In the history of music, there are harmonic implications to Irish or Westernized traditional melodies. They may not be apparent at first but they are there. There are suggestions for basic harmonization built into the tunes but there is no restriction for re-harmonizing.
There is no restrictions for anything for that matter and if you want to play Greensleeves with a boogie-woogie bass you can do that. The question becomes one of taste.

Thanks Mark, I'm sure these concepts of harmony are pretty well known and assimilated without having to think about them too much.

The idea of selecting chords to play to a tune (any tune) is pretty individualistic and jazz musicians have been known to come close to blows over such things as the "right" chord changes or rhythmic tempos. I think that in the interest of knowing about the musical form that is being performed, there are certain restrictions that must be made harmonically for it to sound pleasing to most ears.

I think that here consensus rules in the musical world amoung musicians and in the public acceptance of such things. You could conceivable harmonize Drunken Sailor for example starting with an Fa major seventh as a substitute for the A minor chord which would sound kinda' jazzy. Irish bands have used that progression...F maj 7,to G back to A minor as accompaniment for modal "chunes".

You could justify the following progression for Drunken Sailor...F major 7 in place of A minor, E minor 7th in place of G major, then you could go to a D minor seventh, winding up with a G chord back to an A minor. You could even end up with a Picardie Third, an A major chord. All these chords might be out of character for the feeling a a sea chantey but would work in a symphonic orchestration of the work. I guess the point here is what is in the appropriate taste for the song? Some would say no chords at all but I think that's a pretty narrow view.

Frank Hamilton