Doepfer

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]
>