Episode Three is online:
Correction #1 - I refer to modulating the amplitude of an audio signal with another audio rate signal as Ring Modulation (RM). I should have said Amplitude Modulation (AM).
RM is certainly related to AM, but there's a distinct difference. RM is implemented in such a way that the carrier and modulator's frequencies are eliminated from the signal. You only hear the sums and difference frequencies of the carrier and modulator, but not the original carrier and modulator frequencies.
Interestingly enough, the AC-coupled circuitry that does RM is ring shaped.
Correction #2 - Neither RM nor AM add harmonic frequencies. They add sidebands of inharmonic frequencies - hence the metallic and dissonant sound.
(Thanks to Javier and Peter on MatrixSynth comments.)