One of the basic principles of the twelve-tone technique is the utilization of all twelve chromatic pitches before the repetition of the first. Therefore one constructs twelve-tone rows for the execution of this concept. Therewith we receive the perfect equality of pitches resulting in an atonal environment.
At one point I decided to build a series of polymodal structures resulting in the usage of all twelve half-steps. Because of my symmetrical thinking, as presented in the theory, we can rethink the building of a twelve-tone environment.
One clear example is to choose a heptatonic mode, and superimpose a “sister mode” upon the other symmetrical axis. This mode would be as well a heptatonic mode and in the case of the tritone, is built upon the augmented fourth of the original mode.
Also the “sister mode” should consist of the five pitches which are not found in the original mode. An example in letters would be as such.
C-Db-E-F#-G-A-Bb is the original mode. The polymodal “sister mode” is built as such.
When I apply this technique I purposely leave the F# and B# out of the sister mode because this tritone is already in the original mode. The result is a twelve-tone structure.
I personally reserve registers for each mode which brings the dichotomy into this technique. We can with a transpositional scheme order each modal transposition through the ordering of a given tritone as proposed in the opening of my theory and at the same time we can exercise the principles of dodecaphony. When the original mode is used as a sound chamber and the sister mode as a melody one can clearly hear a logical harmonic movement through the structured symmetries. In a contrapunctal approach the same result is possible when the two modal structures maintain their identity.