Klarinet Archive - Posting 000254.txt from 2001/02

From: George Kidder <gkidder@-----.org>
Subj: Re: [kl] Combination tones......
Date: Thu, 8 Feb 2001 09:51:24 -0500

Tom and all,

Yes, indeed, and this seems to be the crux of the matter. A single tone
(the fundamental) passed through a perfect (linear) system will result in
only the fundamental; there will be no additional tones produced. A single
tone through a non-linear system will contain harmonics (2, 3, 4 ,,, times
the fundamental) and the sums and differences between these harmonics.
However, this harmonic series is all octaves, and the differences between
members of this series are also octaves, so there is no tone produced which
is lower than the fundamental except for the (theoretical) zero-frequency
tone, which of course does not exist. However, when two tones (which are
not octaves) are passed through a non-linear system, the system generates
harmonics of each, and the difference frequencies between some of these
harmonics can produce tones lower in frequency than either fundamental. To
return to Tom's radio example, the single-tone sort of distortion is called
"harmonic distortion", while the two (or more) tone sort is
"intermodulation distortion", or in jargon, "intermod." =20

For example, suppose two tones of 1000 and 1200 Hz. The first tone
produces harmonics at 1000, 2000, 3000 .... The second tone produces
harmonics at 1200, 2400, 3600 .... 1200 - 1000 =3D 200, 2400 - 2000 =3D 400=
,
2000 - 1200 @-----. Also, these resultant tones can interact; 200 +
400 @-----.=
=20

Bottom line - a whole cacophony of tones can be produced by interactions of
two pure sine waves in a non-linear system The ear is such a non-linear
system. A vibrating panel (wallboard, sheet metal) is a non-linear system.
And (to go back to the initial observation) it is likely that the tuner is
also non-linear, at least for loud input tones. And to further complicate
the matter, the fundamental tone from a musical instrument is not a pure
sine wave, but already contains harmonics (at least) and other frequencies.

I guess what surprises me with the organ example is not that difference
tones are produced, but that there aren't so many of them that the result
is a mess!=20

BTW, the "beats" phenomenon referred to below is, as stated, amplitude
changes only, does not generate any additional tones, and does not require
a non-linear system.

At 08:26 AM 02/08/2001 -0500, Tom Wood wrote:
>
> " ....anyway, the confusion between 'difference tone' and
>'interference' is this: When two waves add (or subtract), they are
>merely combining their amplitudes to create larger and smaller
>amplitudes as they drift 'into phase' and then 'out of phase'. They
>are not creating a new frequency component. They are only reinforcing
>or cancelling existing peaks and valleys."
>
> =20
>I wonder if this is about what we call 'inter modulation' in Ham Radio?
>
>
>
>
>
>
> Main Entry: in=B7ter=B7mod=B7u=B7la=B7tion
> Pronunciation: -"m=E4-j&-'lA-sh&n
> Function: noun
> Etymology: International Scientific Vocabulary
> Date: 1931
> : the production in an electrical device of
>currents having
> frequencies equal to the sums and differences of
>frequencies
> supplied to the device or of their harmonics=20
>
>Tom W
>
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>=20
-----------------------
George Kidder
MDIBL
gkidder@-----.org

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