Diatonic hearing vs JI hearing

So I've been conducting an experiment. For the last month, I've been
in Miami, going back and from Haiti, and I had no instruments but a
31-tet guitar. So I basically got to "purify" myself of 12-tet for a
little bit (although I'd still hear stuff on the radio in 12-tet), and
I came to some interesting conclusions. One is that it has converted
me from thinking that functional consonance and dissonance - in my
view the most "important" kind of consonance in music - doesn't come
from JI, but rather the diatonic/chromatic "map" that we are used to
hearing things in.

The gurus here will no doubt have figured this out years ago, but for
us sophomores - here's the evidence that has basically converted me
over:
- Play a minor scale in 1/3-comma meantone or 19-tet. Better yet, make
it dorian. I really like dorian.
- Now play it in some wide fifth superpyth tuning where the minor
thirds approach 7/6. Let's say 22-tet or 27-tet.
- Although you'd have to be deaf to not hear the difference, if you're
like me, these two basically sound like different tunings of the same
underlying "thing." Just like 378 cents and 400 cents sound like
mistunings of the same underlying "thing," these two scales sound like
two different tunings of the same underlying "thing" as well.
- All of this despite the fact that we're using a completely different
JI interval for the minor thirds here.
- In fact, to my ears, 6/5 and 7/6 themselves sound like two different
variations of the same "thing," and yet 5/4 and 6/5 don't. And 7/6 and
8/7 don't either.

And the same principle applied for my going from 12-tet for 31-tet. At
first, the major seconds sounded flat, but after playing a little
chunk of the circle of fifths, my brain seemed to "rewire" itself to
hear them as sounding normal. That is, although they didn't sound as
"stable" as 12-tet's, they finally started to assume the same
function, instead of just sounding like flat messed up 12-tet fifths.
And when going back to 12-tet, the major thirds would sound terribly
sharp, but as soon as I started playing a little chunk of the circle
of fifths again, my brain remapped itself and they started to sound
like major thirds again.

So the question is - how does this work? Paul basically turned me onto
the idea that it's not that we're used to 12-tet per se, but that
we're used to hearing "diatonically" (or perhaps "chromatically" these
days). That is, we're used to hearing this underlying diatonic
"template" which can be instantiated in 12-tet or 31-tet or 22-tet or
anything else. I think it might have something to do with 3-limit
hearing... any ideas? I've read Rothenberg's papers at this point, but
it seems to me like JI must be involved on SOME level...

-Mike

Mike wrote:

> So the question is - how does this work? Paul basically turned
> me onto the idea that it's not that we're used to 12-tet per se,
> but that we're used to hearing "diatonically" (or perhaps
> "chromatically" these days). That is, we're used to hearing
> this underlying diatonic "template" which can be instantiated
> in 12-tet or 31-tet or 22-tet or anything else. I think it might
> have something to do with 3-limit hearing... any ideas? I've
> read Rothenberg's papers at this point, but it seems to me like
> JI must be involved on SOME level...

We discussed this offlist, so you know I agree that our
framework for hearing music (e.g. the backdrop against which we
perceive puns) is probably more learned than innate, and more
to do with Rothenberg equivalence classes than the JI lattice.
Actually since even 7-ET can be used "diatonically", it may
even be that Rothenberg equivalence classes are pretty subtle,
and the stronger equivalence is simply the octave division.
Erv Wilson may be implying this with the term "modulus".

But anyway, one think I think we can do re. JI is recognize
the identity of a pitch in an otonal chord. For this I point
to the situation, often encountered in SATB voice leading,
where two adjacent chords share one or more common tones.
For instance, in FM->CM, the pitch C changes from 3rd harmonic
to fundamental. And there may be something to puns requiring
only a pair of chords, like the tritone substitution, related
to that, I dunno...

-Carl

On Tue, Aug 17, 2010 at 3:03 AM, Carl Lumma <carl@...> wrote:
>
> We discussed this offlist, so you know I agree that our
> framework for hearing music (e.g. the backdrop against which we
> perceive puns) is probably more learned than innate, and more
> to do with Rothenberg equivalence classes than the JI lattice.
> Actually since even 7-ET can be used "diatonically", it may
> even be that Rothenberg equivalence classes are pretty subtle,
> and the stronger equivalence is simply the octave division.
> Erv Wilson may be implying this with the term "modulus".

And 8-ET can be used octatonically as well...

> But anyway, one think I think we can do re. JI is recognize
> the identity of a pitch in an otonal chord. For this I point
> to the situation, often encountered in SATB voice leading,
> where two adjacent chords share one or more common tones.
> For instance, in FM->CM, the pitch C changes from 3rd harmonic
> to fundamental. And there may be something to puns requiring
> only a pair of chords, like the tritone substitution, related
> to that, I dunno...

When you say the "identity" of a pitch in an otonal chord, do you mean
that we can still hear that it's "C" in both chords - aka 261 Hz?
Because to me "C" already seems to imply the existence of a map, which
might not be JI at all...

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > But anyway, one think I think we can do re. JI is recognize
> > the identity of a pitch in an otonal chord. For this I point
> > to the situation, often encountered in SATB voice leading,
> > where two adjacent chords share one or more common tones.
> > For instance, in FM->CM, the pitch C changes from 3rd harmonic
> > to fundamental. And there may be something to puns requiring
> > only a pair of chords, like the tritone substitution, related
> > to that, I dunno...
>
> When you say the "identity" of a pitch in an otonal chord, do
> you mean

I mean in the Partchian sense, whether it is a 3rd harmonic
or a 2nd harmonic etc.

> that we can still hear that it's "C" in both chords - aka 261 Hz?

Obviously we can hear it's the same pitch. "C" has nothing
to do with what I'm talking about however.

-Carl