Originally named the Ookpik Waltz, this tune was written in 1965 by British Columbian fiddler Frankie Rodgers (1936-2009). It is also known as the Eskimo Waltz because of rumors that it was composed by an Eskimo, probably as a result of the fact that Ookpik is an Inuktitut word for "arctic owl."
Authorship of this tune is uncertain, but it is primarily of Welsh origin. It may originally have been based on a composition by Turlough O'Carolan called Beauty in Tears, and it was certainly in O'Carolan's repertoire. However, Beauty in Tears may also have been written by John Parry, a Welsh harpist. The confusion may stem from the fact that both Parry and O'Carolan were blind harpists living in the first part of the 18th century. The tune may in fact be much older, since it also resembles a tune called Constant Billy that was published in Playford's Dancing Master in 1665.
The Tombigbee is a river in Mississippi and Alabama. The name comes from a Choctaw word meaning "box maker" or "coffin maker." This tune was used as the melody for a song named Gum Tree Canoe that seems to describe the romance and serendipitous escape of two cotton field slaves. Although this tune originated in the mid 19th century in the southern US, it has been adopted and played in many other traditions, as far away as Australia.