In 1983, FM synthesis was the Next Big Thing. By 1993, it was as dead as last week's newspaper. FM synths were popping up in garage sales and at flea markets.

Fast-forward to 2006:

It's ba-a-a-ck.

Why the change? Several reasons.

In the late 1980s, FM (frequency modulation) was supplanted by sample-playback keyboards. (A sample is a brief digital recording.) While these instruments were superior to FM at producing certain types of realistic sounds, such as string sections, after a few years musicians began to realize that sample playback is an imperfect technology as well. For one thing, a sample is pretty much set in stone, so it doesn't respond well to real-time control inputs.

Second, FM is a versatile, efficient way of producing a huge variety of sounds. It's superior to sample playback when it comes to responding to MIDI velocity (how hard you strike the keys), which is the most important factor in expressive playing. This is because velocity changes can alter an FM tone in many different ways, not just by making it louder and/or brighter.

Yamaha DX7

The Yamaha DX7, released in 1983, became the most popular synthesizer in history thanks to its distinctive FM sound. Though stripped-down versions of its technology in early soundcards and cell phones gave FM a bad name, today's software FM synths are pushing the sonic frontier again.

That FM Sparkle

FM is a general-purpose synthesis method, and can handle almost any musical task. But it's especially good at producing sounds with crisp high-end detail. That makes it an excellent choice for emulating mallet percussion (marimba and vibraphone), steel drums, and electric piano. The bell-like Rhodes sound in the Yamaha DX7 was so heavily used in 1980s pop recordings that it became a clich≥. Plucked sounds, such as jazz guitar and round-wound electric bass, are also easy to generate with FM.

You can hear the DX7 presets on Synth Mania's DX7 page. For a more musical context, listen to the Yamaha PLG150-DX demo song.

Yamaha PLG150-DX

Yamaha's PLG150-DX daughterboard brings the crisp, expressive DX7 sound to select host synthesizers.

Modern FM synths include resonant filters and a choice of waveforms, which allows them to produce many of the timbres associated with analog synthesis. However, oscillator sync and oscillator pulse width modulation, two of the popular techniques for tone color animation in modeled analog synths, are not possible with FM.

Third, now that computers are fast enough to do real-time synthesis, software developers search eagerly for ways to make good-sounding tones. FM is relatively easy to implement in software.

Fourth, while Yamaha owned the patent on hardware-based FM, which meant that until recently no other manufacturer could offer competing FM instruments, nobody owns FM when it's running on a computer. Each developer can put a fresh spin on the FM concept.

In this article, I'll explain how FM synthesis works, how can you program your own sounds, and how to choose from the four leading FM-based softsynths. For more background on what makes FM special, see the sidebar "That FM Sparkle."

FM in a Nutshell

Most real-world sounds are complex. That is, they contain numerous partials. (A partial is sound energy at a particular frequency.) We can identify sounds, such as an oboe or clarinet, because our ear and brain effortlessly detect and decode the frequencies and relative loudness of the partials.

Together, the partials in a sound make up its timbre, or tone color. Typically, the loudness balance of the partials in a sound changes over time, thus giving each note an expressive shape.

One way to produce complex timbres is to record and play back actual sounds. This technique is called sampling. Frequency modulation (FM) synthesis takes a very different approach. In FM, one simple sound--often a sine wave, which is the simplest sound of all--is used to modulate (alter) another equally simple sound. The results can be surprisingly colorful and varied. Figure 1A shows a sine wave.

In its simplest form, FM requires two oscillators. One oscillator, called the carrier, is the one whose output we hear. The other, called the modulator, is not heard directly. Instead, its output is used to modulate the frequency of the carrier.

Again, "modulation" is just a fancy word for "change." In frequency modulation, it's the frequency of the carrier that increases and decreases. The output of the modulator is a waveform, which means it has peaks and troughs. When the modulator's waveform is at a peak, the carrier's frequency will rise. When the modulator's waveform is at a trough, the carrier's frequency will fall.

This effect is most clearly visible in Figure 1B. In this figure, we're looking at the carrier's waveform, not the modulator's. Where the modulator's wave is in a trough, the carrier's wave spreads out. (In other words, its frequency drops.) Where the modulator's wave is at a peak, the carrier's wave bunches up. (Its frequency rises.)

If the modulator is in the sub-audio range (below about 20Hz), we can actually hear the frequency of the carrier rise and fall. This type of FM is well known--it's called vibrato. But when the frequency of the modulator is faster, we can no longer hear the fluctuations in pitch. Instead, what we hear is a change in the tone color of the carrier. (Listen to Example 1.) This phenomenon is perhaps a bit like looking at stills from a film: if one image replaces one another slowly enough, we see them as separate, but when the images replace one another quickly, we have the illusion that we're seeing continuous movement.

The tone color produced by a carrier/modulator pair depends on three things: the amplitude of the modulator (that is, how much modulation is being applied), the ratio between the frequencies of the two oscillators, and the waveforms selected for them. The relationships among these factors are complicated, and involve college-level math. For everyday musical purposes, though, it's enough to know that as the amplitude of the modulator increases, the waveform produced by the carrier will acquire more and stronger partials. In other words, cranking up the amplitude of the modulator increases the brightness and complexity of the resulting waveform.

