Posted by Dan Masi on July 18, 2002 at 13:21:26:
In Reply to: Re: Re: Ear buzzing when playing in quintet posted by Math Doctor on July 08, 2002 at 08:45:41:
"The frequency of the pitch generated is the greatest common divisor (GCD) of the frequencies, not the difference. "
Not true. In nonlinear mixing, you get a sideband spectrum that is made up of sum and difference frequencies.
"For example, playing 440 Hz (tuning note A) and 550 Hz (C# a slightly flat major third above tuning note A) produces 110 Hz (two octaves below tuning note A). Playing 330 Hz (slightly sharp E a 4th below tuning note A) and 550 Hz (C# above tuning note A) also generates 110 Hz (GCD), not 220 Hz (difference)."
It generates both, in fact. Given sinusoidal input frequencies of F1 and F2, the nonlinear mixing of these frequencies produces a spectrum which consists of all frequencies Fo which solve the following for integer values of i and j:
i*F1 + j*F2 + Fo = 0 (both 110Hz and 220Hz are solutions in your example)
This is merely a realization that not only to the fundamentals mix to provide sum and difference sidebands, but that their harmonics mix as well.
If there were really some mechanism that only allowed the GCD frequency to be
heard, then you certainly wouldn't hear a 2Hz "beat" when trying to tune 999Hz
and 1001Hz instruments...
-dan