Disposition of the 4 Strong Modes

The best disposition seems that of the Platonic regular tetrahedron,
          an equilateral triangular-based pyramid, seen from above,
     with the Flattening Diatonic Major (+++, indicated M) centrally placed at the apex,
     and with the three other modes (+--), placed at the base around it,
          the Sharpening Diatonic Minor (indicated w) top-left,
          the Sharpening Chromatic Major (indicated W) top-right,
          the Flattening Chromatic Minor (indicated m) below.

Disposition of the Parameters

The Window Parameter is placed on the ridges :
     between the two Diatonic Modes with its + line, and
     between the two Chromatic Modes with its - line ;
The Mode Parameter is placed on the ridges :
     between the two Major Modes with its + line, and
     between the two Minor Modes with its - line ;
The Direction Parameter is placed on the ridges :
     between the two Flattening Modes with its + line, and
     between the two Sharpening Modes with its - line .

Choice of Transformation

The only way to transform the Primary +++ Mode into the three other Secondary +-- Modes,
          is that of symmetrical inversion, with a choice of two possible levels of inversion.
     1. The large, global, tonal, level of the complete Window, the Full-inversion,
               along the + ridge of the Window Parameter,
,           transforms the Flattening Diatonic Major (C) into the Sharpening Diatonic Minor (Am),
               with the note correspondents D-D, G-A, C-E, F-B.
     2. The small, nucleus, modal, level of a half-window, the Half-inversion,
               along the + ridge of the Mode Parameter,
,           transforms the Flattening Diatonic Major (C) into the Sharpening Chromatic Major (C),
               with the note correspondents E-E, D-F, C-G, B-A(b), A-B(b).
          NOTE the flats in parentheses (b),
               which only apply to the TONIC/DOMINANT Swing of the Chromatic Mode (Fm⁶/C⁷),
                    and not to the TONIC/COUNTER Swing (G⁷/C⁶).
     3. The application of both inversions (full and half in either order, +-, or +-)
          transforms the Flattening Diatonic Major (C) into the Flattening Chromatic Minor (Am),
               which would have been unreliable with any kind of direct parallel transformation,
                    especially if one relied on scales, instead of swings and circles.

Observations and Conclusions

Metamorphoses
There is a striking similarity between this Inversion Generation and Metamorphoses 4 and 1 -
     1. Metamorphosis 4 changes a chord of C⁶ into a chord of Am⁷,
               changing both the Mode (from major to minor)
               and the direction (from sharpening to flattening);
          the Full-inversion generates the Diatonic Minor Mode from the original Diatonic Major Mode,
                    bringing about a TONIC chord of Am⁷ from a TONIC chord of C⁶,
               thus producing a change of Mode (from major to minor)
               and a change of Direction of the mode (from flattening to sharpening),
               but leaving the Window unchanged (still Diatonic).
     2. Metamorphosis 1 changes a chord of C⁶ into a chord of C⁷,
               changing both the Window (from Diatonic to Chromatic)
               and the direction (from sharpening to flattening);
          the Half-inversion generates the Chromatic Major Mode from the original Diatonic Major Mode,
                    bringing about a TONIC chord of C⁷ from a TONIC chord of C⁶,
               thus producing a change of Window (from Diatonic to Chromatic)
               and a change of Direction of the mode (from flattening to sharpening),
               but leaving the Mode unchanged (still Major).

Direction
In this process of mode generation,
     the Full-inversion changes the Mode (from Major to Minor)
     the Half-inversion changes the Window (from Diatonic to Chromatic)
     both inversions change the Direction.
The parameter of Direction is thus a product, a result of the other parameters,
          and not a generative parameter like the two others (Mode and Window).
               Its 2 ridges (++++ and - - - -) DO NOT appear in the generation diagram.
     There seems to be no basic, generative relationship between modes of the same direction -
          The Diatonic Minor Mode and the Chromatic Major Mode are in the same direction
               merely because they are each a generation away from the original Diatonic Major.
          The Diatonic Major Mode and the Chromatic Minor Mode are in the same direction
               merely because the latter is two generations away from the original Diatonic Major.
It is high time to dismiss the myth of the Chromatic Minor being a parallel form of the Diatonic Major.

Alternative 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