What makes a good Improvisation ?

We almost always distinguish musician who play jazz from musician who play classical music.
It is quite a rare thing to see classical musician play jazz, and often they must do a lot of training before being able to improvise in jazz.

What is it that makes a person who knows his instrument be able to improvise or not ?


COMMUNICATION ! 
The first thing, and probably the most important, is being able to communicate !
Dave Liebman explains in this article that playing together means listening to one another and reacting (or choosing not to react) to what the other musician plays.
In fact, as he explains, there is a lot of band of so-called jazz musician, who just play their part but do not listen. The result is tasteless music, barely hearable. Indeed, how can one musician be able to do something that sounds good with what the others do, if he doesn't know what they are doing ?

Hearing the other musicians is one thing, knowing what they are doing is another. It takes a lot of concentration and of training to be able to know what notes one musician plays when you hear him play. Being able to do that in real time is even harder. Being able to do that in real time, while thinking of what your next note will be then seems impossible...

TRAINING ! 
Musician and researcher Charles Limb got interested in this question. He wanted to know what happens in the brains of a musician when he improvises. So he put on in a MRI with a tiny electronic piano, played a little melody and watched what happend when the musician answered to his melody with another improvised melody.
When looking at the results, he noticed one thing : one area of the brain of the musician was particularly active, the  area dedicated to language.
This means that the improviser knows his scales, his intervals etc... so much that he has assimilated them as a language. In fact this confirms something that improvisers have always known : it takes a lot of work to train the ear to recognize a musical object and to be able to express with your instrument the sounds you want to play.

We can also understand the difference between playing written music and improvised music : in improvisation you have to internalize the context, and know how to react to it, whereas when playing written music, you have to express something that you are told to express, that you haven't internalized. Of course, great classical musicians internalize the music before playing it, that makes it more lively, more human, but there are still a lot of musicians (even well known !!) who don't do that.