Keeping the carrier-to-modulator frequency ratio constant preserves FM timbre across pitches

The structure of FM sidebands depends on the ratio c:m = fC/fM. If this ratio stays constant while both frequencies scale by the same factor, the relative sideband positions are preserved — the timbre remains consistent. For MIDI-playable FM instruments, both carrier and modulator frequencies must scale together with each note. A common error is fixing the modulator frequency while scaling the carrier, which shifts sideband positions and changes timbre across the keyboard.

Examples

c:m = 1:2, fC = 200 Hz, fM = 400 Hz. Raise pitch an octave: fC = 400 Hz, fM = 800 Hz. Ratio stays 1:2, timbre is preserved. Fix fM at 400 Hz while fC doubles: ratio changes, timbre changes.

Assessment

A patch has fC = 300 Hz, fM = 100 Hz. What modulator frequency should you set when the carrier rises to 450 Hz to preserve timbre?