beats me

Paul Erlich wrote:

>Bram, I don't think you're understanding the phenomenon of beats...

There are really two kinds of "beats" being discussed: one is a
physical wave phenomenon and the other is a psycho-acoustic
phenomenon.

The physical kind is what you get when you have (say) two sine
waves of slightly different frequencies sounding at the same time.
The result is a wave with frequency at the average of the two and an
amplitude envelope whose frequency is the difference of the two.
Thus (for example) a sine with frequency 100 Hz and another with
frequency 101 Hz when sounded together appear to be a single wave
at frequency 100.5 Hz with a beat rate (amplitude modulation) of 1
Hz. This is the kind of beating that Bram is (I think) trying to cancel
by adding back in appropriately chosen waves. This is also the kind
of beating that Ed Foote is listening to when he tunes a pair of piano
strings.

The second kind of beating is what happens inside the ear, and is
closely related to difference frequencies that arise due to
nolinearities in the ear-brain complex. This is a more subtle
phenomenon usually associated with high amplitude sounds, and
clearly cannot be readily "cancelled out" by adding in other sinusoids,
if only because it cannot be measured outside of the ear itself.

I see no theoretical reason why Bram's suggestion shouldn't be do-
able. But whether you can actually measure the waves, do the
calculations, and output the appropriate beat-cancelling sound in real
time -- may be tricky.