Re: Virtual pitch

Hans Aberg wrote:
As for the "acoustical root" mentioned here, the "Harvard concise
dictionary of music" mentions "acoustic bass", where organ pipes of
pitches of intervals 1 and 3/2 produce the effect of a pipe
with pitch 1/2. It thinks of it as "difference and summation tones", and
also has an article "combination tone", which claims it is
a physiological phenomenon, produced in the inner ear (cochlea).

I think though it might just be the same phenomenon that the brain
recognizes the fundamental of a tone,

Where did you hear that the brain recognizes the "fundamental of a tone"?
To my way of thinking, single tones *are* fundamentals, they don't *have* fundamentals.
But when you have two or more tones forming intervals and/or chords, the tones involved form freq ratios with one another. And these ratios suggest a harmonic series of fundamental tone that may or may not actually be sounding.
You're a math guy. What's the term used to described the entity that a ratio is based on?
Eg. In the ratio 3:2, what is the term used to describe "1"?
"Denominator"?

even if it is not there
acoustically.

How can the fundamental of a single tone be missing?

Call this absent fundamental "virtual fundamental" or
"virtual root".

You're on the right track. But you should be talking about two or more tones sounding simultaneously. Not single tones.

Then I thin a requirement for the virtual fundamental or root be produced
when using more than one tone generator, is that they have the same
inharmonicity in a way that their overtones in the
particular combination used, line up.

The qualities of the overtones of two or more tones, when sounded together, will affect the degree to which an acoustical root is felt to be active. The proportions of these overtones may serve to reinforce the root or they may serve to obscure it.

Otherwise, I think the brain will
probably recognize that there are two different instruments playing. In
other words, one can probably not produce it by combining an organ pipe
with a string, as they have negative (resp. positive) inharmonicity.

Not true.
If I play C3 on a an organ and you play G3 on a viola the acoustical root C1 comes into play. But it might depend somewhat on which stops you have pulled on the organ.

And if one recognizes the virtual root of a chord,

If you want to call them "virtual roots" that's fine with me.

then it is probably
just computed by taking the lowest common denominator.

It's not computed (although it can be after the fact). It's felt to be in play.

That is, if one
writes a Just major chord 4:5:6, then it is the pitch 1 that is the
virtual root.

Again, what is the mathematical term used to describe "1" in a ratio like that?

And as above, if one writes the interval above used for
organs as 2:3, then it is against 1.

For you that have worked with this intuitively, does it works out so?

What is it that you think I've been talking about out here for years?


--
Joey Goldstein
http://www.joeygoldstein.com
http://www.soundclick.com/bands/joeygoldstein
joegold AT sympatico DOT ca
.

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