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Klarinet Archive - Posting 000462.txt from 2001/02

From: (Tony Pay)
Subj: Re: [kl] Combination tones......
Date: Mon, 12 Feb 2001 18:07:03 -0500

On Mon, 12 Feb 2001 13:13:52 -0700, said:

> I realize that a degree in chemistry with a minor in music doesn't
> exactly qualify me as an expert in acoustics, but I was taking the
> sine wave addition as a description of the physical change in air
> pressure. In other words, the wave pattern that results is the
> physically measurable sound, regardless of the ear's nonlinearity. If
> you run both sine waves into a speaker, the added waveform is what the
> speaker produces (assuming a perfect speaker, of course).

But, as I said in another post, the added waveform can produce the
amplitude modulation only as the *product* of two terms (see below). So
the amplitude modulation *isn't* an added waveform. It *is* a beat,
though, which is a different thing from a difference tone.

> > In fact, a general non-linear system, from stimulation at two
> > frequencies P and Q, generates heterodyne frequencies 2P, 3P...; 2Q,
> > 3Q...; P-Q, P+Q; (2P - Q), (2Q - P); (3P - 2Q).....etc. etc. etc,
> > including sums and differences of all of those. (Most of them are
> > very weak, of course.)
> >
> > I think from your previous post you know how it goes from here:
> > multiples of (P-Q) are strongly represented in the above list. Our
> > neural processing systems are tuned to recognise, and group,
> > *harmonic* patterns; (survival value in that!-) and multiples of
> > (P-Q) form the harmonic series for the frequency (P-Q). So the
> > upshot is that that frequency (as well as others, more weakly) is
> > perceived.
> Yes, the description above also appear in Benade (which I *can*
> locate). It explains why you hear beats between a sine wave (which
> has no upper harmonics) at 200 Hz when played against a tone at 403
> Hz.

No, it doesn't explain why you hear beats. It explains why you hear
difference tones between two frequencies.

Of course, you do hear beats between a sine wave at 200 Hz and a tone at
403 Hz as well.

> I think my original statement regarding different tones and beats
> wasn't sufficiently precise (although it does describe what one
> hears). The waveform of two close sources that are slightly out of
> tune resembles a single wave at the average frequency that rises and
> falls in amplitude: this is what the ear hears. If you play 440 Hz
> while the musician on the next stand plays 442 Hz, you hear 441 Hz
> that beats once per second (1 Hz). If you gliss the pitch from 442
> Hz up to 660 Hz, you'd hear the frequency of beating increase to a
> burr, eventually ending up with a difference tone. Both the beating
> and the difference tone are produced by the same physical phenomena,
> although the ear perceives them somewhat differently.

No, this isn't true. But I do understand how it's a seductive
viewpoint. I wrote about that in an earlier post:

_________ Tony Pay
|ony:-) 79 Southmoor Rd
| |ay Oxford OX2 6RE GMN artist:
tel/fax 01865 553339

... Ancient Greeks made dolphin-killing punishable by death.

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