Moonlight Sonata

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 practised it on the piano for 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 identify the name of the piece, but the famous sonata is clearly recognisable in both.