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


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