[sdiy] Harmonic bandwidth

[Ben Lincoln]

ASSI wrote:
> If you take care that audacity doesn't normalize the amplitudes, 
> eliminate the DC offset error you just introduced and that there is 
> also no overflow or clipping from adding the two waves you will most 
> certainly not hear a difference.  You can test this most easily with a 
> sawtooth, provided you can make a wave from a spectrum: a sawtooth has 
> a 1/n spectrum.  If all the spectral coefficients have the same sign 
> the resulting wave will actually look like a sawtooth.  When you flip 
> the sign of any of the coefficients it doesn't necessarily look 
> anything like a sawtooth anymore, but it still sounds like one.  If you 
> do everything correctly and can still hear a difference, submit 
> yourself to your favourite psychoacoustics lab - they will be really 
> interested to run tests with you.
>   

I suspect that I am not using the right terminology here. I have a 
background in music, but I haven't worked much with audio in a number of 
years. When I describe altering the phase, I am not meaning that I am 
inverting signs (necessarily). I mean that I am adjusting the offset of 
one or more of the component sine waves by less than an entire cycle of 
that wave, so that its phase relative to that of the fundamental 
frequency is different.
For example, I created a sawtooth-like wave in Audacity using 32 sine 
waves (100 Hz fundamental and then the next 31 integer harmonics) - so 
more accurate than my Seiko DS would produce, but not as accurate as I 
could get out of my K5000. It's got an exponential curve instead of 
being a linear line because I didn't want to take the time to adjust the 
amplitudes of each component properly. In order to make the effect as 
apparent as possible, I picked a random offset (again, of less than one 
cycle) to adjust each of the harmonics to, rather than just using one or 
two like I did earlier today.
Here's an mp3 file of the original versus randomized phases:

http://www.eventualdecline.com/Normal_versus_Phased_Harmonics.mp3

Besides the obvious difference in sound, If you look at it in a spectral 
view, you can see that the two sections are very similar in terms of 
their basic content, but the second section appears "smeared". So if I 
am using the incorrect terminology, I think that the author of the 
PADsynth software is using it in the same incorrect way, because that is 
what I took away from his discussion of "harmonic bandwidth".