I heard John Carty playing this in the lovely key of E, as I’ve attempted to notate here. There is a jig cited as "The Jointure" on Kevin Crawford’s album, "Carrying the Tune." I am not certain where the tune originated from, or with whom it may be associated.
The Jointure, X:2
Kevin Crawford’s setting from Carrying the Tune.
Re: The Jointure
Should’ve added that this is reputedly a composition of the harper Thomas Connellan and is the jig part of ‘The Jointure and Jig’. Kathleen Loughnane has a very nice recording of it which is part of her CD and book of the music of Connellan (available here https://www.itma.ie/digital-library/sound/jointure-loughnane-cannon). Gráinne Hambly and Simon Chadwick have also recorded these.