Example 3

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FM synthesis:

ChucK code

SinOsc c => Gain amp => dac; // carrier
SinOsc m => blackhole; // modulator 
0.3 => amp.gain;
550 => float mf => m.freq;
300 => float cf => c.freq;
2 => float index;

while( true )
{
    cf + (index * mf * m.last()) => c.freq;
    1::samp => now;
}

SuperCollider code

{
	var cf, mf, index;
	cf = 300;
	mf = 550;
	index = 2;
	SinOsc.ar(cf + SinOsc.ar(mf, mul: mf * index), mul: 0.3).dup // .dup = duplicate = cheap stereo
}.play;

SC actually has a PM UGen (Phase Modulation synthesis and Frequency Modulation synthesis are basically the same sound), so this example could also look like this:

{PMOsc.ar(300,550,2,mul:0.3).dup}.play;

from DT here: this is super cool Jascha! there is also a ChucK FM synthesis ugen:

http://chuck.cs.princeton.edu/doc/program/ugen_full.html#FM

from JN: neat-o - this should totally be added to the ChucK code section as an alternative approach. i couldn't immediately see how to use it - can you post an example?

from DT: well, FM by itself doesn't actually work, which is silly (it's meant to be a superclass only), but ChucK is full of silliness. however, FM synthesis is possible very simply and efficiently using the .sync method, which many UGENS have, and which tells the UGEN how to interpret its input. so, here's a very simple example, from the ChucK examples:

SinOsc m => SinOsc c => dac;

300 => c.freq;
550 => m.freq;
2 => m.gain;
 
2 => c.sync;
 
while( true ) 1::second => now;

and, just to be clear, this is equivalent to a slightly different version of your original ChucK FM synth:

SinOsc c => Gain amp => dac; // carrier
SinOsc m => blackhole; // modulator 
0.3 => amp.gain;
300 => float cf => c.freq;
550 => float mf => m.freq;
2 => float index;

while( true )
{
    cf + (index * m.last()) => c.freq;
    1::samp => now;
}