Anton Schindler, Beethoven's first biographer, secretary and acquaintance, claimed that the Triple Concerto was written for Beethoven's young royal pupil Archduke Rudolf (the same Archduke that Beethoven dedicated his Piano Trio In B-flat Major, Opus 97 to). The piano part of the concerto does not equal the difficulty of the other soloists, a fact that has lead some to agree with Schindler, as the Ardchduke was a young teenager when the concerto was written and would not have had the technique for anything more difficult. But Beethoven scholars have shown over the years that Schindler was a man whose words needed to be taken with a grain of salt. There is no evidence that the Archduke ever played the work (which is not to say that he didn't) which had its first public performance in 1808. When it was published, the concerto had a dedication to someone else, another one of Beethoven's royal patrons, Prince Lobkowitz, but Beethoven could be fickle (not to mention absentminded) about such things. The concerto is in three movements:
I. Allegro - The concerto begins quietly and gradually builds in volume. There are three main themes introduced by the orchestra alone. The cello is the first soloist to enter with the first theme. Violin and cello expand upon the first theme, and the piano enters with the theme. Each of the soloists has a turn with the three themes, or parts of them. The development gives the trio of soloists further opportunity to dialogue with each other. The orchestra asserts itself a few times but for the most part remains in the background. The recapitulation has the soloists review the themes, which leads to a coda that quickens the tempo and while the orchestra plays full chords the soloists bring the movement to a close.
II. Largo - The orchestra begins this movement (in the key of A-flat major) in a solemn, quiet mood. The cello enters with the theme of the movement, the piano embellishes it. The violin and cello play the theme in a duet as the piano gently accompanies. A short, dark section for orchestra leads to the soloists playing fragments of other themes, which leads to the last movement without pause.
III. Rondo alla polacca - As with the first two movements, the cello is the first soloist to play the main theme of this movement which is in the style of a polonaise, a Polish dance. Themes abound in this movement, all of them rhythmically in keeping with the 'polacca' designation. The music takes a minor key turn as the soloists take turns playing thematic material and accompaniment while the orchestra adds color. The polonaise returns, has its say until the tempo quickens. The soloists play together without the orchestra, and then the soloists wind up the movement by playing rapid figures as the orchestra supplies the punctuation until the end.
Writing for three soloists offered Beethoven many challenges, not least of which was how to have each soloist shine without making the work too long or undermining form. Compared to the 'Waldstein' and 'Appassionata' piano sonatas and the Third Symphony that he was composing at about the same time, the Triple Concerto may appear small potatoes to some. But the Triple Concerto has to be looked at (and heard) in a different way. Beethoven did more than extend the concerto grosso and sinfonia concertante traditions with this work. There is a kind of synthesis between concerto, symphony and chamber music (specifically in the form of the piano trio). This is a quite remarkable achievement, a showcase of Beethoven's huge talent and craftsmanship that's hardly small potatoes.