I'd argue that you don't actually need to embellish Irish tunes with too much harmony, if at all. A bit like Bach's unaccompanied cello suites, which have many passages without even double-stopping, harmony is "suggested" in the mind's ear when you hear the tunes well played. Not that I'm saying that Irish tunes as as good as that, but the argument still applies.
   poppycock, what about o carolans tunes, an important part of the irish tradition, often played on the harp and played with chordal accompaniment which is harmony.
in fact the irish harp and the uilleean pipes both use harmony to a greater or lesser degree.
Steve,you remind me of Le Petomane