Adding a small constant to the FM modulating frequency creates a beat or tremulant effect

In a perfectly integer c/m FM patch, reflected lower sidebands land exactly on upper sidebands and cancel or reinforce precisely. If a small constant frequency offset (e.g., 0.5 Hz) is added to the modulating frequency, the reflected sidebands no longer fall exactly on the positive components; instead they beat against them at a rate equal to twice the offset (e.g., 1 Hz beat/tremulant). This technique introduces subtle natural variation — a slow modulation of individual partial amplitudes — that makes synthesized tones sound less mechanical. It is a simple but effective realism technique applicable to any FM voice simulation.

Examples

A woodwind patch with m=300.5Hz instead of exactly 300Hz produces a 1Hz amplitude tremulant across all components, mimicking the natural breath variation of a wind instrument.

Assessment

If the modulating frequency is offset by 0.3Hz, what is the tremulant beat rate? Explain the mechanism using reflected sideband arithmetic.