FM Synthesis Explained – What is FM Synthesis?

FM Synthesis Basics What is FM Synthesis?

In this post we’ll answer a most important question: What is FM Synthesis? What is it about? How do we use it in make music?

We’ll understand, in simple terms so that the layman comprehend, what this really interesting form of audio synthesis, and how it is used in electronic music.

All while keeping it from being too technical and complicated.

Let’s dive in!

Read the other articles on audio synthesis:

Introduction to FM Synthesis

Synthesis is at the heart of modern music production and modern music making. Learning how to use a synthesizer, whether hardware (like mini synths) or their software equivalent, is an important part of your music production education.

That said, it’s not difficult to understand, once you know the fundamentals of what you’re working with…

The Basics of FM Synthesis

FM Synthesis is short of Frequency Modulation Synthesis. It is a type of synthesis that produces sounds electrically or digitally by altering, (ie. “modulating”) the original generated sound wave produced by an oscillator. As an instrument, they can either be hardware or VSTi plugin variants. In either case, they work based on the same principle just mentioned.

How FM Synthesizers Work

To know how an FM synthesizer works, we need to review the basics of a synthesizer.

For now, just know that a synthesizer is a device that produces sounds by creating sound waves. If the sound wave is between 20 Hz to 20,000 Hz, you will be able to perceive these sounds as “pitches”. The part of the synthesizer that creates these frequencies is called a frequency oscillator. Or just “oscillator” for short (jargon #1 down).

To illustrate, do you know middle C on the piano? Let Wikipedia show you and then get right back here.

On your DAW piano roll, it would be labelled as “C4.”

Now, that note, or “pitch,” produces an oscillation of 262 Hz because the string, or piano wire, which struck by the hammer, cases it to vibrate back and forth 262 times per second.

In the case of a piano, the string would be called the “oscillator.”

Spoon used to illustrate a frequency oscillator
Why are you looking at a spoon? Well, it’s a magic spoon. Keep reading to see why…

In even more words, let’s say that there is a spoon next you. You see this spoon and decided to take it up and suddenly you’re endowed with the superhuman power of speed. With that power, start banging that magic spoon on the table 262 times per second for a few seconds. The result of that superhuman high-speed banging would be that same exact note on the piano. Amazing, isn’t it? Let’s keep going…

Illustration of a soundwave in audio synthesis
The darker parts would be like the bangs of a spoon on the table. The top loop is the waveform we use to understand the number of times that sound frequency oscillates for each second.

A synthesizer, then, is just a device that bangs a spoon on a table so many times per second you get a pitch. Each bang, boom, or bust, is an oscillation.

Now, with that in mind, knowing that we can create a pitch by banging things at a super fast rate, with each bang being a “cycle”, these cycles of up “up-down-up-down” can be visualized into what we call “soundwaves.”

Knowing what a soundwave is, we can find ways of having some fun with that wave, and maybe even accomplish some other sounds from that single sound wave or frequency we’ve created with our magic spoon banging.

How? you may ask. Well, let’s find out…

Frequency Modulation – Or, Let’s Modulate that Pitch

Imagine that you were able to slow down that superfast banging just a little and then speed it up again. That would be called “modulation”. In other words, you’ve modulated the rate at which you were banging your spoon against the table from fast to slow. The modulator, then, is a separate oscillator that changes the frequency in pitch created by the first oscillator.

Continuing with the magic spoon banging analogy. Imagine that you were first banging it at 262 times per second, then 130 times per second (which is the C an octave below the middle C, or C3). Let’s say you repeat that fast-slow rate over time, you’re now “modulation your frequency” a few times every few seconds.

Frequency Modulation Wave Curve
Here are three different waveforms to illustrate FM waves. The top wave is a standard waveform. The middle wave is illustrating what is called “amplitude modulation,” where the intensity of the wave varies. The bottom waveform is a frequency modulation wave, where the speed of the wave varies.

Now, with that image in mind, let’s say, in another feat of superhuman awesomeness, you were able to modulate the rate of change at which you could bang it out fast-slow-fast-slow. Imagine that you could go fast-slow-fast-slow 20 times for the second. Guess what?

Still with me?

You’ve just created another frequency that is within the range of human hearing.

And you’ve done that by just taken your original frequency sound wave (tap-tap-tap) and used it to make another frequency sound wave by altering (modulating) the how fast and slow you tap-tap-tapped that table per second.

That is what FM synthesis is. It takes your original sound wave, modulates it over time at such a rapid rate that you have created another pitch.

In other words, you’ve created frequencies inside of frequencies. #mindblown

This final pitch, note, or sound that you’ve created is an entirely new frequency from just a combination of the two frequencies we’ve initially created: the original being the rate of spoon banging, and the second frequency is the rate that we slowed and sped up our spoon banging.

See this example video of what we’re talking about. Our FM synthesizer starts out with a basic tone, then modulates the pitch of that tone high and low so fast we ended up with another sound. Play the video.

If you’re curious about the software used, it is the Thor synthesizer which comes standard in Propellerhead’s Reason (discussed in this DAW guide).

Properties of FM synthesis

So, now you know the very basics of how an FM synthesizer works.

Now, time for a little more technical jargon to make you sound educated at your mom’s next dinner party.

Carrier Frequency

The original frequency is called a “carrier frequency” (jargon #2). This was the sound created by banging your spoon so fast you ended up with the humanly perceivable note middle C.

This sound can be originated using any other sound, as long as it is repeated over and over again over time at a super fast rate to create your first note which shall “carry” the frequency’s modulation.

There are different kinds of carrier frequencies. There are sine waves, square waves, triangle waves, and sawtooth waves. Each of these waves has their own kind of sound to them.

