<html> Bob Scott wrote: <blockquote type=cite class=cite cite>The process of making wav files includes time-sampling and quantization, both of which are somewhat non-linear.  If there is a 500 Hz resultant in Don's wav file, it is probably an artifact of the imperfections of the recording process.  If it were possible to record 20 kHz and 20.5 kHz tones and mix them with no distortion at all, then there would be no 500 Hz resultant.  Since it is hard to find such a perfect recording system, then the theory can perhaps be tested by finding a poorer recording system - one with more distortion.  If my theory is correct, the resultant tone should be even stronger when played on such a system with more distortion.</blockquote> Not sure what makes you say that the resultant would only be created by distortion or imperfections, Bob.  Are you saying that beats are only audible if distortion is present?  Or that beats themselves should not be audible if the interacting tones are too high in frequency? Excuse me while I ruminate on this a little.  If the speaker diaphragms are the source of the non-linearity, then that would mean that the beating of the high pitches is essentially causing the speaker to produce the 500 Hz tone because there is a strong beat in the high pitches.  That seems like just another way to say that the beat is audible. The same seems true in the air.  There are beats in the air, which act on our eardrum by alternating the surface between small excursions and large at the rate of 500hz.  All the inner ear can respond to is a 500 Hz movement in the eardrum - and we hear the pitch. In the case of the organ resultant I mentioned, the 16Hz beat is strongly felt in one's chest, if not heard.  Higher resultants in the 20 - 30 Hz range are clearly audible as pitches. I have attached a small jpg to this message.  You can see a small piece of the waveform of the file I made.  The left part is the 20kHz tone, then the 20.5kHz tone is added.  The amplitude modulation you can see (which is another way to look at beats), when put into the air, is moving the air in a pattern of a 500Hz sine wave - just what one hears.  It is my opinion that, even though the two high tones themselves are not easily audible in this test, the amplitude modulation of the tone at 500Hz becomes audible on its own. Don Mannino</html>