I've mentioned Galicia's strong Celtic roots in other threads.  The language is galego, a precursor to Portuguese, but they are in Spain. 

You'd recognize many of the tunes as traditional Irish and Scottish.  Some of their music evolves from the additional influence of Spain and further south, Morrocco.  

I found a wonderful group, "Luar Na Lubre" - they perform unique music besides many common Celtic tunes. 

Here's one of their mesmerizing, evolved tunes I think anyone could learn by ear & enjoy playing.  I can't tell if it's about a Miller's wife or not(?)

"La molinera" (on my list!).  Check out their YouTube site for other tunes. 

Had a hard time deciding where to best share this tune... I still hear quite a bit of Celtic here, but maybe it could end up in an International Folk Music genre(?)

- Emily