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Klarinet Archive - Posting 000519.txt from 2001/02

From: Tony@-----.uk (Tony Pay)
Subj: Re: [kl] Difference Tones
Date: Wed, 14 Feb 2001 13:03:05 -0500

On Tue, 13 Feb 2001 23:08:35 -0500, bhausmann1@-----.com said:

> At 10:33 PM 2/13/2001 +0000, Tony Pay wrote:

> > (I wrote:)

> > > If it IS caused by non-linearity, then both the microphones,
> > > walls, and human ears/bodies (for sub-audible frequencies) are
> > > nonlinear in the same way. Curious coincidence, eh?
> >
> > Bill, all 'non-linearity' means in this context is, 'generates
> > combination tones'.
> >
> > But that's only because *linearity* means, 'preserves simple
> > addition as the rule of combination of frequencies'.
> >
> > Benade is good background reading for all of this. And, it's not a
> > question of opinion.
>
> The point I was trying to make is that there is only ONE way for a
> system to be linear, and nearly INFINITE ways for it to be NON-linear.

Yes, that's true. But the effect of these different nonlinear systems
on a sine wave of frequency P is the same, namely to generate extra
vibrations in the system at frequencies 2P, 3P etc, called 'harmonics'
of the original frequency; and on two tones of frequencies P and Q to
generate extra combination tones. Different nonlinearities generate
different amounts of these extra vibrations, but they are of the same
frequencies.

> In any case, if a difference tone can be generated that makes physical
> objects shake, including eardrums, microphone diaphragms, walls, etc.,
> I just have to believe that it exists in space beyond my own head.

If a physical object encounters two pure sine waves P and Q, and has a
non-linear response, then instead of just shaking with frequencies P and
Q combined additively, it shakes at frequencies P, Q and other
frequencies combined additively too, including (P-Q), as I said above.

THIS is the case for the middle ear.

But if the physical object *doesn't* have a nonlinear response, then it
*doesn't* shake with frequency (P-Q).

THIS is the case for the eardrum.

So what sense does it have to say that the frequency (P-Q) is *present*?
In one case it's generated, in the other not, that's all.

As well say that you're always saying 'ouch!', just because you *do* say
'ouch!' when you bang your thumb with a hammer.

Tony
--
_________ Tony Pay
|ony:-) 79 Southmoor Rd Tony@-----.uk
| |ay Oxford OX2 6RE GMN artist: http://www.gmn.com
tel/fax 01865 553339

... 24 hours in a day and 24 beers in a case. Hmmmm.....

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