The Shakespeare originals we dont know for sure what musicthey used: though people wrote down the tunes being used in theatres a hundred years later, and they may be the "right" tunes. But some songs in Shakespeare plays can be found in contemporaary publications as well, so we do know those tunes. I had a very nice edition of Hamlet once, with copious footnotes on the tunes used for the songs, in the 17th and 18th century theatre.Not sure where that books gone.