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...
The system is based on the assertion that in a 13th chord, all the notes in the scale are represented. Therefore, it is logical to conclude that (taste aside) any combination of notes in the scale can be "substituted" for the 13th chord. It can also be derived that any diatonic chord based on the scale can be treated likewise. Thus, any fully diatonic chord may be substituted for any other diatonic chord. This concept is called "diatonic extensions".
For example, the chords:
Cmaj7 Dm7 Em7 Fmaj7 G7 Am7 Bm7b5 are all essentially the same chord.
Now, following up on that that is that the V chord (G7) is the most important chord in the series. The strongest resolution between any 2 chords in the diatonic sequence is the V‐I relationship. This is because the 3rd of the V chord wants to resolve up to the root of the tonic and the 7th of the V chord wants to resolve down to the 3rd of the tonic. Try it and you should hear what I'm talking about. Whether you believe me or not... Bear with me and take the following road…
I used to hear 'Trane playing Dm7 Fm7 and Abm7 runs over the G7 chord. I wondered where this came from. Of course I could analyze the notes over the G7 chord and they all made sense but occasionally he would "lay" on F# notes which I "knew" were wrong :‐) Eventually, my small mind figured out that he was simply playing standard 'Trane licks built on the 5th, b7, and b9 of the V (G7) chord. It started coming to me…
Let's use the Abdim7 chord and how it relates to dominant 7th chords. Take a look at the notes in the Abdim7 chord enharmonically spelled as (Ab B D F). Now this chord also happens to be, G7b9, Bb7b9, Db7b9, and E7b9 chords. Notice that going from the Abdim7 chord to any other chord in the sequence involves simply adjusting one note:
G B D FG7
Ab Bb D FBb7 Ab B Db FDb7 Ab B D EE7
These 4 chords are related through the Ab diminished chord and are found by harmonizing the Diminished scale (symmetrical in half and whole steps). Understanding this Relationship is key to understanding what 'Trane was doing in the '60s.
We've already diagramed the diatonic extensions of G7 Let's do the same for the other 4 chords in the sequence:
(Note the V chord in each sequence) (Bb7)
Ebmaj7 Fm7 Gm7 Abmaj7 Bb7 Cm7 Dm7b5 (Db7)
Gbmaj7 Abm7 Bbm7 Cbmaj7 Db7 Ebm7 Fm7b5 (E7)
Amaj7 Bm7 C#m7 Dmaj7 E7 F#m7 G#m7b5
Now put all the chords together (1/4th of the dodecaphonic system) and you have the following table:
Cmaj7 Dm7 Em7 Fmaj7 G7 Am7 Bm7b5
Ebmaj Fm7 Gm7 Abmaj7 Bb7 Cm7 Dm7b5
Gbmaj7 Abm7 Bbm7 Cbmaj7 Db7 Ebm7 Fm7b5
Amaj7 Bm7 C#m7 Dmaj7 E7 F#m7 G#m7b5
This produces a table or formula of chords that are essentially synonyms for each other. *NOW* what you do is this. Take a chord progression such as
|Dm7 G7 | Cmaj7 A7 |
Use the table to produce some substitutions for the original progression. Note that this is not just for comping but is also used for improvisations. In fact, at first you should learn to "hear" these synonyms over the original progressions. I suggest using a sequencer or tape recorder and have the chords playing in a loop while you take a certain sequence of synonyms and practice them over the original progression. Take small steps at first such as using the standard chord\scales for all but 1 of the chords...The dominant being the place to start with. For example, we'll take the IV chord from the 2nd row (Abmaj7) and use that in place of the G7 chord in the original sequence:
| Dm7 Abmaj7 | Cmaj7 A7 |
(Leave the A7 alone until you become more proficient). Again remember that you should be practicing melodic lines over this, not necessarily chords although the concept works both ways.
Try different parts of different tables as well. Don't shy away from chords that sound "funny". The first time I heard the ii chord row 4 of full table (Bm7 over the G7), I hated it. It had the F# in it after all, and I was taught that there was no more wrong chord than an F# over a G7 chord. I couldn't have been more wrong. If you "live" with the Bm7 chord over the G7 for a while, you will understand how it wants to resolve and it will begin to sound more "inside," same for all the other chords in the sequence. In fact, the point is to get your ear used to hearing things that it did *NOT* hear the day before.