As we can decipher many modes which are nondiatonic have in many instances multiple tritones or perhaps as well an augmented triad which coexist in a given mode. One example could be the formula I-bII-III-#IV-V-VI-bVII. This mode has a total of three tritones found between its members. The first of course is I-#IV, the next is between bII and V and lastly we have the tritone bVII-III.

One application could be the limiting of transpositional possibilities resulting in no repetition of a given tritone. An example with this particular method could be C-Db-E-F#-G-A-Bb<> Ab-A-.C-D-Eb-F-Gb<>Eb-E-G-A-Bb-C-Db<>G-Ab-B-C#-D-E-F-<>Db-D-F-G-Ab-Bb-Cb<>A-Bb-C#-D#-E-F#-G<>D-Eb-F#-G#-A-B-C.

Here we will invert the transpositions giving us another row without repetition. I will begin this time with F# as our first starting point. F#-G-A#-B#-C#-D#-E<>Bb-Cb-D-E-F-G-Ab<>Eb-E-G-A-Bb-C-Db<>B-C-D#-E#-F#-G#-A<>F-Gb-A-B-C-D-Eb<> A-Bb-C#-D#-E-F#-G<>E-F-G#-A#-B-C#-D<>.

I will now derive all three unequal symmetric modes from the original and begin these modes all with C. “Mode 1” will remain C-Db-E-F#-G-A-Bb “Mode 2” begins from Db however from C it appears as such C-D#-E#-F#-G#-A-B. “Mode 3” begins on Bb and it shows itself as C-D-Eb-F#-G#-A-B.

Now we will use all three variants as starting points. Each mode of course is constructed with the tritone as the nucleus and varying planets. This gives us the possibility of various transpositional schemes without always using simply the original mode.

An exposition of this technique shows that each mode in the thesaurus, although some may have the same intervallic construction can be utilized to create an alternative logical schematic.

This is what I mean when I say only the tritones which are ordered bring about this structuring.

I will now present a scheme with all three modal variants. We will see that the transpositional scheme is solid and that “Mode 1” can be found in each mode however “Mode 1” will in total not in any way form a logical set of transpositions. It is only with the usage of “Mode 2” and “Mode 3” that the logic comes to be.

Here is an example.
C-Db-E-F#-G-A-Bb (mode 1) E-F#-G-A#-B#-C#-D# (mode 3)D-F-G-G#-A#-B-C# (mode 2)
Bb-Cb-D-E-F-G-Ab (mode 1) Ab-B-C#-D-E-F-G (mode 2) Db-Eb-Fb-G-A-Bb-C (mode 3)

The above is my first part of the scheme, now I will invert the transpositions from F#. Once again “Mode 1” will not be the binding force.

F#-G-A#-B#-C#-D#-E (mode 1) D-E-F-G#-A#-B-C# (mode 3) E-G-A-A#-B#-C#-D# (mode 2)
Ab-A-C-D-Eb-F-Gb (mode 1)Bb-C#-D#-E-F#-G-A(mode 2) F-G-Ab-B-C#-D-E (mode 3).

This demonstrates the validity of the entire thesaurus’ generation of modes, as each modal construct can be individually used in schematic planning.