As "Modal Color Theory" describes (pp. 25-26), each distinct scalar "color" is determined
by its relationships to the hyperplanes that define the space. For any scale, this
function calculates a sign vector that compares the scale to each hyperplane and returns
a vector summarizing the results. If the scale lies on hyperplane 1, then the first
entry of its sign vector is 0. If it lies below hyperplane 2, then the second entry
of its sign vector is -1. If it lies above hyperplane 3, then the third entry of its
sign vector is 1. Two scales with identical sign vectors belong to the same "color".
Arguments
- set
Numeric vector of pitch-classes in the 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.
Value
A vector whose entries are 0, -1, or 1. Length of vector equals the
number of hyperplanes in ineqmat.
Examples
# 037 and 016 have identical sign vectors because they belong to the same trichordal color
signvector(c(0, 3, 7))
#> [1] -1 -1 -1
signvector(c(0, 1, 6))
#> [1] -1 -1 -1
# Just and equal-tempered diatonic scales have different sign vectors because they have
# different internal structures (e.g. 12edo dia is generated but just dia is not).
dia_12edo <- c(0, 2, 4, 5, 7, 9, 11)
just_dia <- j(dia)
isTRUE( all.equal( signvector(dia_12edo), signvector(just_dia) ) )
#> [1] FALSE