What is FM Synthesis?

Maybe you’ve already picked through our Synthesizer Buyer’s Guide and been left wondering what exactly FM synthesis is. If so, you’re in the right place. Basically, FM synthesis is a sound-creating method that, according to a lot of people, isn’t the easiest of methods to work with and is best avoided. But anyone who does avoid it, is really missing out. Despite its tricky reputation, FM synthesis is well worth getting to know, and the more you know it, the more you’re likely to love it.

A Little Slice of History
Playable FM-Synthesizers
Is FM Synthesis Still Used?
Why FM Software?
Surely There Are Textbooks on FM Synthesis Now?
The Pros & Cons of FM Synthesis
The Essence of FM Synthesis
Just Vibrato
Fast Vibrato
Sine or Sinusoid?
The Control Options of FM Synthesis at a Glance
See also…

A Little Slice of History

FM synthesis, where FM stands for Frequency-Modulation, was first developed almost by accident by John Chowning in the early seventies. While busy experimenting with an analogue synthesizer at Stanford University, he discovered that very high vibrato frequencies were able to change the timbre of a basic waveform, and there you have it: FM synthesis! Later, Yamaha would produce a massive array of more accessible FM synthesizers, and while they weren’t the first of their kind, they were the most successful. When the first Yamaha DX7 synths hit the market halfway through the eighties, they transformed the musical landscape for all time.

Playable FM-Synthesizers

With the dawn of FM synthesis, we were no longer tied to the beautiful but limited sound palette of analogue subtractive synthesizers and the often incredibly expensive early samplers. FM synthesis opened a door, so suddenly anyone could create endlessly unique sounds. However, within a few years, samplers and ROMplers became more affordable, knocking the FM method off the throne. Much later, software-based synthesizers (including the first VST formats) became popular and helped bring FM synthesizers back, and it was only then that FM synthesis really started to take off.

Is FM Synthesis Still Used?

Any recent keyboard, workstation or synthesizer won’t be based on FM synthesis, so if you look at it that way, FM isn’t exactly mainstream. Things were very different in the eighties, when you could build a house with the amount of FM-based keyboards and synthesizers that came out during that time, and sure, these days there are still a lot of synthesizers with FM on board, including the Yamaha Montage workstations, and the still fairly young and compact Yamaha Reface DX, but if you want the most comfortable experience of FM synthesis, then there’s no better option than software. You have a lot to choose from as well. There are loads of VST FM synthesizers you can download, and some of them are even free. My personal favourite is the Native Instruments FM8, which is probably the best algorithmic softsynth that I know of. This is not just because of the mass of sound options it has on offer, but because the CPU usage is laughable. There are doubtless VSTs that maybe sound a little more pure and are a little more extensive than the FM8, but if you’re already eating 30% of your CPU by hitting a simple chord (even on a high-end and powerful system like the Intel i7 Series), then I have to draw the line. With FM8 you can use dozens of instances, which is enough to build complete tracks. FM8 comes included as standard with the renowned Native Instruments software packages, Komplete and Komplete Ultimate.

Why FM Software?

FM synthesis has the reputation of being hard to work with, but that’s not 100% true. While it is true that, because the DX7 was a complex beast loaded with a difficult set of controls, the motivation of writers and producers working in the eighties to start hammering out their own sounds was all but killed off, meaning that they tended to just stick to the factory sounds. However, while the DX7 was a problematic FM synthesizer, that doesn’t mean that FM synthesis is difficult. The problems with the DX7 were the result of a really limited interface that wasn’t really designed to support the joys of experimentation, and while there are other reasons that FM synthesis can be confusing in certain situations, that’s something to be covered in another blog.

In general, I feel confident when I say that FM synthesis is not difficult, it’s just really extensive!

‘Extensive’ is a term that can cause issues when you want to develop a hardware synth, since it means you’re obliged to build a massive cockpit littered with an army of control elements. In terms of production budget, this simply wasn’t feasible: every rotary knob and fader costs money. So, instead of a mountain of controls, the DX7 synth provided nothing more than one data fader and a row of diaphragm buttons. In practice, the results were unfortunately lacking, especially since this synth was in fact a game-changer that, in terms of sound generation, did things very differently from the analogue synthesizers that everyone was already familiar with.

Software has since solved this problem. When developing an FM-softsynth, it costs nothing extra to ‘fit’ an extra bank of virtual rotary knobs, buttons and faders, meaning that the interface you see laid out on your computer monitor is able to offer everything that the DX7 never could.

Surely There Are Textbooks on FM Synthesis Now?

Sure, and some of the articles you can find were actually written by scientists for their peers. If you really want to, you can really dive into the technicalities of FM synthesis, learn all of the mathematical terms involved and really confuse your fellow musicians. Here however, we’ll keep things as simple as possible because, to be honest, you really don’t need to be well versed in all the maths that go into it to understand what you’re doing. All it takes is a good set of ears and the time and will to experiment and eventually, the penny will drop. So, if you do come across terms like ‘bessel function’ on the internet, then you’re free to run as fast as you can, because, unless you’re a PHD mathematician, you simply don’t need to know about it.

