extemporize
\ik-STEM-puh-rahyz\
verb
1. to speak with little or no advance preparation: He can extemporize on any of a number of subjects.
2. to sing, or play on an instrument, composing the music as one proceeds; improvise.
Quotes
I began to understand how he'd been able to extemporize an oration that first day we met: because he was constantly shaping monologues from his ideas and memories and fact-findings as if at any moment he might be called upon to address the joint houses of Congress.
-- Joseph O'Neill, Netherland, 2008
Origin
Extemporize can be traced to the Latin phrase ex tempore meaning "out of the time." It entered English in the mid-1600s.
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