Moonlight Sonata

The Moonlight Sonata was a Beethoven symphony that the Sixth Doctor attempted to play on the piano before stumbling and giving up, regretting turning down Elton John's lessons. (AUDIO: Project: Twilight)

The composition played in 2007 on John Ellis' 1950s radio; John smiled at the tune. (TV: Out of Time)

Behind the scenes
Neither story identifies the name of the piece, but the famous symphony is clearly recognisable in both.