Applies subset_varieties() not just to a particular subset shape but to all possible subset shapes
given a fixed cardinality. For example, finds the specific varieties of all trichordal subsets of
the major scale, not than just the varieties of the tonal triad. Comparable to intervalspectrum()
but for subsets larger than dyads.
Arguments
- set
The scale to find subsets of, as a numeric vector
- subsetcard
Single integer defining the cardinality of subsets to consider
- simplify
Should "inversions" of a subset be ignored? Boolean, defaults to
TRUE- mode
String
"tn"or"tni". When defining subset shapes, use transposition or transposition & inversion to reduce the number of shapes to consider? Defaults to"tn".- 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 list whose length matches the number of distinct subset shapes (given the chosen options). Each entry of the list is a matrix displaying the varieties of some particular subset type.
Details
The parameter simplify lets you control whether to consider different "inversions" of a subset shape
independently. For instance, with simplify=TRUE, only root position triads (0, 2, 4) would be considered;
but with simplify=FALSE, the first inversion (0, 2, 5) and second inversion (0, 3, 5) subset shapes would
also be displayed.
Examples
c_major_scale <- c(0, 2, 4, 5, 7, 9, 11)
subsetspectrum(c_major_scale, 3)
#> $`0, 1, 2`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 2 1
#> [3,] 4 3 3
#>
#> $`0, 1, 3`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 1 2
#> [3,] 5 5 6
#>
#> $`0, 1, 4`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 1 1
#> [3,] 7 7 6
#>
#> $`0, 2, 3`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 4 3 4
#> [3,] 5 5 6
#>
#> $`0, 2, 4`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 4 3 3
#> [3,] 7 7 6
#>
subsetspectrum(c_major_scale, 3, simplify=FALSE)
#> $`0, 1, 2`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 2 1
#> [3,] 4 3 3
#>
#> $`0, 1, 3`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 1 2
#> [3,] 5 5 6
#>
#> $`0, 1, 4`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 1 1
#> [3,] 7 7 6
#>
#> $`0, 1, 5`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 1 2
#> [3,] 9 8 8
#>
#> $`0, 1, 6`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 2 1
#> [3,] 11 10 10
#>
#> $`0, 2, 3`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 4 3 4
#> [3,] 5 5 6
#>
#> $`0, 2, 4`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 4 3 3
#> [3,] 7 7 6
#>
#> $`0, 2, 5`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 4 3 3
#> [3,] 9 9 8
#>
#> $`0, 2, 6`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 4 3 4
#> [3,] 11 10 10
#>
#> $`0, 3, 4`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 5 6 5
#> [3,] 7 7 6
#>
#> $`0, 3, 5`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 5 5 6
#> [3,] 9 8 9
#>
#> $`0, 3, 6`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 5 5 6
#> [3,] 11 10 11
#>
#> $`0, 4, 5`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 7 7 6
#> [3,] 9 8 8
#>
#> $`0, 4, 6`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 7 7 6
#> [3,] 11 10 10
#>
#> $`0, 5, 6`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 9 9 8
#> [3,] 11 10 10
#>
subsetspectrum(c_major_scale, 3, mode="tni") # Note the absence of a "0, 2, 3" matrix
#> $`0, 1, 2`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 2 1
#> [3,] 4 3 3
#>
#> $`0, 1, 3`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 1 2
#> [3,] 5 5 6
#>
#> $`0, 1, 4`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 2 1 1
#> [3,] 7 7 6
#>
#> $`0, 2, 4`
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 4 3 3
#> [3,] 7 7 6
#>