[sdiy] Harmonic bandwidth

[Ian Fritz]

At 04:47 AM 1/6/2008, Tom Wiltshire wrote:
>Yes, it's definitely the irregularities in an analog or acoustic
>sound that give it its character - everyone's pretty much agreed on
>that. What we're struggling with is what _kind_ of irregularities.

Hmmm ... I thought it was pretty well accepted that the irregularities come 
from variations in the driving force.  I'm having trouble seeing where else 
they could come from.  Aren't acoustic instruments strictly passive?


>What I was most interested in was the use of IFFT to get from a non- 
>perfect harmonic spectrum with spread harmonics (and even noisy
>smearing at the high end) to a loopable sample that can be used for a
>wavetable. This seems like a good idea. Building a waveform up from
>(say) 50 perfect sine waves at perfect integer multiples is never
>going to give a natural-sounding wave. The 'spread harmonic'
>technique which the page describes gets around this by effectively
>replacing a single sinewave with a cluster, all with very slightly
>different frequencies.

Well, if this is what you want to do and you find it sounds good, then 
that's great. But it's a pretty big leap to suggest there is a physical 
basis for it, just because you like how it sounds.


>  This spread increases as the frequency goes
>up. This could be the difference Karl is talking about between
>'harmonics' and 'overtones'.

The difference between harmonics and overtones is generally that overtones 
do not have to form a harmonic series.  A periodic wave has overtones that 
form a harmonic series.  A wave from a piano or a bell or a drum does not.


>At first, I thought this would be the same as simply using many
>detuned oscillators, since if an oscillator is detuned by (say) 1Hz,
>then its 2nd harmonic is detuned by 2Hz, and the 3rd by 3Hz, etc,
>giving the frequency spread effect that we're after. But this isn't
>quite right. Doing it that way is going to give you as many sinewaves
>at the fundamental (and as much smearing, although not as detuned) as
>at some higher harmonic. The IFFT technique will give you clearer
>lower harmonics (with less sines) and more smearing at higher
>frequencies (with many sines). This _does_ mimic what you see if you
>run an FFT on an acoustic instrument.

OK, that's what I'm unclear on.  Can you give us a reference showing this 
in an acoustic instrument?


>No, this does seem pretty spurious: "Oh, let's just start everything
>from a random phase! That'll make it more acoustic!" I agree some
>physical basis would be nice.
>
>To be fair, I think something got lost in the translation from
>Romanian too. The guy obviously has a brain on his shoulders and some
>interesting ideas, and we could use more people like that.

Well ... there's a huge body of literature on the physics of acoustic 
instruments. I wouldn't ignore all that in favor of what someone not in the 
field puts up on a website.

But that's just how I look at things, of course. :-)

If you could show us some data on this smearing, that would be very 
important for this discussion.

   Ian