Modes,Schillinger

Blackwood does not consider equal-divisions of the octave to be
symmetric modes, nor does he include scales with more than two step
interval sizes. He also said he was disappointed with the dodecatonic
symmetric mode in 18 (6 times [2 1]) as it sounded to him like an
out-of-tune chromatic scale.

Messiaen called scales of these kinds "modes of limited transposition,"
but he limited his use to 12-tet. I think Wilding-Smith or someone
published a complete list in 12, including such things as 4 2 4 2, 5 1 5
1,
3 2 1 3 2 1, 2 1 1 2 1 1 2 1 1 , 3 1 3 1 3 1, etc.

Schillinger's double ET or 144-tet would be good for Aristoxenos's
Greek tetrachords which have intervals quantizable to the 1/24 of
a tone as in the Hemiolic Chromatic Genus 3/8 3/8 1 3/4 tones
(75 + 75 + 350 cents ascending). Most of Aristo's tunings would
work in 72 tet and many would in even 24 or 36.

--John