And i think it is important to point out the main difference between digital oscillator and analogue oscillator, wich will make Fm modulation not the same on both system.
You need to have linear response to Freq modulation to have the "classic" DX7 Fm sound. While on analogue VCO the response is usually exponential(Volt per Octave); (altough some modular give you the choice).
So lets say that the carrier is 400 Hz and the modulator 200Hz (C:M=1:0.5), on a linear oscillator that would be 400 + 200 and 400 - 200 for the first side band : so one octave down the carrier and a something like a 5th up. While on a exponantial VCO (volt/Octave) it would be an octave down and a octave up . So 400Hz and 800Hz for the first sides bands wich make a huge difference in the resulting spectrum.
Same thing for the vibrato.
I just tough it was important to point out this omission in the text about FM. The rest is pretty interesting and very well explained.