Generation of the 4 Strong Modes

In the 4 strong modes, there are -
         2 diatonic modes and 2 chromatic modes,
                   in what we call the Window Parameter
                             remaining within the Window (diatonic), or
                             borrowing from outside the Window (chromatic) ;
         2 major modes and 2 minor modes,
                   in what we call the Mode Parameter (major or minor) ;
         2 flattening (descending) modes and 2 sharpening (ascending) modes,
                   in what we call the Direction Parameter (flattening or sharpening),
                             flattening with a DOMINANT seventh (G⁷ or E⁷), or
                             sharpening with a DOMINANT sixth (Dm⁶ or Fm⁶).
There is an interesting paradox here -
         With 3 parameters (Window, Mode, Direction) of 2 choices each,
                   there should be 8 (2³) possibilities of modes, not just 4.
         The choice is more limited than one might think
                   because, when one knows 2 of the choices, the third is obligatory,
                             example - when the mode is minor and chromatic, it must be flattening.
         One of these parameters might not be generative
                   as will later be discovered.
         How could these parameters and choices be disposed in a table,
                             and how could these choices be identified,
                   so that the imposition of the choice in the third parameter would always be obvious ?

Classifying + / -

By classifying the choices in each parameter as either positive (+) or negative (-),
         the third choice must be the one to produce a total positive result, thus we have -
                   the Flattening (+) Diatonic (+) Major (+) Mode, (No. 1)
                   the Sharpening (-) Diatonic (+) Minor (-) Mode, (No. 2)
                   the Sharpening (-) Chromatic (-) Major (+) Mode, (No. 3)
                   the Flattening (+) Chromatic (-) Minor (-) Mode, (No. 4)
                             each with a total positive result.
                   There is one +++ mode and there are three +-- modes.
         How are these 4 modes to be disposed
                   so that the Primary +++ Mode is placed centrally,
                             in a position to generate the other three Secondary +-- Modes,
                   and what Transformation will adequately produce the desired result ?

Disposition of the Four Strong Modes
1. The Diatonic Major Mode
2. The Diatonic Minor Mode
3. The Chromatic Major Mode
4. The Chromatic Minor Mode
5. Adjacent Chromatic Modes
6. A melodic Example