[sdiy] Harmonic bandwidth

[Scott Gravenhorst]

Sorry Ben, I sent you a blank reply...  here's the real one

"Ben Lincoln" <blincoln at eventualdecline.com> wrote:
>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.

That's what I think too, but I'm not educated or experienced with this.

>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).

That's very interesting, but sounds most certainly counter to the theory.

>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.

I've been working on something sort of close I think, but it is an FPGA project and is
thus digital and could fall prey for the reasons you mentioned above.  What I have is a
synth that implements 32 NCOs.  Each NCO drives a sinewave table.  The frequencies of the
NCOs are set with 2 controls, one is an integer multiplier for frequency, the other is a
fine tune control which can push the otherwise harmonic signal off frequency where it
becomes a nonharmonic overtone.  I do not have, but could probably easily implement a
starting phase register for each NCO.  Unfortunately, I've got a day job that slows
development of this kind of thing.

>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
>
>
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-- ScottG

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-- Scott Gravenhorst
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