In Latin, the phrase “ex tempore” literally translates as “out of time,” but as an idiomatic expression, it refers to something done without preparation, or on the spur of the moment. The phrase was pulled into English to form a group of words related to this spur-of-the-moment concept. To extemporize is to compose, perform, or produce a piece of art or speech without preparation: An improv group can extemporize a skit, and a musician can extemporize a piece of piano music. The adjective “extemporaneous” and the adverb “extemporaneously” apply to speech made off-the-cuff (either formal or casual), or anything else done without preparation. For example, you might invite a date over and impress them by making an extemporaneous dinner, then woo them by extemporizing a love poem.