Great Big Ball has hints of 80's Brookmeyer in a chart that's approachable by advanced HS bands (and on up). It has a medium feel-good vibe, a memorable melody, and paints with fairly broad brush strokes.
This is a a great vehicle for your bari or alto soloist over an infectious four-chord vamp. Your rhythm section can cut loose right along with the sax soloist. Makes an excellent concert or festival opener.
The audio recording below was from a wonderful band I assembled based in Central PA. I'm playing the alto solo.
“Just about one of the happiest pieces of music you’ll ever hear.”
— Chris Merz, Director of Jazz Studies at the University of Northern Iowa
4-5 mins