FM synthesis with integer modulator-to-carrier ratios produces harmonic tones; non-integer ratios produce inharmonic metallic tones

In FM synthesis, one oscillator (the modulator) varies the frequency of another (the carrier). When the modulator-to-carrier frequency ratio is an integer (1:1, 2:1, 3:2), the resulting sidebands land on harmonic partials, producing musical bell-like or metallic-but-pitched tones (DX-style electric piano, marimba, basses). When the ratio is non-integer (e.g., 2.1:1, 3.14:1), sidebands fall between harmonics, creating inharmonic clangorous or harsh tones (neuro growl, metallic percussion, aggressive DX bass). This integer/non-integer distinction is the primary control for moving between musical and inharmonic FM timbres — it produces sounds impossible to achieve with filtering alone.

Examples

FM ratio 1:1 = electric piano-like; 2:1 = bell-like; 2.1:1 = metallic/gong; 7.5:1 = harsh/noisy. Strudel: .fmi(2).fmh(1) vs .fmi(2.1).fmh(1).

Assessment

Explain the difference between integer and non-integer FM ratios in terms of the resulting timbre. Name one musical use for each.