William "Count" Basie's 1 AM network radio show had a theme that possessed no official name. One night while the band was jamming and having a good time prior to broadcast, the engineer was listening, enjoying himself -- and ignoring the clock. At 1 AM, the engineer glanced casually at the clock, went into a panic, pushed the button for the in-house microphone, and yelled to Basie and the band, "It's one o'clock! Jump!" That's how Basie's theme song got its name.
It starts with Jess Stacy's piano solo paying tribute to Basie, who was standing in the wings at Carnegie Hall. Then come solos for tenor sax (Babe Russin), trombone (Vernon Brown), clarinet (Goodman) and piano (Stacy), followed by more piano (Stacy), trumpet (Harry James) and clarinet (Goodman) for the end.