Through the concept of inverted figures upon each given member of a chord, this technique can of course be utilized as well with a chosen modality. For example we could choose any mode presented in my thesaurus and initialize a generation of ordered inversions.
Firstly I will now construct a heptatonic mode C-Db-E-F#-G-Ab-Bb. Then as discussed earlier I will generate inversions in relation to each separate note of the existing mode.
We will then generate a row of seven modes related to the original. This generation can create a string of related melodic patterns that can be polymodally superimposed upon the same exact generation in another register. If the two modal environments retain identity they will function as a transpositional scheme or as a superimposition. The superimposition is of course possible to transpose and can begin from another pitch but will still obtain the original pitch relationships.
In general, as well, I personally utilize a matrix for my transpositional schematics.
This matrix is in itself symmetrical. It looks as such: C-D-Eb-E-F#-Ab-A-Bb. This is also not the only possibility for a logical transposition. We can as well develop inverted forms or otherwise related schemes. An example could be C-Db-E-Eb-Ab-G.
Therefore I could develop the original inverted scheme and then we could simultaneously superimpose the sevenfold collection in the retrograde beginning on perhaps Ab where the original would begin with C.
From the original mode I will now demonstrate our seven inversions. Firstly from “C”
C-B-Ab-F#-F-E-D. Secondly we have “Db” – resulting in Db-Bb-Ab-G-F#-E-D. Thirdly then from “E”-resulting in E-D-C#-B-Bb-Ab-G. Fourthly from “F#”- resulting in F#-F-E-D-C-B-G#. Fifthly we invert from “G” bringing about G-F#-E-D-C#- Bb-Ab. Sixthly from “Ab”
and this results in Ab-Gb-E-Eb-C-Bb-A and seventh and lastly the inversion from “Bb” appears as the
following Bb-Ab-G-E-D-C#-C. Rearranging the notes one will find that we have generated the same mode in varying transpositions all landing on the matrix of the whole-tone gradation. This can exquisitely become our transpositional scheme.
In this way we develop transposed modes as well as possible superimposition that all use the same generative process. We can then take the generated mode and develop seven inversions resulting in the original mode as well found in various transpositions on the matrix of the whole-tone gradation. The environment is polymodal however completely homogenous.