Classical music was a term used to categorise music. By the far future, it seems the term applied to any music written at a significant time in the past.
Vicki, after watching the Beatles perform "Ticket to Ride" on the Time-Space Visualiser, said she didn't know that they played classical music. (TV: The Chase)
In the 42nd century, Elvis Presley and the Beatles were classified as classical music. (TV: 42)
By the year 5000000000, classical music included "Tainted Love" by Soft Cell and the traditional ballad "Toxic" by Britney Spears. (TV: The End of the World)
The Eleventh Doctor showed a fondness for music, and claimed to have played with various composers and musicians. He claimed to have played the triangle for the recording of "L'amour est un oiseau rebelle" from the opera Carmen that was heard in the Parliament of the Daleks. (TV: Asylum of the Daleks) He once called Franz Schubert "Franz the hands", as he claimed he'd been tickled while serving as hands three and four in Fantasia in F minor for four hands. (TV: Dinosaurs on a Spaceship) Amy Pond even once caught him attempting to conceal a euphonium behind his back. (HOMEVID: Good Night)
Behind the scenes[]
In the real world, classical music had differing and arguable definitions. All were much more restrictive than what it came to mean in the DWU.