Zoë Blade's notebook

FM synthesis

FM synthesis, short for frequency modulation synthesis, is a method of synthesis that involves modulating an oscillator's pitch at audible frequencies. John Chowning patented the technique (since expired), and licensed it to Yamaha, who produced a slew of FM synthesisers in the 1980s.

An oscillator generally has a pitch input that tells it which pitch to oscillate at. By combining the control voltages of a keyboard and an LFO, you can add vibrato, sweeping the pitch up and down around the played note. By combining the control voltages of a keyboard and another audio-range oscillator, you can add such a fast vibrato that it changes the shape the first oscillator makes, adding extra harmonics above and also below the fundamental harmonic.

In short, you can connect the output of one oscillator to the pitch input of another oscillator to get more intense sounds. The oscillator you hear is called the carrier. The one affecting it is called the modulator. The louder the modulator, the more intense the sound.

FM synthesis is usually implemented by pairing up each oscillator with its own envelope generator, so the volume of each note can change over time, as can the intensity of its extra harmonics. Yamaha called each combination of oscillator and envelope generator an operator. The more operators each voice has to play with, the more complex combinations you can make of shapes affecting each other.

Most FM synthesisers have either six operators per voice (as with the DX7 range), or four (as with the DX21 and TX81Z ranges). These can be connected together in various different ways, which Yamaha called the algorithm.

In a way, FM synthesis is simpler than subtractive synthesis, as you don't need to learn to use a filter. In practice, it's less intuitive, because "lowpass filtering the sound so that only the low frequencies get past" is easier to fathom than "making the modulator fairly quiet so that only a few harmonics are added".

It probably didn't help this fathomability that, as Yamaha were implementing a whole new method of synthesis anyway, they went full tilt and replaced the familiar ADSR envelope generator with a slightly more complex one. They also replaced the simple linear pitch value, a number that reflects how high the pitch is, with a more flexible curve. Great for expressivity and versatility, not so great for clarity.

Thankfully, the four-operator synths are a bit cut down in these regards too, with envelope generators that are only slightly more complex than the ADSR variety, and simple linear pitch tracking you can use to affect the envelope generators' speed and volume. This makes them at least slightly easier to understand and program.

Using two oscillators and envelope generators, you can experiment with very basic monophonic FM synthesis using an analogue modular synthesiser. (It helps if the carrier oscillator has a linear pitch input, which most don't.) For anything beyond that, it's only really feasible to implement FM synthesis digitally, given the need for multiple oscillators and envelope generators, and a lot of connections between them. If you want polyphony, remember you have to exactly match the whole setup for each and every voice, something purpose-built FM synths handle for you automatically.

It's no coincidence that FM synthesisers came out shortly after the microchip, pairing a custom design made for the purpose with a regular microprocessor to handle tasks like MIDI. On the downside, these synths tend to have a minimal interface that makes programming them even harder, but on the upside, they also tend to support MIDI very well, not only letting the note velocity affect different aspects of the sound, but also letting you tweak all the parameters remotely, from the comfort of a home computer with a friendlier screen, keyboard and mouse.

If you can bypass the awkward interface, and get past learning several new concepts at once (more complicated envelope generators, customisable nonlinear pitch tracking on the fancier models, and adding rather than removing harmonics by connecting oscillators to each other), FM synthesis can be wonderfully versatile and expressive. It can also be clear and delicate sounding in a way analogue subtractive synthesisers can't, allowing polyphony without cluttering up a mix.

In the twenty-first century, the main issue with FM synthesis is overfamiliarity. Yamaha put their FM sound chips in so many different devices, not least of which being the Sega Mega Drive, that you'll have to work hard to make your programs sound like interesting musical instruments rather than old videogames. Still, it's a whole other world of sounds, and worth exploring.


What I heard was something I had not heard with additive synthesis or subtractive synthesis, this life that was happening after you modulated those waves together... We were having the time of our lives. It was like being in a sandbox and making up stuff. After we got past trying to emulate what traditional instruments sounded like, then we started making up our own sounds. That, to me, was the most fun, and still is.

— Don Lewis, 2020[1]


  1. "Don Lewis — Programming the DX7" Rob Puricelli, Sound On Sound, Feb 2023





Modulation: FM synthesis | Frequency-shift keying | Frequency shifter

Types of synthesis: FM synthesis

FM synthesisers: DX7 | DX21 | TX81Z