Except we know that we're only getting closer to the original sound. We're making a lot of guesses based on surviving instruments (in some case only known from paintings or woodcuts in books though) and surviving texts about how to play music, or diary notes, or notations on scores which were used by people teaching or learning. We don't actually know how any of it really sounded.

Which is, really, the same problem we've got with Shakespeare. Without really good footage of several performances, we can't really know how Shakespeare plays were really performed, we can just get as close as we can from the surviving evidence.

If I ever got a lift with the Doctor I would ask to go back to the 16th century and record as much music as possible.