What are jazz-musicians thinking while improvising do they allow their brains to do the work or do they analyze the harmony as they play?

For me, most of the thinking happens during practice sessions. Jazz musicians often learn the vocabulary just as a person learns a language. They learn short phrases and put them together into longer phrases. Similarly, jazz musicians learn short phrases that work over a particular chord or harmonic passage and as they get more fluent and to be able to get creative with the phrases, they begin to develop longer phrases and to be able to turn them inside out and begin to hear the lines as ideas in the form of colors and shapes and not as “licks”.

The more deep you go with learning the vocabulary the more interesting your solos will be and the more freedom you will experience. Many musicians are constantly working at “getting in the zone”. That’s that place where there’s absolutely “no” thought going on. One of the most exciting things about the best jazz musicians is that they can produce more interesting solos spontaneously than if they spent days trying to compose an interesting solo.

In order to develop the ability to learn how to play over chord changes and “get in the zone”, it is essential to be able to hear the chord tones and the scales and melodic lines that are derived from the chords and scales, not to mention all the rhythmic possibilities etc. That’s the “brain work” and that’s why the geniuses like Charlie Parker, John Coltrane and Michael Brecker often practiced 8 hours a day. It takes time to work out your ability to “hear the changes” and to make solos sound lyrical.

Of course, there are as many approaches to improvising as there are people on this planet. Some improvisors never leave the text book approach to improvising. They are constantly playing lines that they practiced over and over and they play their preconceived ideas as they go from chord to chord. Just like a great speech makers, some write it out and give their speech word for word, some follow an outline but do a little improvising, and some of the best speeches are made simply by knowing the important points they want to make but the rest is completely improvised.