Saturation parameterizes scale structures along a single degree of freedom
which corresponds to size of the vector from the "white" perfectly even
scale to the scale in question. Variation in a scale's saturation minimally
affects its structural properties. The function saturate() takes
in a scale and a saturation parameter (r) and returns another scale
along the same line (i.e. including the scale's hue and its scalar
involution–see "Modal Color Theory," 32).
Arguments
- r
Numeric: the relative proportion to (de)saturate the set by. If r is set to 0, returns white; if r = 1, returns the input set. If 0 < r < 1, the saturation is decreased. If r > 1, the saturation is increased, potentially to the point where the set moves past some OPTIC boundary. If r < 0, the result is an "involution" of the set.
- set
Numeric vector of pitch-classes in the set
- edo
Number of unit steps in an octave. Defaults to
12.
Examples
lydian <- c(0, 2, 4, 6, 7, 9, 11)
qcm_fifth <- meantone_fifth()
qcm_dia <- sort(((0:6)*qcm_fifth)%%12)
evenness_ratio <- evenness(qcm_dia) / evenness(lydian)
desaturated_lydian <- saturate(evenness_ratio, lydian)
desaturated_lydian
#> [1] 0.000000 1.931569 3.863137 5.794706 6.965784 8.897353 10.828921
qcm_dia
#> [1] 0.000000 1.931569 3.863137 5.794706 6.965784 8.897353 10.828921
ionian <- c(0, 2, 4, 5, 7, 9, 11)
involution_of_ionian <- saturate(-2, ionian)
convert(involution_of_ionian, 12, 42)
#> [1] 0 4 8 19 23 27 31
asword(ionian)
#> [1] 2 2 1 2 2 2 1
asword(involution_of_ionian)
#> [1] 1 1 2 1 1 1 2