There’s a whole variety of synthesis types available ranging from things you’ve probably come across like subtractive, wavetable and granular to lesser known techniques like additive, phase distortion, Karplus-Strong and vector. For the longest of times I had thought Frequency Modulation was only capable of making thin and papery computer game sounds, cheesy brittle electric pianos and laughably cheesy marimbas. How wrong was I?

Yes frequency modulation (FM) has been around for a long time, and yes it’s the same thing we use(d) to transmit radio signals with. It is responsible for some drab patches that were totally rinsed during the 80s and yes it can be quite complicated BUT it’s also capable of some incredibly rich and kinetic sounds. FM has just had bad PR.

This is an article I hesitated writing for ages because each time I drafted it I found another excellent resource to include and while I want it to be comprehensive I want it to be understandable by someone with little to no previous experience with FM before.

There is a lot of content about FM synthesis out there both on blogs, YouTube and education papers and here I want to collect what I consider to be the best bits in one place while offering some (hopefully) original insight and keeping the content suitable for users of all abilities.

What is Frequency Modulation?

Before diving into the synthesis side of things, let’s first clarify exactly what frequency modulation is and what it has been used for historically. Older readers might remember the days before digital radio when FM and AM (amplitude modulation) were the de facto way of listening to radio stations. But what is frequency modulation? Wikipedia describes it as the…

…encoding of information in a carrier wave by varying the instantaneous frequency of the wave.

Confused how you can encode signals on to one another? Here’s a quick description from Techquickie. I’ve embedded from 2.26 where the presenter talks specifically about FM radio but you can rewind if you want to learn about AM too.

While this clears up some of the fog, I found this public broadcast video from the Department of Defence from 1964 a little more helpful in explaining exactly what’s going on. Naturally it goes into a little more detail however at just short of 30 minutes I would understand if you just précis it by skipping through. A lot can be skimmed from this but it’s not all entirely relevant to musical applications. Worth a watch if you want a more holistic understanding.

Frequency Modulation Synthesis

I’ll admit that FM was something I struggled with for a long time, even with a medium-to-good grasp of subtractive synthesis I couldn’t really get my head around the sonics of this.

The easiest way I’ve began to understand FM is comparing it to a simple vibrato sound. Vibrato is an effect employed by singers, guitarists, other string instrumentalists and others. It’s a subtle modulating of the pitch. Jazz and opera singers are masterful of using this technique to add some shimmer to longer held notes.

It’s commonly found on synthesisers too, with a modulation wheel or similar adding vibrato to sounds. But how do we patch it? It helps if you have an at least rudimentary understanding of the signal path of an analog synth to get this so read this if you don’t.

We route an oscillator to an amplifier (or, VCA) and take a low frequency oscillator (LFO) and modulate the oscillator’s pitch. Simple as that.

LFOs are sub sonic and therefore inaudible. They typically range from between ~0.01 and 20 Hz. Depending on the amplitude (volume or wave strength) of the LFO, the original tone or pitch can still be perceived at lower amplitudes with the vibrato straddling it, moving slightly above and below.

The more you increase the amplitude the more the sound strays from a vibrato and moves closer to a laser-like sound, with the pitches either side of the original pitch becoming further and further apart. Here’s a quick (two minute) explanation of frequency modulation using eurorack modular to demonstrate a quick patch.

For a little more of an eloquent and romantic summary, here’s John Chowning, credited as the father of FM synthesis explaining a little about how he discovered a musical usage for the technique:

Let’s try and visualise what’s happening here. I’m using Native Instruments Reaktor as it has this flow chart-like architecture than can help you imagine the signal and modulation passing through the synth.

In the below example we have a 1 Hz LFO controlling the pitch of a sine wave (single harmonic waveform) and the amplitude of the LFO is being turned up slowly. At first we hear a subtle undulation and as it increases the LFO creates a sound more akin to a dub siren.

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As we gradually increase the rate of this LFO from 0.01 Hz up to around 11 Hz, it becomes harder to hear the nuanced changes in pitch. At slower rates we can still easily count the cycles and even determine the underlying note pitch but as the amount of modulation and speed of the modulation increases it becomes harder to hear the original tone.

Eventually as the LFO approaches audio rate (> 20 Hz), and the original tone becomes almost imperceivable. This creates a series of complex additional harmonics – this is frequency modulation. In the example below, our LFO rises from 11 Hz to 100 Hz:

Whilst this is FM in a nutshell, is it musical…? The pitch of an oscillator is tracked by our keyboard input, meaning it responds to changes in pitch when you go higher or lower down the keyboard. However our LFO is static, as the frequency is fixed. Yes we can change the rate of the LFO manually but it has no relationship to the keyboard and therefor has an arbitrary relationship to our oscillator. Let’s play a basic major scale and hear how the LFO at a rate of 100 Hz effects each note:

Some notes don’t sound too bad – for example the 2nd, 4th and 7th notes sound quite pleasant to my ears but the rest sounds almost accidental and quite grating. This is why FM synthesisers have different interfaces for tuning oscillators compared to an ordinary subtractive synth but we’ll get to that later when we start looking at specific examples.

Logic’s EFM1

Before getting into operators and terminology more commonly associated with frequency modulation techniques nowadays, I want to start with the concept of carriers and modulators – as this is how I learnt about FM, through Logic’s EFM1.

