improv (n.)

"act of improvising musically," 1786, from French improvisation, from improviser "compose or say extemporaneously" (17c.), from Italian improvisare "to sing or speak extempore," from Latin improviso "unforeseen; not studied or prepared beforehand," ablative of improvisus "not foreseen, unexpected," from assimilated form of in- "not, opposite of" (see in- (1)) + provisus "foreseen," also "provided," past participle of providere "foresee, provide" (see provide). From music the sense expanded to a general meaning "do or perform on the spur of the moment."