In many past articles I've tried to analyze lines of the masters, with a view to understanding their procedures, but I know only too well that actually applying the ideas gleaned from them when playing at speed is a different matter. I confess I feel very far from solving this problem--both pedagogically and for myself--but here are a few comments.
As I comment in this issue's Style Analysis, some players such as Wynton Kelly and Bobby Timmons well exemplify the use of a certain "basic" vocabulary of melodic figures. But I feel that even a more "outside" or idiosyncratic jazz style has to be based on a good mastery of these building blocks.
Triadic figures and riffs
All players (speaking of the mainstream) frequently make use of the basic triad tones and their neighbors, in figures that are familiar and recognizable. You should certainly be able to play figures like these instantly, in any key:
[Ex. 1]
The sixth and ninth are added to the triad for a host of figures which run through all of jazz history.
[Ex. 2]
These examples are more than just triadic figures, they are riffs, used again and again since the 30s and even the 20s. (I think something that distinguishes the masters, like Bud Powell and Monk and McCoy, is an almost unconscious grounding in the great styles that preceded them, the 30s New York and Kansas City swing. It's important for us in the younger generation to listen to Count Basie, the boogie-woogie players, and so on.)
Blues figures, which we've discussed many times before, are based on triad figures, with added chromatic "blue" notes. Again, we should certainly master figures like these in all keys:
[Ex. 3]
Many of Monk's blues heads are based on deeply fundamental riffs, though with a certain original touch.
Scale work
Triad figures with added notes obviously shade into scale passages:
[Ex. 4]
The "bebop" scales, with one chromatic step added to a major, minor or dominant scale, are increasingly important in jazz education. Barry Harris teaches them and the bebop masters certainly used them a great deal:
[Ex. 5]
It's been pointed out in many contexts that eighth-note lines tend to be constructed so that the chord tones fall on strong beats. The be-bop scales accomplish this.
The many specialized jazz scales, such as whole-tone, diminished, and altered, as well as the packaged "runs" favored by some (not all) players such as Oscar Peterson, are used in a slightly different way, to cover ground on the key board or for various effects. Also, with familiarity, small portions of these scales can find their way into melodic lines.
Neighbor figures
I discussed these in No. 7, p 68. The tonic note is very often sidled up to with a neighbor enclosure:
[Ex. 6]
By practicing, you should develop comfort with the interrelationship between the triad tones of each chord and their neighbors. This is a basic exercise to master in all keys:
[Ex. 7]
etc.
Use an improvised left hand chord voicing, if you can.
Improvised melody
In order to improvise, these elements must be brought together according to artistic principles of balance, contrast, imitation, sequence, implied counterpoint, silence. I haven't been able to define any method of teaching these things, except for the universal advice to listen to a lot of jazz; but perhaps just contemplating the existence of these factors may be enlightening.