With due respect to Humphrey Lyttleton, composing completely without preparation is the fundamental element in free jazz. And there are any number of players in more mainstream sounding jazz who usse the same technique to jump into a tune and go with whatever happens--often a bent groove, or a peculiar sound--Monk did this a lot.

A lot of old blues players did this, as well, and could spontaneously improvise variations on floating verses, and so could play the same song, three times in a row, different every time.

At any rate, as evidenced above, it is more difficult to describe the process than to actually do it--