The Butterfly is a traditional Irish tune, and more precisely a slip jig, that is to say a jig in 9/8 time.
It’s a beautiful, haunting melody. You can find many versions of it on the Internet. I especially like the harp versions. Search “The+Butterfly+Harp” on YouTube to listen to a few ones.
Here is my own version, played on a two-row G/C Castagnari Niko. Not the best choice to play Irish music, but I quite like the result after all.
And here is the tab!