Moonlight Sonata
From Tardis Wiki, the free Doctor Who reference
The Moonlight Sonata was a common name of Beethoven's Piano Sonata No. 14 in C-sharp minor "Quasi una fantasia".
The Sixth Doctor attempted to play it on the piano before stumbling and giving up, regretting turning down Elton John's lessons. (AUDIO: Project: Twilight)
The Silver Turk played it on the piano at the Vienna Exposition in 1873. (AUDIO: The Silver Turk)
The composition played in 2007 on John Ellis' 1950s radio; John smiled at the tune. (TV: Out of Time)
Behind the scenes
None of the stories identifies the name of the piece, but the famous sonata is clearly recognisable in both.