According to Virginia Tech Multimedia Music Dictionary, "A country dance of Scotland and Northern England related to the jig. The rant is in duple meter and binary form. Surviving examples are dated from the 17th and 18th centuries."

According to the Scots glossary here at Mudcat:
rant = romp+ sing a tune+ fuss+ complain
rant = to rollick

So.... it's about the feel and tempo of the tune, and about what the listeners will do, upon hearing it?

~Susan