Fig. 1: FM Waveforms

Figure 1. As the frequency of the modulator increases, the waveform of the carrier changes. All four of these images show the same sine-wave carrier, and all are at the same zoom magnification. The only change is in the frequency of the modulator, which increases progressively in B, C, and D. This waveform, captured in Steinberg Cubase SX 3, is heard in Example 1.

Try It

The easiest way to begin to understand FM synthesis is to try changing the frequencies of the carrier and modulator and the strength of the modulator for yourself and listen to the results. If you have access to an FM-capable synth, follow these steps:

  1. Turn off all effects.
  2. Turn off all but two of the oscillators. Give each of them an organ-type envelope (instant on, full sustain level, instant off).
  3. Configure the synth's signal routing scheme so that one of the two oscillators is the carrier and the other is the modulator.
  4. Tune both oscillators to the same frequency.
  5. While playing a note to hear the result, gradually increase the amount of the modulator.
  6. Retune either of the two oscillators to a different frequency, and listen again.

Example 3 is an identical phrase played with five different carrier/modulator ratios--1:1, 2:1, 5:1, 1:9, and 13:9.

Need a synth to get started? If you have a program that can act as a VST host, you can download a demo of LinPlug Octopus, install it, and put this patch (4K .zip file) in the appropriate folder. (In Windows, you'll find the Octopus Data/Banks folder in your VST plug-ins folder.) For links to more FM synths, see the sidebar "More FM Goodness."

LinPlug Octopus

Figure 2. After launching the Octopus demo, you can experiment with FM by adjusting the indicated parameters. The value in the grid (A) controls the level of oscillator 2 (the modulator) applied to oscillator 1 (the carrier). After selecting either oscillator 1 or oscillator 2 for editing (B), you can adjust its tuning with the ratio parameter (C). You can add overtones to the waveform using the Amplitude graph (D). (Click to enlarge.)

Real FM Patching

Before we go further, we need to distinguish between a real FM synth and a synth that gives you a little FM in combination with other ways of making complex tones. If your synth has a knob in the oscillator section labeled "FM," it's in the latter category. You'll be able to try the experiment above with such a synth, and the presence of the FM knob undeniably increases the instrument's palette of sounds, but creating the complex timbres available in real FM synths won't be possible.

A basic FM synth has at least four oscillators. Many instruments have six or more. Typically, each oscillator is paired with its own envelope generator, which controls the oscillator's output amplitude. The oscillator and envelope together are called an operator.

By giving a modulator a different envelope, you can change the tone of the carrier during the course of the note. This is the key that unlocks the mysteries of FM programming. For instance, three modulators with different tuning and different-shaped envelopes might all be modulating the same carrier at the same time. This would produce complex tone color changes in the carrier during the course of each note.

Giving a modulator a different envelope is the key that unlocks the mysteries of FM programming.

All FM synths allow the operators to be configured in various ways. For example, you might be able to set up three carrier/modulator pairs, or apply a single modulator to three different carriers. These configurations are called algorithms. Basic FM synths will give you a selection of fixed algorithms. More capable instruments allow you to create your own algorithm using a completely user-configurable signal-routing matrix. But there are no rules that will tell you which algorithms to use for which types of sounds--experimentation is the key.

Yamaha's original FM instruments, manufactured in the 1980s, lacked filters. But most modern FM synths include analog-style filters and other advanced features. The operators in early FM synths generally produced only sine waves (though Yamaha's rackmount TX81Z had a choice of eight different waveforms). The ability to create your own waveforms is a feature of two of the instruments in our roundup. You do that by separately defining the amplitudes of a number of different harmonics, as in additive synthesis. Example 4 illustrates both a carrier with an additive waveform and a very short attack transient created by a modulator whose envelope has an instant attack and a quick decay to zero.

Many FM synths employ operator output scaling to allow various regions of the keyboard to have different tone colors. (For example, you might set the level of a particular operator to increase as you play higher notes, brightening the sound.) Another important feature of modern FM instruments is the ability to define rhythmic multi-segment envelopes. You can use these to generate complex patterns by holding a single key on the keyboard.

Four Top FM Softsynths

The four software instruments described below all specialize in FM synthesis, but while they're popular, convenient, and good-sounding, they're not the only options. For example, the Alesis Fusion keyboard includes a full implementation of six-operator FM, and Yamaha offers an FM plug-in board (the PLG150-DX) for their Motif keyboards.

Ableton Operator ($149)

Operator is a basic four-operator, one-filter synth. It's available as an optional add-on for Ableton's popular Live music production software, and can be used only in Live, not in other hosts. Operator has other significant limitations, as well. Its ability to respond to real-time controllers arriving via MIDI is less than adequate, and it's the only synth in our roundup that provides fixed algorithms rather than letting you roll your own. Its envelopes can do loop playback, but they're ADSRs (attack-decay-sustain-release), and can't be programmed with extra segments.

