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”.
\version "2.24.0"
%% http://lsr.di.unimi.it/LSR/Search?q=schenker
%% last improvement Feb. 2014.
%% updated by P.P.Schneider Feb. 2014.
%here starts the snippet:
\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 }
