Frequency modulation drives a carrier oscillator's frequency with a modulator, generating sidebands at C±kM
Modulation synthesis uses one oscillator (the modulator) to vary a parameter of another (the carrier). In ring modulation the two signals are simply multiplied (carrier * modulator); amplitude modulation is the same but with a unipolar (always-positive) modulator. In frequency modulation (FM) the modulator is plugged into the carrier’s frequency input. When the modulator runs at audio rate, FM produces an infinite series of sidebands at frequencies C + kM (C = carrier freq, M = modulator freq, k any integer), whose strengths depend on the modulation index. Small integer C:M ratios give harmonic (tonal) spectra; irrational ratios give inharmonic, bell- or metallic-like timbres. FM is cheap yet spectrally rich, which is why it dominated 1980s digital synthesis.
Examples
// FM: modulator into carrier frequency
{SinOsc.ar(440 + SinOsc.ar(110, 0, 200), 0, 0.2)}.play
// ring modulation: multiply two signals
{(SinOsc.ar(440) * SinOsc.ar(113)) * 0.2}.playAssessment
Build an FM patch with a controllable C:M ratio and modulation index. Set C:M to 1:1 and to 1:1.41 and describe the difference in spectrum; predict where the first three sidebands fall for C=200, M=150.