For applications of the Discrete Fourier Transform to pitch-class set theory, it's typically convenient to represent musical sets in terms of distributions rather than lists of their elements. (See Chapter 1 of Amiot 2016, doi:10.1007/978-3-319-45581-5.) These functions convert back and forth between those representations. s2d() and d2s() are shorthands for set_to_distribution() and distribution_to_set(), respectively.
Usage
set_to_distribution(set, edo = 12, rounder = 10)
distribution_to_set(
distro,
multiset = TRUE,
reconvert = TRUE,
edo = 12,
rounder = 10
)
s2d(...)
d2s(...)Arguments
- set
Numeric vector of pitch-classes in the set. May be a multiset, in which case the result is different from the corresponding set with repetitions removed. Entries must be integers.
- 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.- distro
Numeric vector representing a pitch-class distribution.
- multiset
Boolean. Should distribution_to_set() return a multiset if element weights are greater than 1? Defaults to
TRUE.- reconvert
Boolean. Should the scale be converted to the input edo? Defaults to
TRUE.- ...
Arguments to be passed from s2d() or d2s() to unabbreviated functions.
Value
set_to_distribution() returns a numeric vector with length
edo, whose ith entry represents the weight assigned to pitch-class
i in the distribution. distribution_to_set() returns a (multi)set
represented by listing its elements in a vector. (Non-integer weights are rounded
up to the next highest integer if multiset is TRUE.)
Examples
set_to_distribution(c(0, 4, 7))
#> [1] 1 0 0 0 1 0 0 1 0 0 0 0
s2d(c(0, 4, 7)) # Same result but quicker to type
#> [1] 1 0 0 0 1 0 0 1 0 0 0 0
s2d(c(0, 4, 4, 7)) # The doubled third is reflected by the value 2 in the result
#> [1] 1 0 0 0 2 0 0 1 0 0 0 0
minor_triad_distro <- c(2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0)
distribution_to_set(minor_triad_distro)
#> [1] 0 0 3 7
d2s(minor_triad_distro, multiset=FALSE)
#> [1] 0 3 7
# distribution_to_set automatically converts to 12edo, which
# can sometimes be undesirable, as in this case:
tresillo_distro <- c(1, 0, 0, 1, 0, 0, 1, 0)
d2s(tresillo_distro)
#> [1] 0.0 4.5 9.0
d2s(tresillo_distro, reconvert=FALSE)
#> $set
#> [1] 0 3 6
#>
#> $edo
#> [1] 8
#>