Vibrato is one oscillator gently wobbling the pitch of another, a few times a second. Speed that wobble up until it is itself a note, and the sound stops wobbling and changes colour instead: new overtones appear that were in neither oscillator. That is frequency modulation, FM, and it was found by ear.
An evening in 1967
John Chowning was a percussionist working at Stanford's new artificial intelligence laboratory on how to move a sound around a room. For that he needed sounds with some internal motion, so one evening in the autumn of 1967 he set up two sine oscillators on the mainframe, one altering the pitch of the other for vibrato, and pushed the rate and depth past anything a hand could do. Out came tones he had not programmed. He has said since that it was a discovery of the ear, not of equations; he took it to a maths student afterwards to find out why. He published the method in 1973 in the Journal of the Audio Engineering Society, volume 21, pages 526 to 534.
Carrier, modulator, sidebands
The oscillator you hear is the carrier; the one bending its pitch is the modulator. Modulating the carrier's frequency adds sidebands: new components at the carrier frequency plus and minus every whole-number multiple of the modulator frequency. Two knobs set what you get.
| Setting | What it does | Sets |
|---|---|---|
| Ratio (C:M), the carrier's frequency against the modulator's | Whole-number ratios such as 1:1, 1:2 or 1:3 put the sidebands on a harmonic series, so the result sounds like a pitched note. Ratios that are not whole numbers scatter them: bells, metal, clangs | Where the overtones fall |
| Modulation index, how far the carrier's pitch swings divided by the modulator's frequency; in practice, the modulator's level | Low, and only the nearest sidebands matter, close to a plain tone. Raise it and more sidebands appear and the original carrier fades | How many there are |
Put an envelope on the modulator's level and the index moves over the life of the note: bright at the attack, plain by the end. That is the FM electric piano, the FM bass and the FM bell in one sentence.
Keeping those ratios exact is the catch. Analogue oscillators drift, and a ratio that is nearly 1:2 sounds nothing like one that is exactly 1:2, which is why FM is almost always done digitally.
Operators and algorithms
Draw an oscillator together with its envelope as one block and call it an operator. A two-operator FM patch is one modulator feeding one carrier. Yamaha's DX synths carry six sine-wave operators per voice and 32 fixed wirings of them, the algorithms: in algorithm 1, operator 2 modulates carrier 1 while operators 6, 5 and 4 modulate each other in a chain down to carrier 3. Modulators can modulate modulators, and the outputs of several carriers are simply mixed. Yamaha's own additions were feedback, an operator's output routed back into its input for more harmonics without more operators, the 32 algorithms themselves, and velocity control.
From a mainframe to the DX7
| What happened | When |
|---|---|
| Chowning hears the effect at Stanford | 1967 |
| The method is published in the Journal of the AES | 1973 |
| Stanford offers the patent to US organ makers; none take it. Yamaha licenses it | Early to mid-1970s |
| Yamaha's first FM product, the Electone F70 organ, seven years after the licence; the GS1 keyboard follows with two four-operator FM voices | 1981 |
| The DX7: six operators, 32 algorithms, sixteen-note polyphony, a velocity-sensitive five-octave keyboard | 1983 |
| The Stanford patent expires; by then it had earned the university about 20 million dollars | 1995 |
The DX7 sold more than 200,000 units, the first synthesizer past 100,000, and was the first commercially successful digital synth. Few people learned to program it, so its presets did the work: the E Piano 1 sound on the power ballads, the Bass 1 on "Danger Zone". Brian Eno was one of the few who went deep, and shared his patches in Keyboard in 1987.
Sources
Every date, name, figure and definition on this page comes from these pages, read on 2026-11-05.
- Yamaha: Discovering digital FM, John Chowning remembers
- CCRMA, Stanford: The synthesis of complex audio spectra by means of frequency modulation (1973)
- Sound On Sound, Synth Secrets: An introduction to frequency modulation
- Sound On Sound, Synth Secrets: More on frequency modulation
- Wikipedia: Frequency modulation synthesis
- Wikipedia: Yamaha DX7