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Piano Sonata No. 32 in C minor, Op. 111, is the last of Ludwig van Beethoven's piano sonatas. It was dedicated to his friend, pupil, patron, and protector, Archduke Rudolf (who, by the way, received fourteen other dedications from Beethoven). [<ref>Solomon, Maynard, Beethoven, Schirmer Books, NY (1977) p. 306.</ref>]

'''Piano Sonata No. 32 in C minor, Op. 111''', is the last of Ludwig van Beethoven's piano sonatas. It was dedicated to his friend, pupil, patron, and protector, Archduke Rudolf (who, by the way, received fourteen other dedications from Beethoven). [<ref>Solomon, Maynard, Beethoven, Schirmer Books, NY (1977) p. 306.</ref>]

This sonata was probably composed in 1821 and 1822, when Beethoven was 50 and 51.

This sonata was probably composed in 1821 and 1822, when Beethoven was 50 and 51.

The three piano sonatas, Opus nos. 109, 110, and 111, “form a set as coherent as any of his previous groups of three works, and … contain many subtle links ….” [<ref>Cooper, Barry, Beethoven, Oxford University Press (2000), pp. 288-89.</ref>]

The three piano sonatas, Opus nos. 109, 110, and 111, “form a set as coherent as any of his previous groups of three works, and … contain many subtle links ….” <ref>Cooper, Barry, Beethoven, Oxford University Press (2000), pp. 288-89.</ref>

The sonata Opus 111 has only two movements:

The sonata Opus 111 has only two movements:

2.  Adagio molto semplice e cantabile (C-major, 9⁄16 [initial] time signature)  

2.  Adagio molto semplice e cantabile (C-major, 9⁄16 [initial] time signature)  

“[T]he first movement is perhaps surprisingly conventional, echoing the mood of several other C minor works. … The second movement, by contrast, possesses an extraordinary visionary quality, transcending all previous piano music and even challenging the limits of the notational system in which it was written.” [<ref>Cooper, Barry, Beethoven, Oxford University Press (2000), p. 290.</ref>]

“[T]he first movement is perhaps surprisingly conventional, echoing the mood of several other C minor works. … The second movement, by contrast, possesses an extraordinary visionary quality, transcending all previous piano music and even challenging the limits of the notational system in which it was written.” <ref>Cooper, Barry, Beethoven, Oxford University Press (2000), p. 290.</ref>

The metrical scheme of the second movement is highly innovative.  Because a three-beat rhythm plays a significant role in the movement, Beethoven uses unusual time signatures of 9/16, 6/16, and 12/32 to mark various passages.  In fact, according to Cooper, “no modern time signature is capable of indicating a bar consisting of three beats each of which divides into four sub-beats which in turn divide into three.” [<ref>Cooper, Barry, Beethoven, Oxford University Press (2000), p. 290</ref>]

The metrical scheme of the second movement is highly innovative.  Because a three-beat rhythm plays a significant role in the movement, Beethoven uses unusual time signatures of 9/16, 6/16, and 12/32 to mark various passages.  In fact, according to Cooper, “no modern time signature is capable of indicating a bar consisting of three beats each of which divides into four sub-beats which in turn divide into three.” <ref>Cooper, Barry, Beethoven, Oxford University Press (2000), p. 290</ref>

Among the many astonishing aspects of the second movement is the simplicity of its theme:

Among the many astonishing aspects of the second movement is the simplicity of its theme:

From these three notes, Beethoven builds a lovely and monumental structure of twenty minutes’ duration.

From these three notes, Beethoven builds a lovely and monumental structure of twenty minutes’ duration.