What are Sidebands?
While we could just brush over exactly what sidebands are I think to do the topic of FM justice it’s useful to talk about what they are. This might get a little abstract for some readers but just remember it’s not key to understand everything in immaculate detail, but you can do no harm by being on at least nodding terms with it.
So what are sidebands? Sidebands are the bi-product of frequency modulation and we actually get sidebands in other processes such as ring modulation and amplitude modulation. These are the additional frequencies produced by modulating two waveforms together at audio rate. Wikipedia describes them as:
…band[s] of frequencies higher than or lower than the carrier frequency, containing power as a result of the modulation process. The sidebands consist of all the Fourier components of the modulated signal except the carrier. All forms of modulation produce sidebands.
But how do we calculate them? And do we need to? One of the better definitions I’ve heard is from this video by YouTuber and sound designer Composing Gloves. This playlist is a whole series on explaining the nuts and bolts of FM and it’s fantastic so well worth a watch. To paraphrase his explanation:
…sideband frequencies are equal to the carrier frequency +/- a number multiplied by modulating frequency.
It’s actually a little more complicated than that because the amplitude and phase of the waveforms will also make a marked difference but this is just a basic description without jumping too far into the maths, which is honestly beyond even me.
N.B It’s worth noting too that some synths are bandlimited while others allow aliasing and others have oversampling options. These will all have a direct affect on the upper registers of the spectrum potentially adding harmonic distortion or wave folding-like qualities to the sound, so listen out 💀.
In reality this information isn’t whizzing through my mind when I’m making sounds but there’s no harm in better understanding a process.
There are primarily two ways in which we can change the content of the sidebands and affecting our timbre. One is by changing the ratio combinations of our oscillators and the other is by changing the amplitude of those oscillators (sometimes called the modulation index).
I’ve lifted this .gif from an excellent imgur post I found on Reddit that neatly visualises the sidebands created from a 1 Hz carrier bring modulated in increments from 1 to 10 Hz.
As you can see that the sound starts off looking not too dissimilar to wave folding and we can see gradually the discontinuity in the wave increases. The further away from a sine something looks (generally speaking) the brighter or richer it will sound.
Here is an audio example I’ve made using EFM1 to try and demonstrate what the above .gif might sound like:
What does this mean practically? As a musician and not a mathematician this is tough for me to express but it’s actually an easy concept.
If we consider an example of just two oscillators for a second, the way I think about it is that the simpler the two numbers can be expressed as a fraction the more harmonious it will sound.
Ratio combinations of 1:1, 2:1, 3:2, 5:4, 4:1, 5:1, 6:1 etc will all sound relatively pleasant as they are simple rational numbers and the fractions have small(er) denominators when written in reduced form.
If we increase the complexity of the fraction introducing numbers further away from zero or further apart from each other, the brighter and potentially harsher the sound will become. Ratios such as 10:9, 11:10, 30:31 and so on will produce more complex sidebands.
Where it gets a little complicated is that we can actually accept a margin of error, much as we can with harmony. I mentioned before our 12tet system of equal temperament – none of the intervals contained within the octave are mathematically pure in relationship (except the octaves themselves) and by using the12√2 we get semitones that are slightly out of tune with each other. However, the margin of error is less than 10% so our ear accepts this.
Similarly with frequency modulation – if we took two operators with ratios of 2:1 and detuned them both ever-so-slightly, our ears wouldn’t hear 2.0792938:1.0542847 – we would naturally round it up as the margin of error is small enough.
Further Reading: I actually spoke to professor of physics at Nottingham University Dr. Philip Moriarty and Math YouTuber 3Blue1Brown about this topic to try and find a mathematically water-tight definition that was understandable by laypersons (such as me), and while we couldn’t exactly nail it, these resources were quite useful to me. Firstly this on instruments with non-harmonic overtones and this on music and measure theory.
In researching this subject I also found this mind-melting section from an old Future Music magazine (written by Robbie Stamp/Cyclick), the math is a little beyond me but it goes some way to explaining what we perceive to be dissonant .
So let’s think about what increasing the amplitude of our modulating oscillator does to our sound, or to put it more simply, increasing the FM depth. What happens when we increase that? Something else that resonated was this passage from an instruction manual on a eurorack modular unit called FM Aid by Happy Nerding. It explains:
By increasing the “FM [amount]” amount the user shifts additional harmonics proportionally further from the main tone, so the sonically perceived brightness of the sound and complexity increases too.
FM amounts at 0, 5, 10 dial positions and their respective spectrums. 100 Hz sawtooth wave is used as a Carried and Modulator. The whole manual can be found here.
The image on the left is lifted from a radio electronics site and it maps linear frequency on the x-axis and amplitude on the y-axis.
N.B Viewing frequency on a linear scale is useful for viewing relationships between harmonic. Spectral analysers like Voxengo SPAN and other use a logarithmic scale.
It shows how increasing the modulation index introduces more complex set of sidebands that eventually get spaced further apart from our fundamental tone.
