It's a nice article, but I think there are some important things to note here:<p>Typically, what we call "FM synthesis" is implemented as phase modulation -- instead of modulating the frequency of the carrier, you modulate a phase offset. That way, the amplitude of the modulator won't have to be scaled with the frequency of the carrier for a uniform timbre over the whole frequency.<p>My second note is that most FM synthesizers (the whole Yamaha range, basically) don't define the frequency ratio increments in octaves or quarter octaves, but simply as multiples of the base frequency, producing a harmonic series. Most implementations do this in integer increments, but others like the DX7 and TX81z let you use fractional frequency multiples.