svzero_fingerprint {musicMCT} | R Documentation |
Distinguish different types of interval equalities
Description
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 |
edo |
Number of unit steps in an octave. Defaults to |
rounder |
Numeric (expected integer), defaults to |
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)
svzero_fingerprint(hex1)
svzero_fingerprint(hex2)
# Their brightness graphs make their difference more apparent:
brightnessgraph(hex1)
brightnessgraph(hex2)