A short piece of instrumental music that is improvisatory (9)

I believe the answer is:

impromptu

(Other definitions for impromptu that I've seen before include "Extempore" , "Spontaneously, off the cuff" , "Unplanned; unrehearsed" , "Without much planning" , "With little or no preparation or forethought" .)

I've seen this clue in The Independent.

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