musicMCT (version 0.1.2)

howfree: 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)

Value

Single non-negative integer

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 "white," "roth", "pastel," or "rosy", giving the ineqmats of make_white_ineqmat(), make_roth_ineqmat(), make_pastel_ineqmat(), and make_rosy_ineqmat(). For other arrangements, the desired inequality matrix can be entered directly.

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.

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")