Frequency Modulation (FM) with Web Audio API
greweb.me
greweb.me
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.
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.
When you say modulating a phase offset instead of frequency, does this mean you have like 2 oscillators A and B set to the same frequency, where you modulate the offset of A, and you connect both A and B to the audio output?
About your second note, you are so right! Actually it was a mistake in my article, this is what I've done actually but my explanation was a bit wrong. My first demo is a multiple of the frequency. My second demo is a multiple of (carrier frequency/4). Nothing related to octave, I shouldn't have mentioned that (I will fix it ASAP).
carrier = sin((f + modulator) * pi)
carrier = sin(f * pi + modulator)
The reason for doing this to begin with is probably that simply adding an offset in a sin table readout is probably a more effective design than adding the offset to the phase accumulator, especially if you want a consistent timbre without scaling the modulator amplitude along with the carrier frequency, and don't want to deal with negative frequencies.
Another nice thing you get for free with phase modulation is that you can do stable feedback modulation. In essence, you use the last calculated sample value for an operator (envelope * oscillator) as a modulation source in itself. In code, something like
float generate_sample() {
sample = envelope * sin(f * pi + old_sample * feedback_level);
old_sample = sample;
}
To hear the sound click the speaker on the right (works at least with Chrome).