[sdiy] Screwing with Square Waves

[rburnett at richieburnett.co.uk]

>> How about sound examples? Ok, these waves would all sound the same 
>> anyway, but many people would not believe that until they heard it.
> 
> They really would sound very much the same.  Any differences would be
> due to quirks and inaccuracies in how they are generated, how they are
> processed, how they are reproduced, and only then, the listener.

It is a general assumption that the human ear isn't sensitive to the 
phase of harmonics and that as long as the harmonics have the desired 
roll-off all of those candidate waveforms would sound the same.  It can 
be true, but isn't always.  Particularly at low frequencies where the 
oscillation period starts to approach the integration time of the ear, 
then the waveshape becomes important.

For instance if you bring the frequency down into the bass region your 
ear can easily distinguish between the hard discontinuities in the real 
squarewave (with all of its harmonics aligned in phase) and the much 
softer shape of the waveforms where you've buggered about with the 
phases of the harmonics.  At even lower frequencies where the tone is 
reduced to a series of machine-gun clicks, the different waveshapes 
start to sound very different.  (Compare the sound of an impulse and a 
chirp.  They both have the same power spectrum but the phases of their 
harmonics are different.  Under what conditions do they sound the same, 
and when do they sound different!?)

You don't always need a non-linearity, reverberation or whatever to make 
the "identical spectrum waveforms" sound different.  The human ear is 
very sensitive to what's happening during transients.

-Richie,

PS. Very cool web programming though!  I agree that it would be neat if 
you could interactively adjust the frequency of the tone and the phases 
of the partials, watch the waveshape change and then click to hear the 
result!