Your basic core is the numerically-controlled oscillator, which consists of a phase accumulator and a wave shaper which converts the phase to the desired wave (

Your basic core is the numerically-controlled oscillator, which consists of a phase accumulator and a wave shaper which converts the phase to the desired wave (basically a sine wave lookup table). phase accumulator -> wave shaper Yamaha FM just lets you add other signals to the wave shaper input: other signal -------\ (+)-> wave shaper phase accumulator --/ For example, instead of getting sin(x), you get something like sin(x + sin(x)). You start adding parameters like “a sin(b x + c sin(d x))” suddenly there are millions of possibilities. “Why it sounds that way” can get really deep if you like, but basically, as you increase the modulation level you get more harmonics, and if you increase it too much you start losing the fundamental frequency. This is one of the reasons why it’s nice to have a 6-operator FM system (like in the DX-7). With the 4-operator FM, once you turn the modulation “all the way up”, there’s nowhere to go, but with 6-operator FM you have some extra operators around for modulating modulators.