make_black_ineqmat: Define hyperplanes for transposition-sensitive arrangements

In musicMCT: Analyze the Structure of Musical Scales

Define hyperplanes for transposition-sensitive arrangements

Description

The "black" hyperplane arrangement compares a set's scale degrees individually to the pitches of edoo(card) (where card is the number of notes in set). This primarily has the purpose of attending to the overall transposition level of a set. Most applications of Modal Color Theory assume transpositional equivalence, but occasionally it is useful to relax that assumption. Sum class (Straus 2018, \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1215/00222909-7127694")}) is a natural way to track this information, but the "black" arrangements do so qualitatively in the spirit of modal color theory. make_black_ineqmat() returns only the inequality matrix for the "black" arrangement, while make_gray_ineqmat() for convenience combines the results of make_white_ineqmat() and make_black_ineqmat().

Usage

make_black_ineqmat(card)

make_gray_ineqmat(card)

Arguments

card	The cardinality of the scale(s) to be studied

Value

A card by card+1 inequality matrix (for make_black_ineqmat()) or the result of combining white and black inequality matrices (in that order) for make_gray_ineqmat().

See Also

make_white_ineqmat()

Examples

# The set (1, 4, 7)'s elements are respectively below, equal to, and
# above the pitches of edoo(3).
test_set <- c(1, 4, 7)
signvector(test_set, ineqmat=make_black_ineqmat(3))

# The result changes if you transpose test_set down a semitone:
signvector(test_set - 1, ineqmat=make_black_ineqmat(3))

# The results from signvector(..., ineqmat=make_black_ineqmat) can
# also be calculated with coord_to_edo():
sign(coord_to_edo(test_set))
sign(coord_to_edo(test_set - 1))

musicMCT documentation built on June 21, 2026, 9:06 a.m.