Where did you get your transcription from, Falkbeer?
I think this is the tune of a song sung in Irish by Michael O’Donnell on the first Bothy Band album.
See also the setting in Tomas O’Canainn’s Traditional Slow Airs of Ireland (#40) which is much more accurate (correct time signature, for a start, though I know that’s a vexed issue with transcribing slow airs, and I’m not generally a fan of that book….), though at a different (and I think preferable for flute/whistle) pitch - a 4th higher, in A dor. FWIW, one can play it in 3/4 as the OP offers it - the notation is not "wrong" in terms of technical inconsistencies, but I think it loses the feel of the tune as sung/played in most of the renditions I’ve heard.
“definitve” song rendition?
Check this out: http://www.youtube.com/watch?v=bULfyxCVEvw
I’m learning this tune on tin whistle and this version is awful. Barely relates at all to how the tune should sound. @Jemtheflute thanks for posting an accurate rendition of the tune/song.
Re: Eanach Dhúin
Jemtheflute - thanks a lot!