Make Stunning Schenker Graphs with GNU Lilypond

In the early twentieth century, Heinrich Schenker developed a method of analyzing tonal music that ties a piece's melody, harmony and form to a simple underlying musical idea. To illustrate his theory, he created a notational system that clearly depicts these relationships. Schenkerian Analysis, as it is called today, is a staple of music theory, but it is notoriously difficult to notate using the industry-standard, proprietary music notation applications Finale and Sibelius.

The Open Source world, however, has an excellent music typesetter in GNU Lilypond, which now runs natively on Linux, Mac OS X and Microsoft Windows. Lilypond not only produces beautiful sheet music, it also puts a great deal of control at the user's fingertips. Additionally, its text-to-music rendering method makes it easier for a typesetter to control hidden elements. This makes Lilypond a powerful tool for creating Schenkerian notation graphs, which—by their nature—require extreme control of positioning, as well as the masking and hiding of notational elements.

In this article, I cover the creation of a Schenkerian graph that contains all of the most common Schenkerian notational elements, with explanations of what each element signifies and the code required to produce it. I assume that the reader has at least a basic knowledge of Lilypond, and thus give instructions only for the nonstandard code used for Schenker graphs. I also assume that the user is using Lilypond 2.6, though most of the tools I cover are valid for any 2.x version of Lilypond. Armed with a working knowledge of Lilypond and with the techniques explained in this article, any user should be able to produce beautiful Schenker graphs—and some other forms of advanced musical notation—in less time, with less effort and difficulty than when using a graphical music notation application.

There are a few simple steps to understanding a Schenker graph and how it represents an analysis of a piece. Two cardinal principles of tonal music form the foundation of Schenker's theory as an intrinsic part of the way we hear and perceive music. The first principle is the supremacy of the tonic (I) chord and the dominant (V) chord in the harmonic structure. That is, the chords built on the first and fifth notes of the scale. In the key of C major, this would be the C-major chord (I) and the G-major chord (V). The second principle is that the melodic structure is built upon a descending line, which ends on tonic (the first note of the scale).

A Schenkerian graph notates the structure of a piece in two main ways. First, rhythmic values are used to denote the structural importance of a note, not the length for which it should be played. Second, various musical markings—such as slurs, ties, beams and lines—are used to show the relationship of notes that have little structural importance to those that have greater structural significance. Schenkerian graphs also typically contain analytical markings such as Roman numerals for the harmony, scale-degree numbers and occasionally figured bass and analysis brackets.

As an example, let's use an excerpt of an analysis of J.S. Bach's Organ Chorale Prelude Wenn wir in hoechsten Noten sein, from Gene Biringer's book Schenkerian Theory and Analysis: A Bridge from Traditional Harmony, Counterpoint, and Form to Advanced Studies in the Analysis of Tonal Music (unpublished, Lawrence University Conservatory of Music). I chose this example because it clearly illustrates many of the standard Schenkerian notation elements, and I have made a few slight modifications to the graph to demonstrate the notation more completely. For the complete Lilypond file for this graph, see the on-line Resources.

Figure 1. J.S. Bach: Organ Chorale Prelude Wenn wir in hoechsten Noten sein

In this example, note the use of different rhythmic values—half notes, quarter notes and eighth notes. In this case, as in most Schenker graphs, the half notes are the notes of the fundamental structure, and they are also beamed together to highlight the structure most clearly. Next, observe the use of ties, beams and slur marks in the graph. Slurs are used to connect notes of lesser structural significance with the fundamental structure. In the above example, the second and third notes in the upper staff are slurred showing that the F-sharp is a neighbor tone (marked by N) to the more structurally important G. The tie between the two Gs surrounding that F-sharp shows that the second G is a prolongation of the first G. Dotted slurs and ties are also used by some theorists to show extended prolongation of a note. In Figure 1, three dotted slurs or ties show extended prolongations of notes with other forms of embellishment between.

Lastly, observe the diagonal lines between the two staves. These lines are used to connect a melodic note and a bass note that coincide structurally, but they are not performed simultaneously in the piece. When examining the graph in Figure 1, one can see that every note in the example can be connected via slurs, ties or beams to the fundamental structure of the piece, thus showing the role of every note in the structure of the piece.