To disturb someone's calm or peace of mind; to make someone feel uncomfortable or anxious.
From prefix dis- (opposite of) + compose (from Latin com- 'together' + pausare 'to stop'). First appeared in English in the 16th century to describe breaking someone's emotional composure.
Musicians and actors understand 'discompose' intimately—it's what happens when your nerves make you forget a line or lose your focus, literally 'decomposing' your calm state. It's the emotional opposite of being composed.
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