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 + / -

 Parameters \ Signs + - Window Diatonic Chromatic Mode Major Minor Direction Flattening Sharpening

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.
Let's try putting these 4 Strong Modes in order of popularity and common usage - 1. the only +++, the Flattening (+) Diatonic (+) Major (+) Mode, 2. the Direction +, the Flattening (+) Chromatic (-) Minor (-) Mode, 3. the Window +, the Sharpening (-) Diatonic (+) Minor (-) Mode, 4. the Mode +, the Sharpening (-) Chromatic (-) Major (+) Mode, This might seem a little far fetched at first, but it seems the only way to make the pieces fit, and placing the modes in this order, with academic theory only teaching the first 2, seems a promising start at quantification.<-->      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 ?