Well, I just read this page at the Traditional Tune Archive with this comment, so there appears to be another version of the tune.

"There are two main versions of the tune: one can be found in the collections of the Neals, Thumoth, James Oswald and Edward Bunting, while the other is to be found in the manuscripts and publications of Dow, Balcarres, Wemyss and MacFarlane."