FM Synthesis

FM synthesis is short for frequency modulation synthesis. Simply put, FM synthesis uses one signal called, the “modulator” to modulate the pitch of another signal, the “carrier”, that’s in the same or a similar audio range. This creates brand new frequency information in the resulting sound, changing the timbre without the use of filters.

FM synthesis can create both harmonic and inharmonic sounds. To synthesize harmonic sounds, the modulating signal must have a harmonic relationship to the original carrier signal. As the amount of frequency modulation increases, the sound grows progressively complex. It was discovered in the 1967 experiments of John Chowning at Stanford University. At first, Chowning was using complex waveforms to modulate the pitch of simple sine waves. This resulted in supersonic signals at frequencies over a million Hertz.

[FISEA 1988] Workshop: John Chowning, Zack Settel & Ernst Bonis – FM-Synthesis/Psycho-acoustics.

Yamaha's engineers began adapting Chowning's algorithm for use in a commercial digital synthesizer, adding improvements such as the "key scaling" method to avoid the introduction of distortion that normally occurred in analog systems during frequency modulation, though it would take several years before Yamaha released their FM digital synthesizers, the massively popular Yamaha DX7. And thus, FM synthesis was born.

Yamaha had patented its hardware implementation of FM in the 1970s, allowing it to nearly monopolize the market for FM technology until the mid-1990s. Casio developed a related form of synthesis called phase distortion synthesis, used in its CZ range of synthesizers. It had a similar (but slightly differently derived) sound quality to the DX series. Don Buchla implemented FM on his instruments in the mid-1960s, prior to Yamaha's patent. His 158, 258 and 259 dual oscillator modules had a specific FM control voltage input, and the model 208 (Music Easel) had a modulation oscillator hard-wired to allow FM as well as AM of the primary oscillator. These early applications used analog oscillators, and this capability was also followed by other modular synthesizers and portable synthesizers including Minimoog and ARP Odyssey.

Yamaha DX7, manufactured from 1983 to 1989.

With this brief history in mind, let’s look at how exactly FM synthesis works, and why you may want to use it when designing new sounds.

The simple waveforms in an FM synth are produced by something called an ‘operator’. Operators are essentially just oscillators and the number available per-voice depends on the particular FM implementation; six-operator and four-operator are the most common variants. The simple waveforms an operator can produce also depends on the FM implementation, but for the purposes of this discussion, we’ll stick with sine-wave operators, as these are common to all implementations.

Furthermore, these operator groups then interact amongst each other. Each operator is generally set up the same way, and the arrangement of the operators helps determine the final output of the synthesizer. Let’s look at how an individual operator is constructed:

Operators connected to the output are called ‘carriers’ – these are the operators that you actually hear. Operators connected only to other operators are called ‘modulators’ and their output is not directly audible. Most algorithms also provide the facility for one operator to be fed back to an earlier point in the algorithm’s chain.

Most FM synthesizers have at least four available operators. While synths may vary in their functionality, most will allow various ways to arrange these operators.

The way that these operators are arranged is called the algorithm. Some have preset algorithms, while others can create custom ones.