One of your prime concerns should be playing melodically. This does not necessarily mean playing prettily, but there should be some sense of continuity to your lines, and they should be interesting in themselves. You should also be conscious of the rhythmic and harmonic development of your improvisations; I include these concepts in the term “melodic development”. This is hard to teach, and is probably the aspect of improvisation that requires the most creativity. Anyone can learn chord/scale relationships; it is what you do with this knowledge that determines how you sound. Hal Crook’s book How To Improvise has a lot of information on melodic development, especially on rhythmic variation, geared toward the intermediate player, while George Russell’s The Lydian Chromatic Concept Of Tonal Organization For Improvisation and David Liebman’s A Chromatic Approach To Jazz Harmony And Melody contain advanced and very technical discussions on harmonic development.
You should be aware of the contour of your solo. A common way to structure a solo is based on the model of telling a story. You start simply, build through a series of smaller peaks to a climax, and then come to a concluding phrase. This works well in most situations. However, you may wish to vary from this format occasionally. You can decide to start more strongly to introduce your solo, or you may wish to finish right at the climax and forego the denoument. You may wish to keep the entire solo at a low intensity level to convey a lazy feel, although you probably don’t want to bore the listeners, either. You may wish to keep the intensity level at a controlled simmer. Much like a standup comic working a room, you may want to alter your strategies as you assess the mood of the audience. You should strive to be in control of the emotional response you generate in your listeners.
There are some common devices that can be used in structuring your solo. One of the most important is repetition. After a soloist plays a phrase, he often repeats it, or a variation of it. Often the phrase, or a variation of it, is played three times before moving on to something else. The variation might be to transpose the phrase, or to alter key notes within it to conform to a new chord/scale. The variation might consist simply of starting the phrase at a different point in the measure, such as on beat three instead of on beat two. The phrase itself may be altered rhythmically, either by playing it faster or slower.
Related to the idea of repetition is the concept of call and response. Rather than repeat the original phrase, you can consider the phrase as a question or call, and follow it up with an answer or response. This is the musical analogue to asking, “did you go to the store today?”, and then responding “yes, I went to the store today”.
On most instruments, you can increase intensity by playing louder, higher, and faster; playing softer, lower, and slower usually reduces intensity. Playing simple rhythms such as quarter notes and eighth notes where the accents fall on the beats is usually less intense than playing more complex rhythms such as syncopated rhythms, where most accents fall off the beat. A hemiola is a particular type of rhythmic device where one meter is superimposed on another. An example of this is the use of quarter note triplets when playing in 4/4 time.
One long held note can also generate intensity on most instruments, although pianists may have to use trills or rollings octaves to achieve this type of sustain. A single note or short lick repeated over and over can generate a similar sort of intensity. You have to use your judgement in deciding how much is enough.
The relationships between chords and scales should not be seen as limiting or determining your choice of notes. They are merely an aid, a way to help you relate ideas you may have to fingerings on your instrument. Your ideas should not be dictated by the scales, however. Note that very few jazz singers use scales extensively; they generally are able to translate an idea more directly into their voices. For this reason, instrumentalists should practice improvisation by singing, in addition to practicing their instruments. No matter how untrained your voice may be, it is more natural to you than your instrument, so you may find you are able to develop ideas better by singing them than by attempting to play them. Singers also are usually limited in their ability to sing complex harmonic ideas, however, because they do not have well-practiced fingerings to fall back on. Scale theory can indeed be a source of ideas; just make sure it is not your only source.
Try playing scalar lines that are based mostly on steps, angular lines that are based mostly on leaps, as well as lines that combine these approaches. In addition to being concerned over your choice of notes, you try to vary the rhythmic content of your ideas. Beginning improvisers often unwittingly play almost all their phrases with just a few underlying rhythms. Try playing lines that are based mostly on half notes and quarter notes, lines that are based mostly on eighth notes and triplets, as well as lines that combine the two approaches.