I'd previously thought that the Melodic Major Scale was equivalent to the bottom half of the Major Scale combined with the top half of the Minor Scale. In other words, Ionian bottom with Aeolian top. However, while pondering tetrachords, it just occurred to me... The Modal Mirror suggests that the Melodic Major's upper half comes from Phrygian, not Aeolian. The difference is not apparent in the interval spelling, of course, since both of their top halves are the same and the bottom half is being covered by Ionian. By extension, Melodic Major could also be seen as Mixolydian bottom, Aeolian top.
A natural extension of this observation is the following procedure: Here it is: From the Modal Mirror, combine the bottom half of each pair with the top half of its partner, and vice-versa. Yes! Another bona-fide legit musical structure unearthed for the benefit of all.
Eureka encore!
Details for each combo are here:
1,3 Ionian,Phrygian: R 2 3 4 5 b6 b7 8ve = WWHWHWW, a.k.a. Melodic Major
3,1 Phrygian,Ionian: R b2 b3 4 5 6 7 8ve = HWWWWWH, same as 7,4
4,7 Lydian,Locrian: R 2 3 #4/b5 b6 b7 8ve = WWWWWW, a.k.a. Whole-Tone Scale
7,4 Locrian,Lydian: R b2 b3 4 5 6 7 8ve = HWWWWWH, same as 3,1
5,6 Mixolydian,Aeolian R 2 3 4 5 b6 b7 8ve = WWHWHWW, a.k.a. Melodic Major
6,5 Aeolian,Mixolydian R 2 b3 4 5 6 b7 8ve = WHWWWHW, same as Dorian
2,2 Dorian,Dorian R 2 b3 4 5 6 b7 8ve = WHWWWHW, unchanged as Mirror surface
Some interesting developments indeed. There a couple of double occurrences, and a Wholetone scale appeared out of nowhere! The combination of Aeolian bottom with Mixolydian top, to become the same interval spelling as Dorian, harkens back to a prior notion from "Chaos In Boxes" that Mixolydian and Aeolian are the most closely related to Dorian by virtue of only one interval difference. Furthermore, this strengthened association hints toward the development of an expanded version of the Modal Mirror, one which positions each bottom-top mode combo in appropriate order, emanating from Dorian which is of course the center of the entire symetry. Of course, combo 6,5 is closest to 2,2 on the list, which looks like this:
2,2 - 6,5 - 5,6 - 1,3 - 3,1 - 7,4 - 4,7
and whose elements have the following quantities of interval difference from Dorian:
0 - 0 - 2 - 2 - 2 - 2 - 4
In this ordering system, wherever two Mode pairs have the same interval spelling (and therefore the same amount of interval difference from Dorian or "distance from centre"), the deciding factor becomes the interval contents of each constituent mode in its entirety as opposed to only the top or bottom half that got used in the combo. For example, 3 bottom, 1 top is the same as 7 bottom, 4 top; but modes 7 and 4 are each 3 intervals different from Dorian, whereas modes 1 and 3 each differ from Dorian by only 2 intervals, therefore 7,4 is further down the list than 3,1.
Notice that, since interval pairs appear consecutively on the combo list (ie, 6,5 is followed by 5,6, etcetera), it seems feasible and appropriate to re-order the original Modal Mirror according to each distance from Mode 2. The Modal Mirror has the Mode numbers 1 through 7 in consecutive order, arbitrarily clockwise, around the outside of the circle. The new ordering of the Modal Mirror would have Modes 5 and 6 closest to Mode 2, then Modes 1 and 3 further away, and then Modes 4 and 7 at the far side of the circle away from Dorian. Since the Modal Mirror itself does not distinguish or specify which element from each of its pairs takes precedence over the other in any way (that I can currently recall), the new combo list loses a dimension when interpolated or regressed back to the Modal Mirror. That is, the Modal Mirror does not provide a means of accommodating both 6,5 and 5,6. This could be accommodated by making further enhancement to the Modal Mirror. For example, turn the Dorian mirror line to become horizontal and specify that whichever Mode's bottom appears first in the combo list should be shown above the horizontal, and the other below.
Joining the re-ordered Mode numbers in numerical order generates an interesting-looking symmetrical curve.
(refer to culmination diagram)
Q.E.D.
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