Now that you’ve got a handle on the basics of subtractive synthesis, it’s time to tackle something a little more complex – FM, or frequency modulation, synthesis. (And if you aren’t familiar with the subtractive basics, take a minute to read at least the first lesson – you’ll need to understand all of the concepts and the components covered there to understand FM).
As explained in the Types of Synthesis reference, FM creates sounds via audio speed modulation of frequency. In the subtractive lesson, we talked about using LFOs to modulate pitch (or frequency; same thing) to create vibrato. Well, it turns out if you speed that oscillator up to audio speed, instead of vibrato, you get new frequencies (called sidebands). That allows for the creation of complex waveforms from simple waveforms – and those complex waveforms can then go on to modulate other waves, or be layered together, offering even more complexity! By carefully controlling how much modulation each wave gets with envelopes, LFOs and hands-on controls, it becomes possible to create incredibly nuanced and complex sounds via FM.
Enough theory. Let’s look at the tools that make it all happen.
(A quick note: there are a LOT of different FM synths out there and they all implement things in slightly different ways, including differing terminology. Detailing everything that’s out there is well beyond the scope of this series, but if you need help, reach out!)
The Operator
The basic unit of FM synthesis is the operator. An operator is best understood as a combination of an oscillator, an amp and an envelope (in analog, that’s what you need to make an operator; digital is implemented somewhat differently, but conceptually, it’s the same). So a six operator synth, like the classic DX7, has six identical operators, each of which has a dedicated envelope to control the output/amplitude of the oscillator over time. Operators can, depending on the design, use any waveform, but for simplicity’s sake, and because they’re the most commonly used, we’ll stick strictly to sine waves for the initial lessons.
Operators are combined in various ways described as “algorithms” but for now we’re just going to look at the simplest approach – combining two operators into a pair where one is the modulator and one is the carrier. The only one you’ll hear is the carrier – the modulator isn’t connected to the audio output, only to the carrier’s FM input.
The Ratio
Operators can be tuned independently, and are typically tuned in relation to each other to a specific ratio (they can also be set to a fixed frequency). A ratio of 1 (i.e 1:1) means they’re tuned to the base pitch — each individual operator would sound the pitch of the key played on the keyboard. A ratio of 2 (2:1) means one is pitched an octave above the other; a ratio of 3 (3:1) is 3x the pitch (an octave + a fifth), and so on. A ratio of .5 (.5:1) would be an octave below. Instead of being set to a ratio, operators can also be set to a fixed frequency, usually expressed in hertz. This is most typically used in sound effects and some percussion.
The ratio (or fixed tuning) used has a huge impact on the sound created! A ratio of 1:1 creates a spectrum from sine waves to a saw-like wave; to get triangle and square waveshapes, a ratio of 2:1 is what you want. The higher the ratio, the more high harmonics/overtones you’ll get. “Natural” ratios (i.e. whole-number and/or simple ratios like 1.5:1) make for harmonic overtones, while complex/non-integer ratios and fixed frequencies (1.773:1 or 11.23:1 or 610 Hz) make for more clangorous, metallic and weird overtones. Experimentation is the key!
Levels
The level of your carrier will simply determine how loud that operator is – set it to full volume for these first experiments (modulated by the envelope, of course), though later we’ll vary it. The level of your modulator determines the depth of modulation, and thus how much FM is happening – i.e. how complex the waveshape/timbre is and how many harmonics/overtones you hear. If you come from the subtractive world, it can be useful to think of this in terms of a filter opening – a higher modulator level is equivalent to a more-open filter, because more overtones are present. So to execute something like a classic filter sweep, you’d have your carrier envelope open quickly, while the modulator envelope opened slowly and rose to a moderately high level (even with sine waves, very high modulation levels result in a noisy final waveform!) before slowly fading.
Feedback
Operators can also feedback, modulating themselves, depending on the implementation – the original DX7 had a single feedback path per voice, while some modern synths allow any operator to self-modulate via feedback, or allow you to define your own . Feedback unlocks another sound design tool; it frequently gives sounds an edge, and can easily tip a timbre into chaos. It’s also noteworthy that feedback is required to achieve certain fundamental waveshapes, including saw and square waves. Interestingly, a saw wave is possible with just feedback – any self-modulating operator can output a saw wave with ease.
That’s all we need to worry about for now! Two operators, one modulating the other, with a little feedback. We’ll use various settings of the ratio and levels to achieve all of our exercises, and you’ll begin to get an idea of how powerful and flexible FM synthesis can be!
Exercises
- Orient yourself on whichever synth you are using. Locate your operators and the controls for operator tuning/ratio, operator levels and envelopes, and feedback control. Don’t worry much about algorithms yet! We’re just dealing with a simple two-operator configuration, one operator modulating another operator, and nearly all FM synths default to an algorithm that offers that. If your synth offers feedback only on a per-algorithm/per voice basis, make a note of that and know where to access it for later exercises.
- Set your carrier to full volume, with a simple organ-style envelope (instant rise, no decay, full sustain, instant release). Don’t change the ratios; we’ll experiment with those next. Set the modulator envelope the same. Now, while holding a key, slowly raise the modulator volume from zero to full output. Listen as what you hear slowly changes from a simple sine wave to a more complex, saw-like wave. Depending on where your synth levels top off, the highest levels might be pretty noisy/complex. Now switch the modulator envelope to a slow rise and decay, no sustain, and play a note – congratulations, you’ve created a simple FM sweep patch, much like a filter sweep!
- Using those organ envelopes again, set the ratio of the modulation operator to 2, and repeat the exercise. Now, instead of a sawlike wave, you’ll hear something closer to a triangle/square wave. Repeat with a ratio of 3, 4, & 5, listening closely to the differences and noting how each step up produces more higher harmonics, and fewer close to the fundamental. From there, try a few higher ratios – maybe 7, 10 and 13, for example – here you’ll start to hear some of the “glassy” tones that FM is famous for. Following that, switch to non integer ratios – 1.7, 2.3, 3.14, whatever – and note that this produces metallic, noisy and “weird” overtones. Finally, set the modulation operator to a fixed frequency and play up and down the keyboard to get a sense of how that sounds (noisy!). Note that the point here isn’t to memorize all these sounds, but simply to get a sense of how they interact, and to get a sense of how much depth you can create with just two sine-wave operators.
- Now we’ll introduce feedback. Going back to the 1:1 ratio setup from exercise two, with the modulator set to about 60%, add feedback on the modulating oscillator. You should get very close to a saw wave now – tweak the various settings and see if you can get all the way there! Do the same with the 2:1 ratio and you’ll get your square at a similar feedback. Try it with other ratios, as well. (Also, if your synth allows per-operator feedback, try setting the carrier to feedback without any other modulation – you should get a saw at about 70-75% feedback). The takeaway here is feedback allows for some sharper, more defined trones – it’s a final tool in this simple setup to help shape your tone.
- Now it’s time to make some simple patches! Much like we did in the first subtractive lesson, create 5 or so simple, core patches that might be useful in your style of music. Given that we’re dealing with a single operator pair here, these patches may not ever get used in their current form, but you might as well save them, because they will serve as the basis for later, more complex patches once we introduce the remaining operators and the algorithms that define how they interact. A good rule of thumb might be to create a simple bass (experiment with fractional ratios if you like! A modulator at .5 gives you a subharmonic an octave below the fundamental!), a lead or two, a sweep and a pad/keys sound. Percussion is also a good choice for FM, and you can make some crazy effects sounds, if that’s your jam.
If you’d like to go thru this entire lesson, including every exercise, try this stream I did covering the same material: