“Set dances” is a term that has two distinct and totally different meanings in the world of Irish dancing. To the solo stepdancer (you know, those girls with the curly wigs and expensive velvet dresses) a “set dance” is a series of steps that is done to a particular piece of music, such as The Three Sea Captains or Madame Bonaparte. These tunes typically have the feel of a jig or hornpipe, but have an irregular number of bars in either the A or B part (i.e. one or both parts will either be shorter or longer than the standard eight bars). The dancing masters of old devised steps to fit these irregular tunes and they have been danced to the present day in competitions. Usually these set dances have a fixed part that is always danced the same way and another part where the individual dancer can create his/her own particular steps. As Nanohedron mentions, there are apparently 38 set dance pieces that have been approved by the Irish Dance Commission for use in competitions (feisanna). The two I named earlier are on this list, but there are other set dance tunes as well that have not been included there, such as The Drunken Gauger. The Blackbird, which is a very old and very familiar tune with a lot of different versions, is a set dance piece in one of its versions and I have seen it danced on several occasions, usually by older dancers. I’m not sure if it’s on the official competition list or not.
The set dances referred to by djm on the other hand are social dances done in square sets of four couples, much like American square dances. They are descended from the “sets of quadrilles” done in high society in the 19th century, and were adapted by the country folk to be danced to the local jigs, reels and hornpipes - or in Kerry to slides and polkas. There has been a great revival of interest in these sets over the last 25 years in Ireland and beyond, and they have become very popular. The Caledonian, the Plain Set, the Lancers Set and the like are all examples of this type of set dance. These sets all consist of multiple figures (typically the dancers wil stop in between figures of a set, but not always), with each figure being done to a particular type of tune, be it a reel, jig, polka, slide or hornpipe. There are no specific tunes that need to be played for these set dances - if it’s a reel figure, any reel will do, and so forth. (Although because the number of bars of music needed for these set dance figures is quite idiosyncratic, some tunes will work better than others, especially if ending the tune at the same time the figure ends is a concern.)
As for recordings of set dance tunes, for the first kind (the solo dances) there are some excellent versions of a few of the 38 tunes on Eugene O’Donnell’s recording called “Slow Airs and Set Dances”. It was released on Green Linnet many years ago so it may be out of print now, but if you can find it it’s a great one. Eugene O’Donnell was a fiddler from Derry who lived in Philadelphia for most of his life. (AFAIK he’s still alive and living in Derry, but he’s very old and had to quit playing several years ago.) In his youth he was a champion stepdancer, and he carried that over into his fiddling by playing brilliant versions of many of the dance pieces he’d danced to in his younger days. He was also known as a master of the slow air, hence the title of his album.
For the social set dances, the Music for the Sets cassettes and books mentioned by djm are indeed great. Unlike much music recorded for set dancers, which is frequently abominable, this collection is both eminently listenable as well as danceable. It’s great Irish music in its own right, done 20 years ago by musicians who were then virtually unknown but who are now household names. Paul O Shaughnessy, Brendan Begley and Paul McGrattan pre-Beginish, to name just a few who played on this collection. It’s well worth seeking out. It may have made it over to CD at some point, but I don’t know.
Hope this helps to alleviate some of the confusion…