If you still really want to push further with this, I would recommend having a look at this from the University of Indiana titled The Principles of Digital Synthesis.
I’ve linked from page 3 of the FM section. It’s a little bit beyond my comprehension so don’t feel it’s a requirement.
Anyway, back to make wibbly noises.
By far one of my favourite FM synthesisers is Ableton’s Operator. It neatly combines frequency modulation with elements of subtractive and even additive synthesis. It’s both compact and powerful and comes free with Ableton Suite. I find myself reaching for it over the Analog synth or any the other Ableton bundled instruments time and time again.
At this stage is worth confronting why FM synths tend to call their oscillators operators when they seem to perform a similar function. From my understanding it’s because while an operator can behave like an oscillator and produce a periodic waveform at a given pitch, it can also be used as a modulation source whilst also receiving modulation from another operator. Phew!
In EFM1, the routing of our two operators (the carrier and modulator) was fixed, but with Operator we can reconfigure how our four operators are connected, vastly expanding the sound palette available.
Operator is relatively simple once you get the hang of a few basic concepts and its interface. We have two sections either side of a dynamic display. This display changes depending on which shell you click, one of the four operators (A, B, C and D on the left), the LFO, filter, pitch information or global (right).
Below we are viewing the parameters for operator A. FM relies heavily on envelopes, and we can modify the basic ADSR parameters of operator A’s amplitude envelope as well as loop the AD portion, change our waveform (usual candidates here plus some more esoteric ones), restart phase and modify other parameters you might expect to find on an oscillator.
There is also an ‘oscillator’ tab within this display. This is the almost additive element of Operator – we can control the harmonic overtone content of our waveform. Changing these will instantly rename the waveform “user”. Below we are viewing a resolution of just 16 harmonics, but 32 and 64 are available too. This makes operator very powerful indeed.
Here are the four operators will using sine waves. The routing is D modulating C which in turn modules B which modules A. A is the only operator routed to the output. Hear how changing the amplitude (and tuning) of the other three operators changes the overall timbre:
Here I am taking a single harmonic and gradually adding additional harmonics above it. See and hear how it affects the sound:
N.B The clicks and pops you might be able to hear is what’s called zipper noise – it’s something that not designed to be modulated or automated, which is why it sounds clicky.
The bottom right shell is our global tab and that includes a fairly important element: the routing algorithm. This is that collection of pretty coloured squares in the top-middle of the display.
This is a visual representation of the routing of the four operators. The default is D > C > B > A, which means that only A is routed to our master. Additionally we can have D and C modulating B independently before they modulate A. On the very far right we have four operators without any frequency modulation capabilities. Let’s take four operators and record a low MIDI note, changing the routing for each example. Hear how drastically different they are when the modulation is in different orders and combinations:
You can learn more about FM synthesis routing algorithms in the below video. It mainly focusses on the DX7 (more on this later) but it neatly describes the types of routing algorithms, plus a little information on feedback modulation:
If you take into consideration Operator’s routing, additive capabilities, loopable envelope stages and everything else it has to offer, it’s a very useable, flexible and simple synth that (best of all) is free with Ableton Live Suite. I use it for kick drum layering, basses, pads, leads, metallic sounds, risers and a lot else. If you haven’t already I would recommend spending some alone time with it.
Electronic Musician recently published an excellent Operator masterclass which goes into much more detail than this article, so be sure to check that out.
AdLib SoundBlaster Technology
A sound that is very nostalgic to me is that of the DOS computer games I played as a child. Many of the sounds from games like Simon the Sorcerer, Day of the Tentacle and others used simple MIDI soundtracks that triggered the inbuilt chips in many commercially available computers, and more often than not in many situations it was the Yamaha YM3812, which I would hazard a guess that depending on your age may be some of the most familiar sounding FM tones you’ve ever heard.
This is an excellent video by the 8-Bit Keys parent channel 8-Bit Guy, archiving some of the keyboard that were available to buy that also used this chip or similar variations of it.
I loved this sound so much I wanted to see if anyone had made a software version and low-and-behold, they had. The image you see below you is a vst (sorry Logic users!) called JuceOPLVSTi and it’s FREE. Sonically it’s fantastic and I was instantly transported back to 1992.
The architecture is more similar to the EFM1 rather than Operator. It has limited polyphony, some unfamiliar waveforms on offer and the envelope works in a slightly peculiar way, but I really dig it.
WARNING: Sadly, my experience of this plug-in that whilst it sounds fantastic the OSX release seems very unstable and has caused Ableton to crash, and, in some cases cause irreparable damage to certain saves. There seems to be an issue with the buffer size of the project – it will plod along happily at 256 samples but either side of that I’ve not been able to stabilise it.
Here’s a selection of some of my favourite presets from it:
Native Instruments FM8
Next we come to an absolute beast of modern FM synthesis – Native Instruments FM8. I’m not claiming that this is the most powerful of all the FM synths out there but it would certainly stake a claim. As it happens little-known DnB knob twiddlers Noisia claimed if they were stranded on a desert island with just one VST it would be FM8 [paraphrased].
