[MUSIC] So, if the first two movements of Opus 109 are models of economy, the last is spaciousness itself. This is one of so many ways in which the unchallenged dominance of the finale is established. It takes over twice as long to play as do the first two movements together. We have, as you'll remember, been leading to this point. I won't pause for review right now, but if you'd like, go revisit our discussion of the role of the last movement in Opus 7, then in Opus 27, Number 2, and then in the "Lebewohl." Each made meaningful advances, each gave the sonata finale a new role and an increased significance, but none comes close to the last movement of Opus 109 in length or, more significantly, in emotional reach. The movement is a set of variations, but it reinvents the form as profoundly, or perhaps moreso, as the first two movements reinvent or re-imagine sonata form. Let's briefly review the old model for the set of variations. Not invented by Beethoven, but frequently used by him early in life, more or less faithfully, as he did in the first movement of Opus 26. In this model, the first several variations will feature incremental decreases of the note values, which translates as gradual increases in speed. Following this, there is often a variation in a minor key, changing the mood, then sometimes a variation in a slower tempoâusually with a move towards a bell canto vocal styleâ and then a sort of virtuoso finale. Again, the point of this exercise is to, in assorted ways, embellish the theme. Profundity is not out of the question, but it is usually not the point, display being at the forefront. But when Beethoven turns to the variation form in his late periodâand he does so frequently, not only in 109, but in the last movement of Opus 111, the slow movement of the great Opus 131 string quartet, or in the Diabelli Variations themselvesâ he is invariably after something deeper. What was merely embellishment has become psychology. In these late sets of variations we see the theme turned inside out. Again, the theme and variations with its frequent repetitions of the same harmonic scheme, is in a way not conducive to drama. Certainly not structural drama. When I say that these late movements are psychological, I mean that the purpose of the variations is to wring every ounce of possibility from the theme. To find corners and meaning in it that one cannot perceive upon hearing it unadorned. And the theme of the last movement of Opus 109 already has plenty of evident meaning when we hear it initially. [MUSIC] As you can hear, the spaciousness which I mentioned, and which is new to the piece, is established instantly. But in addition to its profound beauty, this theme has another interesting feature, one which has important consequences for the movement as a whole. Again, regardless of the nature of the particular theme, we do not expect a set of variations to provide drama based on harmonic suspenseâout of a need for resolution established over a long period, like we have in the development of the sonata movement. That reality is heightened by the nature of this particular theme, which is notably repetitive in its own harmonic motion. The first half of the theme is subdivided into four groups of two bars each, and each features E moving to B, I moving to V. [MUSIC] In essence. The second half of the theme is one uninterrupted line, and it visits more harmonic outposts, but essentially, it is a movement from V back to I. This has two primary effects. First, given the lack of harmonic variety, of harmonic fodder in the theme, Beethoven will need to be fantastically resourceful in other ways to create sufficient material for the variations. The harmonic outline is generally the consistent factor in this form, variation to variation, so if it is not interesting on its own merits, that increases the burden on the composer to unearth other aspects of the music. Second, and to me, more crucial, is that this I-V is established and re-established absolutely relentlessly. Even if our focus is placed on counterpoint, on rhythm, on color, this most fundamental harmonic motion, I to V, and then back to I, is ever-present. Just as a side note, it is interesting that for a composer who was as enterprising as anyone ever in developing his materialâ some might say wrestling with itâBeethoven is also the first composer to be attracted to the dramatic possibilities that come from mere repetition. I was shocked when a composer told me that he thought of the second movement of the seventh symphony as being the first ever work of minimalism. But I am forced to admit that there is a kernel of truth in the statement. The first three variations do conform, at least on one level, to the old model of the variation set: the first... [MUSIC] the second... [MUSIC] and then the third. [MUSIC] But while these variations are not nearly as revolutionary as what is still to come, they do serve to open it outward, to add dimension to the theme rather than merely decorate its surface. The theme itself is, among other things, a chorale: the voices are all close together, and they move more or less in tandem. In the first variation, this sort of writing is immediately dispensed with, the melody separated by a distance of several octaves from what is now very obviously an accompaniment. And that accompaniment itself... [MUSIC] transforms what was very solemn music into almost a dance, or at least music with a suggestion of dance behind it. In the second variation the voices are made truly independent, with the two lines playing at different times and assuming roles of equal importance. And then in the third variation, Beethoven increases the speed, not only by changing the note values, as would be traditional, but by actually increasing the speed, with the marking becoming allegro vivace. In doing so, he creates a contrast of speed so dramatic, so jarring, that we feel we have not moved just from slow to fast, but from chasteness to wildness. So, these first three variations do, in fact, go beyond the traditional. But it is only with the fourth that the floodgates open. The only way I have ever been able to describe this variation is as a stream of consciousness. [MUSIC] Perhaps the most significant aspect of this is how much territory, not figurative but literal, is covered. Despite its greatness, the theme did have a certain modesty about it. The spacing