isgwf {musicMCT} | R Documentation |
Is a scale n-wise well formed?
Description
Tests whether a scale has a generalized type of well formedness (pairwise or n-wise well formedness).
Usage
isgwf(set, setword = NULL, allow_de = FALSE, edo = 12, rounder = 10)
Arguments
set |
Numeric vector of pitch-classes in the set |
setword |
A vector representing the ranked step sizes of a scale (e.g.
|
allow_de |
Should the function test for degenerate well-formed and distributionally even scales too?
Defaults to |
edo |
Number of unit steps in an octave. Defaults to |
rounder |
Numeric (expected integer), defaults to |
Details
David Clampitt's 1997 dissertation ("Pairwise Well-Formed Scales: Structural and Transformational Properties," SUNY Buffalo) offers a generalization of the notion of well-formedness from 1-dimensional structures with a single generator to 2-dimensional structures that mediate between two well-formed scales. Ongoing research suggests that this can be extended further to "n-wise" or "general" well-formedness, though n-wise well-formed scales are increasingly rare as n grows larger.
Value
Boolean: is the set n-wise well formed?
Examples
meantone_diatonic <- c(0, 2, 4, 5, 7, 9, 11)
just_diatonic <- j(dia)
some_weird_thing <- convert(c(0, 1, 3, 6, 8, 12, 14), 17, 12)
example_scales <- cbind(meantone_diatonic, just_diatonic, some_weird_thing)
apply(example_scales, 2, howfree)
apply(example_scales, 2, isgwf)