[MUSIC] >> So, this revelry leads us towards the fifth and final section of this great, in every sense of the word, movement. And given that we've already had an arioso followed by fugue, and then a second arioso closely related to the first one, it's no great surprise that what comes now is a fugue closely tied to the first one. [MUSIC] >> The presence of this second fugue may be no surprise, but the content of the fugue itself is. In fact, it's a brilliant idea. Whereas the second arioso was in its melodic structure almost exactly the same as the first, the second fugue is a literal reversal, an inversion of the first. The upward fourths are now downward. [MUSIC] This turning the world upside down combined with the remarkable way in which we let into it makes the second fugue seem even more visionary, more like uncharted territory than the first. Once again, this movement takes a step further into the other worldly. And while the first fugue was fairly straight ahead, it played no tricks and its simplicity was its currency, this one treats the subject in a much more complex and sophisticated manner. Four phrases in, the subject is again flipped over so that it is once again in its original upward position. But this time with some serious rhythmic distortion. In the original version, each note was a dotted quarter, a half bar. [MUSIC] Now, we have two voices playing the same subject in eighth notes three times faster, while a third plays it in whole notes twice as slow. [MUSIC] This is like a microscope telescope effect. We simultaneously see or hear the theme as if from very close and from very far. Given that this fugue started in the wrong key and the subject moving in the wrong direction, this continued sense of dislocation makes sense. The subject has righted itself, but the ship hasn't, not quite. Rhythmically, we're all over the place. And we are now in C minor, neither in the home mode or the home key. The route back to A flat major, to safety, is like everything else in this movement, riveting. When the music eventually bends from minor to major, Beethoven asks for a slower tempo, but the note values increase so dramatically at that point it actually sounds faster, not slower. [MUSIC] And when the long awaited return to A flat major comes, we hardly even hear how it happens because the tempo gets faster and faster, robbing us of the time we need to process it. [MUSIC] The modulation is, in fact, completely coherent. Listen to it slowly. [MUSIC] But it goes by in such a flash, we just arrive in E flat major. We don't know how it happened. Nevertheless, it has happened. For the next few lines, maybe because the passage leading us to this point was so odd and compressed sounding, the music still feels as if it's in search of something. But bit by bit, it grows in confidence, and soon the sense of a rival becomes palpable. And when it does, the ecstasy of the moment is something to hear. This movement has been as winding and complex a path as Beethoven ever went down, certainly in an individual movement, certainly up to this point in his life. And it contains some of the most despairing music he ever wrote, not one but two passages of total blackness. So when the resolution comes, the euphoria is hard-earned and really beyond description. [MUSIC] And now, the series of rising forth reaches higher and higher towards infinity. [MUSIC] I've heard it said that Opus 110 is the most theoretical of the last three sonatas, the Holy Trinity. This business of the inversion of the fugue and of the fugue subject being derived from earlier material, these are ideas, which makes it tempting to think of it as an ideas piece. But for me, the emotional immediacy of this music is as great as in anything Beethoven ever wrote. The lows are almost unbearably low and the highs are the kind of highs that only come from someone who has also experienced those lows. They are also a reminder, a reminder that only an artist of Beethoven's stature could provide of the incredible potential for beauty in life. Opus 110 is not theoretical, it is a gift to the soul.