Today we discussed the basic concept of Frequency Modulation Synthesis, in which one oscillator is used to modulate the frequency of another. This is a type of synthesis first popularized in 1983 with the introduction of the Yamaha DX-7 series synths.

In subtractive synthesis and other synthesis methods, we have seen the use of an LFO to create a vibrato effect. This is done by sending the LFO's output to the pitch input of the audio oscillator. When creating the vibrato effect, the LFO typically uses a sine (or triangular) waveform and runs at a rate of 4-7 Hz. But what happens when the modulation rate is increased to audio frequencies?

This question was asked by a Professor at the Stanford Artificial Intelligence Laboratory, John Chowning, in a paper published in the Journal of the AES, entitled The Synthesis of Complex Audio Spectra by Means of Frequency Modulation (September 1973, Vol. 21, No. 7). Chowning discovered that very rich and complex tones could be created with only two sinewave oscillators.

When a carrier oscillator at frequency "C" is modulated by an oscillator at frequency "M," a number of "sideband" harmonics are added, similar to the sum and difference tones of Ring Modulation. In addition to the original frequency, C, sidebands occur at C+M, C+2M, C+3M... as well as C-M, C-2M, C-3M, and so forth. Adding more modulation depth increases the number of sidebands. Any sidebands that would result in negative frequency values "reflect" back into the audio frequency domain. While you would be correct to assume there is a lot of math at the heart of it, the important point to take away from all of this is that FM synthesizers exhibit unusual, but predictable, behavior.

Sideband Frequencies (in blue)

Martin Russ discusses FM in depth (Section 5.1, pp. 224-241) but he breaks it down to the essentials on page 230. The basic timbre of the resulting sound is a function of the frequency ratio between the Carrier and Modulator (C/M) and the Depth (D) of the modulation level. Typically, each oscillator has its own ADSR Envelope Generator. The carrier's ADSR functions as you'd expect, but the Modulator's ADSR determines the rate of timbral change—not amplitude change—since it affects the amount of signal (D) sent to modulate the Carrier.

As an example, say the Carrier is set to the fourth harmonic of the keyboard pitch, and the Modulator is set to the second harmonic. This would produce half a dozen sidebands at modest modulation depth settings:

  • C = 4
  • (M = 2, not audible)

  • C + M = 6
  • C + 2M = 8
  • C + 3M = 10
  • C - M = 2
  • (C - 2M = 0, below audio range)
  • C - 3M = (-2, reflects back to audio range) = 2

We would hear harmonics 2, 4, 6, 8 and 10, with #2 twice as strong. If we maintain this same frequency ratio as we play different pitches on the keyboard, the timbre will stay consistent from note to note. Note also, that the process adds harmonics as the Depth of modulation increases. FM is quite different from subtractive synthesis in that it starts with a sine wave (when modulation depth is zero) and increases in harmonic complexity as modulation is increased. For this reason, most FM synths have no filtering (although there are a couple of later Yamaha models that use LPF's to rein in excessive content). If the sounds you create are too bright, you could always insert an LPF after the FM synth.

One type of sound that FM synthesizers excel at are Bells and other metallophones. Metal objects tend to generate harmonics that are not multiples of a common fundamental frequency. This is easily achieved by setting the Carrier:Modulator ratio to a non-fractional relationship, such as 2:5.647298. Many instruments are easily recreated in FM such as: Chimes, Church Bells, Glockenspiel, Vibraphone (Vibes), Electric Piano (Rhodes), Cowbell, Agogo, Finger Bells, Anvils, Triangles, and so forth.



Nobody really knows how to program FM synths! Sure, some lab-coat wearing geek might be able to bend your ear for an hour about the FC:FM ratio and the Index of Modulation and Bessel Functions and so on, but when it comes down to it, most FM programmers just sit down and experiment until they find something that sounds good.

Often when I use a subtractive synth, I might wail on a control and say "What does this control do?" After I push a knob to its extreme, I'll reduce the amount of it to something more realistic. With FM synthesis, moving one knob just one notch can have a huge impact on the sound of the patch. So instead of experimenting wildly, I simply experiment in a careful, controlled way. Logic's EFM-1 has a randomize function just like the ES-2. Here, however, I tend to randomize by a small percentage to keep the sound somewhat similar to the original texture.

Also, be sure to experiment with slight detuning of the Carrier and Modulator. This can really liven up a patch if done tastefully. The EFM-1 also has a Stereo Detune function to thicken up the sound. If you send a tiny bit of ADSR via the Modulator Pitch knob, you can create dynamic detuning effects.

I would like you to create three patches for the EFM-1.

Assignment: create a minimum of three interesting patches that you would actually use in your own music for the EFM-1. Due next class, March 13th.