I think that Moore wrote My Gentle Harp to another Irish Aire for which I do not know a name. It can be found in "Selections From Moore's Irish Melodies" published by Ossian Publications and still very much in print. ISBN 0 946005 38 9. I used to sing it to the Aire from County Derry when I was on my not liking "Danny Boy" kick. My voice teacher convinced me that it does not fit all that well and I went to the originial aire. There are four stanzas, which seems to me about two stanzas too wordy. The song is whittled down to two stanzas by selecting four halfs of stanzas and mixing and matching. This semi-literate computer klutz will post all the lyrics all strung out if anyone wants them.
Moore did much singing in England. Through his singing songs like this that equate the Harp with Ireland he was able to convince many English listeners to be sympathetic to the cause of Ireland and ending control and persecution.