symmetrical scales

Just as certain chords (the 1-3-#5 augmented triad for example) seem a
bit easier to construe in twelve tone equal temperament than they are
in a purely tuned just intonation framework, I would think that there
must also be a wealth of such scales as well (say the whole tone, or
the Wh/hW diminished scales for example)...

I have in the past used symmetrical scales of two step sizes, by
empirically listening to sequences of say x & y mod n (where x & y are
the two step sizes and n is the equal division of the octave) that
terminate at an octave.* Here are a couple of examples of I've used in
20e:

x=5 & y=7, and x=5 & y=6, with their minor third major third
sequences, are somewhat analogous to the familiar 2nd degree Dorian of
12e at x=3 & y=4 (mod 12)... but in place of the familiar seven note
diatonic, here we have scales of ten and eleven notes.

x=5 & y=7 (mod 20)
0, 1, 4, 5, 8, 9, 12, 13, 16, 17, 20
0, 60, 240, 300, 480, 540, 720, 780, 960, 1020, 1200

x=5 & y=6 (mod 20)
0, 2, 4, 5, 7, 9, 11, 13, 15, 16, 18, 20
0, 120, 240, 300, 420, 540, 660, 780, 900, 960, 1080, 1200

By using the two minor seconds, you could create the following
thirteen note set that uses both of the above 20e fifths and fourths
(12&7, and 11&9).

x=1 & y=2 (mod 20)
0, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20

0, 120, 180, 300, 360, 480, 540, 660, 720, 840, 900, 1020, 1080, 1200

From the familiar n/2 whole tone and the x4 y1, x1 y4 & x3 y2, x2 y3
Wh & hW diminished scales to the unfamiliar x12 y5 & x5 y2, 9 and
11-note scales of (just) 20e; the possibilities for creating symmetric
sequences of mod n scales seem aplenty...

Dan
________
*Though I would imagine that someone has probably already taken an
in-depth look at these types of scales, as they just seem so
'ready-made' so to speak... I really don't know. So if anyone else
does happen to know of any such work along these lines, I'd certainly
appreciate it if they passed it along - thanks.