c. 1600, "act of mingling," with -ure + admix (1530s), a back-formed verb from admixt "mingled" (early 15c.), a past-participle adjective from Latin admixtus "mixed with," past participle of admiscere "to add to by mingling, mix with," from ad "to" (see ad-) + miscere "to mix" (from PIE root *meik- "to mix"). In Middle English admixt was mistaken as the past participle of a (then) non-existent *admix. The earlier noun was admixtion (late 14c., from Latin admixionem).
c. 1600, "composition, act of composing, constructing, arrangement" (also, in early use, with many senses now given to compound (n.2)), from compose + -ure. Sense of "tranquility, calmness, composed state of mind" is first recorded 1660s, from composed "calm" (c. 1600). For sense, compare colloquial fall apart "lose one's composure."