FM Synthesis — Iris Lab

Frequency Modulation synthesis: a carrier frequency is modulated by a modulator. The modulation index controls timbre richness. Used in Yamaha DX7 and countless classic sounds.

Waveform & Spectrum

Parameters

Carrier frequency fC: 220 Hz Modulator frequency fM: 220 Hz C:M ratio: 1:1 Modulation index β: 1.0 Volume: 60%

Presets (classic FM timbres)

y(t) = A·sin(2π·fC·t + β·sin(2π·fM·t))
Sidebands at: fC ± n·fM, n=0,1,2…
Amplitude: J_n(β) (Bessel functions)

Sideband	Freq (Hz)	J_n(β)

FM synthesis was discovered by John Chowning at Stanford in 1967. A single carrier+modulator pair produces sidebands at fC±n·fM. The amplitude of each sideband is proportional to J_n(β), the nth-order Bessel function of the first kind at β.