Make Stunning Schenker Graphs with GNU Lilypond

GNU Lilypond provides an easy-to-use, yet extremely powerful, tool for generating musical notation, including Schenkerian Analysis graphs.
Cross-Staff Diagonal Lines

Occasionally, a melodic note corresponds to a bass note harmonically, but they are not sounded simultaneously and thus are not aligned vertically in the score. In Schenkerian notation, a simple diagonal line connecting the notes suffices to make this connection. Unfortunately, such a line is not as easy to create in Lilypond as in a graphical editor. However, it can be done rather painlessly with \change Staff. When creating our template, we added the line:

\set PianoStaff.followVoice = ##t

to our file. That line combined with \change Staff=LH or \change Staff=RH creates a diagonal line that follows the voice from one staff to the other. Thus, if you create a new voice in the upper staff with the following code:

\override Stem #'transparent = ##t
\override NoteHead #'transparent = ##t
\override Stem #'length = #0
s1 s4 e4 s
\change Staff=LH
fis,4 s2
\revert Stem #'transparent
\revert NoteHead #'transparent
\revert Stem #'length

you will get the first diagonal line in the Bach example, descending from the upper staff to the lower staff. The transparent noteheads and stems cause Lilypond to render only the diagonal line. Using invisible notes also allows you to alter the pitch of the start and end notes to adjust the height of each end of the line. Though this may seem to be overkill, the entire block of code easily can be cut and pasted to another voice or file, with the necessary adjustments being only height and beat placement, making this an easy solution. (If you really want to click and drag the line onto the graph, open the finished graph in an image editor and add the line there.)

The Unfolding Symbol

Figure 4. The unfolding symbol shows a harmonic connection between two notes in a melody.

The last Schenkerian idiom I cover here is the unfolding symbol. Briefly, this symbol signifies a harmonic connection between two notes in a melody. They typically occur in pairs, showing the use of two concurrent harmonic voices in one melodic line. They are surprisingly easy to create. When two simultaneous notes in a line are to be connected with the unfolding symbol (as in the lower staff of the Bach example), one simply needs two notes connected by beaming brackets, with the commands \stemUp and \stemDown in the appropriate locations. Of course, one must remember to remove stem transparency before creating the unfolding symbol and insert eighth-note skips appropriately to preserve vertical alignment:

\override Beam #'positions = #'(1 . -4)
g8[ s
b8] s

Notice the use of beam positions to adjust the height of the stems and the beam angle. When other notes occur between the two notes to be connected with an unfolding symbol, as in the upper staff of the Bach example, put the unfolding notes in one voice and the independent noteheads in another, with appropriate skips in each voice. For example, if the first voice contains:

\override Beam #'positions = #'(3 . -2.5)
a8[ s s2
d8] s
\revert Beam #'positions

and the other contains:

\override Stem #'transparent = ##t
s4 b c s
\revert Stem #'transparent

the end result will turn out like Figure 5.

Figure 5. Other notes can appear between two notes connected with an unfolding symbol.


Creating Schenkerian graphs in a graphical editor like Finale or Sibelius is enough to make many theorists revert to pencil and paper. The process is long and difficult, making changes to finished graphs is nearly impossible and you must do the same things to each graph every time you create a new one. However, with GNU Lilypond and the above tools, any musician can create beautiful Schenker graphs with minimal headaches and maximum control. Lilypond's text-to-music method makes it easy to edit hidden elements, modify finished graphs, and cut and paste code to future projects. Though the methods take time to learn, in the long run Lilypond saves time, energy and frustration, all the while creating stunning output. The tools and examples in this article should put you well on your way to creating beautiful Schenker graphs and some other forms of advanced musical notation with this great application.

Resources for this article: /article/8583.

Kris Shaffer lives in New Haven, Connecticut, where he is pursuing a PhD in Music Theory at Yale University. An open-source enthusiast as well, he has written for, and Kris is also co-founder of, an on-line community for composers and music theorists, which is making its debut in Fall 2005. His personal Web site is