My band (Oomblik) plays all originals, so it's even harder to characterize the style -- I usually say "progressive rock", but there's a bit of jazz in it too. Since jazz is in my background, I think I bring that out a bit.
The song was called Newton, then Newton's Apple, then Newton's Apple Sauce. I band member wants it to be Knuten's Apple Sauce, but I nixed that.
You can find the sheet music and an MP3 (actually an m4a) at the URL link below. It was the band's second time playing the song, so it's still pretty rough, and there isn't a good ending yet.