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Show numbers in musical notes in Lilypond

Music is amazing but notation can be confusing. It doesn't have to be. Expressing musical notes as numbers makes the relations between them much more straightforward. As much as I want a revolutionary notation system based on 12 numbers[1], there is currently no implementation.

As I was searching for techincal solutions, I came across this blog post which included a snippet from Lilypond documentation. Lilypond is an open-source software for making sheet music based on text[2]. It supports adding note names (A~G) to note heads. In particular, the snippet shows how the note heads could be customized to show the degrees of notes in a scale using numbers 1~7. With some simple tweaking, I changed the numbers to 0~11 in a chromatic scale.

Due to the small size of the note heads, the numbers are a little hard to see. But they are still very helpful as an aid for reading music or learning music theory. It could also serve as a smooth transition path to the future notation system based on numbers. This method only requires adding a few lines to existing Lilypond files, which is the simplest acceptable solution to me.

The difference between "absolute" and "relative" is equivalent to the difference between "fixed-do" and "movable-do" solfege. Piano players may prefer the "absolute" system where 0 is always C, so the numbers correspond to piano keys (irrespective of sharps or flats). The "relative" system may be more preferable for isomorphic instruments where numbers map to fingering.

Copy-paste the following code to Hacklily for demo.

lisp
% absolute: 0=C, relative: 0=tonic
% change to ##f for absolute numbers
relative-number = ##t

#(define Ez_numbers_engraver
   (make-engraver
    (acknowledgers
     ((note-head-interface engraver grob source-engraver)
      (let* ((context (ly:translator-context engraver))
         (tonic-pitch (ly:context-property context 'tonic))
         (tonic-number (ly:pitch-semitones tonic-pitch))
         (grob-pitch
          (ly:event-property (event-cause grob) 'pitch))
         (grob-number (ly:pitch-semitones grob-pitch))
     (delta (modulo (- grob-number (if relative-number tonic-number 0)) 12))
         (note-names
          (make-vector 12 (number->string delta))))
    (ly:grob-set-property! grob 'note-names note-names))))))

#(set-global-staff-size 36)

\layout {
  ragged-right = ##t
  \context {
    \Voice
    \consists \Ez_numbers_engraver
  }
}
\markup {
  \bold Relative (0=tonic)
}
\markup \vspace #1
\markup {
  C Major
}
\relative c' {
  \easyHeadsOn
  c4 d e f
  g4 a b c
}
\markup {
  A Major
}
\relative c' {
  \easyHeadsOn
  \key a \major
  a4 b cis d
  e4 fis gis a
}
\markup {
  D Dorian
}
\relative c' {
  \easyHeadsOn
  \key d \dorian
  d4 e f g
  a4 b c d
}

  1. Such as Carrillo notation mentioned in this video, or Jianpu using 12 numbers instead of 7. ↩︎

  2. Another great open-source option is MuseScore, which is WYSIWYG. It supports adding note names or solfeges to the note heads, but there seems to be no customization. Someone could make a pull request or a plugin to support numbers. ↩︎