FM synth 'ratio' is the pitch of an operator expressed as a multiplier of the root note, not in semitones

In FM synthesis, operators don’t have pitch settings in semitones like subtractive synth oscillators — instead they have a ratio. The ratio expresses the operator’s frequency as a multiple of the instrument’s root pitch. A ratio of 1.0 means the operator runs at the same frequency as the note being played; a ratio of 2.0 means it runs at double that frequency (one octave up); a ratio of 0.5 means it runs at half (one octave down). This is a core FM concept because the relationship between carrier and modulator ratios determines the harmonic (or inharmonic) character of the FM spectrum. Integer ratios produce harmonic spectra; non-integer ratios produce inharmonic (bell-like or metallic) spectra. Confusing ratio with a semitone offset is a common beginner error.

Examples

In FM8: operator ratio of 1 = root pitch; ratio 2 = octave above; ratio 1.01 = very slight detuning above root pitch (produces slow beating). Ratio 3 = perfect 5th + octave above. Non-integer like 2.35 produces inharmonic metallic sound.

Assessment

Given a root note of 440 Hz, calculate the frequency of an FM modulator at ratios 0.5, 1, 2, and 1.5; then explain whether each ratio produces a harmonic or inharmonic spectrum.