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."
