FM Synthesis

From Vibrato to FM

Connect an LFO to an oscillator’s pitch input in VCV Rack. Set the LFO to about 5 Hz. You hear vibrato — the pitch wobbles up and down at a rate your ear tracks as movement, not as a new tone.

Now increase the LFO’s frequency. At around 20 Hz, the wobble starts to smear. By the time you reach 100 Hz, then 200 Hz, you are no longer hearing vibrato. The modulating signal is generating new frequency components — sidebands — that your ear perceives as timbre, not pitch movement. The sound gets brighter, buzzier, more complex.

That is FM synthesis in its simplest form. Replace the LFO with a second oscillator running at audio rate, and you have a two-operator FM voice.

Operators: The Building Block

In FM terminology, an oscillator is called an operator. Every operator is a sine wave generator with its own frequency, amplitude, and envelope. The distinction from subtractive synthesis is that operators serve two roles: some produce the sound you hear (carriers), and some modify the frequency of other operators (modulators).

A carrier on its own is a plain sine wave. A modulator connected to a carrier adds harmonic complexity. The modulator’s frequency and amplitude determine which harmonics appear and how loud they are.

Ratios and Harmonicity

The relationship between a carrier’s frequency and its modulator’s frequency is expressed as a ratio. This ratio controls whether the resulting sound is harmonic (musical, pitched) or inharmonic (metallic, bell-like, noisy).

Integer ratios produce harmonic sounds. A 1:1 ratio (modulator and carrier at the same frequency) generates a spectrum with harmonics at integer multiples of the fundamental — similar to what a sawtooth or square wave contains, but with a different balance of harmonics. A 2:1 ratio generates every other harmonic. A 3:1 ratio generates every third. Each integer ratio produces a recognizable harmonic profile.

Non-integer ratios produce inharmonic sounds. A ratio of 1.41:1 or 3.5:1 generates frequencies that are not integer multiples of the fundamental. The ear does not group these into a clear pitch — instead, you hear metallic, clangorous, bell-like tones. This is FM’s unique strength. Subtractive synthesis cannot produce inharmonic spectra from standard waveforms, but FM generates them effortlessly by changing a single number.

In VCV Rack, set up two oscillators as a carrier-modulator pair. Patch the modulator’s sine output into the carrier’s FM input. Set both to the same base frequency (1:1 ratio). Listen. Now change the modulator to twice the carrier frequency (2:1). Listen again. Then try 1.5:1, then 3.14:1. The shift from harmonic to inharmonic is immediate and dramatic.

Modulation Index: How Bright Is the Sound?

The modulator’s amplitude controls how far it pushes the carrier’s frequency. This parameter is called the modulation index, and it determines the brightness and complexity of the resulting timbre.

At a low modulation index, the carrier is barely affected — you hear something close to a pure sine. As you increase the index, more sidebands appear. The sound gets brighter and more complex, gaining harmonics in a way that does not sound like a filter opening. It sounds like new frequencies are appearing from inside the tone, which is exactly what is happening.

This is the FM equivalent of the filter cutoff in subtractive synthesis. Where a subtractive patch sweeps a filter to go from dark to bright, an FM patch changes the modulation index to go from simple to complex. The difference is that FM brightness is not just about removing or revealing existing harmonics — it is about creating new ones.

Attach an envelope to the modulator’s amplitude. Set a fast attack and moderate decay. Now when you play a note, the sound starts bright (high modulation index at the attack) and settles to something simpler (lower index during the sustain). This is exactly how an electric piano works in FM: a bright transient that decays into a warm sustained tone.

Algorithms: How Operators Connect

A single carrier-modulator pair is powerful, but FM synthesizers use multiple operators connected in different configurations called algorithms.

An algorithm defines the signal flow: which operators are modulators, which are carriers, and how they chain together. Some algorithms stack modulators in series — operator 3 modulates operator 2, which modulates operator 1 (the carrier). This produces increasingly complex spectra because each layer of modulation creates sidebands on sidebands.

Other algorithms run operators in parallel — multiple carriers, each with its own modulator, mixed together at the output. This is closer to additive synthesis: you are layering independent timbres rather than building complexity through deep modulation chains.

The DX7 has six operators and 32 algorithms. Some are deeply serial (all six operators in a chain, producing extremely complex spectra), some are fully parallel (six independent sine carriers, essentially an additive synth), and most fall somewhere between. Each algorithm has a distinct character — not because of the operators themselves (they are all identical sine generators), but because of how they connect.

