extemporize

• extemporise (mostly Commonwealth)

extemporize (third-person singular simple present extemporizes, present participle extemporizing, simple past and past participle extemporized)

1. (intransitive) To perform or speak without prior planning or thought; to act in an impromptu manner; to improvise.
   • 1881, George MacDonald, chapter 35, in Mary Marston:

     "Will you please tell me whose music you have been playing?" . . .
     "It's nobody's, miss."
     "Do you mean you have been extemporizing all this time?"

   • 2009 March 5, Peter Baker, “The (very) scripted president”, in New York Times, retrieved 8 November 2011:

     But while some of his predecessors liked to extemporize, Obama prefers the message to be just so.

2. (transitive) To adapt, improvise, or devise action or speech in an impromptu or spontaneous manner.
   • 1860, Nathaniel Hawthorne, chapter 10, in The Marble Faun:

     As the music came fresher on their ears, they danced to its cadence, extemporizing new steps and attitudes.

   • 1879, Samuel Butler, chapter 5, in Evolution, Old & New:

     The small jelly-speck, which we call the amoeba, has no organs save what it can extemporize as occasion arises.

   • 1906, Thomas Hardy, The Dynasts, Part Second, Act Third:

     The wine runs into pitchers, washing-basins, shards, chamber- vessels, and other extemporized receptacles.

   • 2003 August 25, Emily Eakin, “How King Shaped The Dream”, in New York Times, retrieved 8 November 2011:

     His most famous words — "I have a dream" — were extemporized.

• (intransitive): improvise, think on one's feet
• (transitive): devise, improvise

• play it by ear
• off the cuff
• off the top of one's head