[sdiy] Harmonic bandwidth

[Ian Fritz]

At 07:01 AM 1/9/2008, Scott Gravenhorst wrote:
>Ok, now I've done it.  I wrote a C program to generate 3 .wav files using 
>double float,
>one with zero starting phase values and 2 more each with different random, 
>but constant
>phase values.  The program uses 32 harmonics in the series that produces a 
>sawtooth.  I
>was careful to limit clipping and applied the same worst case attenuation 
>value to all
>three.  Each sample is several seconds long.
>
>I most definately hear a difference in timbre.
>
>The question is "why?".

Here are a couple more things to think about.

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.

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.

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.

I'm not pretending to have the answer here, but there are many possible 
spurious effects that need to be considered.

Ian