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There is a special place for the key of C minor in Beethovens output. There were long periods when Lou did not compose and had grave doubts about his art. Then somebody close to him would die, and he would write a piece in C minor that ended forte. This C minor piece would send him off on a long period of composing until his next crisis of faith. During the periods when he was composing just fine, if he wrote a piece in C minor, it would taper off and end piano.
The first of the Opus10 sonatas is the Piano Sonata in C minor, Op. 10/1, and it ends quietly. It even looks back to the sonatas of Mozart and Haydn with a three movement format.
The first movement lacks a speed direction, probably because of carelessness on the part of either Beethoven or his publisher. Its in 3/4 and generally played allegro.
The opening rocking theme in C minor leads to a transitional passage in A-flat and then a second subject in E-flat. The exposition repeats.
At 3:18, Beethoven starts his development of the first subject in C Major, then through a transition into F minor. Its a very short development.
At 4:11, he recaps. This time his transition puts the second subject in C Major, but then he states it in C minor, totally changing the mood. He ends it with a quarter note and fills the remainder of the bar with rests. Its another case of making clear that the end is silence.
His slow movement is marked adagio molto, very slow, and is in A-flat in 2/4. This is a hymn-like melody that is one of his conversations with God. At each stage the ornamentation between notes of the pulse uses faster and faster notes. The central panel turns to E-flat before returning to A-flat. He finishes by staggering each hand one-half beat off the other.
The finale is in sonata format, 2/2 time and is marked prestissimo. He doesnt write a transitional passage but goes straight into his second subject in E-flat. He repeats the exposition
At 16:34, he goes off into a short development of the first subject that takes only a few bars and fewer seconds,
At 16:52, he recaps. His second subject now appears in C Major, but he immediately re-composes it in C minor. In a move that only Beethoven could pull off, he slows it down, returns to A-flat, and makes you question just how he is going to end it. But he jumps back into C minor at high speed, then softens into a quiet C Major end.