifying basic scales and deriving others through combinations, providing a structured understanding of scale relationships.

Contribution

It introduces a novel framework to classify and generate all musical scales from fundamental constituents, advancing the theoretical understanding of scale structures.

Findings

Defined a set of basic scales as foundational elements.

Developed a method to generate all other scales from these basic scales.

Provided a systematic classification of musical scales.

Abstract

We consider the space of all musical scales with the ambition to systematize it. To do this, we pursue the idea to view certain scales as basic constituents and to "mix" all remaining scales from these. The German version of this article appeared in Mitteilungen der DMV, volume 25, issue 1.