[sdiy] Harmonic bandwidth

[Ian Fritz]

At 12:26 PM 1/9/2008, Tom Wiltshire wrote:
>>Room acoustics:  If you play a sawtooth through your speakers you
>>will hear the timbre change as you move your head around.  If you
>>change the phases of the harmonics, then you are introducing
>>different delays which translate to different relative spatial
>>positions of the wave components' loops and nodes. So I think you
>>may hear differences just because of that effect.
>
>I agree that this is a possible explanation, but if it were true,
>then we shouldn't have been told that the human ear can't hear phase,
>since we'd be able to hear phase differences as relative spatial
>positions. So it might be so, but it doesn't explain the discrepancy
>between experiment and theory.

What I'm saying is that the phase differences may be converted into 
amplitude differences, which you may hear.  If you take two sine waves of 
the same frequency, then their sum will vary in amplitude as their relative 
phase changes.  Nobody ever said you couldn't hear that. :-)

In other words, what are the conditions on the statement that you can't 
hear phase?  If relative phase differences lead to relative amplitude 
differences then it seem pretty clear the timbre will change.  Does anybody 
know what the conditions were in the experiments that demonstrated the 
inaudibility of phase?  I'm not finding this in my library collection.


>>Speaker dynamics: If you put a perfect sawtooth into a speaker you
>>would be asking for its displacement to change instantaneously.  If
>>you rephased the harmonics then you would no longer have this
>>step.  Of course you never have exactly this situation, but the
>>transient mechanical response of the speaker to a step should be
>>kept in mind.  For this reason I think the sawtooth does not make a
>>very good test.
>
>We can use any collection of harmonics you like! We've all got
>additive-wave-generating scripts written now!

Yes, I think it would make sense to start with fewer harmonics and to avoid 
singular waveforms. And maybe it would be better to use headphones rather 
than speakers, or at least to compare both ways.


>>An old trick of loudspeaker salesmen is to play at a higher level
>>through the speakers they want to sell.  There was a very large
>>loudness difference in the first pair of examples that were
>>posted.  It is very important when comparing timbre to keep the
>>loudness level the same, probably to within 0.5 dB.
>
>Sorry Ian, but what counts as 'the same loudness'? You're not talking
>about peak level, since the first pair of examples had the same peak
>level, although the average level might have been different, and you
>say there was a loudness difference.
>I'm not trying to nit-pick, I just don't understand what you mean by
>'loudness' in a technical sense. What parameter of the waveform is
>'loudness'?
>I'm sure I can normalise all the phase-altered samples to the same
>loudness to some arbitrary degree of accuracy once I know what I'm
>doing!

Well, what I think is that since the ear is supposed to have a built-in 
Fourier analysis you would want the samples to have the exact same 
amplitudes for each individual harmonic.  (This may not be exact because of 
nonlinearities in the ear.)  So I would say do not adjust the overall wave 
amplitudes at all!  Maybe I shouldn't have called it loudness. Did you 
normalize the original samples to the same peak?

Thanks for the interesting discussion!

Ian