On Thu, 05 Jul 2007 20:02:15 -0600, Bob Myers wrote:
"John Fields" wrote in message

You missed my point, which was that in a mixer (which the ear is,
since its amplitude response is nonlinear) as the two carriers
approach each other the difference frequency will go to zero and the
sum frequency will go to the second harmonic of either carrier,
making it largely appear to vanish into the fundamental.

Sorry, John - while the ear's amplitude response IS nonlinear, it
does not act as a mixer. "Mixing" (multiplication) occurs when
a given nonlinear element (in electronics, a diode or transistor, for
example) is presented with two signals of different frequencies.
But the human ear doesn't work in that manner - there is no single
nonlinear element which is receiving more than one signal.

Sure there is - the cochlea. (well, the whole middle ear/inner ear
system.)

What would the output look like if you summed a 300Hz tone and a 400Hz
tone and sent the sum to a log amp and spectrum analyzer/fft?

Thanks,
Rich

"Rich Grise" wrote in message
news
Sorry, John - while the ear's amplitude response IS nonlinear, it
does not act as a mixer. "Mixing" (multiplication) occurs when
a given nonlinear element (in electronics, a diode or transistor, for
example) is presented with two signals of different frequencies.
But the human ear doesn't work in that manner - there is no single
nonlinear element which is receiving more than one signal.

Sure there is - the cochlea. (well, the whole middle ear/inner ear
system.)

Nope - the point had to do with the inner workings of the cochlea.
You can't consider it as a single element, as the inner workings
consists of what are essentially thousands of very narrowband
individual sensors. There is no *single* nonlinear element in which
mixing of, say, the hypothetical 300 Hz and 400 Hz tones would
take place. John responded that the eardrum (typmanic membrane)
would act as such an element, but I would suggest that any mixing
which might in theory go on here is not a signifcant factor in how we
perceive such tones. The evidence for this is obvious - if presented
with, say, a pure 440 Hz "A" from a tuning fork, and the note from the
slightly flat instrument we're trying to tune (let's say 438 Hz), we DO
hear the 2 Hz "beat" that results from the interference (in the air)
between these two sounds. What we do NOT hear to any significant
degree is the 878 Hz sum that would be expected if there were much
contribution from a multiplicative ("mixing") process.

Bob M.