More 8 tonic theory

In order to fully grasp the workings of the 8 tonic system we must first fully understand four tonic substitutions. Four tonic subs are also called diminished substitutions and the tri-tone substitution is included in this group of subs. If you can imagine that the tonic V7 and the tri-tone is one axis and that the V7 chords a minor third above and below is the other other axis (at a 90 degree angle from the first axis).

In the key of C the V7 is G7 and the tri-tone sub is C#7. The other two dominant chords are Bb7 and E7. These chords are all related to each other because they share the same diminished scale. A G7(b9), Bb7(b9), E7(b9) and C#7(b9) are basically all the same chord if you don’t consider their roots. The tri-tone is used all the time as the most common type of substitution, but the the other two dominant chords (Bb7 & E7) are also very common subs for V7. They are often used as ways to get to the tri-tone sub, this is called a ‘backdoor resolution’. 

For example:

over
D-7   G7    CMaj7

play:
F-7 Ab-7  CMaj7


In fact, we can use the component chords of all four ii-7V7s and combine them freely.

B-7  E7    D-7 G7    F-7  Bb7    Ab-7  C#7

We can use only the dominants or only the ii-7s:

over
D-7       G7          CMaj7

play:
G7 Bb7 E7 C#7   CMaj7


or play:
F-7       B-7         CMaj7

Keep in mind that the Dominant chords all sound pretty close to each other, the related ii-7s are where you start to get more dissonance. Think of the minor third axis  (B-7  E7, F-7  Bb7) as cousins of the tri-tone sub. The chords of the 8 tonic system are simply all of the chords from these these four ii-7V7s. When we are using hexatonics/pairs from these chords we are still basing the harmony these strong four tonic substitutions. The 8 tonic system is simply another way to apply hexatonics/triad pairs to diminished subs. We are just calling the related ii-7 chords Major triads (from the -3rd) or you can also think of them as IVs.