musicMCT (version 0.1.2)

evenness: How even is a scale?

Description

Calculates the distance from a set to the nearest perfectly even division of the octave, which will not be the one with a first entry of 0, unlike almost every other usage in this package. That's because, for most purposes, we do want to distinguish between different modes of a set, but it seems counterintuitive to me to say that one mode of a scale is less even than another. Since this value is a distance from the perfectly even ("white") scale, lower values indicate more evenness.

Usage

evenness(
  set,
  method = c("euclidean", "taxicab", "chebyshev", "hamming"),
  edo = 12,
  rounder = 10
)

Value

Single non-negative numeric value

Arguments

set

Numeric vector of pitch-classes in the set

method

What distance metric should be used? Defaults to "euclidean" (unlike most functions with a method parameter in musicMCT) but can be "taxicab", "chebyshev", or "hamming".

edo

Number of unit steps in an octave. Defaults to 12.

rounder

Numeric (expected integer), defaults to 10: number of decimal places to round to when testing for equality.

Details

Note that the values this function returns depend on what measurement unit you're using (i.e. are you in 12edo or 16edo?). Their absolute value isn't terribly significant: you should only make relative comparisons between calculations done with the same value for edo.

Currently, methods other than "Euclidean" are somewhat experimental.

Examples

evenness(c(0, 4, 8))
evenness(c(0, 4, 7)) < evenness(c(0, 1, 2))

dim_triad <- c(0, 3, 6)
sus_2 <- c(0, 2, 7)
coord_to_edo(dim_triad)
coord_to_edo(sus_2)
evenness(dim_triad) == evenness(sus_2)