s and inharmonicity

[This is a cross-post from tuning-math (message 2462).]

me:
>>Still doesn't explain how. You need a way for data from the
>>combination-sensitive stuff to improve the spectral stuff coming
>>off the cochlea.

Paul:
>There's less ambiguity as to the possible ratio-intepretations.

me:
>I don't think it works that way.

Paul:
>It does. Devise a baby mathematical model for it and you'll see.

Did Goldstein ever do experiments on simultaneous tones?

me:
>>The "accuracy" of the "fundamental" is improved as the spectral
>>components get closer to just, as the harmonic entropy calc.
>>itself correctly models. But to change s in this way is a fudge,
>>in my opinion.

Paul:
>It would be nice to derive the change in s mathematically, and any
>baby model will do so. However, until the model is more fully
>developed, I'm hesitant to put forward any exact formulas about how
>s changes.

Well, here's one person looking forward to when you are.

me:
>>With harmonic timbres, h.e. on the fundamentals is a good
>>approximation of things, but with inharmonic timbres, all spectral
>>components need to be put in to the h.e. calculation. Jacking up
>>s may approximate this, but it would be a fudge.

Paul:
>Again, if the inharmonicities are only about 50 cents, I thing it's
>a pretty darn good one.

Maybe so.

-Carl

Carl wrote,

>Did Goldstein ever do experiments on simultaneous tones?

He _only_ did experiments on simultaneous tones, as far as I know.

>>Did Goldstein ever do experiments on simultaneous tones?
>
>He _only_ did experiments on simultaneous tones, as far as I know.

Jeez. I should have my Mom send me the papers. What I mean to
ask is, did he ever show s shrinking for just intervals, or for
pairs of complex tones (as opposed to simple tones).

-Carl

I'm not sure what you could be thinking as regards s shrinking for just
intervals. As for pairs of complex tones, that would have been well outside
G's subject of research (at least in the few papers of his that I've cited),
which was the perception of virtual fundamentals evoked by small sets of
simple tones. The interpretation of harmonic roots, and thus a component of
consonance, with an analogy of virtual pitch but for complex tones instead
of simple ones, is due to Terhardt and Parncutt, not Goldstein.

-----Original Message-----
From: clumma [mailto:carl@...]
Sent: Thursday, January 10, 2002 1:49 PM
To: harmonic_entropy@yahoogroups.com
Subject: [harmonic_entropy] Re: s and inharmonicity

>>Did Goldstein ever do experiments on simultaneous tones?
>
>He _only_ did experiments on simultaneous tones, as far as I know.

Jeez. I should have my Mom send me the papers. What I mean to
ask is, did he ever show s shrinking for just intervals, or for
pairs of complex tones (as opposed to simple tones).

-Carl

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>I'm not sure what you could be thinking as regards s shrinking for
>just intervals.

You're expanding it for inharmonic timbres. I'm wondering if there
is any basis for this in Goldstein's work.

>As for pairs of complex tones, that would have been well outside
>G's subject of research (at least in the few papers of his that
>I've cited),

Thanks!

-Carl

>>I'm not sure what you could be thinking as regards s shrinking for
>>just intervals.

>You're expanding it for inharmonic timbres. I'm wondering if there
>is any basis for this in Goldstein's work.

The basis is my very strong intuition, I guess. This intuition served me
extremely well getting through AHSMEs and a Yale B.S. with very little work
or studying. So I trust it. I know that I think non-verbally, despite all
the claims that humans think verbally. I "see" this harmonic entropy stuff.
You shouldn't just take my word for it, though -- come up with a toy
mathematical model for it and work it out yourself.

>>You're expanding it for inharmonic timbres. I'm wondering if there
>>is any basis for this in Goldstein's work.
>
>The basis is my very strong intuition, I guess.

Okay.

>This intuition served me extremely well getting through AHSMEs

?

>and a Yale B.S. with very little work or studying. So I trust it.

I tend to trust your intuition, too.

>I know that I think non-verbally, despite all the claims that
>humans think verbally.

All the things I can think of that this could mean seem like
BS to me.

I think it's clear that humans are capable of using language as
a tool to cook up axioms which are more likely to be correct than
random axioms -- few enough to test, and iterate. It also strikes
me as likely that they have spacial processing abilities that they
use in much the same way. One or the other, or both, of these
skills may be more developed in different individuals, for whatever
reasons...

I've tested above average at doing both, but I've tested higher at
the verbal stuff, and, the theory goes, tend to use it as a crutch,
to the exclusion of developing the spatial stuff more. Sounds
corny, but I can't deny that it introspection backs it up.

>You shouldn't just take my word for it, though -- come up with a
>toy mathematical model for it and work it out yourself.

One day, I might. In the meantime, I've made it my place to
harass you. I hope you won't take it personally!

The Berkeley library is in a state, due to seismic retrofitting,
but I promise to deliver the reviews and citations of the
combination-sensitive stuff eventually!

-Carl

>I've tested above average at doing both, but I've tested higher at
>the verbal stuff, and, the theory goes, tend to use it as a crutch,
>to the exclusion of developing the spatial stuff more. Sounds
>corny, but I can't deny that it introspection backs it up.

Sure . . . also, remember the personality tests? I'm a P (perceiving),
you're a J (judging). I guess we make a good team . . .

>One day, I might. In the meantime, I've made it my place to
>harass you. I hope you won't take it personally!

Far from it -- keep it up!!!!

>Sure . . . also, remember the personality tests? I'm a P
>(perceiving), you're a J (judging). I guess we make a good
>team . . .

I remember them, but I don't remember taking it! Was there a
name for the particular test (so I can search the archives)?

-C.

The Myers-Briggs Personality Test, or Indicator, or some such .. .

-----Original Message-----
From: clumma [mailto:carl@...]
Sent: Thursday, January 10, 2002 7:56 PM
To: harmonic_entropy@yahoogroups.com
Subject: [harmonic_entropy] Re: s and inharmonicity

>Sure . . . also, remember the personality tests? I'm a P
>(perceiving), you're a J (judging). I guess we make a good
>team . . .

I remember them, but I don't remember taking it! Was there a
name for the particular test (so I can search the archives)?

-C.

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