Peter,

I think that the myxolydian mode is defined by the chord implications of the melody. The Irish keening songs tend toward this mode. The chords that you would customarilly use would naturally be a I chord and a bVII chord. You can use as Amos has pointed out the relative minors of these two chords. D (I) C (bVII) Bm (VIm of D) and Am (VIm of C).

I believe the harmonic implications of a folk song define it's modality even though the melody might not be harmonized. The musical implications are there though.

Frank Hamilton