Editing 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:

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

Solutions:

# 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.
# 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.
# Harmonic connections are implemented by a note followers in separate “layers”.

<lilypond 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 }
</lilypond>

[[Category:Specific notation]]
[[Category:Tweaks and overrides]]
[[Category:Contemporary notation]]