Buain Na Rainich or Tha Mi Sgith are Gaelic titles used for the same song. It is anonymous since it is an old Gaelic song.
The legend goes, the girl goes out and cuts the bracken for the fire. She meets and falls in love with the Sidhe, or fairy. He also falls in love with her. One day the family find out about this and keep her locked up at home. He, the sidhe, is despondent and sings this song.
However, only the first verse and the chorus were saved. The other five verses that I have, apparently were written by Kenneth MacLeod.
The song was collected by Marjory Kennedy-Fraser for her Songs of the Hebrides Collection.
The Gaelic song and part of this story are told here
Buain Na Rainich
The song is well suited to a number of tempos. You can sing it to the popular tune Ca The Knowes, as well as a fast pace, almost a dance tune, and as a lullaby, from the sentiment.