It doesn't seem clear. Bronson (I, 324) prints the tune and comments "The single tune which has been preserved in two variants for this ballad" [the other being in the Blaikie MS] "may well be, as Scott calls it, 'ancient.' Scott, or his musical editor, writes as if a modern tune was also current in his day; but, if so, it has not been recorded, any more than recent texts that might accompany it."

The 1833 Minstrelsy was edited by J G Lockhart, but I don't know if that included sourcing musical examples (I have an earlier edition). Scott himself was no musician, though given his background I'd expect him to have been musically literate. Perhaps someone will have better information.