Creating a Schenker Graph

The music theorist Heinrich Schenker created a method of analysing tonal music using, what are now known as Schenker graphs or diagrams. These use “normal” musical notation in non-standard ways.

Major problems creating a Schenker graph with lilypond are:

1. Precise alignment of notes between staves needed,
2. Note heads, stems, beams etc are used to notate musical structure not rhythm,
3. A note head may have more than one stem or none,
4. Slurs may be nested arbitrarily and can connect to both left and right of the same note head,
5. Harmonic connection lines may be drawn between staves.

Solutions:

1. By default all notes are eight notes and the (invisible) time signature is 1/8. A “missing” note head is implemented as a transparent note rather than a skip.
2. Most grobs are, by default, invisible. Each staff is structured as a series of “layers”, implemented as voices, containing all the notes, NoteCollision #'merge-differently-headed is set to true. Note heads are only visible in the “notes” voice, note heads are determined by setting NoteHead #'duration-log.
3. Harmonic connections are implemented by a note followers in separate “layers”.

\version "2.24.0"

\header{
  composer = "J.S. Bach"
  title = "Wenn wir in höchsten Nöten sein"
  subtitle = "Analysis from Gene Biringer's Schenker Text, Ex. 5-27"
% "BWV641"
  enteredby = "Kris Shaffer"
}

% See http://kris.shaffermusic.com/tech.html. for more information

% 'Add color...' sections are not the original author's, but added
% afterwards specifically for illustration in LilyPond's Documentation.

I = \once \override NoteColumn.ignore-collision = ##t

staffPiano = \new PianoStaff {
  \set Score.timing = ##f
  \set PianoStaff.followVoice = ##t
  <<
    \new Staff = "RH" { % Right hand
      \clef treble
      \key g \major
      \relative c'' {
        \override Staff.NoteCollision.merge-differently-headed = ##t
          <<
            {
              \override Beam.positions = #'(8 . 8)
              \hide NoteHead
              \override NoteHead.duration-log = #1
              s1 b8[^\markup 
              {
                  \override #'(baseline-skip . 0.5)
                                % Add color to markup in top staff
                                \column { \with-color #red \small { ^ 3 } }
              }
              s4. s1 a8^\markup 
              {
                \override #'(baseline-skip . 0.5)
                              % Add color to markup in top staff
                              \column { \with-color #red \small { ^ 2 } }
              }
              s4. s2 g8]^\markup 
              {
                            % Add color to markup in top staff
                \override #'(baseline-skip . 0.5)
                \column { \with-color #red \small { ^ 1 } }
              }
              s4.
              \revert Beam.positions
              \undo \hide NoteHead
              \revert NoteHead.duration-log
            }
            \\
            {
                % Add color to both Dashed Slurs in top staff
                \override Slur.color = #(x11-color "purple")
              \hide Stem
              s1
              \once \override Slur.height-limit = #6
              \once \override Slur.extra-offset = #'(1.25 . 0)
              \slurDashed
              \I b2_( s2
              \once \hide NoteHead
              b4) s
              \once \override Slur.height-limit = #3.25
              \once \override Slur.extra-offset = #'(.75 . 0)
              a2_( s4
              \once \hide NoteHead
              a4) g2
              \undo \hide Stem
            }
            \\
            \override Staff.NoteCollision.merge-differently-headed = ##t
            {
              \override Beam.positions = #'(4 . -3.25)
              \stemUp
              g8[ s s4 s2
              \stemDown
              \once \hide NoteHead
              \I b8] s8
              \override Beam.positions = #'(3 . -2.25)
              \stemUp
              a8[ s s4
              \stemDown
              c8] s s2 s s
            }
            \\
            {
                % Add color to all remaining Slurs in top staff
                \override Slur.color = #(x11-color "violet")
                \override PhrasingSlur.color = #(x11-color "violet")
              \hide Stem
              \override Stem.length = #0
                          % Add color to text markups in top staff
              g4_\( fis^(_\markup { \with-color #blue \tiny N } g)\)
              a^(^\markup { \with-color #blue \tiny P } b2)
              b4^(^\markup { \with-color #blue \tiny P }
              \stemUp
              \undo \hide Stem
              \override Stem.length = #10
              c8)^( s
              \override Stem.length = #14
              b4) s s
              \override Stem.length = #0
              \hide Stem
              \once \override Slur.extra-offset = #'(0 . 0.35)
                          % Add color to remaining text markup in top staff
              c4^\( b_(_\markup { \with-color #blue \tiny P } a)\) s2
              \revert Stem.length
            }
            \\
            {
              \hide Stem
              \hide NoteHead
              \override Stem.length = #0
              s1 s4 e4 s
              \change Staff = "LH"
              fis,4 s2
              \undo \hide Stem
              \undo \hide NoteHead
              \revert Stem.length
            }
            \\
            {
              \hide Stem
              \hide NoteHead
              \override Stem.length = #0
              s1 s s2
              fis'4 s
              \change Staff = "LH"
              g,4 s s2
              \undo \hide Stem
              \undo \hide NoteHead
              \revert Stem.length
            }
          >>
          \bar "|."
        }
      }

