Modal Color Theory is useful for analyzing scales in continuous pitch-class space with irrational values, but sometimes those irrational values can be inconvenient to work with. Therefore it's often quite useful to find a scale that has the same color as the one you're studying, but which can be represented by integers in some mod k universe. See "Modal Color Theory," 27.
Usage
quantize_color(
set,
nmax = 12,
reconvert = FALSE,
ineqmat = NULL,
target_edo = NULL,
edo = 12,
rounder = 10
)Arguments
- set
Numeric vector of pitch-classes in the set
- 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 the input edo? Defaults to
FALSE.- 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," "black", "gray", "roth", "pastel," or "rosy", giving theineqmats ofmake_white_ineqmat(),make_black_ineqmat(),make_gray_ineqmat(),make_roth_ineqmat(),make_pastel_ineqmat(), andmake_rosy_ineqmat(). For other arrangements, the desired inequality matrix can be entered directly.- target_edo
Numeric (expected integer) determining a specific equal division of the octave to quantize to. Defaults to
NULL, in which any potentialedowill be accepted.- 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
If reconvert=FALSE, a list of two elements: element 1 is set with a vector of integers
representing the quantized scale; element 2 is edo representing the number k of unit steps in the
mod k universe. If reconvert=TRUE, returns a single numeric vector measured relative
to the unit step size input as edo: these generally will not be integers. Values may be NA
if no suitable quantization was found beneath the limit given by nmax or in target_edo (if
specified).
Examples
qcm_fifth <- meantone_fifth()
qcm_lydian <- sort(((0:6)*qcm_fifth)%%12)
quantize_color(qcm_lydian)
#> $set
#> [1] 0 2 4 6 7 9 11
#>
#> $edo
#> [1] 12
#>
# Let's approximate the Werckmeister III well-temperament
werck_ratios <- c(1, 256/243, 64*sqrt(2)/81, 32/27, (256/243)*2^(1/4), 4/3,
1024/729, (8/9)*2^(3/4), 128/81, (1024/729)*2^(1/4), 16/9, (128/81)*2^(1/4))
werck3 <- z(werck_ratios)
quantize_color(werck3)
#> $set
#> [1] 0 1 4 7 9 13 14 18 20 22 26 28
#>
#> $edo
#> [1] 32
#>
quantize_color(werck3, reconvert=TRUE)
#> [1] 0.000 0.375 1.500 2.625 3.375 4.875 5.250 6.750 7.500 8.250
#> [11] 9.750 10.500
quantize_color(j(dia))
#> $set
#> [1] 0 3 5 6 9 11 14
#>
#> $edo
#> [1] 15
#>
quantize_color(j(dia), target_edo=22)
#> $set
#> [1] 0 4 7 9 13 16 20
#>
#> $edo
#> [1] 22
#>