I agree entirely with Andrea, except for her assertion that you need a knowledge of musical theory in order to improvise.  A practised ear is all you need for that.  Musically literate players can improvise too, of course, but they tend to find it harder if they have been trained to rely on musical notation, which in the case of traditional music is, after all, just a way of noting the bare bones of the tune.  A comprehensively notated set of even a relatively uncomplicated tune as played in real life can become so involved that many professionals without experience in that style of playing would be quite unable to reproduce it accurately.  The point is that somebody who can only play from written music probably believes that there is a "right" way of of playing a tune (well, they've seen the sheet music!) -when there is really no such thing; context determines what is right (or, more to the point, appropriate) in any given situation. &nbnsp;This, of course, has nothing whatsoever to do with the original question...

Malcolm