[sdiy] Harmonic bandwidth

[Ben Lincoln]

I have three theories:

- It's an artifact of all of this being done digitally. That is, if we
really were working with mathematically pure sine waves instead of digital
approximations of them, then there would be no difference.
- It's an effect similar to Haidinger's Brush (by which some people can
perceive the polarization of light even though the sensors in our eyes
don't detect it directly).
- It's an artifact introduced by the systems we're listening to them on.

The first seems the most likely to me, but as I said before I'm not very
knowledgeable in this area.

One question I do have is whether Tom, Achim, or anyone else with more
knowledge of frequency analysis than me has re-FFT'd the output of their
sound generation programs to see if the results are what they expect based
on what they put in. When I look at all three of Tom's in a spectral view,
they are very different from each other in ways that correspond to how
they sound to me (e.g. one is missing a lot of frequencies in the middle
of its range).

Part of the reason I'm curious about this comes back to my original
comment about building an additive synth with independent controls for the
phase of each harmonic. I'm sure that the same effect could be obtained by
other means, but there's no reason to not have both at one's disposal,
especially if one or the other is easier to use or implement in different
scenarios.

On Tue, January 8, 2008 6:11 am, Scott Gravenhorst said:
> I was under the impression that this subject has been proven
> mathematically, that
> is, that as long as the phase of each harmonic is constant relative to the
> other
> harmonics that there is no difference in the timbre regardless of the
> exact phase
> angles.  I'm not really a math heavy, so I don't know if such a proof
> exists.
>
> It seems we're diving into a rather subjective hole again with this.  I
> suppose it
> could be argued that I don't hear a difference because I'm old and could
> be deaf in
> the upper range?  My opinion is that using tools like Cool Edit and
> Audacity to do
> these experiments is not optimum and could be flawed.  It's also difficult
> to
> compare our experiences because of wholly different audio systems as well
> as
> different hearing abilities.  And I'll throw in the use of MP3 compression
> as a
> further corruption of the data that could add to the confusion.
>
> -- ScottG