Which hyperplanes affect a given generic interval?

Given an ineqmat (i.e. a matrix representing a hyperplane arrangement), this function tells us which of those hyperplanes affect a specific generic interval size. (One specific application of this is is step_signvector(), which pays attention only to the comparisons between step sizes in a scale.)

Usage

get_relevant_rows(generic_intervals, ineqmat)

Arguments

generic_intervals

A vector of one or more integers representing generic intervals that can be found within the scale. Unisons are 0, generic steps are 1, etc.

ineqmat

The matrix of hyperplane normal vectors that you want to search.

Value

Vector of integers indicating the relevant hyperplanes from ineqmat

Examples

heptachord_ineqmat <- getineqmat(7)
heptachord_step_comparisons <- get_relevant_rows(1, heptachord_ineqmat)

# Create an ineqmat that attends only to the quality of (024) trichordal
# subsets in a heptachord.
heptachord_triads <- get_relevant_rows(c(0, 2, 4), heptachord_ineqmat)
triads_in_7_ineqmat <- heptachord_ineqmat[heptachord_triads,]

# Now, the following two heptachords have different colors
# but the same pattern of (024) trichordal subsets, so their signvector
# using triads_in_7_ineqmat is identical:
heptachord_1 <- convert(c(0, 1, 3, 6, 8, 12, 13), 17, 12)
heptachord_2 <- convert(c(0, 1, 3, 5, 7, 10, 11), 14, 12)
colornum(heptachord_1) == colornum(heptachord_2)
#> logical(0)
sv_1 <- signvector(heptachord_1, ineqmat=triads_in_7_ineqmat)
sv_2 <- signvector(heptachord_2, ineqmat=triads_in_7_ineqmat)
isTRUE(all.equal(sv_1, sv_2))
#> [1] TRUE
subset_varieties(c(0, 2, 4), heptachord_1, unique=FALSE)
#>          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]
#> [1,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
#> [2,] 2.117647 3.529412 3.529412 4.235294 3.529412 3.529412 3.529412
#> [3,] 5.647059 7.764706 7.058824 7.764706 7.058824 5.647059 7.058824
subset_varieties(c(0, 2, 4), heptachord_2, unique=FALSE)
#>          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]
#> [1,] 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
#> [2,] 2.571429 3.428571 3.428571 4.285714 3.428571 3.428571 3.428571
#> [3,] 6.000000 7.714286 6.857143 7.714286 6.857143 6.000000 6.857143
# Both have identical qualities for triads on scale degree 3, 5, and 7,
# which you can see by comparing columns 3, 5, and 7 in the two
# matrices above.