Distinguish different types of interval equalities

Not all hyperplanes are made equal. Those which represent "formal tritone" comparisons and those which are "exceptional" because they check a scale degree twice ("Modal Color Theory," 40-41) play a different role in the structure of the hyperplane arrangement than the rest. This function returns a "fingerprint" of a scale which is like countsvzeroes() but which counts the different types of hyperplane separately.

Usage

svzero_fingerprint(set, ineqmat = NULL, edo = 12, rounder = 10)

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 strings "white," "black", "gray", "roth", "infrared", "pastel", "rosy", "infrared", or "anaglyph", giving the ineqmats of make_white_ineqmat(), make_black_ineqmat(), make_gray_ineqmat(), make_roth_ineqmat(), make_infrared_ineqmat(), make_pastel_ineqmat(), make_rosy_ineqmat(), make_infrared_ineqmat(), or make_anaglyph_ineqmat(). For other arrangements, this parameter accepts explicit matrices.

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

Numeric vector with 3 entries: the number of 'normal' hyperplanes the set lies on, the number of 'exceptional' hyperplanes, and the number of hyperplanes which compare a formal tritone to itself.

Examples

# Two hexachords on the same number of hyperplanes but with different fingerprints
hex1 <- c(0, 1, 3, 5, 8, 9)
hex2 <- c(0, 1, 3, 5, 6, 9)
countsvzeroes(hex1) == countsvzeroes(hex2)
#> [1] TRUE
svzero_fingerprint(hex1)
#> [1] 3 4 1
svzero_fingerprint(hex2)
#> [1] 1 6 1

# Their brightness graphs make their difference more apparent:
brightnessgraph(hex1)

brightnessgraph(hex2)