FM Synthesis

Frequency modulation (FM) synthesizes complex timbres by modulating the frequency of one oscillator (the carrier) with the output of another (the modulator). nkido has no dedicated fm() builtin. You build FM compositionally: feed a modulator signal into the frequency input of osc().

carrier

The carrier is the oscillator whose pitch you hear. It runs at the perceived musical frequency.

// Sine carrier at 440 Hz, no modulation yet
osc("sin", 440) |> out(%, %)

modulator

The modulator is a second oscillator whose output is added to the carrier’s frequency. The modulator’s amplitude (the modulation index) controls how far the carrier’s frequency swings.

// Slow vibrato. Modulator at 5 Hz, ±10 Hz swing
osc("sin", 440 + osc("sin", 5) * 10) |> out(%, %)

index

The modulation index is the modulator’s amplitude. Low values give subtle vibrato; high values create rich, harmonic-dense tones characteristic of classic FM (DX7-style bell, electric piano, brass).

// Bell-like timbre with a high modulation index
osc("sin", 440 + osc("sin", 660) * 200) |> out(%, %)

ratio

The frequency ratio between modulator and carrier determines harmonic content. Integer ratios (1:1, 2:1, 3:1) produce harmonic spectra; non-integer ratios (1.41:1, 1.618:1) produce inharmonic, bell- and gong-like timbres.

// 2:1 ratio carrier:modulator (classic harmonic FM)
freq = 220
osc("sin", freq + osc("sin", freq * 2) * 100) |> out(%, %)

// Inharmonic ratio for a bell
freq = 220
osc("sin", freq + osc("sin", freq * 1.41) * 300) |> out(%, %)

sideband

FM produces sidebands at carrier ± n·modulator for integer n. The modulation index controls how many sidebands are audible: higher index, more sidebands, brighter tone. That’s why a single carrier can move from pure-tone vibrato (low index) to bright, edgy timbres (high index) without changing pitch.

// FM using phasor as modulator (sawtooth-shaped sweep)
osc("sin", 440 + osc("phasor", 5) * 100) |> out(%, %)

harmonic

For harmonic FM, the modulator’s frequency is an integer multiple of the carrier’s. The result has only harmonic sidebands and stays pitched.

// Harmonic FM with modulator at 2x carrier frequency
osc("sin", 110 + osc("sin", 220) * 80) |> out(%, %)

Related: oscillators, modulation, math