Composed between 1817 and 1818. Four movements.
And here’s the biggest one of them all. The weird, titanic, gnarled, joyous, grief-stricken monster that is the Hammerklavier. Where exactly to begin?
With the interval of a 3rd, I guess. It permeates the work at every level, creating close coordination between motivic-harmonic detail, and tonal structure. The main theme of each movement is built from the same motif: a rising and then falling 3rd. In the final movement the 3rd both defies the movement in the bass in the introduction, as well as the shape of the fugue theme: a rising 3rd (10th), following by a scalar figure that is repeated, each time descending by a 3rd. Harmonically, the development section of the third movement is built on a sequence of 3rds, and the trio of the scherzo oscillates between Bb Minor and Db Major, two keys separated by a 3rd.
At an even deeper structural level, the 3rd is all-pervasive. You’d expect, in a Bb Maj sonata, that the dominant key of F would play a major role, but in 40+ minutes of music there is not a single modulation to that key. Instead, Beethoven constructs an intricate system of four keys around Bb, and returns to them time and time again. Three of them, G, D, and F#, are all separated from Bb by the interval of a third. The final, the black key of B Minor, occurs in every movement and functions as an anti-thesis to Bb Major. The struggle between these two keys dramatically frames the entire sonata (just listen to the scherzo’s ending).
There’s lots more to the Hammerklavier than the 3rd. You’ve got structural innovations: in the 1st movement’s recapitulation the return to the stable tonic is heavily delayed (by, yes, the key of B minor), and in the 2nd the development is too short, but the recapitulation varies and decorates the theme so extensively that it becomes a sort of extended development. And you’ve got the sheer contrapuntal and dramatic genius of the last movement, where a huge number of traditional contrapuntal devices are wielded with a jaggedness and fury that belies their conservative associations. It's also worth noting how contrapuntal the writing in the 1st movement is -- one of the most striking features of Beethoven's late work.