Sine waves produce the purest and cleanest sound of them all. It’s the Snow White of waveforms. The other waves are buzzier in sound. Knowing the sounds of each helps you to determine what kind of sounds you’re looking for when sculpting your sound designs.

Think of it this way. A cello is closer to having a sawtooth wave because the string is being pulled back by a bow, and snapped back to place when the bow has taken the string to the point of maximum tension.  If you were to plot this behavior of the string on a graph over time, this pulling and snapping back at a high rate looks like the form of a sawtooth wave, which produces a sounds similar in timbre to a bowed instrument.

Sawtooth Waveform
A sawtooth waveform. Click to hear what a basic sawtooth wave frequency sounds like (opens in new window)

The sound of a reed instrument, like a clarinet, is closer to a square wave. This is because the reed in a reed instrument, the reed (which we could call our oscillator) goes up and down pretty evenly. The air pressure of the blows breath is what causes the reed to vibrate.

Square Wave frequency
A square waveform. Click to hear what a basic square wave frequency sounds like (opens in new window)

And a sine wave is like a human voice singing “Ooo“, because the vocal cords flap smoothly over time. This can be visualized as the wave shaped as a sine wave.

Sine Wave frequency
A sine waveform. Click to hear what at basic sine wave frequency sounds like (opens in new window)

A triangle wave shape is like a combination of a square and sine, in other words, the combination of a human voice and a clarinet or sax.

Triangle Wave frequency
A triangle waveform. Click to hear what a basic triangle wave frequency sounds like (opens in new window)

Modulator Frequency

The second frequency oscillator is what controls the pitch (high to low) of the carrier frequencies just mentioned. This frequency is called the “modulator frequency.” (Jargon #3)

The modulator tells the synthesizer to make that carrier frequency dip and rise in tone, and to do it so fast that it creates an entirely new frequency, resulting what are called “harmonic sidebands.”

Harmonic Sideband Frequencies

When you start modulating the pitch of a sound wave over and over at rapid rates, you’ll begin to notice that at least one new sound splits off from the original carrier wave. These harmonic overtones are what we call “sidebands” (Jargon #4). They can be higher or lower than the original carrier sound wave itself, and can also be either harmonic or inharmonic in sound.

These sidebands and their complexity are what makes an FM synthesizer unique. You can get a wide variety of sounds by a combination of how many harmonic sidebands you create, as well as whether these sideband overtones are harmonic or inharmonic. And since in nature no sound is produces a clean single note, this is what allows FM synthesis to have a sound closer to what we’d consider to sound “natural” from an electronic instrument.

To illustrate, take a look at this video. As you hear the frequency modulate to new pitches, you’ll hear new frequencies breaking off into upper and lower sounds (harmonic sidebands), which are visualized using green lines on the spectrum.

Frequency Ratios

You can control a number of harmonic sidebands as well as their amplitude (simply, their intensity of amplification) by changing the ratio of the carrier frequency to modulator frequency.

If the ratio is even, like 2:1 or 4:1, you end up with harmonic sidebands.

If the ration is uneven, like 1.314:1, you end up with an inharmonic sideband.

Why is this good to know? Keep reading…

What are FM Synths good for? Sonic Textures : )

Because you can create different sounds using at least two oscillators, and manipulate their harmonics via the ratio between these two oscillators (carrier frequency and modulator frequency), an FM synthesizer will be capable of producing a wide range of complex sounds that are tonally rich in timbre.

Sound wave visualised

When you add to that the fact that you can actually modulate not just one carrier wave, but multiple carrier frequency waves at any given time, you can imagine just sound complex and rich the sounds that you could create.

So back to our magic spoon banging example, you and a friend could be banging spoons on a table at the same rate (two oscillators working together), and then one of you decides to change how fast and slow they bang it (that’s the modulation oscillator). Just as you would come up with complex rhythms, at a super fast rate, you’d come up with complex sounds.

Hence, FM synthesizers are often go-to choices for sounds like percussions, bells, metallic sounds, shocks, zaps, sizzles, crashes, noises, drones, you name it. This would otherwise be difficult or close to impossible to accomplish with other types of synthesizers, like subtractive synthesizers, for instance.

Quick sidenote: A subtractive synthesizer works sort of the other way around. It first starts with a wave with plenty of harmonic sidebands, then subtracts frequencies to achieve a particular desired sound. Since the end result is a more focused or definite sound, you’d need a tremendous amount of equipment and synthesis power to create the complexity offered in FM synthesis. Read more about subtractive synthesis here.

Great Examples of Virtual FM Synthesizers (Softsynths)

Included in a Digital Audio Workstation

  1. Sytrus by FL-Studio
  2. Operator by Ableton Live
  3. Thor Polysonic Synthesizer by Propellerhead Reason
  4. Mai Tai by PreSonus Studio One

As a Third-party Plugin

  1. FM8 by Native Instruments
  2. Massive by Native Instruments
  3. Dune 2 by Synapse Audio
  4. Nemesis by Tone2

FM Synthesis – Final Thoughts

And that’s what FM synthesis is.

In this post, you’ve hopefully learned by now the basics of how an FM synthesizer works.

From now on, when using an FM synthesizer, you should be able to make more educated decisions on the sort of sounds you want to use, and where to get them from, as well as how to use your synthesizer for sound designing your electronic music masterpieces.

You learned that FM synthesis requires at least two oscillators, one to generate the carrier frequency, the other to modulate the frequency variation of that carrier frequency over time.

You learned that, in doing this, you create rich harmonic textures, which makes FM synthesis the go-to choice for complex sounds like percussions, metallic, sound, bells, and so on.

If you enjoyed and found this information useful, you can learn a lot more about synthesis and music production from some of these online courses that we recommend.