Wednesday, February 27, 2008

More music theory. Sorry for boring you :)

A little more on Schenker. It'll be brief, because it's cold and I don't have any pants on (trying to fall asleep when this occurred to me).

I was thinking of the possibility of doing my dissertation on analyses of the Beethoven sonatas, looking at sonata form in particular. There are a few interesting anomalies: the
strange second key of the first movement of the Waldstein, the false recap in the first movement of opus 10 no. 2 (at which I'm looking right now), the third movement of the same, with a second theme that scarcely does anything at all, etc.

So I thought of why I would want to do Schenkerian analyses of so much stuff. What's my project?

I'm not a fan of hierarchies, as most of you know, and Schenkerian analysis is often criticized and praised for being hierarchical. Part of my project for the topic I'm working on now is to fix that, but to do so, I have to explain what it means to be hierarchical, or how is Schenker's work so?

We might say Schenkerian analysis is hierarchical in two ways. First, there is are the various layers, from the background to the foreground (or vice versa)--this is what I was talking about in my previous post. This, the most common citation for hierarchy, is hierarchy improperly so-called. A more proper designation would be a continuum. Schenker says "always the same, but never the same way," or something like that. That is, every piece of (tonal) music has the same fundamental structure: the triad. But it is always composed out differently. Implicit in this position is that it is the composing-out of the triad that makes music so swell. On the one hand, then, you have the governing background, which is clearly important (for mystical as well as practical reasons, for Schenker); on the other hand, you have the intricate foreground, which, particularly since Schenker was concerned perhaps first of all with performance, is of unavoidable importance. I would submit that these two extremes, mediated by the myriad middlegrounds, are both extremely important. And while Schenker's rhetoric is not consistent on the matter, I would also submit that neither is subsumed under the other, though perhaps they are both subordinate to one another.

This (non) hierarchy does bring us to the true hierarchy, though. This is the primacy of the top voice (or maybe the soprano/bass counterpoint. I need to work out the details there with the original sources and the quite substantial secondary literature). Since "all" music is a composing out of the tonic triad by means of a descending linear progression, all music is then governed by a single coherent melodic line. Consequentially, all material appearing above this line is simply--or merely--an inner voice that has been displaced (and, significantly, which often then has to work its way back to where it belongs).

I propose that a more useful reappropriation of Schenkerism would be to retain his (non) hierarchical reductionism and his privileging of voice leading at the expense of key relations and functional harmony, but to dispense with his mystical reliance on the tonic triad and it's resultant Urlinie. This seems the most reasonable way to allow the second theme group of a sonata to be equally important in both its manifestations (but also markedly different each time), and is supported by Forte and Gilbert's reading of Beethoven opus 10, no. 1, III. It is also contrary to Charles Smith's position, which necessitates the adoption of numerous new fundamental structures, in the attempt to 1) hierarchize that which I argue above is not in fact hierarchical, and 2) to locate all important formal events on the same level. Reading layers as non-hierarchical allows us to see that Smith's move is not necessary: middleground events are not non-structural, nor a-formal, and re-writing the voice leading to make them so is not a desirable solution.

Friday, February 22, 2008

Introduction to Schenkerian Sonata Form

So the source of my anger is not mine alone. Apparently a few scholars have been trying to grapple with Schenker's inattention to the recapitulation of sonata form. It's like this:

For Schenker, a piece of (tonal) music is made coherent by its relationship to the tonic triad. Specifically, one of the three notes of this triad is chosen by the composer as the starting point, and the piece acts more or less like an elaborated step-wise descent from this top note. So a piece in C would read:

E - D - C
G - F - E - D - C
C - B - A - G - F - E - D - C.

The passing tones, originally a dissonant diminution of the tonic, are made consonant by simultaneous elaborations in the bass, creating new chords and moving to new key areas. These elaborations are in turn elaborated, and through the complicated process of compositional improvisation, the piece comes into being. Fundamentally, though, everything in tonal music is heard, in this model, as deriving from this stepwise descent.

