Monday, August 23, 2010

What's it all about — Wolfie?

When I begin serious musical analysis with my undergraduate theory students, I always invite them to ponder the root of the word "analysis".

The ice thus broken, the games begin. A former teacher and then colleague of mine used to say that conventional musical analysis usually didn't go much further than "making a list of things in a piece that resemble other things in the piece." Yeah, that's about as far as I got in my undergraduate theory. Lists — good. But when you talk about a novel, you don't stop after you count the number of chapters and make a list of the characters. At the very least, you talk about how the form and the interaction of the characters make for a good story, right? Just for starters, anyway.

And so with musical analysis, yes, it's very important to note all of the technical features like keys, harmonic progressions, phrase lengths, odd phrase lengths, types of cadences, relative strengths of cadences, thematic and motivic transformations, formal divisions, modulations — just doing all of that is a buttload of work. It is to living in a house what drawing a picture of a house is.

It gets to the next level when you identify that, for instance, at a certain articulative point the cadence is strong and then ask questions. Why here? Why this cadence? Why not this other cadence, which would on the surface seemed to have worked just as well?

It eventually leads to questions that become progressively more cosmic. With any luck, there will be enough evidence in the piece to form a hypothesis to answer "what is this piece about?" You need pretty good analytical chops to go up the food chain just to get to the point where you can ask such a question.

Consider the slow movement of Mozart's 23rd Piano Concerto. Here are some statistics: it's in F-sharp minor, which is the relative minor of the key of the whole concerto. It is in an A-B-A form with codetta, with the B section in the key of A major. It's in compound time, and takes about 7 to 9 minutes to perform. It is one of only a very few pieces Mozart ever composed in the key of F-sharp minor.

I'll bet you can't wait to go out and listen to it, right?

Let me add some information: it's one of my desert island pieces. It's sad, wandering, gorgeous, and when it's over I always want to hear it again.

A good analysis should try to bridge the two descriptive paragraphs, don't you think? If you really love the music, find a way to show me in the music what makes it sad, what makes it wandering, what makes it gorgeous. What makes it a piece you want to hear over and over again? And if you're a composer — what is worth stealing here?

Well, since we are talking about music — there's not enough hard disk space in the world to hold the complete answer to that question. I've got a few partial answers that I've taught a few times, but of course they can't do much more than scratch the surface.

One of them has to do with a story and a few things that would go into the list of things that I think are true about this piece. Here's something that may be odd, may be not. After the luxuriant chromaticism and lush textures at the beginning of the movement, at the end the movement textures get simpler, and the complex melody of the opening is nowhere in evidence, instead replaced by a bunch of repeated notes.

So how do we get from



One response is tradition and function: the first excerpt is an opening, the second is an ending. Bravo! Brava! Bravi! You're well on your way. Why this ending? Why those repeated notes? Hypothesis: they sound good. Well, yes they do. They sound good an octave lower, too. Repeated D's sound good there, too. Response: it has to be C-sharps. It's the ending, so the note has to be in the tonic triad. Bravo! Brava! Bravi! Why not repeated A's? Or F-sharps? Response: because of what's in the piece that happens before? Okay, let's keep that thought as a metaphorical ball in the air. Response: could it be the, um, apotheosis of that simplifying of texture thing you mentioned before? It sure could. In fact, you seem to be implying that the textural simplification is there to call attention to the repeated C-sharps (by calling it an apotheosis). Response: okay, I guess so. So the gesture itself — triumphal or celebratory in nature? Is that even an affect?

Response: hey, I just noticed. C-sharp is the first note of the piece. The first melody note, that is. Bravoai! But that's not the same C-sharp as at the end of the piece, right? Didn't we decide that the repeated C-sharps "sound good" an octave lower, too?

Okay, let's connect the dots and see if we can follow whatever story is being told, or concluded, by those repeated notes at the end.

Those opening 12 bars: a 4-bar phrase that half cadences, followed by an 8-bar phrase, in which normally there are two harmonies per bar except for a pause before the final cadence where the Neapolitan sixth lingers for two whole bars, supporting an upward arpeggiation of that triad.

Oh yes. The opening passage is for the soloist only. The orchestra sits out until they join in at the final cadence. The orchestra's response is different music, much more regularly phrased.

The opening melody is a compound line, essentially two lines moving in parallel sixths for a while. And the general trajectory of the upper line is downwards, usually moving by step, spanning a tenth in the course of the whole passage.

