Regarding clueless don's post, the Wikipedia article about the Sam Hall song says:

Regarding the metrics and the melody, the version common in the British Isles ("Oh my name it is Sam Hall, chimney sweep...") appeared to be based on the tune "Ye Jacobites by Name" (Roud # 5517), whereas the version more common in the USA ("My name it is Sam Hall, T'is Sam Hall...") is a variant of the tune to "Frog Went A-Courting" (Roud # 16).

So the tune of Sam Hall (in its British version) was a variant on the tune of Ye Jacobites by Name, rather than the other way around.

Both the Wikipedia article about Ye Jacobites by Name and the Wikipedia article about My Love's in Germany state that Burns took the tune for Ye Jacobites by Name from the tune of My Love's in Germany - and the two tunes are indeed identical - for instance there's a youtube recording of My Love's in Germany here.

So the tune seems to have been written for My Love's in Germany, then taken up by Burns for Ye Jacobites by Name, and later switched to the minor key for Sam Hall.

As meself mentioned, this is indeed similar to the way the tune of Oh Dear What Can the Matter Be was switched to the minor key in The Mist Covered Mountains of Home - and that tune was later made even more haunting by Jim McLean in the variant of it that he wrote for Smile in your Sleep. It's fascinating how folk songs evolve over time!

However, the Wikipedia article about My Love's in Germany says it was published in 1794, which was not long before Burns published Ye Jacobites by Name. So the pre-Burns Ye Jacobites by Name song must have had a completely different tune. I can't find any information regarding that tune - I imagine it's lost in the mists of time.