Thom suggested that we add this great Planxty-made-famous tune. It was written by Turlough O’Carolan, the blind 18th Century Irish singer, harpist and composer. I’ve taken the notation for the tune used by Chris Haigh, the London-based fiddle tutor (who has written several excellent books on folk music from Kletzmer to Irish folk) as he has a helpful youTube tutorial on the tune. I really recommend listening to the Planxty version for a while to get the melody in your head and then it doesn’t turn out to be too difficult to learn.
As for the spelling… Si Bheag Si Mhor is often spelt in a variety of ways, but it mostly seems to sound like sheebeg sheemore (which is sometimes how it is written too). It means Big Fairy, Little Fairy, which were probably the names of two hills in Ireland, I believe, and the tune has its own page on Wikipedia. And we have Ray to thank for the chord suggestions.
Thom found some great places to hear it:
Planxty (with nice pictures, but not live)
Sung by the French band, Garlic Bread (from their album O’Carolan’s Dream)
Chris Haigh’s fiddle tutorial
A really slow violin version
An excellent guitar tutorial video by Jerry’s Guitar Bar