      \new Staff = "LH" { % Left hand
        \clef bass
        \key g \major
        \relative c' {
        \override Staff.NoteCollision.merge-differently-headed = ##t
        <<
        {
          \override Beam.positions = #'(-8 . -8)
          \hide NoteHead
          \stemDown
                      % Add color to long beam text markups in bottom staff
          \I g8[_\markup { \with-color #(x11-color 'LawnGreen) \bold I }
                      s4. s1 s s2
          \I d8_\markup { \with-color #(x11-color 'LawnGreen) \bold V }
                      s4.
          \I g,8]_\markup { \with-color #(x11-color 'LawnGreen) \bold I }
                      s4.
          \revert Beam.positions
          \undo \hide NoteHead
        }
        \\
        {
        \hide Stem
          \stemDown
          \override TextScript.extra-offset = #'(-11.75 . -12.25)
          \I g'2 s1 s s2 \I d2 g,2
          \undo \hide Stem
        }			
        \\
        {
            % Add color to all single-note Slurs in bottom staff
            \override Slur.color = #(x11-color "violet")
          \hide Stem
          \once \hide NoteHead
          \override Stem.length = #0
          g'4
          \once \override TextScript.padding = #0.25
                      % Add color to text markups in bottom staff
          a4_(^\markup { \with-color #blue \tiny P } b)
          fis4^(^\markup { \with-color #blue \tiny P } e)
          \once \hide NoteHead
          \once \override Slur.height-limit = #1.5
                      % Add color to remaining text markup in bottom staff
          c4^( d)^\markup { \with-color #blue \tiny N }
          \once \hide NoteHead
          \once \override Slur.extra-offset = #'(0 . 0.5)
          \I fis,4_(
          \undo \hide Stem
          \override Stem.length = #10
          \stemDown
          g4) s
          \once \override Slur.extra-offset = #'(0 . 0.25)
          \I c8_( s
          \hide Stem
          \revert Stem.length
          a4)
          \once \hide NoteHead
          \I d4^( d,4) s2
        }
        \\
        {
            % Add color to all two-note Slurs in bottom staff
            \override Slur.color = #(x11-color "violet")
          \hide Stem
          \hide NoteHead
          \I g'4^( s b) s2
          \undo \hide Stem
          \undo \hide NoteHead
          \override Beam.positions = #'(-4 . 1)
          \stemDown
          c,8[ s s4
          \stemUp
          fis,8] s
          \override Beam.positions = #'(1 . -4)
          g8[ s
          \stemDown
          b8] s
          \revert Beam.positions
          \hide Stem
          \hide NoteHead
          c4^( s d4) s s2
        }
        \\
        {
            % Add color to four-note Slur in bottom staff
            \override Slur.color = #(x11-color "violet")
          \hide Stem
          \hide NoteHead
          \override Stem.length = #0
          \stemDown
          \once \override Slur.height-limit = #3
          \once \override Slur.extra-offset = #'(0 . 0.25)
          \I g4_( s2. e4) s2. s2 s1 s2
          \undo \hide Stem
          \undo \hide NoteHead
        }
        \\
        {
            % Add color to dashed Slur in bottom staff
            \override Slur.color = #(x11-color "purple")
          \hide Stem
          \hide NoteHead
          \slurDashed
          \once \override Slur.height-limit = #6.0
          \once \override Slur.extra-offset = #'(0.5 . -0.25)
          \override Stem.length = #0
          g4_( s2. s1 g,4) s s1 s2
          \undo \hide Stem
          \undo \hide NoteHead
        }
      >>
      \bar "|."
      }
    }
  >>
}

\score {
  <<
    \staffPiano
  >>
  \layout {
    indent = 0.0
    ragged-right = ##f
    \context { \Staff \remove "Time_signature_engraver" }
  }
}

\paper { tagline = ##f }