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FM is not multiplication. FM is driving one Voltage-Controlled Oscillator (VCO) with another. As Chowning points out it's fast vibrato.

AM (amplitude modulation) is multiplication. When you do it fast, you get what's commonly called a ring modulator.



AFAIK, you cannot vary a VCO's control voltage with a frequency similar to its output frequency and get a clean result, so the implementation had to be numeric / digital. But idealized VCOs are a nice mental model for FM synthesis.




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