also off-beat, "unusual," 1938, from off (adv.) + beat (n.). From earlier sense in reference to the second and fourth beats in a four-beat music rhythm (1927), where the stress typically fell on the first and third. Compare upbeat.
ofay
off
offal
off-and-on
off-base
offbeat
off-Broadway
off-camera
off-chance
off-color
off-colour