Reference numbers for scale structures

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 getineqmat(), but can be set to "white," "roth", "pastel," or "rosy", giving the ineqmats of make_white_ineqmat(), make_roth_ineqmat(), make_pastel_ineqmat(), and make_rosy_ineqmat(). For other arrangements, the desired inequality matrix can be entered directly.

signvector_list

A list of signvectors to use as the reference by which colornum assigns a value. Defaults to NULL and will attempt to use representative_signvectors, which needs to be downloaded and assigned separately from the package musicMCT.

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.

Value

Single non-negative integer (the color number) if a signvector_list is specified or representative_signvectors is loaded; otherwise NULL

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.

Examples

colornum(edoo(5))
#> [1] 0
colornum(c(0, 3, 7))
#> NULL
colornum(c(0, 2, 7))
#> NULL
colornum(c(0, 1, 3, 7))
#> NULL
colornum(c(0, 1, 3, 6, 10, 15, 21), edo=33)
#> NULL
colornum(c(0, 2, 4, 5, 7, 9, 11))
#> NULL