Kathleen's setting was in pretty much straight G dorian - all the B's are flat.
She based it on Michael Coleman's version, even pairing it as he did
with "Dowd's Favourite." Hughie Gillespie's 78-rpm version was quite similar, as
he also learned it from Coleman.
But if you listen to the way Coleman himself played it in 1922 (available on the
Topic CD "Irish Dance Music"), you will hear that he shades the B's in the first
part toward B natural, giving that part more of a mixolydian feel. Michael
Hanafin, the Kerry fiddler with Dan Sullivan's Shamrock Band in the 1920's,
wrote out a similar setting in a notebook (a photocopy is in the Boston College
archives), but his was rooted on A and came with the notation "from my
Joe Burke, the great Galway box player, is a big Coleman fan and he also
plays "The Star" in G with B naturals in the first part. You can't really fudge
the intonation on the accordion, however, so it's a more definite B natural
than Coleman employed.