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Transpositional combination & pitch multiplication

Source: R/set_theory.R
tc.Rd

Cohn (1988) doi:10.2307/745790 defines transpositional combination as a procedure that generates a pc-set as the union of two (or more) transpositions of some smaller set. tc() takes the small set and a vector of transposition levels, returning the larger pc-set that results. (Pierre Boulez referred to this procedure as pitch "multiplication", which Amiot (2016) doi:10.1007/978-3-319-45581-5 shows to be not at all fanciful, as a convolution of two pitch-class sets.)

Usage

tc(set, multiplier = NULL, edo = 12, rounder = 10)

Arguments

set

Numeric vector of pitch-classes in the set

multiplier

Numeric vector of transposition levels to apply to set. If not specified, defaults to set.

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

Numeric vector of length \(\leq\) length(set) \(\cdot\) length(multiplier)

Examples

tc(c(0, 4), c(0, 7))
#> [1]  0  4  7 11
tc(c(0, 7), c(0, 4))
#> [1]  0  4  7 11

pyth_tetrachord <- j(1, t, dt, 4)
pyth_dia <- tc(pyth_tetrachord, j(1, 5))
same_hue(pyth_dia, c(0, 2, 4, 5, 7, 9, 11))
#> [1] TRUE