What we now call by shorthand the violin sonata -- a sonata for violin and keyboard, the two instruments being fairly equal partners -- had started out early in Mozart's career as a keyboard sonata with a comparatively inconsequential string part. Through the efforts of Mozart and others, the violin gradually assumed a far more active role. So by 1799, when Beethoven published his first set of violin sonatas, the title-page designation "for the harpsichord or fortepiano with a violin" was already anachronistic in its near-dismissal of the string part. This turned out to be something of a joke, as discovered at the beginning of the set's A-major sonata. The first movement, Allegro vivace, opens with a quick, mechanical little waltz-like accompaniment characteristic of the keyboard writing of the time -- except that here it's taken by the violin, while the piano plays a simple, downward-skipping melody that shortly breaks out in a frantic run, all in a very violinistic idiom!
After this first statement, the instruments effectively trade places, but also continue to trade off melody and accompaniment as true partners. The most memorable phrase of a secondary subject looks forward to Rossini's Largo al factotum; this is followed by a lot of back-and-forth teasing between the instruments, and a creeping, mock-suspenseful episode. The development section suddenly jerks everything into C major, a slightly surprising modulation for the time. The development itself hardly differs from the exposition except in its amusing key transpositions from theme to theme. The coda is extended enough to be mistaken for part of the development, playing as it does on the main subject's appoggiaturas, before petering out to leave the violin's little downward-skipping two-note motif hanging.
The second movement, Andante, più tosto allegretto, is a simple affair. The theme falls into four-bar phrases, with each half introduced by the piano before being appropriated by the violin. This first section is built around a flowing but still guileless melody that eventually becomes sole property of the violin, with the piano offering a modest, staccato accompaniment. The mood darkens in the movement's second half, although neither the thematic material nor the texture becomes any more complex.
The third movement, marked Allegro piacevole, is a relaxed rondo whose recurring theme is a happy whistling tune, with a few wide intervallic leaps and playful turns. Interleaved with this are episodes in much the same character; in fact, the middle section's accompaniment is nothing more than the little cadence from the primary theme's final bar. Beethoven saves one more joke for the end: The instruments move through a decisive-sounding final cadence in full partnership, only for the piano to get in the last word with an "extra" last note.