For what it is worth, I have made a similar work with much less details and very poorly designed, but here are some cool FM instruments: https://github.com/tfjgeorge/jsfm#gong
To hear the sound click the speaker on the right (works at least with Chrome).
It's a nice article, but I think there are some important things to note here:
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.
I have no music background, so thanks a lot, your feedback is really helpful :)
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).
Hey, no problem. FM synthesis is one of my greater interests! With modulating the phase offset I mean that instead of doing
carrier = sin((f + modulator) * pi)
(a typical way of modulating the frequency) you can do
carrier = sin(f * pi + modulator)
The modulator could be scaled by something from 0 to 2 pi but experiment with what sounds best.
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
5 comments
[ 4.9 ms ] story [ 26.5 ms ] threadTo hear the sound click the speaker on the right (works at least with Chrome).
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).
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
It's very effective for brass sounds or harsher sounds like trying to model distorted guitars