FM Synthesis

One sine wave bends the pitch of another, hundreds of times a second, and a bell comes out: bright and clangorous when struck, fading to a pure tone as it rings. There's no filter in this patch. All the harmonics come from frequency modulation, and an envelope on the modulator's level decides how many there are.

Load it: choose 📚 Examples → FM Synthesis in the toolbar. Press ▶ Play, then play the Z to M keys. The patch file is patches/fm-synthesis.json.

Or play it here: press ▶ Play in the corner. The full app is a click away under Open in Soba. A modulator and a carrier, each with its own VCA and envelope.

What it teaches

• Carrier and modulator. The carrier is the oscillator you hear. The modulator is an oscillator you don't hear directly: it wobbles the carrier's pitch so fast that the wobble becomes tone color.
• Ratio sets the character. Whole-number pitch ratios between the two sound harmonic. Other ratios sound like bells and metal.
• Index sets the brightness. The more the modulator moves the carrier, the more harmonics appear. An envelope on the index makes the tone evolve.

Modules

How it's built

Two oscillators, one keyboard

[Note In Pitch] ──> [Oscillator (modulator) V/Oct]
                ──> [Oscillator (carrier) V/Oct]

Both oscillators follow the keyboard, so the ratio between them stays the same on every note and the timbre stays the same up and down the keyboard. The modulator's Semi is +6, a tritone above the carrier. That's a frequency ratio of √2 : 1, about 1.41. No whole-number ratio is that close, so the harmonics it creates don't line up with the carrier's harmonic series. The result sounds like a bell, not a string.

The modulator, through a VCA

[Oscillator (modulator) Out] ──> [VCA (modulator) In]
[ADSR (modulator) Out] ──> [VCA (modulator) CV]
[VCA (modulator) Out] ──> [Oscillator (carrier) FM]
[Note In Gate] ──> [ADSR (modulator) Gate]

The carrier's FM input is through-zero linear FM: it multiplies the carrier's pitch by 1 + FM × input. With FM at 2.5 and the modulator at full level, the carrier's frequency swings well past zero and back on every cycle. That's what produces the glassy, crowded spectrum of a struck bell.

The FM knob has no CV input, so the patch controls the depth from the other side, by turning the modulator down. The modulator's VCA, driven by its envelope, does that: the modulation is at full depth for the strike, then decays over 500 ms to 10%. As it falls, the harmonics fall away, and the bell's clang mellows into a near-pure tone.

The carrier, through a VCA

[Oscillator (carrier) Out] ──> [VCA (carrier) In]
[ADSR (carrier) Out] ──> [VCA (carrier) CV]
[VCA (carrier) Out] ──> [Audio Output Mono]
[Note In Gate] ──> [ADSR (carrier) Gate]

The carrier's envelope is a bell's: an instant strike and a 2-second decay to silence, with a 1-second release if you let go early. Because the modulator's envelope is shorter, the tone gets purer as it gets quieter, the way real bells and struck metal behave.

Variations

Harmonic tones. Set the modulator's Semi to +12 (a 2:1 ratio) or +19 (3:1). The harmonics now line up with the note, giving organ-like and reedy tones in place of bells.

Electric piano. Set the modulator's Semi to 0 (1:1), lower the carrier's FM to about 1.5, and shorten the modulator envelope's Dec to 150 ms. The bright attack becomes a short "tine" over a mellow body.

Gong. Lengthen the carrier envelope's Dec to 8 s and the modulator's to 3 s. Try Oct −1 on Note In.

Shimmer. Add a few cents of Fine to the modulator. The ratio drifts off true, and the spectrum slowly beats and turns.

Brighter or darker. Turn the carrier's FM up toward 5 for a harsher, more metallic strike, or down toward 1 for a gentler one.

Space. Bells want a room. Put a Reverb between the carrier VCA and the Audio Output.

Related

• Oscillator – how through-zero FM works
• Basic Subtractive Synth – the other way to shape harmonics