Specific varieties of scalar subsets given a generic shape

Considered mod 7, the traditional triads of a diatonic scale are all instances of the generic shape (0, 2, 4). They come in three varieties: major, minor, and diminished. This function lists the distinct varieties of any similarly defined generic shape which occur as subsets in some specified scale (or larger set).

Usage

subset_varieties(subsetdegrees, set, unique = TRUE, edo = 12, rounder = 10)

Arguments

subsetdegrees: Vector of integers indicating the generic shape to use, e.g. c(0, 2, 4) for tertian triads in a heptachord. Expected to begin with 0 and must have length > 1.
set: The scale to find subsets of, as a numeric vector
unique: Should each variety be listed only once? Defaults to TRUE. If FALSE, each specific variety will be listed corresponding to how many times it occurs as a subset.
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 numeric matrix whose columns represent the specific varieties of the subset

Examples

c_major_scale <- c(0, 2, 4, 5, 7, 9, 11)
double_harmonic_scale <- c(0, 1, 4, 5, 7, 8, 11)

subset_varieties(c(0, 2, 4), c_major_scale)
#>      [,1] [,2] [,3]
#> [1,]    0    0    0
#> [2,]    4    3    3
#> [3,]    7    7    6
subset_varieties(c(0, 2, 4), c_major_scale, unique=FALSE)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    0    0    0    0    0    0    0
#> [2,]    4    3    3    4    4    3    3
#> [3,]    7    7    7    7    7    7    6
subset_varieties(c(0, 2, 4), double_harmonic_scale)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    0    0    0    0
#> [2,]    4    3    4    4    2
#> [3,]    7    7    6    8    6