One of the ways that a composer will extend the background descent is through more local linear descents and ascents, called linear progressions. This is a process more or less analogous to the background descent, serving to prolong both the active tone of the background and the harmony supporting it. On a deeper level, linear progressions are a motion from an upper voice to an inner voice (or from an inner voice to an upper voice, in the case of the ascent). So a middleground linear progression, when seen closer to the background, can be verticalized, revealing a contrapuntal relationship between two voices in the larger harmonic progression.

An important phenomenon that relates to the fundamental structure, as described above, is interruption. This is when the linear descent is arrested at the second scale degree and has to restart. It looks like this:

E - D || E - D - C
G - F - E - D || G - F - E - D - C

This structure is not available to pieces that descend from the octave, since that interruption would, according to Schenker, simply be an elaborated step up from C to D, with the latter pitch displaced an octave. Instead, the 8-line is often divided thus:

C - B - A - G || G - F - E - D - C

The relationships between middleground linear progressions and the background play an important role in the generation of musical forms. While each piece will manifest these structures and forms differently, in many cases it seems reasonable (both logically and empirically) to expect striking similarities between pieces from certain groups. These expectations are not always unproblematic.

The case I'm looking at is that of sonata-form movements. The formal characteristics of sonata form, particularly its key schemes, pose interesting problems for Schenkerian analysis, particularly since Schenker, like most of his contemporaries, saw sonata form as the pinnacle of musical art.

Sonata form works more or less like this:
Exposition - Development - Recapitulation.

The exposition, often marked off by a repeat sign, usually has four parts: A first theme group, in the tonic key; a transition, which sets up the next part, usually by modulating; a second theme group, often in the dominant or mediant (the latter is most common in minor mode sonatas); and a closing group, which reinforces the second tonal area and closes off the exposition. Often the transition and/or the closing section will be missing, but the first and second theme groups are necessary for sonata form.

The development often makes use of motivic material from the exposition, and has an unpredictable key scheme. Its purpose, according to Schenker, is to either precipitate the descent to the second scale degree, or, if the exposition already brought the background down to the second scale degree, the development will prolong that active tone. The development ends with scale degree 2 as the active tone, and the background structure at this point is interrupted (this means that the 8-line is a structural impossibility for sonata form, a result that is troublesome in itself).

The recapitulation recapitulates the exposition's material, but with an important difference: the second theme group is retransposed into the tonic key. This will often necessitate a reworking of the transition, and will, of course, also move the closing material into the tonic key.

In terms of structure, there are several possibilities to explore. As mentioned before, Schenker's insistence that sonata form involve an interruption, and his assertion that 8-lines cannot be interrupted, but only arrested, rules them out as a background structure. And since deep middle ground structures act to prolong the active tone, this also means that the first theme group will not be an 8-line either (which is almost certainly why Schenker modified his graph of Beethoven, opus 10, no. 2, I, which, in Meisterwerk II [1925] appears as an 8-line and in Der Freie Satz [1935] is treated as a 3-line). So, let us consider the remaining cases (I will only look at situations in which the second theme group is in the dominant or in the mediant, since these are by far the most common cases).

Second theme in the Dominant

In this case, the first theme and transition will bring the fundamental line down to scale degree 2, and the second theme, in the dominant, will prolong 2 with a middle ground descent of a fifth. In C:

G - F - E - D (d - c - b - a - g) ||

In the recap, this is pretty easy to handle. The recap reclaims G as the primary tone, restarting after an interruption. The first theme group is now recontextualized in such a way as to push its descent into the middle ground (although the music often will be exactly the same as it was in the expo, it takes on a different meaning because it's now the recapitulation), and the second theme, now retransposed to the tonic, will complete the descent in the background:

G (g - f - e - d) G - F - E - D - C (coda).

