I must say, I didn't recognise many of the "greatest" melodies mentioned. Anyway, here are my nominations: An Chúilfhionn, Connlach Ghlas an Fhómhair, Sliabh na mBan, a Spailpín, a Rún, Amhrán Phádraig Shéamais / an Chéad Mháirt de Fhómhar. But it's all so subjective, really.