[sdiy] Phase shifts and instantaneous frequency

[Ian Fritz]

At 11:42 AM 7/15/2008, Aaron Lanterman wrote:

>Huh. That shows up when you're working with RF equipment all the
>time... I had no idea that happened in the ear too.

Oh my, yes. This has been known for hundreds of years.  For example, string 
players tune double-stop thirds by listening to the rough difference 
tones.  It has been known since the 1870s that these "combination tones" do 
not correspond to physical vibrations in the air. (For example, they cannot 
be amplified by resonator bottles.)  You can read about all this in 
Helmholz's book, especially in the translator's appendix XX sect 
L.  Article 6 of that section is titled "Influence of difference of Phase 
on Quality of Tone" and discusses the definitive experiments of Konig using 
sirens to show distinct differences in periodic sounds with different 
phases of the harmonics.

It's actually pretty odd that people still perpetuate the myth that the 
relative phases of the harmonics aren't audible.  They clearly are.  As 
Konig put it: "The composition of a number of harmonic tones, including 
both the evenly and unevenly numbered partials, generates in all cases, 
quite independently of the relative intensity of these, the strongest and 
acutest quality tone for the 1/4 difference of phase, and the weakest and 
softest for 3/4 difference of phase, while the difference 0 and 1/2 lie 
betwee the others, borth as regards intensity and acuteness."

Nowadays, these are easily demonstrated with synthesized tones, as was 
discussed here a while back.

   Ian