Non-integer C:M ratios in FM synthesis produce inharmonic spectra for metallic and bell sounds

When the C:M ratio is non-integer (e.g. 1:1.2), the sidebands generated by FM no longer land on integer multiples of a single fundamental. They are displaced off the harmonic series, producing a spectrum that reads as metallic, bell-like, or gong-like rather than a clear pitch. This is because pitch perception relies on harmonic partials fusing into one tone; inharmonic partials do not fuse. The further the ratio departs from simple integers, the more the sound moves from tonal toward clangorous or percussive. This principle is the basis for FM metallic percussion and bell timbres. It is the boundary case of the C:M-ratio concept: integer ratios stay harmonic, non-integer ratios go inharmonic.

Examples

C:M = 1:1 -> clear pitched tone. C:M = 1:1.2 -> the sidebands shift off the harmonic grid, giving the ‘enharmonic’ metallic/bell character the source describes. Pushing further (e.g. an irrational ratio) yields chaotic, gong-like spectra.

Assessment

On an FM synth, set C:M = 1:1, then move the modulator ratio toward 1:1.2 and beyond, keeping the index constant. At what point does the timbre shift from ‘tonal instrument’ to ‘metallic/bell’? Explain why in terms of sideband positions.