The Pros & Cons of FM Synthesis

#1 With a sample-based synthesizer, you’re playing with ‘static’ sounds. FM sounds, on the other hand, are extremely musical and changeable, so you’re not met with the ‘machine gun effect’ that you often hear from sample-based synths. A good example of this phenomena is when you repeat a snare to mimic a drum roll: since the exact same, unchanging sample is repeated, it sounds like you’re just rattling off a machine gun. These days, ‘round robin samples’ are a kind of brute force solution, but a well designed FM synth just won’t have this problem.

#2 Another advantage is that, with FM synthesis you can create a near-limitless range of different sounds. From this perspective, FM synths immediately have more potential than analogue and virtual-analogue synths. FM is also known for being really good at creating bells, clocks and other percussive sounds involving two metal objects striking one another (like vibraphones and xylophones), but this actually sells FM synthesis a bit short. FM can also handle wind instruments, bass, other percussive sounds, even Rhodes pianos, organs and similar instruments with relatively little difficulty. And, naturally, an immense palette of purely synthetic sounds is possible as well. Even better, the simulations of acoustic instruments aren’t far from the reach of FM synthesis either.

#3 So, FM opens up some really wide and versatile sonic scope, meaning that your FM sounds (both subtle and complex) can change in a way that they just can’t when using other methods of synthesis.

Have a listen to the five audio clips below. Each of the sounds is based on a typical DX-EPiano, which is maybe the most familiar FM sound of all time, simply because it comes pre-loaded into almost every keyboard, synth and digital piano you can lay your hands on. However, since this is a sampled version, it has a static quality to it. The variations that follow from the first audio clip include subtle or more complex changes as a result of applying just one or two FM parameter adjustments. This alone should give you a really clear idea of just how versatile FM is when compared to sample-based synthesizers.

Audio Example 1: five EP-sounds

The Essence of FM Synthesis

The following statement is essential when it comes to understanding FM synthesis, so write it down or print it out and commit it to memory:

FM is nothing more than ‘rapid vibrato’.

Since a picture can say a thousand words, let’s try to give you a single picture that can tell you a lot about how FM sound generation works. When it comes to algorithmic synthesizers (including analogue based synths, FM or additive synths), anyone who’s taken a ‘look’ at a bit of audio through an oscilloscope will see a shape, whether its a sine wave, a triangle wave, a sawtooth wave or a square wave (Diagram 1). The repetition of these shapes is referred to as a cycle, so the up and down pattern of the sine wave completes one cycle. A long note will be made up of a specific number of repeats of this cycle, and as you can see in diagrams 2 and 3 below, this cycle can be narrower or wider. The wider the cycle, the longer the cycle duration. In other words: the lower the pitch of the note.

Diagram 1 (from top to bottom): sine wave, square wave, triangle wave, sawtooth wave

Diagram 2: low note

Diagram 3: high note

Just Vibrato

Say that you’re using the modulation wheel of a synthesizer to create a natural vibrato by making the pitch rise and fall. Here, you’re varying the width of the sound wave cycles, making them wider and then narrower. In most audio software, you can even see these shapes in the waveform of a sound when you zoom right in.

In diagram 4 below, you can see that the sine wave shape doesn’t change that much when a natural vibrato is applied. Besides widening and narrowing, it remains recognisable. This is because a normal vibrato sits around the 4 or 5Hz mark, which directly translates into four to five vibrations per second. This might sound fast, but it’s actually really slow when compared to the super-fast cycle that repeats in the waveform of an audible sound. This is why vibrato never has an extreme effect over the shape of a sound wave.

Diagram 4: note with vibrato

Fast Vibrato

Now we come to the fast vibrato of FM synthesis. Rather than applying a 4 to 5 Hz vibrato, let’s try using a 100Hz vibrato. What happens? Here, the cycle is widened and narrowed within every cycle of the 100Hz note. This is the moment where the shape of the sine wave begins to change, resulting in FM synthesis.

Below, you can see that the waveform starts to look like something between a sine wave and sawtooth wave. For those in the know: this also looks a bit like the effect that a low-pass filter has on a sawtooth wave, it also sounds a bit like it.

Diagram 5: note with FM-synthesis

Audio Example 2: An increasingly fast vibrato. This ends in a note that barely resembles the original sine wave.

Sine or Sinusoid?

Here’s another bit of trivia that you’re welcome to forget: in the world of sound synthesis, sine wave is a standard term, but in the world of mathematics and physics, a sine is the ratio of an angle, and therefore the shape should actually be referred to as a sinusoid.

The Control Options of FM Synthesis at a Glance

Hopefully, you already have a better idea of just how extensive FM synthesis is. To really underline that thought, here’s a brief list of the elements you can control:

The frequency of a basic waveform.
The frequency of a fast vibrato.
The depth of a fast vibrato (taking Diagram 5 above as an example, you can more or less set the horizontal relationship of the pink dots above and below).
The shape of the basic waveform (but not every FM synthesizer has the option to select any waveform other than a sine wave. For example: the popular DX7 only has a sine wave).
The waveform of the fast vibrato.

Bear in mind that, despite the mass of settings, you’re still dealing with a remarkably simple foundation made up of nothing more than one basic waveform and a fast vibrato.

Not so complicated, right?

What’s your experience of FM synthesis? Let us know in the comments!