Canceling out beats

On Fri, 2 Oct 1998 A440A@aol.com wrote:
> Paul writes:
>> Actually, thinking further on it, I don't think that would even be
>> possible, considering that the beats don't actually exist physically,
>> but arise because of nonlinearities in the auditory system.
>
> Gee, I must beg to differ, based on two experiences.
[snip buzzes]

Okay. "Physically" was obviously the wrong word for me to have used
there. Of course plenty of physical systems have nonlinearities in them
(I forget which chaos theorist said "talking about non-linear systems is
like talking about non-elephant animals"), and buzzes are a prime
example.

Nevertheless, I remain skeptical about adding sine waves of matching
frequency to eliminate beats. I haven't worked out all the math of it
yet, but it just doesn't feel to me like it would work out.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

> The same thing happens in an airplane when the two engines of a twin get
> out of synch. I have seen drinks and ashtrays throb with the difference
> pulse.

That's definitely not a linear system.

On Fri, 2 Oct 1998, Andrew Bolce' wrote:

> >From: bram
> >
> >Can someone verify for me whether sin(x) and
> >a*sin(x/a) are of the same volume? If they are, I know how to make it
> >exact.
>
> they're not equal. a*sin(x/a) = a(sq.rt.((1-cosx)/a)) or
> sq.rt.((a^2-a^2cosx)/(a))
> i think. 0 would work however. and so would pi. (or would it be 0 and 1?)

I'm not sure what you mean - how does that relate to volume?

My guess is that the volume of a sound is based on the integral of the
absolute value of it's derivative. The integrals of cos(x) and cos(x/a)
(the respective derivatives) never differ by more than a constant amount.

-Bram

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End of TUNING Digest 1543
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