and theres a bunch of "supporting stuff" like computer programs to do the dissonance calculations branching from my homepage at:
http://eceserv0.ece.wisc.edu/~sethares/
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As Paul Hahn mentioned, Bram's idea of cancelling beats in a "noise cancellation" kind of way is not directly related to the minimization of beats via a sensory dissonance calculation (which is what's going on in "Relating Timbre and Tuning").
In any case, one useful formula from trig is:
sin(x) + sin(y) = 2 cos( (x-y)/2 ) sin( (x+y)/2 )
To apply this to the beat cancellation, use this in the form
sin(w t) + sin( (w + dw)t ) = 2 cos( dw t /2) sin( (w+dw/2)t )
where w = one frequency w+dw = other frequency (thus dw = different between the two frequencies) and t is time.
The "amplitude" is thus the slowly varying wave cos(dw t/2) while the basic wave if sin( (w+dw/2)t )