Yahoo Tuning Groups Ultimate Backup mills-tuning-list to PAULE, Major 6 9, subharmonics

[belated reply to Jan 14 message]

PAULE wrote:

> >[Matt Nathan]
> >The "problem" here may be in trying to transfer what in 12tet is considered
> >a
> >consonant chord--a Major 6 9 chord--into JI and trying to make it serve the
> >same purpose.
>
> Well, many JI advocates try to do this sort of thing all the time, equating
> "purpose" with ratios. In fact, it sounds like that's just what you're doing
> here:
>
> >My question would be, "why try to use a structure which doesn't suggest
> >itself
> >musically?".
>
> where by "musically" you mean nothing but "in terms of ratios."

You're putting words in my mouth. Let me paraphrase, first "purpose",
then "suggest itself musically".

What I mean by purpose is the association "a pleasant chord". In 12tet, a
Major 6 9 chord has taken on this association over time just as diminished
chords have taken on the association of "danger". This can happen because
in 12tet a Major 6 9 chord is relatively consonant compared to other
possible structures, even though if you listen closely, it's actually
dissonant. This sort of thing can take place in any limited pitch set, where
there are only so many possible structures, so that there are no competing
"better" choices for producing an effect, and so a particular stucture will
win out.

In unlimited JI, being an infinite pitch set (infinite yet not
containing all intervals of course), relative dissonance or
consonance is based directly on the tuning so this ability to "choose
the lesser of two evils" in creating associations doesn't exist in the
same way.

In JI there are many many more-consonant and more-pleasant structures
than the various approximations of a 12tet Major 6 9 chord.

When people put up examples like this to show me that there's a problem
in JI because, say, a Major 6 9 chord is dissonant in JI, I note that
the problem is in trying to transfer a structure that means something
in another tuning system into JI and expecting JI's various approximations
of this structure to mean the same thing (have the same association,
especially as compared to other structures available in the system).

What I meant by "suggest itself musically" is to play around with
the resources in JI (improvise, if you will, on paper or in real time)
to find out what's there, and see what kinds of consonance-dissonance
relations can be found, and what kinds of associations spring up,
and to use these musically--rather than improvise in 12tet and then
try to translate it into JI. To me, a Major 6 9 chord doesn't
"suggest itself musically" in JI, the way it does in 12tet. Other
structures do "suggest themselves musically".

> >1/1 9/8 5/4 4/3 3/2 5/3 [...] starts to support its own dissonance in a
> really nice way since
> >each little otonal 8:9:10 subset resonates on its own even with the 40/27's
> >and stuff going on between them, at least to my ear.
>
> Yeah, but try the utonal version of this chord -- blech!

I can't hear it in my head, but I'll bet you're right. I tend n
ot to "believe in" utonal structures at this point in my exploring.
I mean, I can use them and hear them, just as I can hear and use
stacks of various arbitrary intervals, but utonality doesn't seem
to have the same self-organizing "pull" that otonality has even
though the math would suggest it. I reserve the right to alter my
position.

> Polytonality is
> much easier to establish with otonal than with utonal units, as every early
> 20th century composer knew.

This is probably because otonality is easier to establish period! The
difference tones in otonality tend to support the same otonality. The
difference tones in utonality tend to disrupt the utonality by producing
difference tones which would support an otonality instead.

Summation tones would tend to support utonality, but I lean
towards the camp that holds that these are rarely heard and
are practically unimportant in the natural hearing process.

I've even read that difference tones may be generated internally,
as part of the hearing process itself, so that even listening to
two sine waves in head phones at low levels, we do some
"otonal"-style internal processing.

After once reading mail from Marshal Tuttle on the Fidonet
Comp 101 echo (BTW, does anyone know how to access Fidonet via
internet?) who said that string players tend to tune major thirds as
pythagorean (81/64) and minor chords 12tet (300 cents), I wanted
to see what JI interval a 12tet minor third is close to. It turns
out to be a close match with 19/16 at 297.5 cents; roughly the
same error as a 3/2 receives in 12tet. Compare this to the generally
accepted standard JI minor third 6/5 at 315.6 cents. The first-order
difference tones for 16:19:24 are 3:5:8, making it possible that these
string players are intuitively aiming for an otonal, not utonal, minor
chord!

> Or you can see this chord as a
> 24:27:30:32:36:40, whose first-order difference tones form a
> 2:3:4:5:6:8:9:10:12:13 chord . . .

Neat. It would probably work well in the high register, to bring this out.

Matt Nathan

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Charles Lucy wrote:

> *
> When I touch a guitar string gently at specific points, I can hear
> tones which are "higher" than the open string or the fretted string.
> *

> Probably everyone on this list has read Helmholtz, most have also
> prolly read Baccus (God of Whine?). They explain the conventional
> wisdom in tuning theory and the arithmetc of musical acoustics.

Spelled Backus.

> What are these tones???
>
>
> Conventional wisdom tells us that these tones are
> HARMONICS.
> Matt Nathan suggests that we call them
> NODES

Actually, I said "nodes" were the places on the string which
you touch, not the complex tones produced.

> ^
> The traditional mathematical model of musical tuning and
> acoustics states that these "ghost tones" (for sake of a better
> term) are found at frequencies which are small integer ratios
> to the fundamental or open string frequency.
> This is the assumption upon which Just Intonation is based.
> ^

Are you talking about partials or complex tones?

Are you talking about an ideal string or a real string?

Matt Nathan

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to PAULE, Major 6 9, subharmonics

🔗Matt Nathan <mattn@...>

🔗Matt Nathan <mattn@...>

🔗Paul Hahn <Paul-Hahn@...>