Piano Sonata No. 32 (Beethoven)  The Piano Sonata No. 32 in C minor, Op. 111, is the last of Ludwig van Beethoven's piano sonatas. Along with Beethoven's "33 Variations on a waltz by Anton Diabelli", Op. 120 (1823) and his two collections of bagatelles—Op. 119 (1822) and Op. 126 (1823)—this was one of Beethoven's last compositions for piano. The work was written between 1821 and 1822. Like other "late period" sonatas, it contains fugal elements. It was dedicated to his friend, pupil, and patron, Archduke Rudolf. The Sonata comprises only two very contrasting movements, with the second, an Arietta with variations, being consecrated in the words of Thomas Mann as a 'farewell to the Sonata'. Nearly ignored by contemporaries, it was notuntil the second half of the 19th century that it found its way into the repertoire of most leading pianists. Rhythmically visionary and technically demanding, it is one of the most discussed of Beethoven's works. The work is in two highly contrasting movements:  Typical performances take 7–10 minutes for the first movement, and 15–20 minutes for the second, though the range of timings is wide. There are a few recordings that take more than 20 minutes for the second movement, e.g. Barenboim (21 minutes), Afanassiev (22 minutes) and Ugorski (27 minutes). "Duration of roughly 9–11 minutes." The first movement, like many other works by Beethoven in C minor (see Beethoven and C minor), is stormy and impassioned—the tempo markings may be translated, respectively, as "majestic" and "brisk, with vigor and passion". It abounds in diminished seventh chords, as in for instance the first full bar of its opening introduction, which may have provided the inspiration for the introduction of Chopin's second piano sonata:  Unlike Beethoven's other C minor sonata-form movements, the exposition of this movement moves to the submediant (A major), not to the mediant, as its second key area. The quiet second theme bears a resemblance to the second theme in the final movement of the fourteenth piano sonata, made even more explicit in the recapitulation where this theme is restated ominously in the bass in minor mode, after initially appearing in C major.