[sdiy] Harmonic bandwidth

[Ian Fritz]

At 08:29 AM 1/10/2008, Ben Lincoln wrote:
>I was also a little surprised to find that the research which was the
>basis for the "harmonic phases are not distinguishable" statement was from
>the middle of the 19th century. While I don't think that means it should
>be entirely discounted, it seems to me like the equipment in 1843 would
>not be nearly accurate enough to use as a basis for that kind of broad
>statement without duplicating the results using modern equipment.

If you are interested, you can actually read some of this literature!  The 
Helmholtz book "On the Sensation of Tone" is available from Dover.  Truly 
amazing work.  He made a series of glass bottle resonators to use for 
Fourier analysis.  His conclusion that phase cannot be heard was based on 
driven tuning forks coupled to resonators with the phase variation provided 
by slight frequency detuning.  However, he did find an exception to these 
results, so in a sense his work is actually self-contradictory. There is 
further discussion in the editor's critical appendix.

There is further 19th century discussion in another book still available 
from Dover, Rayleigh's "The Theory of Sound".  This covers research beyond 
Helmholtz's, such as the work of Konig with specially made sirens.

As far as duplicating with modern equipment, it seems to me that there is a 
lot of agreement.  But read up and draw your own conclusions.

I tried the mistuned octave experiment with a pair of Sin VCOs monitored 
with headphones. I hear beats, but only at high volume.  As the volume is 
turned up, the beats appear at the same point where the pitch sounds like 
it is going flat.  Of course my Sin waves are not perfect, but if the beats 
only appear at high volume, then it seems to me that I am detecting phase 
differences due to nonlinearities in my ear. This would be an easy 
experiment to try with digital waves.  I wouldn't worry too much about 
digital artifacts in this case.

Ian