There is a link to an image file of the music notation there too.
I have not heard the tune played as fast as this midi, and it has a lilting sound when played more slowly which gives it a different feel altogether, but I believe it likely that this is the version from a book published by Ossian Publications and which has a very, very long title: Anon. (1984). Complete Collection of the Much Admired Old Irish Tunes: The Original and Genuine Compositions of Carolan the Celebrated Harper and Composer (1670-1738). Iona Green, Cork, Ireland: Ossian Publications, 21 Iona green, Cork, Ireland.