I actually don’t know much about An Tri is a Rian, and it’s not a “tune from Doolin” as such! I heard a recording of the great concertina player from Dingle Cormac Begley playing it, and loved it instantly. He called it “Mary MacNamara’s” so I assume he learned it from her. It was also recorded by Enda Scahill on his album Pick It Up.
X:1
T:An Tri Is A Rian
R:hornpipe
M:4/4
L:1/8
K:Gmaj
|:G2BG EFGA|BcBA BcBA|GABG EFGB|(3ABA (3GFE DcBA|
G2BG EFGA|Bdef g2fg|ecAG Fddc|1 (3BAG (3AGF G2 (3DEF:|2 (3BAG (3AGF G2Bc||
|:d2df g2ge|dedB G2AB|c2ec B2dB|(3ABA (3GFE D2BA|
G2BG EFGA|Bdef g2fg|ecAG Fddc|1 (3BAG (3AGF G2Bc:|2 (3BAG (3AGF G2 (3DEF||