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Orbit of a scale under symmetries of hyperplane arrangement

Source: R/colors.R
scale_palette.Rd

Given an input scale, return a "palette" of related scalar colors. All the returned scales are the image of the input under some ineqsym(). The symmetry group used to define the orbit comprises the symmetries of the MCT arrangements given by makeineqmat(). Although scale_palette() gives the option of finding palettes with respect to other hyperplane arrangements, note that they may not all have the same underlying symmetries. It may not be the case that all scales in a palette have the same properties with respect to an arbitrary arrangement.

Usage

scale_palette(
  set,
  include_involution = TRUE,
  ineqmat = NULL,
  edo = 12,
  rounder = 10
)

Arguments

set

Numeric vector of pitch-classes in the set

include_involution

Should involutional symmetry be included in the applied transformation group? Defaults to TRUE.

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 strings "white," "black", "gray", "roth", "infrared", "pastel", "rosy", "infrared", or "anaglyph", giving the ineqmats of make_white_ineqmat(), make_black_ineqmat(), make_gray_ineqmat(), make_roth_ineqmat(), make_infrared_ineqmat(), make_pastel_ineqmat(), make_rosy_ineqmat(), make_infrared_ineqmat(), or make_anaglyph_ineqmat(). For other arrangements, this parameter accepts explicit matrices.

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

A matrix whose columns represent the colors in set's palette.

Examples

# The palette of a minor triad is all inversions of major and minor:
minor_triad <- c(0, 3, 7)
scale_palette(minor_triad)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    0    0    0    0    0    0
#> [2,]    3    4    5    5    4    3
#> [3,]    7    9    8    9    7    8

# But 12edo is a little too convenient. The palette of the just minor triad
# involves some less-consonant intervals:
just_minor <- j(1, m3, 5)
scale_palette(just_minor)
#>          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]
#> [1,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
#> [2,] 3.156413 3.863137 4.980450 4.843587 4.136863 3.019550
#> [3,] 7.019550 8.843587 8.136863 8.980450 7.156413 7.863137

# The palette of the diatonic scale includes all 42 well-formed heptachord colors:
dia_palette <- scale_palette(sc(7, 35))
dim(dia_palette)
#> [1]  7 42
table(apply(dia_palette, 2, iswellformed))
#> 
#> TRUE 
#>   42 

# The Rothenberg arrangements do not have the same symmetries as the MCT arrangements,
# so Rothenberg properties are not preserved in a palette:
proper_trichord <- c(0, 5, 6)
roth_palette <- suppressWarnings(scale_palette(proper_trichord, ineqmat="roth"))
apply(roth_palette, 2, isproper)
#> [1]  TRUE  TRUE  TRUE FALSE FALSE FALSE
# Not all the scales in this palette are "proper" even though the input was!