[tjr]

Learning to improvise jazz seems different to Franklin's method, in that you don't listen to a jazz great's solo, put it aside and later try to reconstruct it; you have to play it exactly, writing it out if necessary, and play it over and over until it starts to become intuitive; until the muscles learn it.

I think that this Franklin method is basically how I learned. Jazz solos are not generally random; they are based on particular chords and/or scales/modes. The best improvisers tend to be good composers in general, and improvising is composing real-time. Get a good handle on what chord/mode to center you're composing around, and construct a jazz solo likewise.

[yesenadam]

>not generally random

not generally? "not random", surely. And even if humans try to play randomly they couldn't.

>based on particular chords

Whether the notes used in a section are from the set of all 12, or a particular subset, is nearly, dare I say, orthogonal to the level of randomness. And even playing not based on particular chords can be highly random-sounding or not at all.

I didn't understand your last sentence at all; at least, what do you mean, likewise? Or the first half really.

[tjr]

I did not mean "random" in a literal mathematical sense. If I have absolutely no idea (or purposefully ignore) what the chord progression of a tune is, I could just start playing notes. It might sound good, it might not. It might sound dissonant in a pleasing way. But that playing would not be based on a theoretical understanding of the chord progression; it would be, in some sense, random -- unplanned, escaping traditional theoretical analysis.

You could play any note on any chord, and it might be what you intended. Let's say the chord is C major. You could play a C, for the root. Or G, for the 5th. Or Db, for a flat 9. Or F#, for a sharp 11. Indeed, any of the 12 notes would be fair game, and you could name what they are from a music theory standpoint.

Trying to bring this back around to the Franklin method of learning: what one might do here is listen to a jazz solo, and first transcribe (or obtain a copy of) the chord progression. Instead of trying to copy the solo itself, you can hear that the soloist often played motifs emphasizing the dominant 9th and 11th over minor chords, and the major 7th and major 6th over major chords. You could then make up your own solo with the same emphasis. It would not be the exact same solo, but it would (or could) have a similar sonic color to it.