Notation for describing generic intervals, and also, interesting observation about L/s = 3/2 MOS

We have terms like 1\12 and 1\13 to describe steps out of EDOs. I'm
going to define the following notation:

1) 1\12~ describes the generic interval class that is one generic step
out of a 12-note MOS or a 12-note scale in general. (The ~ means
"approximately.")
2) For greater clarity, 1\7L5s describes the generic interval class
that is one generic step out of the 7L5s MOS.
3) For greater clarity and in a way that describes ratios,
1\meantone[12] describes the generic interval class that is one
generic step out of meantone[12]. (Note for mathematicians: be aware
that this, in general, defines a lattice coset in interval space.)

This is intended to be a useful way to describe generic interval
classes for any MOS. So as an example, in the meantone chromatic
scale, 7\12~ refers to the generic interval class containing both the
perfect fifth and the wolf fifth, and 1\12~ refers to the generic
interval containing both the diatonic and chromatic semitones.

Now then, some interesting food for thought. If you play around with
the "interseptimal interval" of ~950 cents in 19-EDO, you may notice
that it sometimes flip flops between sounding like a "major sixth" vs
a "minor seventh." More precisely, you may note that you sometimes
hear this interval as corresponding to 9\12 and sometimes as
corresponding to 10\12.

This isn't just because you've been abused into only listening to
12-EDO your whole life. You're actually correct with this observation.
In 19-EDO, that interval IS both 9\12~ and 10\12~. In diatonic
terminology, it's both a "diminished seventh," which is a member of
9\12~, and an "augmented sixth," which is a member of 10\12~.

This is basically just a higher-resolution example of the following
observation: the augmented second, and the minor third, which differ
by diesis, both correlate to 3\12~, despite that one is in 2\7~ and
that the other is in 3\7~. It's also the same as noting that the
diminished fifth, which is 4\7~ and the augmented fourth, which is
3\7~ both correlate to 6\12~. In this case, the large 9\12~ and the
large 10\12~ both correlate to 15\19~.

This is a general property of all MOS's of the form L/s = 3/2. We're
all used to thinking about what happens if L/s = 2/1, and a scale
which was strictly proper is now just "proper," and there are
"ambiguous intervals." L/s = 3/2 brings its own form of ambiguity, but
in a deeper, more complex way.

Has anyone given any thought to interesting musical things that you
can do to exploit this property of these scales?

-Mike