FM synthesis

The synth below has two sine waves in it. One you hear. The other you don't hear at all: its only job is to bend the first one, hundreds of times a second. Hold the note and raise Op 2 Level slowly. A plain flute-like tone grows a reedy, hollow edge.

Now switch Op 2 Ratio from 2.00 to 1.41. Before you do: will the note get brighter, change pitch, or turn into a different kind of instrument?

What just happened?

At ratio 1.41, the note stopped sounding like an instrument that plays notes and started sounding like something struck: a bell, a gong, a glass. Nothing random happened. Two plain sines, a fixed ratio, and the result is completely repeatable. Play it again and you get the same bell.

This is FM synthesis: frequency modulation. In the LFO guide you sent a slow wobble to a note's pitch and heard vibrato. You may also have pushed that wobble to 20 Hz and heard it stop being a wobble and start being a growl. FM takes that idea all the way. When one oscillator bends another's pitch hundreds or thousands of times a second, you can't hear the bending any more. You hear new frequencies instead, a new tone colour.

The two oscillators get names. The one you hear is the carrier. The one doing the bending is the modulator. FM synths call each one an operator, a sine oscillator with its own level and envelope, and the wiring between them an algorithm. In the lab, operator 2 modulates operator 1, and operators 3 and 4 are switched off. The diagram under the synth shows the arrows.

Ratio decides where the new frequencies land

When a modulator bends a carrier, new frequencies called sidebands appear on both sides of the carrier, spaced apart by the modulator's frequency. With a 100 Hz carrier and a 200 Hz modulator (ratio 2), they land at 100 plus or minus 200, 400, 600 Hz and so on. The ones that would fall below zero fold back up, and everything lands on 100, 300, 500, 700 Hz.

Look at those numbers: odd multiples of 100. That's the recipe of a square wave, from the oscillators guide. Ratio 2 gives you a hollow, square-like, clarinet-like tone. Ratio 1 would give every multiple, the saw's recipe, for a brassy, buzzy tone.

Now change the modulator to 141 Hz (ratio 1.41, which is the square root of 2). The sidebands land at 41, 100, 183, 241, 324, 383 Hz. Those don't fit any harmonic series a note could have. Your ear hears a cluster of unrelated pitches ringing together, and that's exactly what a bell is: a bell's partials aren't neat multiples of one note either.

So non-whole ratios aren't chaos. They're a precise way of placing frequencies where no harmonic would go. Try the other ratios in the lab: 3.00 and 4.00 stay pitched and get brighter; 1.50 sits somewhere in between, because its sidebands fit a harmonic series an octave below the note you played; 2.83 and 3.53 ring metallic.

Level decides how many you hear

On the modulator, Level isn't volume. It's how hard the modulator bends the carrier, often called the index. A little bending makes a few faint sidebands near the carrier. More bending spreads energy into more sidebands further out, so the tone gets brighter and more complex.

But it doesn't just get "more". Raise Op 2 Level slowly all the way and watch the spectrum: individual sidebands don't simply grow. Some rise and then dip while others take over, so the balance keeps shifting. The sound passes through sweet spots and thin spots. That's why FM can feel tricky to program: the brightness knob isn't a straight line. It's also why FM sounds so alive when that knob moves.

The secret: let the colour decay

Here's what makes FM sound like real instruments. Give the modulator an envelope that fades quickly, while the carrier keeps sounding. The note starts bright and complex, all sidebands, then settles toward a pure sine as the bending dies away. That's how a struck or plucked note behaves in the real world: bright at the moment of impact, mellower as it rings.

It's also the sound of the 1980s. John Chowning worked out FM synthesis at Stanford in the late 1960s, and Stanford licensed it to Yamaha. In 1983 the Yamaha DX7 put it in the hands of everyone. It had six operators and 32 algorithms, and its bright, bell-tinged electric piano preset turned up on countless ballads of the decade.

A few years later, a simpler four-operator FM chip gave the Sega Mega Drive (Genesis) its punchy, metallic soundtrack sound.

Like the DX7, the synth on this page bends phase rather than frequency directly, which is the practical way to do FM and sounds the same.

Start with Op 2 Decay at 2 seconds: a bright, steady, organ-like bass. Bring it down toward 0.2 seconds and every note now opens with a snap and falls into a round, warm body. You didn't touch the volume shape at all. Only the colour moves, and your ear hears it as a pluck.

Where it breaks

Too much index. Push the modulator level very high and the sidebands spread so wide that the tone turns to harsh, noisy hash. That can be exactly right for an aggressive growl, but on a bass it eats the low end. If a patch suddenly sounds thin, back the level off: you may have stepped past a sweet spot.

Too high a note. Bright FM patches throw sidebands far above the note. Play high enough and those can exceed what digital audio can hold, and fold back as sour, unrelated tones. A patch that's clean on low notes needs a listen at the top of its range.

Static colour. An FM patch with no envelope on the modulator sounds like an organ, which can be lovely. If your FM patch sounds lifeless, the first thing to try is a decaying modulator, not more operators.

Same idea, different place: ring modulation multiplies two signals and creates sidebands too, just one pair: the sum and difference of the two frequencies. FM makes a whole family of them. That's why a ring modulator sounds like a single metallic shimmer and FM can sound like a bell with a dozen partials. See Frequency shifting.

Make it yours

Make a bass for something you're working on. Keep both ratios at 1.00 for a solid, pitched low end. Set Op 2 Decay so the snap lasts about as long as your groove's shortest notes. Then reveal Vel → Index, which makes harder-played notes bend more. Press the buttons and play the keyboard soft and hard: a strong hit should come out brighter and more aggressive, a soft one rounder. That's what makes an FM bass feel played instead of programmed.

If you want more edge, open the full panel and try Op 2 Ratio at 2.00 for a hollow, slightly honky bass, or 3.00 for a brighter, more metallic attack. When you like it, open FM Keys from the link at the top of the lab, which carries your settings, and save it as your bass.

Quick check

1. You turn up a knob labelled Level on an FM synth and the sound gets brighter but hardly louder. What is that operator doing? It's a modulator. Its level sets how hard it bends a carrier, so it changes colour, not volume. Carriers are the operators you hear directly.
2. A friend says "non-whole ratios make FM random." You set ratio 1.41 and play the same note ten times. What happens, and why does it sound metallic? The same bell, ten times. The sidebands land at fixed frequencies between the harmonics, which is exactly what makes bells and metal sound like bells and metal.
3. Your FM electric piano sounds like an organ: bright and steady from start to end. Which envelope would you change, and how? The modulator's. Give it a fast decay and low sustain so the brightness fades while the carrier keeps ringing.

Next steps

• Go deeper: Wavetable synthesis. FM moved the colour by moving the index. Could you store a whole journey of colours and just scan through it?
• Explanation: Envelopes. The time shapes that made the colour decay.