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.
Why the ratio matters more than almost anything else
In a typical subtractive synthesiser you shape a pre-existing rich waveform with filters. In FM, the ratio alone creates the waveform — and a tiny change can shift from a warm piano tone to an inharmonic bell with no filter required. That sensitivity is what makes FM both powerful and initially confusing: two otherwise identical patches with C:M ratios of 1:1 and 1:1.01 sound radically different.
This makes the C:M ratio the primary timbre parameter to understand before you touch envelope, modulation index, or velocity curves.
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. For example, a 4:2 ratio reduces to 2:1, whose perceived fundamental is the carrier ÷ 2.
Sideband detail and reflection
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 and the sounds they make
| C:M | Character | Example instrument |
|---|---|---|
| 1:1 | Sawtooth-like, full harmonic series | Organ, brass |
| 2:1 | Hollow, odd-harmonic only | Clarinet, hollow reed |
| 1:2 | Bright, every-other harmonic | Bell-like but pitched |
| 3:1 | Nasal, reedy | Oboe, bassoon quality |
| 1:1.41 | Inharmonic bell / gong | Crotale, tubular bell |
| 1:3.5 | Metallic, atonal | Industrial percussion |
| 1:3.0 | Brassy, clangorous | DX7-style e-piano attack |
The classic Yamaha DX7 electric piano patch leans on ratios near 1:1 combined with fast amplitude envelopes on the operator stack to create that characteristic attack transient and decay. FM bells use deliberately non-integer ratios to scatter the sidebands off the harmonic series. Tuned percussion instruments like vibes and xylophones fall somewhere in between — slightly inharmonic ratios that still have a clear pitch.
The modulation index and brightness
The C:M ratio determines which sidebands are present; the modulation index determines how loud they are. A low index (0.1–0.5) keeps the tone near a sine wave with just a few soft sidebands. A high index (3–10+) makes many sidebands loud and the sound bright, noisy, or even distorted. As an envelope sweeps the index from high to low over the note’s decay, you get the characteristic FM brightness that diminishes as the note fades.
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