Feeling, diatonic maps, Rothenberg, and 3-limit hearing

On Wed, Aug 18, 2010 at 2:04 PM, Michael <djtrancendance@...> wrote:
>
> Gene-replying-to-MikeB>"That's how it feels to you, but you keep assuming your feelings are universal."
>
> But I suspect, though people of course won't think chords "feel" the same, that many will think relatively along similar lines. The most obvious example being a major triad sounding more sweet than a minor one to many if not most people...but I think the logic can extend to more complex chords.

Maybe "feel" is a loaded term. The point I was making here though, is
that 33-et's super-flat meantone diatonic scale is still recognizable
as a diatonic scale. And the I, IV, and V chords still sound like I,
IV, and V - even though they're neutral. They still, to me, "sound"
like they retain the gestalt sound or "function" of the major chord,
despite not being tuned to 4:5:6. And this is even more notable with
superpyth tunings where the major thirds are closer to 7:9 and the
minor thirds are closer to 6:7, because the fifths don't have to be so
far out.

Therefore, part of the overall "schema" that we have for a "major"
chord is how it can be placed within some diatonic scale (pick a mode,
any mode), and thus relate to other nearby chords. And also, this part
of the schema can be activated even if the chords aren't tuned to
4:5:6. And, thusly therefore and thus, when we talk about "mood," we
might sometimes be talking about this way of hearing as we are about
harmonic stability.

One half-assed theory that I have is that the real defining
characteristic of "diatonic" hearing, as far as cognitive processing
is concerned, is that everything is accessible by a few fifths. Note
that with superpyth, meantone, and this ultra-flat meantone, every
note retains its same 3-limit relationship to the root, but that its
direct harmonic relationship to the root changes. If you mess around
with superpyth minor triads, you will clearly hear that they have a
very different subtle "flavor" than 1/3-comma meantone minor triads -
but are still recognizable as diatonic "minor triads" of some kind. I
think that the former has to do with the absolute harmonic
relationship involved, and that the latter has to do with this
fifths-based hearing.

Whether the fifths-based hearing has to do with some kind of inborn
3-limit JI map, or a learned 3-limit JI map, or has nothing to do with
JI and more to do with the fact that a detuned fifth is a sort of
consonant sounding generator, is beyond me.

-Mike

MikeB>"The point I was making here though, is that 33-et's super-flat meantone
diatonic scale is still recognizable
as a diatonic scale."
Super-flat? Yeah its around 12 cents or so flat...but I wouldn't call that
super-flat: it's call 19/13 or some sort of diminished-ish-5th super-flat
(something from a whole different tonal class)...then again a tuning with those
certainly wouldn't qualify as mean-tone.

I agree it's recognizable as a diatonic scale...but I'd hardly say that's a
miracle considering how close the 5th is to pure. However you're right...if I
get your drift...the way a "compressed" major triad third from that scale (IE
one obviously with 20+ cent difference from pure) sounds like a regular one does
seem to suggest the brain does some heavy-duty rounding that makes it "feel
normal".

MikeB>"One half-assed theory that I have is that the real defining
characteristic of "diatonic" hearing, as far as cognitive processing is
concerned, is that everything is accessible by a few fifths."

Meaning within a certain number of fifths on a circle of fifths?
If so...then what on earth happens when you get Mohajira or something where one
of the "fifths" is distinctively not in the circle (IE near 13/9)?

Also, I notice that 12TET's "awful" (to me) sounding 6th is generated by just
three chained fifths and then dividing by the octave AND 9/8 is generated by
just two chained fifths. This would not seem to imply that low in the chain of
fifths IE "accessible by a few fifths" means relaxed sounding. That is...even
though a chain of about four fifths produces 5/4.

I think Charles Lucy mentioned something similar...about location along the
chain of fifths determining "resolved-ness".

On 8/18/10, Michael <djtrancendance@...> wrote:
> Super-flat? Yeah its around 12 cents or so flat...but I wouldn't call
> that
> super-flat: it's call 19/13 or some sort of diminished-ish-5th super-flat
> (something from a whole different tonal class)...then again a tuning with
> those
> certainly wouldn't qualify as mean-tone.

I mean super flat as in we're dealing with on the order of 1/2 comma
meantone. For a meantone, those fifths are really flat. And it
definitely would qualify as meantone if you map 3/2 as one of these
flat fifths and 5/1 as 4 of them.

