Rich Grise wrote:
`On Mon, 23 May 2005 11:27:28 -0700, Jack// ani wrote:`

```How is harmonics generated? Why are they integral multiple of the
fundamental frequency?
```

```The way I understand it, the harmonics are generated by different
vibration modes of the string happening simultaneously. In this
case, they're called "overtones". The same thing happens with an
air column in a woodwind, and so on.```

Why they occur in electronic stuff like oscillators and amplifiers
is because of nonlinearities that "distort" the signal, and make it
be something other than a pure sine wave. If you put a pure sine
wave through a speaker, it's a very boring sound, like, "oooooooo....".
The overtones, or harmonics, give it tone coloring, or timbre, like "eeeeeee" or "ahhhhhh" and so on. Say "errrr" into a mic on a
spectrum analyzer sometime, and I can guar-awn-tee that you will be surprised.

```I can't answer "why are they ..." any more than I can answer, "why
is the sky blue?". They just are. It probably has something to do
with phase relationships and Laplace transforms and Fourier transforms
and heavy arithmetical stuff like that. But suffice it to say, when
a signal is distorted, the distortion can be seen on a spectrum
analyzer as other frequencies that just plain happen to be integral
multiples of the fundamental.```

Maybe it's just that the ones at integral multiples don't get cancelled
out with the ones that _aren't_ integral multiples, but that's just as much of a non-answer as saying "The sky is blue because it isn't red."

`Hope this helps!`

```Cheers!
Rich```

read "the cuckoos egg" by Clifford Stoll. Apparently the sky is blue because of a PhD thesis involving dipole moments.

```Cheers
Terry
.```