FM synthesis varies one oscillator's frequency with another to produce complex sidebands

Frequency modulation (FM) synthesis uses one oscillator (the modulator) to rapidly vary the frequency of another (the carrier). When the modulator is at audio rate (above ~20 Hz), sidebands appear in the spectrum at carrier ± modulator frequency and their multiples. The ratio of carrier to modulator frequency (C:M ratio) determines whether the sidebands are harmonic (integer ratio → pitched tone) or inharmonic (non-integer → metallic, bell-like). Modulation depth (index) controls how many sidebands appear: low index = subtle brightness; high index = dense, complex, or harsh spectrum. FM at low modulator rates blurs into vibrato; at audio rates it is timbre synthesis. Digital FM synthesizers (DX7) use this principle with precision; modular FM is rougher and continuous.

Examples

VCO A (carrier, 440 Hz) FM’d by VCO B (modulator, 440 Hz, 1:1 ratio): harmonic spectrum, extra overtones. VCO B at 550 Hz (5:4 ratio, non-integer): inharmonic, bell-like. Increasing modulation depth dramatically increases spectral complexity.

Assessment

Explain why a 1:1 integer C:M ratio in FM produces a harmonic spectrum while a non-integer ratio produces an inharmonic one. Describe how modulation depth (index) affects the number of audible sidebands.