"If there had been such a song, harpers everywhere would know about it by now."

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Erm, yes, there is and they do. Didn't you read the posts above about Alison Kinnaird? As well as recording this piece she's also published it, as an air & variations in her book of old harp tunes, titled The Harp Key, issued by herself and her husband Robin Morton under the imprint Kinmor Music, ISBN 0 9511204 0 9

Incidentally, Donal O'Sullivan's Carolan: The Life Times & Music of an Irish Harper is the definitive source for his tunes and historical info, and is where the websites etc have got their material from, so I think it's only fair to give his book (now re-published and again available) a mention here.