Minimal voice leadings to all transpositions of some Tn-type mod k

Given a starting set (source) and some tn-type as a voice leading goal (goal_type), find the minimal voice leading to every transposition (in some mod k universe) of the goal. If a goal is not specified, the goal is assumed to be the tn-type of the source set. This lets you see, for example, the minimal voice leading from C7 to other dominant seventh chords mod 12. I couldn't think of a suitably serious and clear name for this information, so the metaphor behind "rolodex" is that these voice leadings are the contact information that source has for all its acquaintances in goal_type.

Usage

vl_rolodex(
  source,
  goal_type = NULL,
  reorder = TRUE,
  method = c("taxicab", "euclidean", "chebyshev", "hamming"),
  edo = 12,
  rounder = 10,
  no_ties = FALSE
)

Arguments

source: Numeric vector, the pitch-class set at the start of your voice leading
goal_type: Numeric vector, any pitch-class set representing the tn-type of your voice leading goal
reorder: Should the results be listed from smallest to largest voice leading size? Defaults to TRUE. If FALSE results are listed in transposition order (i.e. \(T_1\), \(T_2\), ..., \(T_{edo-1}\), \(T_0\)).
method: What distance metric should be used? Defaults to "taxicab" but can be "euclidean", "chebyshev", or "hamming".
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.
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.

Value

A list of length edo, each entry of which represents a voice leading (or group of tied voice leadings). List entries are named by their transposition level.

Examples

vl_rolodex(c(0, 4, 7))
#> $`0`
#> [1] 0 0 0
#> 
#> $`4`
#> [1] -1  0  1
#> 
#> $`8`
#> [1]  0 -1  1
#> 
#> $`1`
#> [1] 1 1 1
#> 
#> $`3`
#> [1] -2 -1  0
#> 
#> $`5`
#> [1] 0 1 2
#> 
#> $`7`
#> [1] -1 -2  0
#> 
#> $`9`
#> [1] 1 0 2
#> 
#> $`11`
#> [1] -1 -1 -1
#> 
#> $`2`
#>      [,1] [,2] [,3]
#> [1,]    2    2    2
#> [2,]   -3   -2   -1
#> 
#> $`6`
#>      [,1] [,2] [,3]
#> [1,]    1    2    3
#> [2,]   -2   -3   -1
#> 
#> $`10`
#>      [,1] [,2] [,3]
#> [1,]    2    1    3
#> [2,]   -2   -2   -2
#> 

vl_rolodex(c(0, 4, 7), reorder=FALSE)
#> $`1`
#> [1] 1 1 1
#> 
#> $`2`
#>      [,1] [,2] [,3]
#> [1,]    2    2    2
#> [2,]   -3   -2   -1
#> 
#> $`3`
#> [1] -2 -1  0
#> 
#> $`4`
#> [1] -1  0  1
#> 
#> $`5`
#> [1] 0 1 2
#> 
#> $`6`
#>      [,1] [,2] [,3]
#> [1,]    1    2    3
#> [2,]   -2   -3   -1
#> 
#> $`7`
#> [1] -1 -2  0
#> 
#> $`8`
#> [1]  0 -1  1
#> 
#> $`9`
#> [1] 1 0 2
#> 
#> $`10`
#>      [,1] [,2] [,3]
#> [1,]    2    1    3
#> [2,]   -2   -2   -2
#> 
#> $`11`
#> [1] -1 -1 -1
#> 
#> $`0`
#> [1] 0 0 0
#> 

#Multisets sort of work! Best resolutions from dom7 to triads with doubled root:
vl_rolodex(c(0, 4, 7, 10), c(0, 0, 4, 7))
#> $`0`
#> [1] 0 0 0 2
#> 
#> $`3`
#> [1]  3 -1  0  0
#> 
#> $`5`
#> [1]  0  1 -2 -1
#> 
#> $`6`
#> [1]  1  2 -1  0
#> 
#> $`8`
#> [1]  0 -1  1 -2
#> 
#> $`9`
#> [1]  1  0  2 -1
#> 
#> $`11`
#> [1] -1 -1 -1  1
#> 
#> $`1`
#> [1] 1 1 1 3
#> 
#> $`2`
#> [1]  2 -2 -1 -1
#> 
#> $`4`
#>      [,1] [,2] [,3] [,4]
#> [1,]    4    0    1    1
#> [2,]   -1    0   -3   -2
#> 
#> $`7`
#>      [,1] [,2] [,3] [,4]
#> [1,]    2    3    0    1
#> [2,]   -1   -2    0   -3
#> 
#> $`10`
#>      [,1] [,2] [,3] [,4]
#> [1,]    2    1    3    0
#> [2,]   -2   -2   -2    0
#>