source file: m1543.txt
Date: Sat, 3 Oct 1998 18:19:55 -0700 (PDT)

Subject: Re: beating the beats

From: bram <bram@gawth.com>

On Fri, 2 Oct 1998, William Sethares wrote:

> 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 )

I thank that's the right sort of 'flavor' of formula for what I'm trying
to do, but not the exact right one. I think I'm looking for a formula
which somehow involves cos(w*t/d)

A note for the mathematically inclined - trigonometric identities are a
lot easier to verify using the formulas - 

sin(x) = i*(e^(-i*x)-e^(i*x))/2

cos(x) = (e^(i*x)+e^(-i*x)/2

Both of which are based on the formula

e^(i*x) = cos(x) + i*sin(x)

-Bram