Translate a hyperplane arrangement to a new center

By default, the various hyperplane arrangements of musicMCT treat the "white" perfectly even scale as their center. (It is the point where all the hyperplanes of the MCT, white, and black arrangements intersect, and although the Rothenberg arrangements do not pass through the scale by definition, it is still a center of symmetry for them.) This function let you construct hyperplane arrangements that have been shifted to treat any other set as their center. (Details on why you might want this to come.)

Usage

make_offset_ineqmat(set, ineqmat = NULL, edo = 12)

Arguments

set

Numeric vector of pitch-classes in the set intended to be the center of the new arrangement

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 the ineqmats of make_white_ineqmat(), make_black_ineqmat(), make_gray_ineqmat(), make_roth_ineqmat(), make_pastel_ineqmat(), and make_rosy_ineqmat(). For other arrangements, the desired inequality matrix can be entered directly.

edo

Number of unit steps in an octave. Defaults to 12.

Value

A matrix with the same shape as the ones that define the standard arrangement of type ineqmat

See also

makeineqmat() for modal color theory arrangements; make_white_ineqmat(), make_black_ineqmat(), and make_roth_ineqmat() for other relevant arrangements.

Examples

# When used for the sign vector with any central arrangement, the
# input `set` will have a sign vector of all 0s:
viennese_trichord <- c(0, 1, 6)
signvector(viennese_trichord, ineqmat=make_offset_ineqmat(viennese_trichord))
#> [1] 0 0 0

# Where does melodic minor lie in relation to major?
major <- c(0, 2, 4, 5, 7, 9, 11)
melmin <- c(0, 2, 3, 5, 7, 9, 11)
signvector(melmin, ineqmat=make_offset_ineqmat(major, ineqmat="white"))
#>  [1]  0 -1  0  0  0  0 -1  0  0  0  0  1  1  1  1  0  0  0  0  0  0