That's "Gianni" by Robert Silverberg.
Giovanni Pergolesi is one of the lesser-known geniuses of music. He wrote prolifically in his short life, then died in 1736 at the age of 25. Some high-minded scientists in 2008 use a machine to pluck the composer from just before his death into the future so they can allow his talents to develop as if he had lived longer. Then Gianni discovers pop music... After all, in his day, opera was pop music.