The Trip To Clarina
As played by Mick Mulcahy.
Probably better written in E dorian, with the c naturals in the 1st part being the accidentals, and with the c sharps in the second part being part of the natural scale for the tune.
is from the playing of Brian Holleran And Brian Bigley on the flute and the pipes:
@Dargai: There are no c naturals in this setting, so your intuition about the tune being actually in E dorian seems to be right! You can still change the key signature BTW.
Setting #1 E dorian
Thanks Sebastian. That was niggling me. All sorted now.