Recommended Reading
Here are a few exercises to work on improvising concepts in jazz. When performing, you should put all of this out of your head and play as your ear directs you. However, in practice it is useful to address specific aspects of improvisation in order to develop the skills to be able to play stylistically and musically.
Interpreting a melody
A solo should be in the context of the tune you are playing. Being really familiar with the tune you are improvising on is essential to delivering an effective solo.
On a standard, experiment with interpreting the melody. Choose something with fairly straightforward harmony and impose restrictions like beginning key phrases a full bar later than they are written (make sure you have some sort of accompaniment). Think about how you want to control the tension and release across the phrases and chord sequence.
Phrase map exercise
On any tune, some sort of pre-planned phrase map or plan is a really good way to practice improvising without getting too caught up in the detail of the phrases (we'll worry about that later).
Over a blues: play a simple 2 bar phrase, then 2 bars rest. Over chord IV, repeat (or adapt to fit) your phrase, then 2 bars rest. Over the last four bars, play a 4 bar phrase. You can develop this into a two person exercise, doing question and answer phrases over a sequence.
Voice leading
Voice-leading is linear harmony; (on a single line instrument) how the notes you play relate to the chords when they change. How you approach this has a profound effect on how strong your lines are in the context of the chord sequence. Improvising stylistically and coherently over a chord sequence is virtually impossible without clear voice-leading.
Over a standard blues, play the guidetones (3rd & 7th of each chord) and make sure you are clear which notes they are and how they sound in context. Practise taking solos where every time the chords change you play the guidetone voice-leading, that is you play the 3rd or 7th of the chord and then when the chord changes you go to the nearest 3rd or 7th of the new chord. For pianists, make sure this is done with a single line (and all the other exercises too). Make sure you work at a tempo that you can achieve, regardless of how slowly this is. Your progress will be much faster if you don't let yourself get away with mistakes.
Developing motives
The Sonny Rollins solo on St. Thomas is a great example of this. There are loads exercises you can do to work on different kinds of motivic development:
-take a simple idea (probably no longer than 3 or 4 notes to start) and repeat it through a sequence (for at least a whole chorus), transposed to fit the changes.
-take the same idea, but this time adapted to fit the changes.
-start the idea on different beats of the bar at different points through the sequence (this can be hip if you start it on a different quaver so the swing switches round).
...all of this can be done before you've even started thinking about extending the motive at all, or developing it in any way other than the stated methods. Freestyle motivic development should be the last exercise on this.
Good luck!
