there are basically three approaches to improvising on jazz standards: melodic paraphrasing, improvising with the harmony, and motivic development which may overlap the previous two.
agreat many jazz musicians approach the harmonic implications in three ways: harmonic specificity, harmonic generalization, or ignoring harmonic implications.  

harmonic specificity: careful attention to implications of harmony. reliance on proper thirds, sevenths resolving appropriately. adhering to alterations called for by the chord symbols or melodic implications of the composition.

harmonic generalization:  rather than deal with the specifics of the implied harmony, reliance on blues ideas and scales. in the instance of  a ii v progression, it is often generalized as a i chord. for example: with the progression
| dmi7    | g7    | c major 7    |
the c major triad or c major blues is used for the entire phrase.

ignoring the implications:  this can be the result of the improvised line following the direction of motivic based improvisation; the improviser choosing to impose alternate harmony over pre-existing harmony; the improviser choosing to create tension by deliberately playing notes foreign to the implied harmony.

experienced jazz plays move in and out of the above areas. they are always able to play harmonically specific, and often after being general or vague they will return to the specifics. when an experienced jazz improviser plays deliberately vague, he does so knowing the harmonic implication and therefore what tones to avoid.
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very good thoughts.

i remember someone telling once, "don't play outside until you know how to play inside!"

that is, don't ignore harmonic implications or even do harmonic generalization until you are good at harmonic specificity otherwise there's nothing to base your "art" on.
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what you are calling "harmonic generalization" is what i call and what countless others and countless textbooks call "horizontal"  as opposed to "vertical" when  you consider each chord seperatly when improvising.  eash approach being equally valid just different ways of approaching a set of chord changes to improvise one.  playing "horizontally" is often just as inside as playing "vertically".  coleman hawkins for example was known for prefering to aproach changes "horizontally"... hardly an outside player.
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