mod. cool; easygoing. (Compare this with upbeat.) : He is sort of a downbeat character—no stress.
Dictionary of American Slang and Colloquial Expressions by Richard A. Spears.Fourth Edition. Copyright 2007. Published by McGraw Hill.
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1876, in ref. to downward stroke of a conductor's baton; 1952 in fig. sense of "pessimistic," but probably just from the association of the word down, since the beat itself is no more pessimistic than the upbeat (q.v.) is optimistic.