Dodecaphonic staff with accurate ledger lines

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. Ledger lines follow the same pattern as the staff lines. Though such notation does not have to be microtonal, some quarter-tones have been added to show that they still work. Improvements are welcome.

\version "2.24.0"

\paper { tagline = ##f }

%% http://lsr.di.unimi.it/LSR/Item?id=619
%% for a different approach see: http://lsr.di.unimi.it/LSR/Item?id=694 and http://lsr.di.unimi.it/LSR/Item?id=755

% LSR originally contributed by Graham Breed for version 2.11.65
% Correct ledger line pattern added by Paul Morris (at version 2.18.2)

% 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)
    \override StaffSymbol.ledger-positions = #'(-5 -3 0 2 4 7)
    \override StaffSymbol.ledger-extra = #1
  }
}
\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
  }
}