FM synthesis builds complex tones by having one oscillator (the modulator) rapidly vary the pitch of another (the carrier). The single most important parameter is the frequency ratio between them. This tool classifies any C:M ratio as harmonic or inharmonic and shows the sidebands it produces.
How it works
When a carrier at frequency C is modulated by a modulator at frequency M, the spectrum is a set of sidebands at:
C, C +/- M, C +/- 2M, C +/- 3M, ...If the ratio C:M reduces to small whole numbers, every sideband lands on an integer multiple of a common fundamental, so the ear fuses them into one clear pitch — a harmonic tone. If the ratio is irrational or a large/awkward fraction, the sidebands miss the harmonic series and the result is inharmonic: bells, gongs, and metallic timbres.
Finding the perceived fundamental
For an integer ratio the perceived fundamental is the carrier frequency divided by the carrier number of the reduced ratio. The tool reduces the entered C:M to lowest terms (using a gcd for integer inputs) and reports both the classification and the fundamental.
Sideband detail
Negative-frequency sidebands (where C - nM goes below zero) reflect back as positive frequencies with inverted phase, which is why low carrier numbers still produce a full spectrum. The tool lists the first several sideband frequencies, folding reflected ones back into the audible range.
Classic ratios
| C:M | Character |
|---|---|
| 1:1 | Sawtooth-like, full harmonic series |
| 2:1 | Hollow, odd-harmonic, clarinet-like |
| 1:2 | Bright, every-other harmonic |
| 3:1 | Nasal, reedy |
| 1:1.41 | Inharmonic bell / gong |
| 1:3.5 | Metallic, atonal percussion |
The classic DX7 electric piano leans on ratios near 1:1 and 14:1 stacked across operators; FM bells use deliberately inharmonic ratios.
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