Fee, Fi, Fo, FM: Explore the World of FM Synthesis
Pages: 1, 2, 3, 4

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.

• Example 3. Changing the ratio (392K MP3)

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."

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.

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.

• Example 4. Timbre envelope (84K MP3)

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.