Here's the tune used by Dermot Hegarty. The tune sounds like a very familiar song tune (not this song!).

Mick

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X:1
T:Connemara Rose
C:Jimmy McGee and Dermot O'Brian
S:Dermot Hegarty
D:Dermot Hegarty: Connemara Rose
N:Transposed from Bb mix to C mix
Z:MCP
L:1/4
Q:3/4=56
M:3/4
K:Cmix
E/D/ | C2 c | B2 c | G2 E | F F G | F2 E | C2 C | C3- | C2
w: Well I|met a|girl from|Conn- e-|ma- ra Far|West from|Gal- way|town_
G | c2 d | e2 d | c2 B | G2 A | B2 B | (A G) F | G3- | G2
w:Her|blue eyes|shone with|beau- ty|and her|red hair|flow_ ing|down|_
G | c2 d | e2 d | c2 B | G2 A | B2 B | (A G) F | G3- | G
w: She|lives a-|mong the|mount- ains|where the|wild wild|heath_ er|grows|_
E D | C2 c | B2 c | G2 E | F2 G | F2 E | C2 C | C3- | C2 |]
w: And her|name it's|Kate O'|Har- a|she's my|Conn- e-|ma- ra| rose|_|]