> That's why you can think of the ring modulation
> also as the multiplication of two signals.

Both VCAs and ring mods multiply their two input signals, but it is the _range_ of allowed input signals that causes the difference. In a VCA, the input signal (which can swing both positive and negative) is multiplied by the gain-controlling voltage, which must always be *positive* - if this CV goes negative, the VCA shuts off, and the output is zero (this is called 'two quadrant multiplication'). This is enough to give you the usual amplitude modulation.

In a ring mod, this restriction is removed - if the control signal does go negative, it can now _invert_ the input signal, so the output doesn't stay at zero, but actually changes sign (this is 'four quadrant multiplication').

Ollie's description is confusing (though mathematically correct enough), as the sense of 'F1 & 'F2' changes from *inputs* here:

> By ring mod-ing two signals with frequency F1 and F2...

to *outputs* here:

> adding the two output frequencies: Fout = Fout1+Fout2
> = cos(F1*t)+cos(F2*t)...

thus presenting an additional algebraic challenge to the unwary!

Tim