There is what is presumably an old English tune for the ballad in Chappell's Popular Music of the olden Times at p170.

It would be impossible to pin down geographically Musgrave and Barnard as they are both very old aristocratic families who held widely spread properties in both England and Scotland. The earliest versions go back at least to the 1620s. Even if the ballad was based on some real event there have probably been numerous liaisons between the 2 families over the centuries. If you want to PM me with your email I can scan you a copy of the tune.