musicMCT (version 0.2.0)

set_to_distribution: Convert between pitch-class sets and distributions

Description

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(...)

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.)

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.

Examples

set_to_distribution(c(0, 4, 7))
s2d(c(0, 4, 7)) # Same result but quicker to type
s2d(c(0, 4, 4, 7)) # The doubled third is reflected by the value 2 in the result

minor_triad_distro <- c(2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0)
distribution_to_set(minor_triad_distro)
d2s(minor_triad_distro, multiset=FALSE)

# 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) 
d2s(tresillo_distro, reconvert=FALSE)