You may have come across carries and modulators with ring modulation or vocoding, and you can still find some more basic FM synths that use this terminology. For a small interface and just two oscillators with minimal modulation capabilities, the EFM1 packs quite a punch, and for that reason it’s a great place to start.

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Let’s begin with some basics. The carrier oscillator is routed to the amp/output and produces a sine wave. With FM it’s quite easy to create brittle, bright, metallic and hollow sounds by just modulating sine waves.

The modulator oscillator isn’t connected to the amp/output and is actually connected to the carrier much like the LFO was in our vibrato example, only the difference is the modulator oscillator is tracked by our keyboard input. Changing specifics of the modulator oscillator’s pitch, volume or harmonic content will in-turn affect the timbral qualities of our carrier.

In EFM1, both the carrier and modulator use Harmonics to tune rather than more conventional octaves, tones and semitones. We also have a bi-polar fine tuning control (in cents, or 100ths of a semitone) for a more ordinary detuning effect. Lastly we have a button to fix the frequency of the oscillator which is useful for drones, risers, drum synthesis or other FX.

But hold up… why do we tune is harmonics and not normal intervals? For the longest of times this stumped me. Let’s clarify first what harmonics are first. Harmonics are whole number ratios of a frequency obtained by multiplying the note by an integer.

That might sound more complicated than it is, but it’s really not. It’s quite simply multiplying a frequency by whole numbers such as 1, 2, 3, 4 and so on. They appear naturally in the Harmonic Series and are the building blocks of western harmony. They also have an intrinsic link to our intervalic system. Doubling the ratio from 1 to 2 will raise the pitch by an octave, doubling that again to 4 and in turn 8 would raise it by octaves again and again. Halving the ratio from 1 to 0.5 would drop the pitch by an octave.

But what about the ratios that aren’t 1, 2, 4, 8, 16 etc? These produce other harmonious intervals; multiplying by 3 would produce an interval close to a and octave plus a perfect fifth and multiplying by 5 would be an interval close to a two octaves plus a major third etc.

The reason we use use ratios is that they are mathematically pure compared to our equal tempered (12-tet) system of tuning we use in western music. In equal temperament we divide the octave in to semitones using the 12√2 – as there are 12 semitone in the octave, each semitone is 1 x12√2 higher than the previous.However the 12√2 is an irrational number and deviates slightly from the perfect ratio system.

While it’s possible to find some FM synths that can use equal temperament the sound produced by using the harmonic series tends to be more sonorous to our ears. I would strongly suggest familiarising yourself with harmonics in general as they crop up in lots of different areas of both music and music tech.

So do we blindly pick ratios? Well yes and no, and that really comes down to your experience with FM and a healthy dose of intuition. Below is an excellent (albeit slightly dated) video that explains a little bit about what to expect from certain ratio combinations.

The video is embedded from where the topic is picked up but watching the whole thing is not only great revision for frequency modulation in general but also contains a very comprehensive guide to subtractive synthesis at the start.

As you saw, the FM section of the video is focused around the legendary DX7 (more on this later) and some while some of the patch examples might sound a little sterile to our 2017 ears, the theory is top-notch and it’s well worth spending some time this video.

Anyway, back to EFM 1. Here’s our carrier in isolation with the harmonics slowly being turned from 1 up to 36 and then back down again. It should be a sound you are familiar with as it the harmonic series appears in nature:

The FM knob in the middle (unsurprisingly) controls that amount of frequency modulation on the carrier via the modulator. Here it is being turned to maximum and them down again with the harmonics of both oscillators set to 1:

The modulator on the left has the same harmonics and fine tune control as our carrier but also has a basic wavetable index. This scans through a small selection of interpolated waveforms containing different harmonic signatures which produces a whole range interesting timbres when modulating our carrier.

Let’s modulate the harmonic, fine tune and wave one by one, hearing how each in turn affects our carrier’s sound. I’ve left the FM dial at around 12’o’clock:

Here are some example patches I knocked up to demonstrate some of what this synth can do starting off with a simple retro bass sound synonymous with a lot of commercial UK house music at the moment. The sound is achieved by using envelope modulation to increase the FM amount at the front of the sound (no attack, short decay, no sustain), giving it a percussive transient knock. What’s really happening is just amplitude modulation – but it’s the amplitude of the modulation oscillator:

Here are some metallic, shimmering bells. The in-built unison adds that sheen and sparkle. Again there’s envelope modulation and some inharmonic detune between the oscillators from the ‘fine’ control. There are no spatial or time-based effects applied to this:

Next up is a soft, ethereal pad. I love FM for these types of sounds as you can start with sine wave and gradually shift their timbres into something kinetic, glassy, warm, cold, whatever. Even with just two oscillators there’s a lot going on:

Last off is an industrial-like drone. Atonality is relatively simple with FM while these types of sounds might be near impossible at best a struggle with subtractive synthesis:

As you can hear there’s a huge plethora of sounds available and considering this is a dead simple synth with limited functionality, you can begin to imagine what’s possible with more modulation capabilities.

So what’s actually going on here? Subtractive synthesis takes harmonically rich geometric waveforms such as sawtooths, pulses and noise and uses filters to attenuate their harmonics. FM works in the opposite manner starting with basic waveforms and increasing their complexity. The additional overtones created you can hear are called sidebands. Let’s have a look at what they are.

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