The FM fundamental frequency equals fC/N1 = fM/N2 when the carrier-to-modulator ratio is N1:N2

When the carrier-to-modulator ratio is the rational number N1/N2, the perceived pitch is f0 = fC/N1 = fM/N2. This formula lets you design FM patches to play a specific pitch: set fC = N1·f0 and fM = N2·f0. It also explains why different c:m ratios at the same modulator frequency produce different pitches. Knowing this is essential for programming FM synthesizers to track MIDI notes correctly across the keyboard.

Examples

A4 (440 Hz) with c:m = 1:2: fC = 440 Hz, fM = 880 Hz. Same pitch with c:m = 2:1: fC = 880 Hz, fM = 440 Hz. Both produce a 440 Hz fundamental.

Assessment

Derive the fundamental frequency for fC = 600 Hz, fM = 400 Hz. Then state what fC and fM to use for a 330 Hz note with c:m = 3:2.