Projects a scale onto the nearest point that lies on a target flat
of the hyperplane arrangement. project_onto() determines the target
flat from a list of linearly independent rows in ineqmat which define
the flat. match_flat() determines the target by extrapolating from a
given scale on that flat. Note that while the projection lies on
the desired flat (i.e. it will have all of the necessary 0s in its
sign vector), it will not necessarily belong to any particular color.
(That is, projection doesn't give you control over the 1s and -1s of
the sign vector.)
Usage
project_onto(
set,
target_rows,
ineqmat = NULL,
start_zero = TRUE,
edo = 12,
rounder = 10
)
match_flat(
set,
target_scale,
start_zero = TRUE,
ineqmat = NULL,
edo = 12,
rounder = 10
)Arguments
- set
Numeric vector of pitch-classes in the set
- target_rows
An integer vector: each integer specifies a row of
ineqmatwhich helps to determine the target flat. The rows must be linearly independent.- 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.- start_zero
Boolean: should the result be transposed so that its pitch initial is zero? Defaults to
TRUE.- 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.- target_scale
A numeric vector which represents a scale on the target flat.
Value
A numeric vector of same length as set, representing
the projection of set onto the flat determined by target_rows or
target_scale.
Examples
minor_triad <- c(0, 3, 7)
project_onto(minor_triad, 3)
#> [1] 0.0 3.0 7.5
project_onto(minor_triad, 1)
#> [1] 0.0 3.5 7.0
project_onto(minor_triad, c(1, 3))
#> [1] 0 4 8
# This last projection results in the perfectly even scale
# because that's the only scale on both hyperplanes 1 and 3.
major_scale <- c(0, 2, 4, 5, 7, 9, 11)
projected_just_dia <- match_flat(j(dia), major_scale)
print(projected_just_dia)
#> [1] 0.000000 1.946930 3.893860 5.026535 6.973465 8.920395 10.867326
# This is very close to fifth-comma meantone:
fifth_comma_meantone <- sim(sort(((0:6) * meantone_fifth(1/5))%%12))[,5]
vl_dist(projected_just_dia, fifth_comma_meantone)
#> [1] 0.04915723