Schenker claims that most major-key sonatas are 3-lines, and he analyzes the first movement of the Eroica as such. This is when, as posted earlier, he ignores the second theme in the recap. We shall now see why:

As before, the first theme will descent to 2, and the second theme, again a 5-line will prolong. This will be followed by the recap reclaiming 3 again, and the second theme descending from 5, above the fundamental line (just as in Meisterwerk III):

E - D (d - c - b - a - g) || E - D (g - f - e - d) - C (coda)

The clear problem with this is that Schenker says that linear progressions, like the 5-line in the second theme group, always prolong their highest pitch, and represent a motion into an inner voice. This means that either the 5 in the second theme groups of the recap is the primary tone all along, or that linear progression is strictly cover: an inner voice superimposed on top of the primary melodic line. In the former case, it becomes quite difficult indeed to make sense of the material preceding the second theme groups reprise (which is most of the piece). The latter case pushes the second theme group close to the foreground, subordinating it to the point that one gets the impression that its return--the focus of sonata form's dramatic momentum--is trivial. This is interestingly consonant with how I presume many of Scalatti's keyboard sonatas (most of which are not in sonata form) would pan out.

Second theme in the Mediant

Schenker asserted that most mediant-directed sonata forms would be 5-lines. The scheme seems as though it would work like so (in A minor):

E (d- c- b -[a]) - (e - d- c) D - C - B || E - D - C (b - [a]) C - B - A (coda)

This works out much differently than the dominant cases above. The descent to 2 does not happen until the end of the development, rather than in the exposition, and the second theme of the exposition prolongs the primary tone, rather then scale degree 2. In the recap, the primary tone now descends to scale degree 3 in the first theme (with a middleground descent to 1 or 2 to close the theme group) and the retransposed second theme closes the primary line. The second theme fits nicely into this scheme, but the primary theme in the recap behaves quite strangely. One alternative possibility would be for a middle ground descent from 5 in the first theme of the recap, followed by a background descent to 3 during the transition (I don't mean to suggest trying to force this into an analysis, but rather suggest that some pieces might do this).

This is something Schenker did not try, although it's problems are similar to a dominant-directed 3-line.

In the exposition, we expect either a middle ground descent to 1 or 2 with the first theme group. This is followed by a phenomenon similar to that which we saw in the recap of the second theme above: the second theme comes in above the primary tone, either at scale degree 7 or 5, and descends to 3, which is still the active tone. 3 descends to 2 in the development, for the large-scale interruption. In the recap, 3 is regained, and the first theme is a middle ground descent again. Theme 2 is either a 3-line descent (this is the lest problematic case) or a 5-line, in which case we yet again have a superimposition:

C (b [a]) - ([g - f] - e - d -) C - B || C (b [a]) - [e - d] - C - B - A (coda).

Some closing remarks

Only one of these cases is unproblematic, and it's curiously one that Schenker did not consider viable. Two possible reworkings salvage the form.

1) Allen Forte suggests that not all descending linear progressions serve to prolong the highest note. Instead, they can prolong the low tone. This solves the earlier problems of overlap, in suggesting that a superimposed voice can act to prolong the upper voice (which is actually being covered up), and, at least to my mind, prevents the second theme group from being pushed too far to the foreground.

2) Abandon the background. This is what I'm working on. Instead of a fundamental descending line, why not a reduction based only on voice-leading. The fundamental structure is based upon the belief that all tonal music is organic, and flows from the mystical qualities of the triad. Schenkerian analysis is useful because it reveals the importance of voice-leading on more than just note-to-note events. Wedding it to an outdated (and in Schenker's case, quite chauvinist)
philosophy of organicism mires voice-leading in a structure that sonata form does not seem to support.

I'll have more on this possibility later, I hope. I need to actually write it down.

Thursday, February 14, 2008


I'm angry.

I'm trying to find out how Schenker reconciles the connection between the second theme of a sonata with the background structure during the recapitulation. In the exposition, the second theme appears either in the dominant or the mediant (usually). In these cases, the second theme can either prolong the second scale degree (in the former case) or the fifth (in the latter). However, once the recapitulation rolls around, and the second theme returns in the tonic key, it can't work out the same.

So I read Schenker's analysis Beethoven's 3rd symphony, a major key movement in sonata form that moves to the dominant for the second theme. Wanna know how Schenker solves the problem of the recapitulation? He skips it. Completely. He doesn't have it in his forground graph and in the prose he just doesn't mention it at all. He doesn't even apologize for skipping it. He's just hoping no one notices?


Monday, February 4, 2008

Just a Quickie.