anazero_fingerprint: Are regularities within or between sets in a pair?

In musicMCT: Analyze the Structure of Musical Scales

Are regularities within or between sets in a pair?

Description

As for other hyperplane arrangements, it is useful to consider the number of entries which equal 0 in an anaglyph signvector. However, such entries can represent three different types of regularity: regularity within the first set, regularity within the second set, or regularity in the comparison between them. This function distinguishes between those three types of hyperplanes.

Usage

anazero_fingerprint(set, edo = 12, rounder = 10)

Arguments

set	A vector of even length representing a pair of sets
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 with three entries, representing regularities in the first set, regularities in the second set, and regularities between them.

See Also

make_anaglyph_ineqmat(), svzero_fingerprint()

Examples

maj <- c(0, 4, 7)
sus2 <- c(0, 2, 7)
anazero_fingerprint(c(maj, sus2))

# The first entry shows that the major triad has 0 regularities.
# This is equivalent to:
countsvzeroes(maj)

# The second entry shows that the sus2 trichord has 1 regularity.
# This is equivalent to:
countsvzeroes(sus2)

# The final entry shows that the major triad's perfect fifth
# equals the size of the *two* perfect fifths in the sus2 trichord.
# We can visualize the whole set of relationships using a brightness
# graph:
brightnessgraph(maj, sus2)

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