Feedback

Some FM algorithms include a feedback path, where an operator’s output is routed back into its own frequency input. This is an operator modulating itself.

At low feedback levels, the sine wave develops a slight edge — it starts to resemble a sawtooth. At higher levels, the sound becomes increasingly noisy and distorted. Feedback on a carrier adds grit. The DX7 uses single-operator feedback on specific algorithms, and it is a significant part of the instrument’s timbral range — many DX7 bass and organ sounds depend on feedback to add harmonic richness that pure sine-to-sine modulation cannot produce.

Building FM Tones in VCV Rack

Start with two operators. In VCV Rack, use two sine-wave oscillators. Patch operator B’s sine output into operator A’s FM input. Operator A is the carrier (connect its output to your audio). Operator B is the modulator.

Electric piano: Set the ratio to 1:1. Attach an envelope to the modulator’s amplitude (or to a VCA controlling the modulator’s output level). Fast attack, moderate decay, low sustain. The envelope controls the modulation index over time — the attack is bright, the sustain is warm. Add a second modulator at a 14:1 ratio with a very fast, percussive envelope for the key click. This two-stage approach — a transient modulator for the attack and a slower modulator for the body — is how nearly every DX7 electric piano patch works.

Bell: Set the ratio to a non-integer value — try 1.41:1 or 2.76:1. Moderate modulation index. Long release on both the carrier’s amplifier envelope and the modulator’s envelope. The inharmonic ratio produces metallic partials. The long release lets them ring. Bells in FM are almost absurdly easy once you know that inharmonic ratios are the key.

Metallic bass: Set the ratio to 1:1. High modulation index on the attack (fast envelope with sharp decay on the modulator amplitude), low sustain. The result has a hard, biting transient that decays into a simpler tone. Increase the ratio to 3:1 for a more aggressive edge.

Evolving pad: Use three or four operators in a chain (if your VCV setup supports it) or parallel pairs with slow-moving LFOs on the modulation indices. The LFOs cause the harmonic spectrum to shift continuously. Because FM spectra are so sensitive to modulation index changes, even a gentle LFO produces noticeable timbral movement.

FM vs. Subtractive: When to Use Which

FM and subtractive synthesis are complementary, not competing. Each handles certain sounds with ease and struggles with others.

Use subtractive for warm basses, classic leads, pads that need filter sweep movement, and any sound where the timbral evolution follows a “bright to dark” or “dark to bright” arc. Subtractive is predictable in a good way — you always know roughly what you will get.

Use FM for metallic and bell-like tones, electric pianos, glassy textures, percussive attacks, and any sound that needs inharmonic content or a harmonic spectrum that changes in a way filters cannot produce. FM excels at tones that need to start complex and decay into simplicity.

Many sounds combine both. A common approach is to build the basic timbre with FM, then run it through a subtractive filter for further shaping. The FM engine generates the raw complexity; the filter tames and sculpts it. This is how a lot of modern sound design works, and it is the direction the guide will continue moving — combining synthesis methods rather than treating them as isolated techniques.

What to Practice

• Build a two-operator FM voice in VCV Rack. Start with a 1:1 ratio and sweep the modulator’s amplitude from zero to maximum while holding a note. Listen to how the timbre evolves. Repeat with 2:1, 3:1, and 1.41:1 ratios.
• Create an electric piano sound using the method described above. Focus on getting the envelope on the modulator right — the attack brightness and the rate of decay into the sustained tone are what sell the sound. Compare your result with a DX7 preset in Dexed if you have it installed.
• Create a bell sound using a non-integer ratio. Experiment with different ratios: 1.41, 2.76, 3.14, 7.5. Each produces a different bell character. Notice how even small changes in the ratio dramatically alter the sound — this sensitivity is both FM’s power and its challenge.
• Download Dexed (free from KVR Audio). Load some classic DX7 patches — the factory ROM set is a good starting place. For each sound you find interesting, look at the algorithm, the ratios between operators, and the envelope shapes. Try to understand why the patch sounds the way it does based on what you have learned in this chapter.
• Try building a three-operator chain: operator C modulates operator B, which modulates operator A (carrier). Listen to how the added layer of modulation increases complexity. Adjust operator C’s amplitude to control how much of that additional complexity reaches the output.
• Build one sound that subtractive synthesis cannot produce — something metallic, inharmonic, or with a spectral evolution that does not follow a simple bright-to-dark arc. This is the exercise that will cement why FM exists alongside subtractive rather than replacing it.