carlos_step: Define a step size for one of Wendy Carlos's scales

In musicMCT: Analyze the Structure of Musical Scales

Define a step size for one of Wendy Carlos's scales

Description

For her album Beauty in the Beast, Wendy Carlos developed several non-octave scales whose step sizes are calculated to optimize approximations of three intervals: the 3:2 fifth, the 5:4 major third, and the 6:5 minor third. The alpha, beta, gamma, and delta scales differ in terms of how strongly they privilege each of those just intervals. The basic step size for each scale is created by calling this function with the appropriate name argument (e.g. "alpha"). You can also choose your own weights for the three approximated just intervals, in which case the name argument is overridden.

Usage

carlos_step(name = "alpha", weights = NULL, edo = 12)

Arguments

name	Which of Carlos's four scales to create: "alpha", "beta", "gamma", or "delta". Defaults to "alpha"
weights	Numeric vector of length 3 assigning the number of steps that correspond to 3:2, 5:4, and 6:5, respectively. Overrides name if specified.
edo	Number of unit steps in an octave. Defaults to 12.

Value

Single numeric value containing the step size for the desired scale

Examples

alpha_scale <- (0:31) * carlos_step()
practically_12tet <- (0:24) * carlos_step(weights=c(7, 4, 3))

musicMCT documentation built on June 21, 2026, 9:06 a.m.