Dodecaphonic staff

This twelve-note staff demonstrates a contemporary notation described by Erv Wilson. It works similarly to a piano keyboard: black notes are on the lines and white notes are in the spaces. Though such notation does not have to be microtonal, some quarter-tones have been added to show that they still work. Ledger lines do not follow the same pattern as the staff lines. Here they have been made as thin as possible for now; a better hack would be to draw them a bit higher, so that they're above the note head for C. (And draw them a bit lower below the staff so that the first one's under B.) Improvements are welcome.

\version "2.24.0"

\paper { tagline = ##f }

%% http://lsr.di.unimi.it/LSR/Item?id=619


% LSR originally contributed by Graham Breed for version "2.11.65"

% Dodecaphonic notation, after Erv Wilson, but probably an earlier idea.

\include "english.ly"

% set the nominals to be 12-equal
#(ly:set-default-scale (ly:make-scale '#(0 1/2 1 3/2 2 5/2 3 7/2 4 9/2 5 11/2)))

% Set the pitches to 12-equal with enharmonic equivalences
% keep the original pitch names.
% Preserves quartertones as half-sharps.
dodecaPitchNames =
  #(map
    (lambda (pitchname)
      (let* ((pitch (cdr pitchname))
             (nominal-steps
               (vector-ref '#(0 2 4 5 7 9 11) (ly:pitch-notename pitch)))
             (fractional-steps
                 (+ nominal-steps (* 2 (ly:pitch-alteration pitch))))
             (steps (inexact->exact (floor fractional-steps))))

        (cons (car pitchname)
              (ly:make-pitch
                (ly:pitch-octave pitch)
                steps
                (/ (- fractional-steps steps) 2)))))
    pitchnames)

#(ly:parser-set-note-names dodecaPitchNames)

\layout {
  \context {
    \Score
    \override StaffSymbol.line-positions = #'(-5 -3 0 2 4)
    % hack to suppress ledger line, seems to have a lower limit
    \override StaffSymbol.ledger-line-thickness = #'(0.0006 . 0)
  }
}

\score{
  \new Staff
    \relative c' {
    c d e f
    g a b c
    c, cs d ds
    e f fs g
    gs a as b
    c1
    c4 b bf a
    af g gf f
    e ef d df
    c1
    c4 cqs cs dqf
    d dqs ds eqf
    e eqs f fqs
    fs gqf g gqs
    gs aqf a aqs
    as bqf b bqs
    c1
  }
}