I’m sort of a theme & variations junkie. From Bach to Coltrane, they show just what a musician can do when taking a single melody and running with it. A while back I posted Bach’s Goldberg Variations, which didn’t really improvise the main melody but came up with new ones while repeating the bass line. Subsequent composers usually varied the melody by elaborating on bits of it, like in this Beethoven set. This set came about after the musician and (more importantly) publisher, Anton Diabelli, sent a waltz melody to the leading German composers of the time and requested each of them to write a variation on it. Beethoven thought the melody was garbage and ignored it at first. One story has him changing his mind when he learned that other respected composers (Czerny and Hummel, a sometimes rival) were doing it. Or maybe he decided that the melody was pliable enough to accomplish something. Most likely Diabelli simply offered Beethoven money to compose multiple variations; he knew they’d sell. Beethoven wrote 33 variations. Like Coltrane working a show tune, these 33 get pretty far out there, way ahead of their time. There’s everything from mockery of the melody (“this melody is shit”) to transcendance (“look what I can do with even a shitty melody”) and, well, who knows what to call it. There have been plenty of great theme and variation works since, but none have put a melody through the wringer quite like this.
Beethoven was a master of improvisation; he wrote other such sets, but also worked variations into his symphonies, piano sonatas, string quartets, etc. If you want a shorter example, try the second (and final) movement of his piano sonata #32, his last, where he twists a hymn-like melody all over the place before landing in long, brutal, and otherworldly trills that would cripple a normal hand. The second movement starts at 9:00 if you don’t want to hear the first.