Are you looking to beef up your understanding of FM synthesis? Are you at a complete loss when sitting down to program an FM synthesizer? In this article, we’ll dive into the power of FM synthesis and demystify the complexity of this breakthrough technology.
History
The earliest record of Frequency Modulation synthesis can be traced back to the mid-1960s, when Don Buchla implemented the technology in his analog modular setups. Analog FM is a powerful sound-design tool, but it was difficult to keep it stable, especially when playing up and down the keyboard. FM as we know it today was created by university professor Jon Chowning, at Stanford University, in 1967, and later patented in 1975. The initial design was intended for radios to transmit voice by modulating one waveform’s frequency with another, hence the name “FM” radio.
Yamaha licensed the technology and began adapting it for use in a commercial digital synthesizer, adding several enhancements including key scaling, which allowed for the sounds to remain stable over multiple octaves. In 1983, Yamaha released the DX7, which became the ubiquitous sound throughout the ’80s. When the patent expired in 1995, digital FM synthesis could be freely implemented by anyone. FM synthesis can frequently be heard in popular music, movie soundtracks, video games, cell phones.
Today, the most popular form of FM is found in software, such as Native Instruments FM8, Logic Pro EFM1, and Ableton Live Operator. However, there has been a resurgence of hardware synthesizers and you can find several manufacturers embracing FM synthesis, including the Yamaha Montage and the Korg Kronos. Even the Dave Smith Prophet 12 offers linear FM with four Operators. For more budget-minded, there are options, including the Yamaha Reface DX, the Korg Volca FM and the Elektron Digitone.
The Basics
FM synthesis is not all that complicated. It garnered a reputation for being difficult to program, which stems from the DX7’s menu-driven programming structure. Most musicians at the time of the DX7’s release were familiar with analog synthesizers. The DX7 used different terminology with a less “hands-on” approach and very few physical controls. If you are brand new to synthesis, please read the Guide to Analog Subtractive Synthesis, which covers a broad spectrum of concepts, including the properties of sound and the circuits of a synthesizer that allow us to control them.
An analog mono-synth can be broken down into a few circuits. The voltage-controlled oscillator (VCO) generates different types of wave forms with varying degrees of harmonic content (Saw, Square, Triangle, Sine). The signal is passed through a voltage-controlled filter (VCF), which removes and shapes the harmonic content, depending on the type of filter used (LP, HP, BP, and Notch). The signal is then passed on to the voltage-controlled amplifier (VCA), which controls the amplitude of the signal.
Additionally, there are typically two more circuits, the LFO and the Envelope Generator, which help shape and modify the VCO, VCF, VCA. The low-frequency oscillator (LFO) is like the VCO, because it generates a waveform, but at a rate that is usually below human hearing. By routing an LFO to the VCO, VCF, and VCA, we hear cyclical changes, which create staple effects such as vibrato, wah-wah, and tremolo. The envelope generator (ADSR) allows us to shape these same circuits over time. With longer attack and release times, an envelope is great for pads and strings, while shorter attack and release time are essential for percussion and bass sounds.
Conceptually, FM synthesis is essentially the same as an LFO modulating a VCO. However, if we raise the frequency of the LFO into audio rates, we don’t hear the cycling of pitch (vibrato effect), but rather a constant waveform with added harmonic content. FM synthesizers package an oscillator, envelope, and amplifier into what is called an Operator. An Operator can generate sounds, modulate sounds, or both simultaneously. They can even modulate themselves creating a type of feedback loop.
The Yamaha DX7 features six Operators and, to simplify the setup, the instrument features 32 pre-configured algorithms with each offering a different suitable application. For instance, algorithm one, with only two audible Operators, might be well suited for a bass or lead sound, while algorithm 20 might be more appropriate for pad or strings.
Working with the FM8
Let’s have a listen to some audio examples of FM synthesis using FM8. To simplify things, let’s only use two Operators. To clear up the nomenclature, an Operator that generates sound is considered a “carrier,” while an Operator that is modulating the carrier is called a “modulator.” It is possible to have all six Operators as carriers, but this would layer each signal, rather than modulate them. Once we initiate the modulator to affect the carrier, harmonics are introduced much like a wave shaping on an analog synth. It’s also worth mentioning that the original FM synthesis only offered sine wave oscillators. Sine waves are only fundamentals and do not have any harmonics. It is the closest to a pure tone in nature.
