optc_test: Does a scale lie in the canonical fundamental domain for OPTC...

In musicMCT: Analyze the Structure of Musical Scales

Does a scale lie in the canonical fundamental domain for OPTC symmetries?

Description

Modal Color Theory is capable of describing "scales" (perhaps "melodies" might be more accurate) which do all sorts of non-scalar things, like repeating notes, ascending and descending inconsistently, not observing octave equivalence, and so on. This function tests whether an input has a 'well-behaved' form in that it starts on 0, only ascends, doesn't repeat pitches, and doesn't go above the octave. If you find an interesting scale structure represented by a set that doesn't satisfy these constraints, you can always desaturate it until it does (i.e. call something like saturate(.1, my_scale_with_bad_OPTCs)).

Usage

optc_test(set, edo = 12, rounder = 10, single_answer = TRUE)

Arguments

set	Numeric vector of pitch-classes in the set
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.
single_answer	Should the function return a single value of TRUE or FALSE? Defaults to TRUE. If set to FALSE, returns a vector of 4 Boolean values that indicate whether the scale individually passes O, P, T, and C criteria for being in the fundamental domain.

Value

Either a single Boolean value or a vector of 4 Boolean values, depending on the single_answer argument.

Examples

major_triad_normal_form <- c(0, 4, 7)
major_triad_open_spacing <- c(0, 7, 16)
major_triad_voice_crossing <- c(0, 7, 4)
major_triad_on_des <- c(1, 5, 8)
major_triad_doubled_third_omit_5 <- c(0, 4, 4)
example_triads <- cbind(major_triad_normal_form,
			   major_triad_open_spacing,
			   major_triad_voice_crossing,
			   major_triad_on_des,
			   major_triad_doubled_third_omit_5)

apply(example_triads, 2, optc_test)
optc_test(major_triad_voice_crossing, single_answer=FALSE)

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