From www.mutopiaproject.org

The Piano Sonata No. 17 in D minor, Op. 31, No. 2, was composed in 1801–02 by Ludwig van Beethoven. It is usually referred to as The Tempest, but the sonata was not given this title by Beethoven, or indeed referred to as such during his lifetime. The name comes from a reference to a personal conversation with Beethoven by his associate Anton Schindler in which Schindler reports that Beethoven suggested, in passing response to his question about interpreting it and Op. 57, the Appassionata sonata, that he should read Shakespeare's Tempest; some however have suggested that Beethoven may have been referring to the works of C. C. Sturm, the preacher and author best known for his Reflections on the Works of God in Nature, a copy of which he owned and, indeed, had heavily annotated. Although much of Schindler's information is distrusted by classical music scholars, this is a first-hand account unlike any other that any scholar reports. The British music scholar Donald Francis Tovey says in A Companion to Beethoven's Pianoforte Sonatas:With all the tragic power of its first movement the D minor Sonata is, like Prospero, almost as far beyond tragedy as it is beyond mere foul weather. It will do you no harm to think of Miranda at bars 31–38 of the slow movement... but people who want to identify Ariel and Caliban and the castaways, good and villainous, may as well confine their attention to the exploits of Scarlet Pimpernel when the Eroica or the C minor Symphony is being played.
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