inversionally-identical chords (Monzo)

>This relates to the "inversionally similar" chords
>I posted yesterday (actual they should be referred
>to as "inversionally identical"). Perhaps utonalities
>that are most favored are the ones which are
>inversionally identical when described otonally.
>Has anyone ever investigated this property in
>chords before?

I'm not sure I know what you're getting at... but if it's what I think it
is, there's no such thing as a inversionally-identical utonality. What
we're looking at here is the order of the interior intervals of a chord...

7-limit otonality is 5/4 -> 6/5 -> 7/6
10-12-15-18 is 6/5 -> 5/4 -> 6/5

The reason the 10-12-15-18 is inversionally identical is because the list
of its interior intervals has reflection symmetry. This is never the case
for Partchian O and U tonalities because the same interval never appears
twice. The Utonality is what you get when you invert the Otonality anyway.

This can be likened to palindromes. Mom=Mom, Dad=Dad, but Mad =/= Dam.

Carl