In this image, we see the main window of FM8, which is a six-Operator FM synthesizer with each Operator being assigned a letter (A-F). At the moment, only Operator F is active and being used as a carrier signal. Listening to the audio file, we can hear a simple sine wave.
Keep in mind: FM synthesis uses ratios to change pitch, instead of coarse and fine-tuning (semitones and cents.) A doubling of the ratio is like raising the pitch by an octave. For instance, at ratio 1.000, the operator will play the note pressed by the keyboard. If you increase the ratio to 2.000, the signal will play one octave above. At 4.000, it will play 2 octaves above and at 8.000, the result is 3 octaves above. If you wish to pitch a carrier set to 1.000 down two octaves, you would change the ratio to 0.2500.
Using the root note of C4:
Note / Ratio
C3 = 0.5000
C4 = 1.0000
C5 = 2.0000
C6 = 4.0000
C7 = 8.0000
C8 = 16.0000
In this example, I have made Operator E the modulator and increased the amplitude level to 80. The ratio is set very low (0.0200), to hear the modulation. This is very much like a vibrato effect on an analog synthesizer, where the LFO is modulating the main oscillator’s pitch.
In example 3, I’ve changed the ratio of Operator E to 2.0000, which creates a rich, even-ordered harmonic waveform. By modulating the carrier by a multiple of a whole number, the sound is less atonal, maintaining a coherent pitch with lots of character. This approach is well suited for leads, bass, pads and strings.
If we modulate the carrier by a random modulated frequency (Operator E – Ratio 2.5351), the timbre of the sound features odd-ordered harmonics and is much more atonal and dissonant, much like ring modulation. This approach is excellent for bell-like tones.
FM synthesizers traditionally don’t offer filters to help control the harmonic content. If you recall, each Operator offers an amplifier, which either controls level of the carrier or controls the depth of the modulator being routed to the carrier. With the amp level all the way down, the modulator is effectively off. If we raise the level to 100%, we are hearing the full breadth of the modulated carrier.
In sound example 5, we can listen to what happens when we slowly lower the amp level of the modulator over time. The sound gets duller, much like a low-pass filter on an analog synthesizer. This allows us to dial-in the exact number of harmonics.
Using Envelopes
Now let’s add the envelope of each Operator to shape the signals. This allows us to change the amp level automatically over time, much like an envelope generator that’s controlling a filter on an analog synth. Operator F, which is the carrier, is using a standard ADSR envelope with a fast attack, medium decay and medium sustain, and a short release. Operator E, which is the modulator, is using one of FM8’s stock envelope shapes (called DBR), which has a fast attack, short decay, very little sustain, and a short release. The results heard in sound example 6 are a classic bass often heard in house music.
In this example, I’ve created a basic snare drum. If we think about what sonic components make up a snare drum, we find the body of the drum and the snare rattle. Operators D, E, and F are being used as carriers, which allow for the layering of their signals. I started with Operator F with a low sine wave ratio of 1.0000 for the bottom end, while Operator E is set to a ratio of 2.0000 for a midrange harmonic. Operator D is set at a ratio of 4.0000, which is being modulated by the Operator C at a ratio of 6.3100 for some dissonant noise. Additionally, I’m using the “X” noise source as a separate layer, giving the sound a burst of white noise. X is also routed to Operator C for some added complexity. All the envelopes are set with a fast attack and decay. This snare drum example demonstrates how we can imagine and approach the building of a sound from scratch. Each Operator can be added or layered into the sound, much like additive synthesis, but with far greater control.
As you can see, FM synthesis can be an extremely powerful sound-design tool and this article only scratches the surface on what is possible. Now that you understand how each Operator functions and how they can affect each other, it should be a bit easier to understand more complex patches. People have spent years delving into this technology, so don’t beat yourself up if it isn’t as immediate as analog subtractive synthesis. It takes patience and practice. But before long, you’ll be able to translate the sounds in your head into whatever software or hardware you are using. I hope you have enjoyed this article on FM synthesis and that it helps you in your production work. If anyone has experience programming FM synthesis, please share some tips in the Comments section, below.
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