Moonlight Sonata
From Tardis Wiki, the free Doctor Who reference
The Moonlight Sonata is a piano sonata by Ludwig van Beethoven. The Sixth Doctor attempted to play this piece on the piano before stumbling and giving up, regretting turning down Elton John's lessons. (AUDIO: Project: Twilight)
Furthermore, this composition was played in 2007 on John Ellis' 1950s radio. Consequently, John smiled at the tune. (TV: Out of Time)
Behind the scenes
Neither story identifies the name of this piece, but this noteworthy piano sonata is clearly recognizable in both.