Right after the OP on the first episode, 11 year-old Kousei is shown playing the piano.
What music is he playing? Is this an existing music, or was it something made for the series?
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Thanks to this MAL post I just found out it's Ludwig van Beethoven's Piano Sonata No. 14 in C-sharp minor "Quasi una fantasia", popularly known as the Moonlight Sonata's third and last movement, Presto Agitato.
Here's a video of the music, played by Wilhelm Kempff.
And here another video by one Brandon Ethridge, filmed from the top. This ones makes it look - at least for me - like the animation was done accurately (or at least the progression of the right hand along the keyboard in the animation intends to suggest a minimum of accuracy).