webern (0.1.0)

Elixir library for creating and working with 12-tone rows

API

Creating objects

Webern.row/1 provides a helper function to generate a new tone row consisting of pitch classes from the 12-tone semitone chromatic scale

Webern.matrix/1 accepts a row as an argument and returns a displayable matrix based on the row.

Transforming tone rows

Webern also provides functions for the standard serial transformations:

• prime - the original form of the row

• retrograde - the row backwards

  • if the prime form begins with pitch class indices [3, 5], the retrograde form will end with pitch class indices [5, 3]

• inverse - the row with the interval between each set of pitch classes flipped

  • if the first two pitch classes in the prime form of the row are [3, 5], the first two pitch classes of the inverse form will be [3, 1]; the upward step of 2 semitones becomes a downward step of 2 semitones

• retrograde_inverse - a compound transformation, acheived by taking first the inverse of the prime form, and then the retrograde of the resulting form

• inverse_retrograde - another, less common compound form, acheived by taking first the retrograde of the prime form, and then the inverse of the resulting form

For more information about twelve tone technique and transformations, see Twelve-tone technique on Wikipedia

Output

Both Webern.Row and Webern.Matrix implement the String.Chars protocol:

  iex> row = Webern.row([0, 2, 1, 3, 4, 6, 5, 7, 8, 10, 9, 11])
  iex> to_string(row)
  "c   d   cs  ef  e   fs  f   g   af  bf  a   b"

  iex> matrix = Webern.matrix(row)
  iex> to_string(matrix)
  "c   d   cs  ef  e   fs  f   g   af  bf  a   b
  bf  c   b   cs  d   e   ef  f   fs  af  g   a
  ...
  cs  ef  d   e   f   g   fs  af  a   b   bf  c"

Webern.Row.to_list/2 allows for more customized output of a row’s contents. Passing only the row to to_list/2 will return the pitch classes as integers

  iex> row = Webern.row([0, 2, 1, 3, 4, 6, 5, 7, 8, 10, 9, 11])
  iex> Webern.Row.to_list(row)
  [0, 2, 1, 3, 4, 6, 5, 7, 8, 10, 9, 11]

Passing the option to_pitches: true will convert the pitch classes to their lilypond formatted pitch class names, with 0 == c

  iex> row = Webern.row([0, 2, 1, 3, 4, 6, 5, 7, 8, 10, 9, 11])
  iex> Webern.Row.to_list(row, to_pitches: true)
  ["c", "d", "cs", "ef", "e", "f", "fs", "f", "g", "af", "bf", "a", "b"]

Passing a pitch class name as the option zero_pitch works as above, but will set 0 == zero_pitch

  iex> row = Webern.row([0, 2, 1, 3, 4, 6, 5, 7, 8, 10, 9, 11])
  iex> Webern.Row.to_list(row, to_pitches: true, zero_pitch: "fs")
  ["fs", "af", "g", "a", "bf", "b", "c", "b", "cs", "d", "e", "ef", "f"]

Webern provides the Webern.Lilypond protocol and its to_lily/1 function. This function embeds a valid LilyPond represenation of the row or matrix inside a full lilypond document string. For a row, this returns a result almost identical to calling to_string/1 on the row (the only change being octave markings for the pitch classes). For a matrix, the document will contain 60 rows, each of the five row transformations listed above for each chromatic semitone.

While Webern.Lilypond.to_lily/1 can be called on its own to return the LilyPond document string, Webern.to_lily/2 exists, which writes that document to a file (whose name is passed as the second argument) and compiles it to a PDF document, provided LilyPond is installed on your system.

  iex> row = Webern.row([0, 2, 1, 3, 4, 6, 5, 7, 8, 10, 9, 11])
  iex> Webern.to_lily(row, "my_row")
  :ok #=> this creates `my_row.ly` and `my_row.pdf` in your current working directory

Installation

1. Add webern to your mix.exs dependencies

    defp deps do
      [ {:webern, "~> 0.1"} ]
    end

2. Run mix do deps.get, compile

Dependencies

Most of Webern‘s functionality requires only an Elixir installation, but if you wish to use the Webern.to_lily/2 function provided, make sure LilyPond is installed on your system using the links and instructions found here.