[sdiy] Harmonic bandwidth

[Tom Wiltshire]

On 6 Jan 2008, at 01:05, Ian Fritz wrote:

> Well, I have to say it isn't very clear to me what is going on  
> here.  Irregularities in musical sounds have been studied  
> extensively in the past. (I have mentioned the Keefer paper on  
> clarinet unsteadiness several times before).

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.

> My old Roland rompler has an "analog feel" control that adds some  
> nice variation to the sounds.

Many instruments have similar knobs, and sometimes they help and  
sometimes they're rubbish, but mostly all they're doing is adding  
some random pitch variation into oscillators - at least, that's as  
much as anyone admits to. I'd be interested to hear the details of  
any successful 'analog feel' algorithm.

> But can you understand why you would look at this in terms of the  
> individual harmonics?

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

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.

I'm interested to know if anyone has tried/knows of an instrument  
that has tried this technique of using IFFT to produce wavetable  
samples. Is this chap alone?

> I'm especially unclear on "Put random phases to each frequency of  
> the spectrum".  Is this really how acoustic instruments work? It's  
> true that nonlinearities can introduce anharmonicities, as in piano  
> strings, but I don't see how this leads to random phases.
>
> Oh well. <shrug>

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.

Regards,
Tom