colornum {musicMCT} | R Documentation |
Reference numbers for scale structures
Description
As described on p. 28 of "Modal Color Theory," it's convenient to have a
systematic labeling system ("color numbers") to refer to the distinct colors
in the hyperplane arrangements. This serves a similar function as Forte's
set class numbers do in traditional pitch-class set theory. Color numbers
are defined with reference to a complete list of the possible sign vectors
for each cardinality, so they depend on the extensive prior computation
that is stored in the object representative_signvectors
. (This is a large
file that cannot be included in the package musicMCT itself. It needs to be
downloaded separately, saved in your working directory, and loaded by entering
representative_signvectors <- readRDS("representative_signvectors.rds")
.
Color numbers are currently only defined for scales with 7 or fewer notes.
Usage
colornum(set, ineqmat = NULL, signvector_list = NULL, edo = 12, rounder = 10)
Arguments
set |
Numeric vector of pitch-classes in the set |
ineqmat |
Specifies which hyperplane arrangement to consider. By default (or by
explicitly entering "mct") it supplies the standard "Modal Color Theory" arrangements
of |
signvector_list |
A list of signvectors to use as the reference by
which |
edo |
Number of unit steps in an octave. Defaults to |
rounder |
Numeric (expected integer), defaults to |
Details
Note that the perfectly even "white" scale is number 0
for every cardinality
by definition.
The function assumes that you don't need to be reminded of the cardinality of the set you've entered. That is, there's a color number 2 for every cardinality, so you can get that value returned by entering a trichord, tetrachord, etc.
Value
Single non-negative integer (the color number) if a signvector_list
is specified or representative_signvectors
is loaded; otherwise NULL
Examples
colornum(edoo(5))
colornum(c(0, 3, 7))
colornum(c(0, 2, 7))
colornum(c(0, 1, 3, 7))
colornum(c(0, 1, 3, 6, 10, 15, 21), edo=33)
colornum(c(0, 2, 4, 5, 7, 9, 11))