Off the top of my head, I don't think the set of square waves forms
an orthogonal basis, so that a decomposition in terms of square
waves is not unique. In other words, in the square wave basis,
the "overtones" present are not unique. Not sure how you could apply
a filter in this case, since the idea of a filter is to strip out
members of the basis independently of the others.

Beyond this I think our senses confirm the decomposition of
vibrations in terms of sine waves, and this is simply a matter of
experience agreeing with theory. I think if the ear were to
experience a sound and we were expected to think about it in terms
of the various contributions of square waves it would be difficult,
because the contribution of each square wave in a particular sound
is not unique. You could think about a sound being composed of two
(or more) different sets of square waves, and the answer to the
question would become ambiguous. Two or more, or many answers would
be correct. In the case of sine waves, there is only one answer.

Hopefully I am correct in this and not muddying the waters.


Thanks,
Doug

--- 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]
>