I first heard this in Brighton, but it is apparently from the playing of Pat O’Connor, and normally played with John Naughton’s Reel, (the one in E Dorian that goes E F# G A B E D E | G E B E G E D E…) and the Laccaroe reel, followed by this one. This tune is so difficult or impossible to find on the internet to listen to or get the music for that have finally transcribed it myself! I love this tune, especially with the set mentioned above. It is worth noting that I have written it here as I first heard it, in Amix with the first two tunes played in Edor, but on D pipes I would play it all a whole tone down to suit the pipes tunings. I love the modulation; the B part is based on C major, the A part in Amix(can’t spell myxcsaliidyainn). But then most of Mandy Murray’s tunes from Co. Clare seem to do this, and I love them all!
Compare with "Gan Ainm" https://thesession.org/tunes/7788
Bill Malley’s reel
Yes, it’s similar! Apparently ‘Gan Ainm’ means ‘Unnamed’.