Generalized Carlos Scales

TL;DR

This paper generalizes Wendy Carlos's unique musical scales, which emphasize thirds and fifths over octaves, by extending Benson's derivation to create a broad family of similar scales.

Contribution

It introduces a generalized framework for creating Carlos-type scales, expanding the original three scales into a wider class of musical scales.

Findings

Derived new scales inspired by Carlos's original scales.

Provided a mathematical framework for scale generalization.

Expanded the understanding of alternative tuning systems.

Abstract

In 1986, composer Wendy Carlos introduced three unusual musical scales she called alpha, beta and gamma, equal temperament-inspired scales that de-emphasize the octave as the primary interval in favor of the major and minor thirds and the perfect fifth. A derivation of the alpha, beta, and gamma scales due to David Benson is generalized to produce many Carlos-type scales.