A variant spelling of assai; a musical term meaning 'very' or 'extremely' (very fast, very slow, etc.).
From Italian 'assai,' which may derive from Latin 'ad satis' meaning 'to sufficiency' or 'very much.' This musical terminology entered English in the 17th-18th centuries alongside Italian musical vocabulary.
Musicians see 'assai' (and its variant 'assahy') in sheet music to mean 'really, truly' the thing you're supposed to play—so 'allegro assai' means 'really fast,' making this Italian word essential to how composers communicate intensity to performers.
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