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The Collaborative International Dictionary
Composedness

Composed \Com*posed"\, a. Free from agitation; calm; sedate; quiet; tranquil; self-possessed.

The Mantuan there in sober triumph sate, Composed his posture, and his look sedate.
--Pope. -- Com*pos"ed*ly, adv. -- Com*pos"ed*ness, n.

Wiktionary
composedness

n. The state or quality of being composed.