Dodecaphonics is the representation of music based on the chromatic scale where each note is of equal importance. More to the point of this discussion is the study of chord substitution theory and the idea that you can play any note or chord over any other chord.
The following constitutes part I of a system of theory that I have used in my teaching practice. I am (re)‐ posting this in order to share information about improvisation and to establish a dialog. I have played jazz guitar for over 30 years and have studied with Pat Martino, Howard Roberts, Andrew White, Mark Copeland, Herb Ellis, etc. Dodecaphonics is the name of a "System of Harmony" that I derived from my various studies and is particularly inspired by the works of John Coltrane.
Dodecaphonics is the 12 tone application of chord substitution. This Applies to soloing and comping concepts. About 20 years ago, I started cataloging various ways to play over certain chord progressions. I had random bits and pieces of formulas that worked over different chords. For some, I had theoretical practices to back them up, and for others, I just knew they sounded good. As I became a more proficient improviser and my tastes grew to include some of the modern masters of jazz such as Eric Dolphy and John Coltrane, I knew that there had to be more than the standard theory that I knew from college. I began to develop a system…
Note that in these systems, the harmonic components you are playing over DO NOT need to be present in the music. You are creating the chord progression in your improvisation, much as John Coltrane utilized countdown changes in 1959 over a 2-5-1 that DID NOT EXIST in the music. (Listen to his playing on the Cannonball Adderly recording of limehouse blues at 1:15)
Over | Dm7 | G7 | CMaj7 | he was playing countdown changes (Dm7 Eb7 AbMaj7 B7 Emaj7 G7 CMaj7) as well as Giant Steps changes.
By virtue of your studies of this harmonic system, you are redefining the harmony even while the rhythm section is playing something completely different. Again, this is not new and radical stuff. Charlie Parker created bebop by redefining what you could play over a chord progression. i.e. he played a NEW chord progression and not strictly over what the rhythm section did.
These systems will allow you to ultimately go beyond functional harmony though the first two systems are fully within the realm of functional harmony. It's a process…