The main advantages of Operator are that it has an excellent library of presets (many of them programmed by my colleague Francis Preve) and that it integrates well with Live. Live's handy device group feature, in which a plugin instrument is linked with plugin effects in a preset that can be recalled with a single click, works only with Ableton's own instruments, not with third-party software.

Fig. 3: Ableton Operator

Figure 3. Ableton Operator has four operators (on the left), graphically editable ADSR envelopes (center), and a multimode filter (center right). The four colored boxes in the bottom gray rectangle on the right show the currently selected algorithm; modulators are in the top row, and the carrier is in the bottom row.

Image-Line Sytrus ($179)

It's a close call, because Octopus is excellent as well, but on balance, I feel Sytrus is the best instrument in this roundup. Unfortunately, it's not available for the Mac OS. Sytrus has six operators, three multimode filters, and effects (three highly programmable waveshapers, a rich multi-voice chorus, a full-featured reverb, EQ, and three delay lines). You can define up to 128 overtones in the waveform editor, which also includes parameters for things like tension and skew. Plucked-string synthesis is part of the package, as are ring modulation (RM) and a two-dimensional mousable control surface.

One of Sytrus's strengths is its generous complement of envelopes and LFOs (more than 50 of each). You can copy and paste envelopes, and the program includes numerous templates to aid programming. Sytrus's arpeggiator is versatile, though it's implemented in a way that makes it less than intuitive to program: the break points of looping envelopes can be defined as arpeggiator steps.

Fig. 4: Image-Line Sytrus

Figure 4. Image-Line Sytrus has dozens of envelopes and LFOs. After selecting an operator (top row), you choose the aspect of its operation that you want to control (PAN, VOL, MOD, etc.; second row) and then edit the envelope, LFO, keyboard scaling curve, velocity scaling, response to the two-dimensional X/Y controller, and so on. The matrix at the right routes signals from one operator to another, or to and from the filters.

LinPlug Octopus ($149)

The prize for most oscillators (eight) goes to Octopus (see Figure 5). This synth also has a sample playback oscillator, whose output can either be listened to or used as an FM modulator, plus two filters and a waveform designer with 32 overtones.

Rather than pair oscillators with envelopes in hardwired operators, Octopus defines its envelopes (up to 32 of them) in a separate part of the panel. A given envelope can be used to control the outputs of many oscillators at once. This makes for an efficient use of DSP resources, but makes Octopus a bit more difficult to program, even than other FM synths. Octopus has no LFOs; instead, looping envelopes are used for LFO-type control.

Also included in the feature set are chorus, delay, reverb, EQ, a pair of step sequencers, and the ability to load microtuning files. (A huge assortment of tunings is included.) In its 1.1 release, Octopus is not entirely free of bugs, but it also has a lot going for it.

LinPlug Octopus

Figure 5. LinPlug Octopus packs eight oscillators, each with adjustable feedback. (Click to enlarge.)

Native Instruments FM7 ($339)

The first software-based FM synth, FM7 is closely patterned on the venerable Yamaha DX7 in certain respects, from the controller input implementation to the panel graphics. FM7 is the oldest instrument in this roundup, and set the standard in the field with its multi-segment envelopes and the use of a freely configurable algorithm matrix. Only 32 preset waveforms are provided, and FM7 has one dual-filter module rather than two or three separate filters. A distortion "operator" is included; the only other effect is a delay line.

Like Sytrus, FM7 can load DX7 patches in a system-exclusive file format. Thousands of these patches are readily available online (though the quality of the free downloads is not uniformly good).

You can run FM7 as a standalone softsynth or as a VST effect plugin rather than as a synth. (Whether these capabilities justify the high price is for you to decide.) When it's operating as a plugin, the audio input can either be processed by its distortion and filters or used as a carrier or modulator. That's useful for producing a variety of metallic and distorted effects; the main limitation is that most VST effects can't receive MIDI note messages from the host. An important exception is Mackie Tracktion, which would be an excellent host for FM7 or any other plugin synth that has audio inputs for effect use, because it can route MIDI directly to effects.

Native Instruments FM7

Figure 6. The sliders and buttons on Native Instruments FM7 look a lot like those on a first-generation Yamaha DX7. You select operators with the buttons along the top. The graphic area on the right can be switched from the envelope-and-keyboard-tracking display (shown) to the algorithm matrix. (Click to enlarge.)

You Ought to Be on FM

FM synthesis is a complex subject. In this brief article we've only scratched the surface. The good news is, if you'd like to explore FM, you have more good software options than ever before. Today, a good FM synth is capable of both analog subtractive synthesis (similar to old-style Moog and ARP instruments) and a basic form of additive synthesis (building up a complex tone by stacking overtones manually). Thus, it's a worthy choice for almost any musical task, especially when you're looking for an extra helping of expression or sparkle.

Cyndustries Zeroscillator

More FM Goodness

ThMan's All Free VST Plugins Database has links to scads of FM softsynths, though most are Windows-only.

OPLX features links and information about the OPL FM chips that voice millions of cell phones and Sound Blasters.

Feeling handy? Here are directions for building a hardware FM synth based on OPL chips.

And for analog FM experimentation, there's the Zeroscillator from Cyndustries (at right).

David Battino

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