Operators Are Standing By

Image placeholder title

Despite its age, FM (frequency modulation) synthesis remains a popular technique for desktop musicians. In fact, composers and sound designers have more choices than ever when it comes to FM. Native Instruments FM7, which has been around for several years, has recently been joined by Image-Line Sytrus and the Operator add-on for Ableton Live. In addition, numerous analog-style and modular synths offer basic FM as part of their sound palette.

Image placeholder title

FIG. 1: This figure shows an algorithm in Native Instruments FM7 with three modulator/carrier pairs. The audio outputs are in the bottom row, so any operator connected to that row by a vertical line is a carrier. The signals from modulators travel down and to the right to enter the modulation inputs of the carriers.

Though FM is capable of producing a wide variety of sounds, programming your own FM presets is not always easy. In this column, I'll cover the basics of FM programming, with an eye toward making useful sounds. If you're curious about the theory behind FM synthesis, see “Square One: FM Basic Training” in the April 1999 issue of EM and “Master Class: Smooth Operators” in the June 2003 issue; both are available at www.emusician.com.

It Takes Two

Most FM synths have either four or six operators. (An operator is a software construct that combines an oscillator and its amplitude envelope.) These are combined in various ways to produce complex sounds. An excellent way to start learning FM is to take a preset you like, and mute and unmute the operators one at a time to hear the contribution that each makes to the sound (see Web Clip 1). It's easier to hear what's going on if you also switch off any filters or effects in the preset.

The three most important characteristics of an operator are its frequency, its amplitude, and the shape of its amplitude envelope. Let's look at each in turn.

Changing the frequency of an operator affects the tone color in an immediately obvious way. To experiment with this, mute all but two of the operators, and make sure they're patched as a carrier/modulator pair. Give them both full-on organ-type envelopes (instantaneous attack and release), and set the amplitude of the modulator to a moderate value. (If the modulator also has a direct audio output, turn it down to zero.) Then experiment with the relative tunings of the two (see Web Clip 2).

Next, try slowly increasing and decreasing the amount of signal coming from the modulator (see Web Clip 3). As the modulation amount increases, the number of sidebands (sine wave components above and below the carrier frequency) in the signal increases, as does their loudness. At first, this may sound rather like raising and lowering the cutoff frequency of a lowpass filter. If you listen closely, however, you'll hear that some sidebands increase and then decrease in loudness while the amount of modulation increases steadily. The mathematical reasons for this are complex and have to do with phase cancellation. In general, though, increasing the amplitude of the modulator creates a brighter sound. At extremely high modulator amplitudes, frequency modulation produces so many sidebands that the composite waveform turns to noise.

Experiment with various envelope shapes for the modulator. An instant attack and quick decay back to zero produces a plucked sound. A modulator with a long attack time can add a subtle bit of color to the sustain portion of a tone (see Web Clip 4). By applying three modulators with different envelopes to a single carrier, you can change the carrier's harmonic spectrum in complex ways over the course of each note.

Slow Pitch

One feature found on some FM synths is the ability to change the pitch of individual operators under envelope or LFO control. Changing the pitch of one operator rather than changing them all together would cause the frequencies of the sidebands to become inharmonic, which produces a sound usually lacking in a clear pitch. Detuning one operator slightly from another, however, produces a pleasing chorused quality, much as it does in analog synthesis.

If your FM synth has only one general-purpose LFO, you can create a separate vibrato LFO by setting an operator to a low, fixed frequency and using it to modulate other operators. This works because FM synthesis is based on the same concept as vibrato. The main difference is that most FM patches have modulating waves that are in the audio frequency range (above 20 Hz).

Advanced FM Techniques

Controlling the amplitude of a modulator from MIDI Velocity is extremely useful. Because each modulator can add different partials to the tone, playing harder and softer can change the timbre in ways that would be extremely difficult to duplicate using an analog-style filter.

Instead of tracking the keyboard, an FM operator can be tuned to a fixed frequency. Tuning a modulator to a fixed high frequency can add formants to the tone (see Web Clip 5). A formant is a frequency or a group of frequencies that doesn't change as the fundamental changes. Another option is to tune the carrier to a fixed subaudio frequency (around 1 Hz). That will give the tone of its modulators a rolling chorused quality (see Web Clip 6).

Classic FM uses sine waves for both the carriers and modulators. But as early as the Yamaha TX81Z (a 4-operator module that was released soon after the original DX7), operators with a choice of waveforms were provided. Choosing anything but a sine wave as a carrier or modulator multiplies the number and intensity of the sidebands, because each overtone in a more complex wave serves as a separate carrier or modulator, generating new sidebands that are added to the mix.

If the carrier is tuned to a high frequency and the modulator to a lower one (though still above 20 Hz), the modulator will provide the fundamental for the composite waveform. If you place an envelope on the modulator's amplitude, the carrier's high tone will be left exposed as the modulator decays toward zero (see Web Clip 7). This technique can be used to emulate the sound of an electric guitar feeding back.


The operators in an FM synth can be configured in a number of ways. For instance, with only four operators you can have either two carrier/modulator pairs, one modulator affecting three carriers, or three modulators all affecting one carrier. These configurations are called algorithms. Some FM synths have a fixed set of algorithms that the user selects from, while others allow users to design their own algorithms.

Choosing the right algorithm is an essential part of FM sound design. For a rich pad sound, you'll want three carriers that are slightly detuned from one another. Many bass sounds, on the other hand, use only a single carrier, because the phase cancellation caused by detuning can cause a bass to lose punch.

On Track

Another feature of FM synthesizers that dates back to the early days is keyboard tracking. When a keyboard-tracking curve is applied to an operator, its output has a greater amplitude in one region of the keyboard than in another.

Keyboard tracking can tame the output of an operator in a region where it would create too many prominent sidebands. Reducing a modulator's amplitude at the low end of the keyboard, for example, produces bass notes with fewer overtones, which is helpful because it prevents the bass from overpowering instruments that are playing in the midrange. Many acoustic instruments sound quite different in different pitch ranges, so keyboard tracking is useful in emulating acoustic instruments using FM.

Reducing the modulator's level at the high end of the keyboard helps prevent aliasing (see Web Clip 8). Aliasing is a form of digital distortion in which the tone acquires new partials that are not harmonically related to the fundamental. The clangorous (bell-like) tones produced by aliasing can occasionally be useful for a special effect, but aliasing is generally undesirable. Aliasing is produced in FM synthesis when the modulation produces sidebands that are higher than the Nyquist frequency. (The Nyquist frequency is equal to one-half of the sampling rate. If the synth is operating at 44.1 kHz, the Nyquist frequency is 22.05 kHz.)

If you're curious about FM, there's no need to remain in the dark. Both FM7 and Sytrus are available in demo downloads. Freeware synths that do FM include Green Oak's Crystal (www.greenoak.com/crystal/download.html), which is cross-platform, and the Windows-only Oxe from Daniel Moura (www.oxesoft.com/products.php). FM is well suited to experimentation, so why not give it a try?

Jim Aikin has played and written about hundreds of synthesizers, but he still remembers the first day his ears were opened by a Yamaha DX7.