Jazz is mainly an improvisational music. All "rules" derive from this. But improvisation itself has some rules too. The main rule is the so called "phrasing". Phrase in music has the same meaning as in spoken language: a comprehensive idea that has beginning and end. A phrase might be a part of a sentence, but definetly is more than a word and by all means is understandable.
Speaking in a musical language, the phrase must have an internal structure and two phrases may (or better should) have pauses between them. Pauses must be an integral part of musical thinking and not a frustrated "now what do i do?" moment in the solo. This statement doesn't apply to the duration of a phrase. A small phrase can be divine as a huge one could be. Better though, not to start from big ones, as the first concern is to organize what we know in theory, so let's keep the duration under control.
We finally played 16th notes on a Ab Pentatonic at 180 beats. Splendid! Now if we stick only to automated exercises, we will gain speed but we will definetly lose the spontaneus innovation that Jazz (as other musical expressions also) needs.
Once we reach a satisfactory level in a single scale-chord playing, we have to try others and multiplex them. This really means that a continuous scale that uses steps and jumps (horizontal and vertical playing) using fluently all that we initially study statically, is paying back much grater than a programmed scale ascending-descending and then move-on-to-the-next pattern. Automation seems to pay back greater only because it is easier. In the long run though, flexibility really pays back.
Many styles have spawned from Jazz, as Jazz itself has been greatly benefited from the surrounding musical expressions in every era. The Blues for example has been an integral part in Jazz since the beginning. What we should have in mind is that different styles have slightly or completely different principles considering arrangement, articulation, synchopation, harmony, structure, mood etc. It is a great failure if we solo in a bebop tune and the audience begins to snore, or on the other side, use too asymetric and difficult "sit down and listen" sharp-aggressive phrases while our audience is in a romantic dancing mood, or worse, in a post dinner pre-digestive phase!
In most grave situations like the above, there is nothing wrong to the technique or the education of the players. The main problem is on the initial disposition of the individual musicians or the whole band. And this issue is solved when automation steps down and choice stands up. A 6 months band with a strong disposition will sound really better than a 5 year bored band that plays mindlessly (only by reflex). This applies also to solo playing.
Be interactive. It is better to hear and play one chord that to enclose in one's self and play 5 times more. As this is an integral part in Jazz, no further explanation is required. If you change the word "chord" to another suitable one, then this paragraph doesn't apply only to pianists :)
Trying to expertise in Jazz, I have to state that the primary difficulties in this music are related primary to rhythm. Rhythm as articulation and as a "vehicle" in which a phrase is based on. Focusing on the time issue will help in any direction or role (solo, accompaniment etc.)
Furthermore, time itself "lives" in other aspects. For example, if I wanted someone to "describe" the changes in a great piece like "Stella By Starlight", it would not be real difficult. But describing or thinking of them is a stop-time action. When this piece starts playing in 200 bpm, stop time becomes real time and just "understanding" the harmony isn't enough anymore. When the tempo is an issue, time is mercyless.
Finally, time is not an objective experience. Has it occured to you finishing listening to a great solo and realizing that time seemed to have stopped? When improvizing, we must "take" with us the listener to a trip that seems to be endless (not as a torture :), and not to "tell" that we solo because it's our turn and finally time will pass and we'll end out turn to pass it to another musician. This is the final objective for any Jazz musician: carry the audience along the trip.
I am proud for having accompanied (in the piano) Sheila Jordan and Cameron Brown in a recent seminar in Athenaeum Conservatory. It's the second one we had in two years with her and I still remember her initial phrase in the first one.
"Today we will talk about dedication"! What followed and what she did was a build up of the first sentence. Jazz does not necessarily bring money or fame, and a musician has to make a lot of effort just to be at least satisfied.
Jazz is a very useful qualification for any musician and usually musicians take what they can and use it in other styles. But really occupying oneself with Jazz is a major task by itself and requires great love for the "sport". If you are the "sporty" type, dedicate yourselves. I try to.
"Neo, sooner or later you are going to realize just as I did, that there is a difference between knowing the path and walking the path."
- Morpheus, Matrix.
----------- Jazz issues out ----------