This type of tune is of cause very common in the UK bagpipe traditions, including the Northern English 3/2 Hornpipes.
It's a common phenomenon for vocal traditions to be greatly influenced by instrumental scales and intonation, I think that this kind of tune that we might these days, associate with Scotland because of the persistence of the Big Pipes there when they became extinct in the rest of the UK, would have been much more widespread in the 16th and 17th centuries.
The subject of Irish Clan Marches is a fascinating one; I've done quite a bit of musical research in this area. I don't know how accurate the title Clan March is, but from a musical perspective there is a body of Big Pipe tunes definitely separate from the Dance tradition. The March of the King Of Laoise is a good example, a version of this tune is found in Playford's EDM 1657 additional tunes under the title of Washington's March.

TTFN
PP