RE: [tuning] The great Helmholtz in the kitchen

>Back re-reading Helmholtz again (after 15 years!). The topic here is
>"synthetic" perception... meaning the perception of tone as a "fused"
>element... ie. a sound comprised of a basic tone and all its
>accompanying Fourier partials that lend it's timbre as a single
>sensation.

>From the text, it seems as if the entire concept of a tone with
>accompanying harmonic partials that determine its timbre is a "new" idea
>at that time.

>This was not an "original" idea with Helmholtz, was it?? What is the
>history of this concept?? Paul?? Anybody??

My understanding was that the idea dated back 200 years but was still
controversial. I could be totally mistaken.

>In any case, the theory seems new and Helmholtz is looking for examples
>to back it up. He unfortunately wanders into the realm of taste... or
>is it tastelessness (??)

>[snip]

>(Some of this makes our short-lived "Mark C." interchanges maybe not
>quite so weird after all!)

Joseph...you must be joking.

I wrote,

>My understanding was that the idea dated back 200 years but was still
>controversial. I could be totally mistaken.

I meant it was still controversial in Helmholtz's time, of course.

----- Original Message -----
From: Joseph Pehrson <josephpehrson@compuserve.com>

> Back re-reading Helmholtz again (after 15 years!). The topic here is
> "synthetic" perception... meaning the perception of tone as a "fused"
> element... ie. a sound comprised of a basic tone and all its
> accompanying Fourier partials that lend it's timbre as a single
> sensation.
>
> >From the text, it seems as if the entire concept of a tone with
> accompanying harmonic partials that determine its timbre is a "new" idea
> at that time.

This is interesting because a simple description of the movement of air
during a sound shows no evidence of partials - you either have to perform a
FFT mathematically or use the FFT that is built into our nervous system.
Sometimes I find it amazing that our ears/brains are able to do a Fourier
analysis of sound - where the hell did that come from? I have a painter
friend who says that when he sees a color, he can "see" the mixture of red,
green or whatever that is in the color, but I'm not sure if this is
analogous.

In the Aristotelian Problemata 4.16 (8) we find "Why does the low-pitched
(string) contain the note of the high pitched?" Barker remarks: "This might
refer to the higher harmonics heard simultaneously with a sound's
fundamental pitch. But I have not found any unambiguous references to this
phenomenon in Greek sources"

More likely, it is related to what Descartes says in his Abrege de la
Musique, pg60 "Sound is to sound as string is to string. Each string
contains in itself all other strings shorter than it, but not those which
are longer. Therefore all high sounds are contained in low ones, but low
ones, conversely, are not contained in high ones."

When he says "all high sounds are contained in low ones", rather than mearly
"all shorter strings are contained in longer ones", he seems on the brink of
the recognition of partials.

What Helmholtz actually says about partials is "..we meet with a strange and
unexpected phenomenon, long known indeed to individual musicians and
physicists, but commonly regarded as a mere curiosity, its generality and
its great significance for al matters relating to musical tones not having
been recognized."

He also remarks that it was Ohm who "first declared that there is only one
form of vibration which will give rise to no harmonic upper partial tones."
Fourier, of course, lived from 1768-1830, so the question is not "when was
it first realized that periodic vibrations are analyzable into composite
sines" but "when was it realized that this was perfectly audible to a
"naked" ear in a musical tone."

Thats all I can dig up. I seem to recall something about Tartini and the
seventh partial? Does anyone know what that might have been about?

Dante

Rosati wrote,

>He also remarks that it was Ohm who "first declared that there is only one
>form of vibration which will give rise to no harmonic upper partial tones."
>Fourier, of course, lived from 1768-1830, so the question is not "when was
>it first realized that periodic vibrations are analyzable into composite
>sines" but "when was it realized that this was perfectly audible to a
>"naked" ear in a musical tone."

...in the form of the perception of timbre.

>In the Aristotelian Problemata 4.16 (8) we find "Why does the low-pitched
>(string) contain the note of the high pitched?" Barker remarks: "This might
>refer to the higher harmonics heard simultaneously with a sound's
>fundamental pitch. But I have not found any unambiguous references to this
>phenomenon in Greek sources"

>More likely, it is related to what Descartes says in his Abrege de la
>Musique, pg60 "Sound is to sound as string is to string. Each string
>contains in itself all other strings shorter than it, but not those which
>are longer. Therefore all high sounds are contained in low ones, but low
>ones, conversely, are not contained in high ones."

>When he says "all high sounds are contained in low ones", rather than
mearly
>"all shorter strings are contained in longer ones", he seems on the brink
of
>the recognition of partials.

Both could be nothing more than a reference to the natural harmonics
obtained by lightly stopping the string at a nodal point.

----- Original Message -----
From: Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>
>
> Both could be nothing more than a reference to the natural harmonics
> obtained by lightly stopping the string at a nodal point.

Then, when was it first realized that those harmonics are audible in the
sound even if you don't stop the string?

>Then, when was it first realized that those harmonics are audible in the
>sound even if you don't stop the string?

I thought Mersenne was the key . . . I could be wrong . . .

Dante wrote,

>This is interesting because a simple description of the movement of air
>during a sound shows no evidence of partials - you either have to perform a
>FFT mathematically or use the FFT that is built into our nervous system.
>Sometimes I find it amazing that our ears/brains are able to do a Fourier
>analysis of sound - where the hell did that come from? I have a painter
>friend who says that when he sees a color, he can "see" the mixture of red,
>green or whatever that is in the color, but I'm not sure if this is
>analogous.

It's analagous to how we all see color -- our retinal cells are specifically
tuned to three different frequencies of EM, with rough bands (sort of like
critical bands on the cochlea) around each, and the perception of "color" at
a given point in the visual field is a mapping onto "frequency" based on the
data from the three types of cells near the corresponding point on the
retina. The cochlea seems more miraculous, though, in that it is capable of
resolving thousands of frequencies at once, while a point in the eye cannot
so much as resolve two different frequencies at once. The eye compensates by
being able to resolve millions of distinct points in two dimensions, while
with only two ears we only have a rough idea of where a sound is coming
from. The differences are a product of the vastly different wavelengths of
audible sound vs. light.