Polytonality in 12-equal and necessarily-tempered harmony

In septimal meantone, C-G-E-A#-B-F# (interval pattern: P5-M3-A4-M2-P5)
is a necessarily marvel-tempered chord.

I stumbled on chords like this in 12-equal before getting into
microtonal music, and loved the way that they blended different colors
together into the sound of something new, much like the way a pinch of
salt can add to the flavor of something sweet like a cake. In this
case, I'd usually play something like C-G-E-Bb, which would sound kind
of like a 7-limit bluesy dominant 7 chord, and then I'd throw the B-F#
on top of it and it'd "activate" a new sound I'd never heard before,
connecting things in different ways.

If you don't think that 12-equal is accurate enough to really give you
7-limit harmony, you can try for yourself loading it up in 22-equal or
31-equal and seeing that the "feeling" stays the same, while the
intonation improves. For example, I did a similar excursion here, at
the end of this porcupine-tempered Happy Birthday piece:

http://soundcloud.com/mikebattagliamusic/happy-birthday

I played a few trippy chords like this when I went up to Paul Erlich's
place a while ago. I'm now realizing that what I discovered without
knowing it were higher-limit "dyadic chords," and that the way that
they mix flavors together is similar to the way that an
875/864-tempered diminished chord mixes the flavor of "diminished" and
"rooted/otonal" together (because three 6/5's makes a 7/4, giving you
7/4 on the outer dyad).

Such explorations in 12-equal have generally been known as
"polytonality," but a lot of the most beautiful polytonal harmonies
seem to make sense as higher-limit necessarily tempered harmonies in
this way. I note that Stravinsky managed to hit these sorts of
sonorities more than other people, who treated polytonality more
aleatorically and didn't "get it." So it might be worthwhile to go
back through some polytonal compositions and see how they lay out in
this fashion, retuning the "polytonal chords" as higher-limit tempered
chords with greater accuracy.

-Mike