Expressing overtones in squarewaves is not correct.
Because the squarewave has a large number of overtones.

The (perfect) sine is the purest tone you can achive. It has no overtones.
that is the way mathematics looks at it.
If you would look in with a spectrum analyzer the (perfect) sine shows up as
a needle sticking out at one place.
In truth most sine oscillators are not entirely perfect so they do have
slight tendencies to have a few tiny overtones.
If you would analyze the squarewave this way you see a whole blur over the
with of the spectrum

The only way to create a sine out of a squarewave is by using a lowpass
filter.
Mathematically seen you could consider the lowpass filter an integrator.


If you are interested doing research in these fields I would advise you to
take a look at Cycling 74's Max/MSP software.

On Thu, Jul 3, 2008 at 8:50 PM, 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 <Doepfer_a100%40yahoogroups.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]
> >
>
>
>


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