minimize_vl: Smallest voice leading between two sets

In musicMCT: Analyze the Structure of Musical Scales

Smallest voice leading between two sets

Description

Given a source set and a goal to move to, find the voice leading from source to goal with smallest size.

Usage

minimize_vl(
  source,
  goal,
  method = c("taxicab", "euclidean", "chebyshev", "hamming"),
  no_ties = FALSE,
  edo = 12,
  rounder = 10
)

Arguments

source	Numeric vector, the pitch-class set at the start of your voice leading
goal	Numeric vector, the pitch-class set at the end of your voice leading
method	What distance metric should be used? Defaults to "taxicab" but can be "euclidean", "chebyshev", or "hamming".
no_ties	If multiple VLs are equally small, should only one be returned? Defaults to FALSE, which is generally what an interactive user should want.
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.

Details

Unless method="hamming", it is assumed that the minimal voice leading should be strongly crossing-free, so you might get strange results if your source and goal are not both in ascending order.

Using method="hamming" in principle should only care about preserving common tones, with no other restrictions on how voices move. This gives a profusion of tied voice leadings, which is not generally useful. This function therefore eliminates many of the options by requiring that the voices which aren't common tones make a minimal voice leading by the taxicab metric. Nevertheless, for multisets, method="hamming" can still return many tied possibilities.

Value

Numeric array. In most cases, a vector the same length as source; or a vector of NA the same length as source if goal and source have different lengths. If no_ties=FALSE and multiple voice leadings are equivalent, the array can be a matrix with m rows where m is the number of equally small voice leadings.

Examples

c_major <- c(0, 4, 7)
ab_minor <- c(8, 11, 3)
minimize_vl(c_major, ab_minor)

diatonic_scale <- c(0, 2, 4, 5, 7, 9, 11)
minimize_vl(diatonic_scale, tn(diatonic_scale, 7))

d_major <- c(2, 6, 9)
minimize_vl(c_major, d_major)
minimize_vl(c_major, d_major, no_ties=TRUE)
minimize_vl(c_major, d_major, method="euclidean", no_ties=FALSE)

minimize_vl(c(0, 4, 7, 10), c(7, 7, 11, 2), method="euclidean")
minimize_vl(c(0, 4, 7, 10), c(7, 7, 11, 2), method="euclidean", no_ties=TRUE)

natural_hexachord <- c(0, 2, 4, 5, 7, 9)
hard_hexachord <- c(7, 9, 11, 0, 2, 4)
minimize_vl(natural_hexachord, hard_hexachord, method="hamming")

musicMCT documentation built on June 21, 2026, 9:06 a.m.