In traditional pitch-class set theory, concepts like normal order and
primeform() establish a canonical representative for each equivalence
class of pitch-class sets. It's useful to do something similar in MCT
as well: given a family of scales, such as the collection of modes or a
scale_palette(), we can define the "primary color" of the family as the
one that comes first when the scales' sign vectors are ordered lexicographically.
primary_hue() uses ineqsym() to return a specific representative of
the primary color which belongs to the same palette of hues as the input.
Because primary_hue() focuses on hues rather than colors, it may not
highlight the fact that two scales have the same primary color. Thus, for
information about broader families, primary_colornum() returns the color
number of the primary color, primary_signvector() returns the sign vector,
and primary_color() itself uses quantize_color() to return a consistent
representative of each color.
Usage
primary_hue(
set,
type = c("all", "half_palette", "modes"),
ineqmat = NULL,
edo = 12,
rounder = 10
)
primary_colornum(set, type = "all", ...)
primary_signvector(set, type = "all", ...)
primary_color(set, type = "all", nmax = 12, reconvert = FALSE, ...)Arguments
- set
Numeric vector of pitch-classes in the set
- type
How broad of an equivalence class should be considered? May be one of three options:
"all", the default, uses the full range of
scale_palette()relationships"half_palette" uses
scale_palette()withinclude_involution=FALSE"modes" uses only the n modes of
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 theineqmats ofmake_white_ineqmat(),make_roth_ineqmat(),make_pastel_ineqmat(), andmake_rosy_ineqmat(). For other arrangements, the desired inequality matrix can be entered directly.- 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.- ...
Arguments to be passed to
primary_hue()- nmax
Integer, essentially a limit to how far the function should search before giving up. Although every real color should have a rational representation in some mod k universe, for some colors that k must be very high. Increasing nmax makes the function run longer but might be necessary if small chromatic universes don't produce a result. Defaults to
12.- reconvert
Boolean. Should the scale be converted to 12edo? Defaults to
FALSE.
Value
A numeric vector representing a scale for primary_hue(); a
single integer for primary_colornum(); a signvector() for
primary_signvector(); and a list like quantize_color() for
primary_color().
Examples
major_64 <- c(0, 5, 9)
primary_hue(major_64)
#> [1] 0 3 7
primary_hue(major_64, type="modes")
#> [1] 0 3 8
viennese_trichord <- c(0, 6, 11)
# Same primary color as major_64:
apply(cbind(major_64, viennese_trichord), 2, primary_signvector)
#> major_64 viennese_trichord
#> [1,] -1 -1
#> [2,] -1 -1
#> [3,] -1 -1
# But a different primary hue:
primary_hue(viennese_trichord)
#> [1] 0 2 5
# Only works with representative_signvectors loaded:
primary_colornum(major_64) == primary_colornum(viennese_trichord)
#> logical(0)
primary_color(major_64)
#> $set
#> [1] 0 1 3
#>
#> $edo
#> [1] 6
#>
primary_color(viennese_trichord)
#> $set
#> [1] 0 1 3
#>
#> $edo
#> [1] 6
#>