> I agree it's recognizable as a diatonic scale...but I'd hardly say that's
> a
> miracle considering how close the 5th is to pure.

Right, but the major thirds are in 16/13 territory. Thus the tuning of
the fifth seems to be more important to the recognizability of the
scale than the tuning of the major thirds.

And if you really want to test this hypothesis, mess around with
mavila[5]. You'll hear that even though 5/4 and 6/5 switch places, the
whole thing still resembles the normal pentatonic scale. This doesn't
seem to work as well with mavila-7 though.

> However you're right...if I
> get your drift...the way a "compressed" major triad third from that scale
> (IE
> one obviously with 20+ cent difference from pure) sounds like a regular one
> does
> seem to suggest the brain does some heavy-duty rounding that makes it "feel
> normal".

But what about superpythagorean minor triads? Those are 6:7:9. Is it
really that the brain is rounding them to 10:12:15, or is something
else going on?

> Meaning within a certain number of fifths on a circle of fifths?
> If so...then what on earth happens when you get Mohajira or something where
> one
> of the "fifths" is distinctively not in the circle (IE near 13/9)?

I'm just talking about diatonic hearing. I am not fluent enough with
mohajira to know how it works yet. I'm just saying that "diatonic
hearing" is often defined as anything matching some kind of LLsLLLs
template, but perhaps the real important characteristic is that it's
an octave-equivalent set of 7 fifths. For example, mavila-5 and
meantone-5 can sound very equivalent.

> Also, I notice that 12TET's "awful" (to me) sounding 6th is generated by
> just
> three chained fifths and then dividing by the octave AND 9/8 is generated by
> just two chained fifths. This would not seem to imply that low in the chain
> of
> fifths IE "accessible by a few fifths" means relaxed sounding. That
> is...even
> though a chain of about four fifths produces 5/4.

I agree and never meat to imply that it does. Just that with diatonic
hearing, the only JI ratio that seems to matter is 3/2. Whether this
is because it's the generator, or there are no other nearby JI ratios
that conflict with it, or because of some inborn or learned or
conditioned 3-limit JI hearing, is beyond me.

-Mike

And, if you really want to see an example that will put this to rest,
then go to 22-et and play the C harmonic minor scale. Tell me whether
of not it is recognizable as a harmonic minor scale, or sounds like
some brand new xenharmonic thing.

Assuming that you can hear that it's just another instance of the same
harmonic minor scale we all know and love, check what approximate
ratio the augmented second is. Then check the minor thirds. You will
be surprised - and that is just how unimportant JI is in the grand
scheme of things.

--
-Mike

MikeB>"Assuming that you can hear that it's just another instance of the same
harmonic minor scale we all know and love, check what approximate
ratio the augmented second is. Then check the minor thirds. You will
be surprised - and that is just how unimportant JI is in the grand
scheme of things."

I'll tell you one thing...the triads (both major and minor!) sound virtually
indistinguishable across these two to me with a piano and not-to-far-off with a
guitar! :-D
It's as if each tuning's very strong 5th helps align the rather high (in
12TET) and low (in 22TET) minor and major thirds.

But try a chord like C D D# G or C D# A or C F A A#...and I'm betting you'll
notice a huge difference in brightness of the chord sound between the two. Not
that they can't be interchanged but...the effect seems similar to switching the
type of instrument used in a song from, say, a distorted guitar to a flute.

MikeB>"I agree and never meat to imply that it does. Just that with diatonic
hearing, the only JI ratio that seems to matter is 3/2."

Seems to me the obvious pattern that having a fairly strong 3/2 at the edge of
a chord gives a lot of slack to errors so far as other intervals in that chord.
Do you think that's a fair assumption or can you find examples to disprove
that?

>"Whether this is because it's the generator, or there are no other nearby JI
>ratios
that conflict with it, or because of some inborn or learned or conditioned
3-limit JI hearing, is beyond me."
I'd lean toward "because it's the generator" IE it's one thing the brain can
quickly identify as a pattern.
Quick way to test this: compare scales generated by generators that are within
13 cents of each other that produce scales that do NOT have anything near a
fifth. I remember on this list ages ago someone said a PHI scale was shown to a
bunch of Kindergarten students and "even" they instantly pointed out PHI as to
period/"octave" or special relation when they heard it.