If you go back and look at most of those old tunes that the early New Orleans jazz players worked with, many of the tunes and a lot of the lyrics come from the Anglo/Irish Ballad tradition--

A single example will suffice--St. James Infirmary Blues, a Jazz standard if their is one, has a melody that is closely related to "The Star of the County Down", a lyric that is closely linked to "The Bard of Armagh", and if that isn't enough, refers to one "Big Joe McKennedy" in the verse.