"to make cheerful, lively, or merry; render glad or joyous," 1530s, from Latin exhilaratus "cheerful, merry," past participle of exhilarare "gladden, cheer," from ex "out, out of; thoroughly" (see ex-) + hilarare "make cheerful," from hilarus "cheerful" (see hilarity). Related: Exhilarated; exhilarating.
"act of enlivening or cheering; state of being enlivened or cheerful," 1620s, from Late Latin exhilarationem (nominative exhilaratio) "a gladdening," noun of action from past-participle stem of exhilarare "gladden, cheer," from ex "out, out of; thoroughly" (see ex-) + hilarare "make cheerful," from hilarus "cheerful" (see hilarity).
1721 as a musical term, from Italian allegro "brisk, sprightly, cheerful," from Latin alacrem (nominative alacer) "lively, cheerful, brisk" (see alacrity). The same Latin word came into English 17c. as aleger "lively, brisk," from Old French alegre, from Latin alacris; and Milton used "L'Allegro" in its literal sense as a poem title (1632).