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offbeat (adj.)

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.

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Definitions of offbeat from WordNet
1
offbeat (n.)
an unaccented beat (especially the last beat of a measure);
Synonyms: upbeat
2
offbeat (adj.)
(informal) strikingly unconventional;
Synonyms: far-out / kinky / quirky / way-out
From wordnet.princeton.edu