There can be little doubt that music theorists value consistency as much as any epistemic value. The reasons for this are clear enough.
Claiming that something and its opposite are both true creates dif-ficulties in making predictions; though prediction may not be the sole purpose of scientific inquiry, it is always the bottom line. To quote Quine: “[Prediction] is what gives science its empirical con-tent, its link with nature. It is what makes the difference between science, however high flown and imaginative, and sheer fancy.”1 When we confirm a theory, we do so through “the verification of its predictions.”2 The more predictions we verify, the more confident we will be about using our theory. The same can be said about building and testing music theories, as Schenker made perfectly clear near the start of Kontrapunkt I. According to him:
In this study, the beginning artist learns that tones, organized in such and such a way, produce one particular effect and none other, whether he wishes it or not. One can predict this effect: it must follow. Thus tones cannot pro-duce any desired effect just because of the wish of the individual who sets them, for nobody has the power over tones in the sense that he is able to demand from them something contrary to their nature. Even tones must do what they do.3
Several pages later, Schenker reinforced the point by noting that he was primarily interested in describing the abstract effects that a particular tone might have on the motion of a voice and not the psychological effects it might have on a listener: “Tones mean nothing but themselves; they are as living beings with their own social laws.”4
Although Schenker went to great lengths to ensure the consis-tency of his theory, he repeatedly ran into problems in one particular
area: the treatment of parallel perfect octaves and fifths. To under-stand the source of these contradictions, it is important to remember that tonal voice leading is founded on the notion that contrapuntal lines tend to move in contrary motion or in parallel thirds and sixths. In strict counterpoint, if a given pair of lines moves in the same direction, then they can never produce parallel perfect octaves and fifths between successive notes. But in functional monotonal-ity, a given pair of voices can contain parallel perfect octaves and fifths provided that those lines involve doublings and figuration or combinations of harmonic and non-harmonic tones. This subtle change from strict counterpoint to functional tonality is an essen-tial component of ‘The Heinrich Maneuver.’ We can also infer from Schenker’s motto, semper idem sed non eodem modo, that this principle applies consistently at all structural levels.
At least, that is what we are led to believe. Unfortunately, Schenker was not always able to preserve the laws of tonal voice leading from one level to the next; he ran into particular difficulties maintaining the laws prohibiting parallel perfect intervals. William Benjamin has described the problem as follows:
[O]n the one hand, [Schenker] accounts for certain foreground events in terms of the need to get rid of parallel fifths or octaves at a middleground level; on the other, he justifies certain parallel fifths and octaves in the fore-ground by noting that they are no longer present once a reduction to the next-higher level (a middleground) is accomplished.5
For his part, Schenker was perfectly aware of these inconsistencies;
in par. 161 of Der freie Satz, he claimed that the foreground “funda-mentally prohibits parallel octaves and fifths,” but was forced to concede that “the middleground frequently displays forbidden suc-cessions, it is then the task of the foreground to eliminate them.”6
We can illustrate the problem with a simple example. Figure 3.1 shows mm. 1–16 of Minuet II from Bach’s French Suite I in D Minor, BWV 812. As shown in figure 3.1a, the passage has two eight-bar phrases, each of which ends with a cadence in D minor. Each phrase is sequential in nature. These sequences are normally explained either in terms of the texture’s outer-voice counterpoint, in this case the repeating intervallic pattern 5–10–5–10, or in terms of local bass motion—in this case the repeating pattern of descending
fifths transposed by descending seconds. Such explanations are the ones we normally encounter in undergraduate theory classes or har-mony textbooks.7
Nevertheless, difficulties arise when we try to reconcile such explanations with a Schenkerian derivation of the music. From a global perspective, the most striking feature of the sequences is that they both support a stepwise descent in the upper voices from A to D, with A ornamented by B, G by A, and F by G. If we remove the ornamental notes and their supporting harmonies, then we are left with a chord succession I–VII–VI–V–I that violates the law prohi-biting parallel perfect octaves and fifths (see figure 3.1b, ‘The Parallel Problem’). These inconsistencies suggest that our common-sense distinction between structural and ornamental tones conflicts with the general laws of tonal counterpoint. This conflict, which we will refer to as ‘The Parallel Problem,’ is particularly vexing for those who believe that Schenkerian analysis give us “artistic statements, in music, about music.”8After all, how can we support such a view if our analyses include relationships that do not typically occur in tonal surfaces?
This is not, however, the only problem with sequences. If we take the distinction between structural and ornamental notes a step further, then we might suppose that the first chord in each portion of the sequence has priority over the second (see figure 3.1c, ‘The Top-Down/Bottom-Up Problem.’). According to this scheme, the A chord in m. 7 should have priority over the D chord in m. 8. But this reading is unconvincing; as the goal of the entire phrase, the final tonic D in m. 8 surely has priority over the dominant in m. 7.
Thus, describing sequences in “bottom-up” terms as some sort of repeating melodic, contrapuntal, or harmonic pattern conflicts with treating the phrase in “top-down” fashion as a prolongation of the tonic D. This topic, which we will refer to as ‘The Top-Down/
Bottom-Up Problem,’ is significant because it suggests that there may be inherent differences between the conventional ways in which we describe musical surfaces and the more radical ways in which Schenkerian theory derives them.
In short, sequences present us with some thorny questions. Can we, in fact, generate sequences like the one in figure 3.1 without violating the basic laws of tonal voice leading? Can we resolve
Figure 3.1. Sequences.
a. Bach, French Suite in D Minor, BWV 812, Minuet II, mm. 1–16
‘The Parallel Problem’ and ‘The Top-Down/Bottom-Up Problem’
using Schenkerian theory? This chapter sets out to answer these questions. Part 1 takes another look at sequential patterns like the one in figure 3.1 and suggests some concrete ways to overcome the hazards mentioned above. Next, Part 2 shows how these solu-tions can be grounded in familiar principles of counterpoint and in Schenker’s own concept of combined linear progressions; among other things, it shows that there are interesting connections between sequences and pedals. Part 3 then considers the analytical conse-quences of these ideas and presents detailed readings of several pieces, including the Minuet shown in figure 3.1.