The following is a direct quote from an "Ulster Scots" correspondence list. It might help to answer the question.
"This is purely a personal opinion it should not be viewed as the USHC's interpretation nor are the examples meant to be exhaustive.
Ulster-Scots music and song is as follows: 1.. Tunes thats use is proven on either side of the North Channel (In older Scots music books it is common to find a tune listed with a note that it is also found in Ulster or part of it as well as the Burns ) The music in the Lowlands especially Dumfires and Galloway will be of importance in the 16-19th century considering the persistent flow back and forth (beyond actual settlement). 2. Music and song written by Ulster-Scots (eg the large number of modern piping tunes that are written to the large number of songs written by theRhyming weavers of modern country rhymers) 3. Music and song about Ulster-Scots places people or communities. 4. The Scotch-Irish/Appalachian music and its modern development Bluegrass."
Under all that there are hundreds of tunes and songs (regrettably many inaccessible) but plenty to be getting on with.