[sdiy] Harmonic bandwidth

[Tom Wiltshire]

On 6 Jan 2008, at 13:35, ASSI wrote:

> On Sonntag 06 Januar 2008, Tom Wiltshire wrote:
>> 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.
>
> No. OK it seems like a good idea, but actually isn't.  Sorry, I'm not
> trying to mock you, but this is a pitfall that has claimed many  
> victims
> in the past and seemingly will eternally.  If a sample is looped, it
> becomes periodic and you get a discrete spectrum by definition.

Yes, and you're quite right to point this out. I did a very definite  
demonstration of this the other night by looping a short sample of  
noise generator output. Although the sampled source had no definite  
pitch, the looped sample clearly did.

>> Building a waveform up from
>> (say) 50 perfect sine waves at perfect integer multiples is never
>> going to give a natural-sounding wave.
>
> I contest there even is such a thing as a natural sounding wave.  A  
> wave
> is a one-dimensional thing and nature sure isn't.

No, you're probably right - a simple singlecycle waveform is never  
going to have enough complexity to be 'natural'. However, there's  
still a very obvious difference between what you see on a  
oscilloscope when you look at a natural waveform or acoustic sound  
and what you see when you listen to a synth. It's never going to be  
the whole story, but it seems to me that we need to be trying to get  
the same level of richness and detail into our basic waveforms that  
nature manages. Getting the dynamic changes in there might be a  
separate problem or it might be part of the same problem.

Just so my aims are clear, my concern is not with trying to model  
acoustic instruments, and even if it were, direct copying of the  
sound production methods of a given instrument might not be the only  
way to do it. People did manage some nice, realistic string sounds  
_before_ the Karplus-Strong string model, for example. Instead, I'm  
interested in the richness and complexity of natural and acoustic  
sounds, and how we might capture (parameterize) that for use in new  
synthetic sounds. The ultimate goal for me is new sounds that cannot  
be identified as acoustic or synthetic - is that unheard-before noise  
some kind of Indonesian woodblock instrument, or a synth? I reckon  
that currently you can still (mostly) tell the synth from the reality.

>> 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.
>
> The smearing you see in an FFT of acoustic instruments has much  
> more to
> do with the limitations of the method itself.

Yes, I wondered if this might be the case. If the assumptions made by  
FFT analysis skew the results, then any resynthesis based on the  
results of that analysis are also all screwed up.

There's some examples of FFT analysis of real instruments at:

http://www.computermusicresource.com/spectrum.html

If you look at the banjo spectrum for example, you'll see the obvious  
peaks of various harmonics, fading into a low-level background noise  
above about 1KHz. Even the harmonics (or overtones or partials or  
whatever - please don't let's get into an argument over terminology)  
don't appear as the single neat line found on the theoretical graphs.  
Now, how much of that is an effect of the limitations of FFT, and how  
much is an effect of acoustic instruments not being as pure as theory  
suggests?
Our friend in Romania has assumed that the FFT results are valid and  
that that is what acoustic instruments are doing, and used that as a  
basis to generate richer sounding waveforms. Whether his assumption  
is valid or not, his results are good, which is itself interesting if  
the assumption is wrong.

Regards,
Tom