I don't believe you can create a sine by adding signals with overtones. You can transfer the
energy around in the spectrum with specific phase cancellations. But every time you
cancel an overtone you create or reinforce another.

In nature, sine functions are prevalent everywhere. On the other hand, square waves are
non-existent and must always be synthesized. It would very atypical for nature to miss
something as mathematically elegant as sines in favor of something more convoluted.

--- In Doepfer_a100@yahoogroups.com , "Monroe Eskew" <monroe.eskew@...> wrote:
>
> I'm curious about harmonics. I've been looking for an explanation of why
> different waveforms have different overtones. One explanation offered is in
> terms of Fourier series. Every periodic function can be expressed as an
> infinite sum of sine waves of increasing frequency and decreasing amplitude.
> If we look at the Fourier series for a given curve (like a sawtooth or
> square wave), then we can find the overtones by looking at the terms in the
> sum.
>
> Now I like mathematics, but I'm not satisfied by this explanation. We can
> express a function as a Fourier series, but we can also express it in other
> ways. Perhaps a sine wave can be expressed as an infinite series of square
> waves. Then a sine wave should have a lot of overtones.
>
> Here's my guess-- Qualitatively, different waveforms have different sounds,
> and this does not necessarily need to be interpreted as having overtones.
> However FILTERS are what truly reveal overtones. But the function of a
> filter is determined by the fact that its resonant frequency is always a
> sine wave. If we had square wave resonance, then we'd have totally
> different filters, with the square wave being the least affected by the
> filter.
>
> Is that more or less correct
>
> Also, does the Fourier expression make the most sense to the human ear
> (i.e. Does the human ear have something akin to sine wave resonance )
>
> Thanks,
> Monroe
>
>
> [Non-text portions of this message have been removed]
>