Afraid I dont know the tune. I expect everyone's thought of this, but in case not: try a few spellings of kathryn. I live with someone called Kathryn and I know well there are about a hundred ways of spelling the name.
   The only catherine Douglas I've heard of (might have something to with tune?) is the woman who saved the life of some Scottish king by barring a door with her arm when some baddies were trying to get in and kill him. It must have been one of those doors with big staples to put a wooden bar through, and someone had thrown the bar on the fire becaues they were cold. Anyway, it bust her arm a lot, but it apparently saved the day. This is story is used to expalin (not totally believably) the proverbial phrase "Katy bar the door".