source file: m1543.txt Date: Sat, 3 Oct 1998 13:11:36 -0500 Subject: beats me From: sethares@eceserv0.ece.wisc.edu (William Sethares) 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.