Use the word lilt to describe a swinging kind of tempo in music. You might love old fashioned big band jazz because of its distinctive lilt.
Upbeat, rhythmic music of any kind has a lilt, and you can also describe certain ways of speaking as having a lilt. In this case, the lilt is either the rhythm of a person's speech, or her accent — an Irish accent is often called an "Irish lilt." Lilt can be a verb, too, as when you lilt out a song. The earliest meaning of the word was "to lift up one's voice," from the West Midlands lulten, "to sound an alarm."