1.3 The different elements of a background graph
Now I am going to introduce some technical terms which describe different components of the background graph. The new terms introduced in Example 5 become more important when we analyse a more complicated piece of music, and they will enable you to follow the discussions below of other sections of Beethoven's Eighth Symphony.
The techniques of voice-leading analysis were first developed in German-speaking scholarship. One result is that technical terms exist in both German and English. This course uses the English translations of terms.
As you saw just now, the form of a tonal piece of music is based on one particular note of the tonic triad, which is prolonged (normally through the bulk of the piece) in the top voice of the harmony. This note is called the primary tone (or the head-note). In Example 5, A (the third of the tonic chord F major) is the primary tone.
The primary tone is made to descend, step by step, down to the tonic in order to close the form. This step-wise descending shape is called the fundamental line. The notes of the fundamental line are shown in a graph as unfilled noteheads with stems, and their number in the tonic scale is indicated above them with a caret (in Example 5, as a 
descent).
The fundamental line and the bass voice that harmonises it together make a piece of simple two-part counterpoint. The second-to-last note of the fundamental line is always harmonised by the dominant in the bass (so that in a descent such as Example 5, the bass always moves tonic-dominant-tonic). The two-part counterpoint which underpins the form of the music is called the fundamental structure.
In a voice-leading analysis of form, the background graph can be divided into several phases. At first, the music establishes the primary tone of the form. Sometimes, the primary tone is the first note of the piece; but often, the top voice of the music moves up to it gradually. This initial part of the graph is called the initial ascent.
Then, the primary tone remains the point of reference for the middle part of the graph (which is often the bulk of the piece) until it descends to the tonic note. We call this central part of the graph the prolongation of the primary tone, followed by the structural descent. The descent of the fundamental line to the tonic note is often a short, decisive move, though it may be more spread out; but the final move from 2 to 1 is termed the structural cadence or structural close of the form.
Sometimes, the cadence that completes the fundamental structure is the final cadence of the piece; but often (especially in longer pieces) the final tonic degree is prolonged for some time. We can call this last section the structural coda, and it serves to establish the finality of the close of the piece. It is not, of course, the same as the ‘coda’ in a traditional account of form: it may be the same section of music, but it may be much longer or shorter.
You can see that Example 7, although it describes only a short section of music, contains all the elements identified above. A short initial ascent is followed by a prolongation of the primary tone which covers most of the section, with the last two notes of the fundamental line coming close together in bars 73 and 74, and a brief structural coda, with hunting-horn type arpeggios on the horns and clarinets, emphasises the tonic F major triad at the end.
This trio is structured around a descent in the fundamental line, as we have seen. In other pieces, however, the fundamental structure can be organised around a descent from either of the other two notes of the tonic chord, as a 
or even an 
structure. In these cases, the structural cadence still takes place at the end of the fundamental line, elaborating the 
descent. The three possible forms of the fundamental structure are shown as Example 8.
There are two important points which are worth bearing in mind at the conclusion of this initial look at background structure.
First, whilst almost any piece of tonal music can be reduced to one of these three fundamental structures, the point of doing this can only be to show how the composer connects this very abstract background structure with the detail at the foreground that makes the piece sound unique. This means that the real value of an analysis of this sort lies in the elements of the graph or graphs which fill in the details of how the fundamental structure holds the piece together. So in Example 5, the harmonic detail that is extra to that contained in Example 8a, strictly speaking the middleground detail, is what begins to explore Beethoven's approach to the form of this short section. On its own, after all, Example 8a could refer to any of thousands of different pieces.
Secondly, the analysis involved in drawing a background graph is rather different from that involved in drawing a foreground graph. At the foreground, there really is very little room for doubt about what is right and what is wrong. Which notes are consonant and which are dissonant, and the difference between main and subsidiary harmonies, are things which only rarely turn out to be ambiguous (even if they can be difficult to track down). This is less true at middleground levels, as you found out in the discussion of three different ways of analysing the structure of the opening theme of Mozart's Sonata in A major K331 (Examples 28, 29 and 30 in OpenLearn course AA314_2 [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] ). At the background, even very experienced musicians may have quite different opinions about where the structural cadence of a piece occurs, and which musical events are structurally the most important. But this does not mean that such analysis is pointless. On the contrary, comparing different analyses of the same piece often reveals subtleties and depths to a composer's way of writing music.
With these points in mind, it is now time to look at other parts of Beethoven's Eighth Symphony. We won't be building up background graphs in the sort of detail that we applied to the trio of the third movement. But you should by now be able to follow a background graph alongside listening to the music or reading the score, and understand the description of the form that the graph represents.