"with a positive mood," 1947, apparently from on the upbeat "improving, getting better," attested from 1934 and a favorite of Billboard magazine headline-writers in the early 1940s, from the musical noun upbeat (1869), referring to the beat of a bar at which the conductor's baton is in a raised position; from up (adv.) + beat (n.). The "optimistic" sense apparently for no other reason than that it sounds like a happy word (the musical upbeat is no more inherently "positive" than any other beat).
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