of its chords is very tight, and its upper voice covers very little ground. From the bottom of its range to the top, it's scarcely more than an octave. Suddenly, in this fourth variation, Beethoven needs three voices, fully independent but woven together, and the entire span of the keyboard to convey where the theme has gone, what it has evolved into. The second half of the variation is still more fantastic in all senses of the word. It grows even larger, feels even more uncontainable. Listen again to the second half of the theme. [MUSIC] And now to the second half of the fourth variation. [MUSIC] Few things could make me feel so powerless as attempting to explain the magnificence of this. Clearly it is drawn out of the theme. And yet everything, even its fundamental shape, is altered. Its skeleton is almost imperceptible. The harmony is essentially the same, but it is obscured by the appogiaturas and the figuration, with this... [MUSIC] becoming this... [MUSIC] Even the climax, and it's a big one, the most crucial moment in the piece thus far, comes in a different place than it does in the theme. This... [MUSIC] versus this... [MUSIC] one bar earlier. When I say that this movement is about psychology, it never feels truer than at this juncture. We are now firmly in the world of dreams. How does Beethoven find his way out of this dream state? With a fugue. This is actually quite an influential idea. In the Romantic era, it became almost standard practice to prove one's mettle with a fugue in the middle of a work's finale. Composers as far afield as Tchaikovsky and Dvorak did it frequently with, frankly, mixed results. But, at the time of Beethoven's Opus 109, the idea is still a new one. [MUSIC] The previous variation irreversibly removed any shackles from the material, but this fugue adds still more to it. The third variation had had a comparable degree of energy and optimism. But this fifth has a questing quality as well. And because here the emphasis on counterpoint is obviously greater than ever, it conveys an increased sense of the music becoming more and more multilayered. There is an additional surprise and one of real significance in this variation. It features an extra repeat. Now, when I played the theme earlier, I did so without the repeats, but each half is meant to be played twice. And as was the custom, every variation up to this point has been shaped identically with two iterations of each half. Sometimes these are literal repeats, other times they are varied and therefore written out. But until this point, nothing interferes with the structural symmetry. But now, suddenly, the second half of the fugal variation appears not twice, but three times. Four variations in, we have structural expectations which have yet to be frustrated. Here, they are. This serves the dual function, one very connected to the other, of making the music seem to reach further into the unknown, and of creating a sense of uncertainty within a variation that was launched with great confidence. This could not be more timely, more appropriate, because it leads us to the last variation, which is as full of wonder as music comes. It resurrects the shape of the theme and returns to its speed. And in fact, at first it resembles the theme far more closely that do any of the variations that have come in the interim. What is new is that, though through virtually the whole variation, and with increasing insistence, there is now either in the bass or in the treble, a pedal point B, V. [MUSIC] It's so fascinating how after all the adventures this music has gone through, none of them really harmonic in essence, in its final moments, it is all about the B needing to resolve to an E. Of course, that basic resolution is always there in tonal music, but it is absolutely spotlighted here. It's highly ironic. In his recent sonatas Beethoven's interest in the ultimate, this ultimate resolution, once the central fact of sonata form, has seemed to be waning. Now, he chooses a theme and variation as his form, making that definitive V-I cadence far less crucial, and he is absolutely obsessed with it. In the last moments of the work, in which, as you will hear, Beethoven tests the possibilities of the instrument as stubbornly as he ever did, he is fixated exclusively on this search for the most fundamental classical resolution. [MUSIC] As you have heard, when this resolution finally comes, it is into the theme itself. Unusually, but not unprecedentedlyâ I'm thinking of the Goldberg VariationsâBeethoven offers us the theme as a recollection to bookend the work. But while the theme does arrive on the heels of a massive V-I cadence, this is not a recapitulation. There is no alteration to the theme here except for the one that has occurred within us, based on everything we have heard and all we have come to understand about the theme through these remarkable variations. Unlike with the sonata form, nothing about the structure here makes the return of the theme a necessity, and again, it is certainly not the norm within variations. But on account of the way in which this theme has been turned inside out, compressed in the third and fifth variations, stretched in every sense in the fourth, grappled with throughout, and finally tethered to this maddening pedal point, we need to hear it in its original form once again. The only difference between the two iterations of the theme, in short, lies in what has occurred. The theme has taken on vast new meaning for what it has been through, through the past it has now acquired. This is such a gateway to the music of the Romantic generation. The need for harmonic resolution has already, thanks to Beethoven's own work, begun to dissipate. And structure, a.k.a., our need for things to follow one another in a particular way, is more and more based on our memory of what we have already heard, even on our nostalgia for it. The reason we come back to great music again and again, as players or as listeners, is that you can barely ever scratch its surface. That is truer than ever in the case of late Beethoven, with its vision of the infinite. I have played Opus 109 for something like 17 years now, and I feel that I have come only marginally closer to it with time. But there is more sense of fulfillment in inching towards this music than there is in playing just about anything else. Let's take a short break for a review question.