Hi Alexandre,

mea culpa, you were right about the modulation index using Phasor! :D

here we are the 2 implementation, one with Phasor and SinOsc sync(1) (in the previous mail I said sync(2) but I meant sync(1) ), and one without Phasor but just with 2 SinOsc:

Phasor phasor => Gain g => SinOsc carrier => dac;
SinOsc mod => g;

carrier.sync(1);
phasor.freq(100);
modInd(5,200); //change parameters here and listen the result

while( true ){
   
   
    second => now;
}

fun void modInd( int i, int fm ){ //arguments: modulation index, modulation frequency
    float am;
   
    i/6.283185307 => am;
    mod.freq(fm);
    mod.gain(am);
}

////////////////////////////////////////////////////////

////////////////////////////////////////////////////////

// m = mod osc;  c = carrier osc;
SinOsc m => Gain g => SinOsc c => dac;
Step cm => g; //cm = carrier freq in Hz


while( true ){
    modInd(5, 200); //change parameters here and listen the result
    cm.next(100);
    second => now;
}

fun void modInd( float i, float f ){ //arg: modInd, freq mod
    float am; 

    i*f => am; //(modInd = Am/Fm), then (Am = modInd*Fm)
    m.freq(f);
    m.gain(am);
}

2017-06-04 13:59 GMT-03:00 mario.buoninfante <mario.buoninfante@gmail.com>:

Now 2pi is needed only if you deal with a ramp, with a phasor. Cause Phasor*2pi gives you a sine. If you already have a sine there is no need to use 2pi.

Hi, let me try to be clearer. Phasor * 2pi going through a sine function gives you a sine wave. SinOsc can also be drive by a Phasor. Such as this.

Phasor p => SinOsc osc => dac;

440 => p.freq;

1 => osc.sync;

4::second => now;

In this case, you get a sine wave and you don't need to multiply the phasor by 2pi, because the input is normalized, from 0-1

What I was trying to say is that if you have a modulating index in phase modulation, and you want to replicate it in frequency modulation, you alsop need to multiply it by 2pi. 

I'm not challenging the math or equations, just adding an implementation detail in Chuck code. I know I wasn't clear about it, sorry. Hope it's clear now. 

But my main point was something else. It is true that if you multiply the index value by the modulation frequency value, such as in your code, you sort of get a similar behaviour than you'd get with phase modulation. But there's another detail missing if you're to really convert it.

One thing about this conversion is that the waveform/function of the modulation signal needs to also be adjusted. In terms of sine waves, if you have the phase signal being modulated by a sine wave, you need to modulate the frequency with a cosine wave. 

With other waveforms it gets more complicated. By the way, the rule of thumb (multiply the index by the frequency) also changes, that is important to note as well.

My main point is just that it's just best to implement via phase modulation, if that's the behaviour you want.

cheers