And in the first four-bar phrase, the upper voice of the compound line drops out at the half-cadence. Why? Here it is greatly simplified:

At the half-cadence, the upper-line's note should be C-sharp. But Mozart withholds that note from us. We don't get to hear it, instead wondering why the D in the previous bar hasn't correctly moved down. Why would he do such a thing? It's obviously the next note of the upper line. And it's a chord tone if this is really a half cadence.

Sleight of hand. The upper line isn't ready to move, and indeed, the second phrase begins on that same D — and that means that line never moved, it's just being picked up exactly where it left off. So the half-cadence resolves from V to vi6? My theory textbook told me never to do that for a deceptive cadence because it ... let me get the tone right ... sounds dumb. Silly, it's not a deceptive cadence — cadences are endings, not beginnings. This is, instead a phrase that begins deceptively. But for what reason? Why all this sleight of hand?

Wait, what about those repeated C-sharps at the end? Aren't we trying to explain those? Be patient, my liege. But I'll return to your point that C-sharp is the first melody note of the piece. You must agree with that because 1) you said it already and 2) it's true.

So consider how Mozart opens on that C-sharp by ornamenting it with an upper neighbor, D, with what came to be known as the "Siciliana" figure — the Siciliana being a kind of dance that also was often associated (ironically) with the Neapolitan harmony.

Mozart being the proud contrapuntalist that he was, he naturally imitated it in another voice — in augmentation! Immediately afterward it happens in the left hand, played by the thumb.

Great, but what does that have to do with the price of eggs in China? And what the heck kind of question is that, anyway?

Maybe Mozart is setting something up. Wouldn't you say that C-sharp to D and back to C-sharp is being established as an important motive here? Response Yes, but what does that have to do with the top voice dropping out at the half-cadence?

Well, let's just say that maybe, just maybe, the reason that D doesn't move correctly down to C-sharp is that it's part of yet a bigger augmentation of the Siciliana motive. Voilà!
Response I think you're onto something. I think it's cool that the left-hand sonority, F-sharp and A, is exactly the same for all three of the notes in what you're calling the "middleground Siciliana figure." So that weird deceptive thing after the half cadence is part of a larger scheme, huh?

As far as I can tell, yes. And note that I already put into this phrase's list of statistics that the harmony changes twice per bar, except on the Neapolitan, which lingers four times as long as "normal". Any idea why? Response I think I see it. While the general trajectory is down for the melody here, there's an upward arpeggiation to the highest note of the whole piece so far, just before it settles much lower, on the tonic.

What is that highest note? Response high D. What does D in the melody do in this piece? Response it resolves downward, by half step, to C-sharp. Where does it do that here? Response It doesn't. Oh wait ...

No, that's correct. That D, unresolved, is hanging there for a very long time. Mozart has already shown the D resolving in three different time spans. This one is part of a fourth, far longer time span. And the resolution of that D – or maybe what we'd call the psychological need for the resolution of that D — causes a very strange anomaly when the opening music returns.

For you see, much later in the piece, the whole beginning is restated, without a single variation, thus restating the problem of the unresolved high D. But this time there is actually a deceptive cadence where there was the final cadence before, seeming momentarily to tonicize the Neapolitan (i.e. VI of F-sharp minor is also V of G, the Neapolitan of F-sharp minor). Oddly, it's the winds that intrude with VI where i was expected, and when they land back on the Neapolitan, the piano is forced to go back in time and repeat what it had played before — down to the Siciliana figure decorating G-natural and the upward arpeggio to D.

But this is not what it plays here. This time Mozart leaves out the arpeggio altogether and isolates the high D that's been causing all these problems, without letting any other notes get near it.

Then the final cadence for this section finally happens properly. So this time in this music, Mozart adds four bars for the express purpose of doubly calling attention to that pesky unresolved high D.

So without even looking at what happens between here and what we know happens at the ending, let's restate the question from earlier. Why this ending? Why those notes? Why not other ones, or the same ones an octave lower?

Response okay, now it's easy. It's that high D finally resolving, which must resolve in its own register, and the gesture is triumphal or even overstated because it has taken so long for the resolution to happen. And perhaps, just perhaps, that texture simplification thing is there so we really, really notice the resolution.

And maybe the textural simplification thing is part of another story, too. Remember when I said that the tutti music that followed the piano solo was different music? We haven't even brought that into the argument yet. It must be important, since Mozart has no other slow movements in his piano concertos that separate the thematic material this way. Response I'll work on that on my own. Any hints?

Yes. Look up the Hegelian dialectic. And when you're done with that, show me what makes this piece so full of sadness and longing. Response Hints? Yes. Start with the fourth species of counterpoint.

Update: I wrote a follow-up to this post.