howfree {musicMCT} | R Documentation |
Count a scale's degrees of freedom
Description
Some scalar structures can vary their specific pitches much more flexibly than others while retaining the same overall "color." For instance, the meantone family of diatonic scales is generated by a line of fifths and can only vary along one dimension: the size of the generating fifth. This literally defines a line in the MCT geometry, and if the scale moves off that line it ceases to have the same structure as the diatonic scale. (Notably, it stops being non-degenerate well-formed.) By contrast, the 5-limit just diatonic scale is defined by two distinct parameters: the size of its major third and the size of its perfect fifth. See "Modal Color Theory," pp. 26-27, for more discussion.
Usage
howfree(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
Single non-negative integer
Examples
c_natural_minor <- c(0, 2, 3, 5, 7, 8, 10)
c_melodic_minor <- c(0, 2, 3, 5, 7, 9, 11)
just_diatonic <- j(dia)
howfree(c_natural_minor)
howfree(c_melodic_minor)
howfree(just_diatonic)
howfree(c(0, 4, 7))
howfree(c(0, 4, 7), ineqmat="white")
howfree(c(0, 2, 6), ineqmat="mct")
howfree(c(0, 2, 6), ineqmat="roth")