Doepfer

Pretty sure my original post on this subject is weak (or worse), but 
I think this article might help. One should be able to construct an 
arbitrary periodic function using a non-trigonmetric basis. In other 
words, you *can* "create a sine by adding signals."

http://ieeexplore.ieee.org/iel5/31/23557/01085543.pdf?
arnumber=1085543

Further, seems to me the ear can be trained to listen for non-sine 
basis functions (aka "overtones"). Take for example, the sound of 
two or more oboes. Pretty sure one could separate the parts by 
pitch, although the parts aren't themselves pure sines. Muting one 
of the oboe parts would be filtering that "frequency", wouldn't it?

I guess I am agreeing with the original poster, and the answer as to 
why we analyse signals in terms of trigonometric basis functions is 
just mathematical (and design?) convenience. 

Doug


--- In Doepfer_a100@yahoogroups.com, "laryn91" <caymus91@...> wrote:
>
> 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]
> >
>