The question is basically whether overtones are objective or just one
interpretation of a wave. Given that there are multiple ways to decompose a
given waveform, why is one decomposition favored as a way of understanding
the overtones If the decomposition corresponds to how the cochlea
physically works, or how the brain processes, or a combination of both, this
may help explain it. Obviously overtones have a functional relationship to
filters, and since filters are sine-wave-based, this leads to the hypothesis
that the ear (and/or brain) shares some characteristics with those filters.

The ear doesn't have to "know" anything; it may physically function in a way
as to break the spectrum into sine components. The cochlea is a complex
thing.

On Thu, Jul 3, 2008 at 3:42 PM, laryn91 < caymus91@... > wrote:

> In your example, what are the "pitch parts" you're separating when
> analyzing the two
> oboes SINE waves - right Not square or some other arbitrary function.
>
> Since I can only read the fragmented summary in the referenced paper, so
> maybe I'm
> understanding it totally incorrectly. But it may not be relevant since the
> harmonic phase
> relations don't appear to be held constant. In other words yes, you can get
> a sine if you
> add two signals of different shape. Which is not what the poster asked.
>
> I believe the poster was wondering if any function can be transformed from
> a non-circular
> plane - like a square or rectangular one. Maybe it's just my limited
> knowledge, but I
> haven't heard of such a thing. I can try to *approximate" a sine from a
> square plane...
>
> --- In Doepfer_a100@yahoogroups.com <Doepfer_a100%40yahoogroups.com>,
> "Doug" <dougc356@...> wrote:
> >
> > 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 <Doepfer_a100%40yahoogroups.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 <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]
> > > >
> > >
> >
>
>
>


[Non-text portions of this message have been removed]