FM8 heavily borrows from Yamaha’s 1983 DX7, FM8 has the power of a monster six operators while having a visual layout that makes it very easy to program compared to its hardware predecessors. FM8’s modulation matrix is by far the clearest display of co-dependant modulation operators I’ve seen and that makes it a hugely flexible synthesiser.
N.B Interestingly enough the DX7 actually not actually a frequency modulation synthesiser and uses something called phase modulation, however sonically they are pretty damned similar.
I want to avoid doing an in-depth “this is exactly how to use every feature of FM8” tutorial as there’s already enough of those out there and I want focus more on what makes is special in the context of what we’ve looked at already. If you really want to get under the skin of this synth I would suggest checking out the official manual which is excellent in terms of quality. Let’s have a look at the layout:
Let’s look at the navigation on the left hand side of FM8. The ‘Browser’ and ‘Attributes’ tabs focus on preset management and the ‘Master’ tab deals with voices, unison parameters, pitch bend information and other global features. The ‘Effects’ tab is unsurprisingly just some effects (minor gripe here: FM8’s effects can’t have their order changed or be modulated, which sadly lets the synth down just a little, otherwise it’s great), and the ‘Arpeggiator’ is self explanatory.
The ‘Easy/Morph’ is a useful tab for making broad changes once you’ve programmed something. We’re looking at the ‘Expert’, this displays our modulation matrix (far right) and either information about our operators, envelopes, modulation, key scaling, pitch and a nice spectral analyser (always a winner with me).
The ‘Ops’ subsection of the ‘Expert’ tab we can see an overview of our six operators A to F. Here we can oversee their tuning as a Ratio (to four decimal places) and an Offset. The Offset allows fixed tunings perfect for linear frequency modulation or creating drums and drones when the Ratio is turned to 0.
We can select the operator’s waveform too – all of the usual candidates are here, sine, triangle, pulse, saw, but also tristate waves, combinations of harmonics, formants and some waves borrowed from the Yamaha TX-series of synths. Additionally here we can invert and restart the phase as well as modulate the pitch and amplitude.
If we click on one of the letters A to F we can see the Operators individual controls:
This is gives us a far-higher level of control including more amplitude modulation settings as well as pan position and a complex envelope stage. The envelopes in FM8 not only allow us intricate shaping of slopes from linear to exponential or logarithmic but we can also virtually do-away with LFOs by having loop-able shapes within the sustain stage.
Operators can be routed directly to the master output and/or to each other as well as self-modulating and there’s additional distortion and filter circuits (X and Z). As if that wasn’t enough it’s possible to route audio from your DAW straight into FM8 to either modulate with the operators or use as a modulation source!
The Matrix itself has a number of preset configurations that are included but it’s far more fun to experiment with your own. The default preset you will see that only operator F is routed to the master.
We first need to switch on other operators, do this by either ctrl + clicking on the operator or right click if your mouse allows. Let’s turn on operator E. Directly underneath operator E and to the left of operator F, click and drag up to increase the modulation.
If you press a MIDI note while doing this you will hear the amount of frequency modulation increase.
This is the maximum modulation you are setting. We can modify operator E’s amplitude envelope to shape that frequency modulation over operator F. By setting a long attack and decay with no sustain, the amount of FM will increase to a point and then decrease. Combing this with the other four operators and different waveforms and ratios can throw up some huge sounds.
What this really has over Ableton’s Operator is the ability to combine our six operators in any combination we want.
Below I’ve made a quick pad sound to show off the multi-stage envelopes in FM8:
All six operators are sent to the master. A and B are both parabolic waves (like soft clipped sines) tuned slightly sharp and flat of the third and fourth harmonic respectively. Using the offset allows us to add a detune that isn’t tracked by the keyboard. This can also function as a more traditional LFO but we wont be using that in this patch.
C and D are tuned (again slightly sharp and flat) of the third and second harmonics. These both employ the 1+2 and 1+3 waveforms. These are 1st and 2nd harmonics and 1st and third, so what we’re actually hearing is 2 x (1+2) equalling 2nd and 4th harmonics, and 3 x (1 + 3) resulting in the third and ninth. A and B are both tuned around the first harmonics and use simple sine waves.
Panning the operators around the stereo field gives us a far wider sound too. We can see A and B are modulating C and D, while C and D module E and F and E and F modulate A and B.
We can see that while all of the envelopes share long attack and release stages, the sustain portions all have differently curved shapes, creating LFO-like amplitude shifts in the frequency modulation. This gives the sense of cascading LFOs all out of sync with one another which has a natural and organic feel to it while feeling celestial and expansive (even if I do say so myself). This patch has no external reverb or effects on it. You can download it here.
FM8’s capabilities go way beyond floaty pads and nice sheeny sounds like that – it’s capable of searing tear-out DnB reese basses, trance arpeggios, thick analog-sounding basses and pretty much anything you can do with a subtractive synth, but to avoid going too much into making this just about FM8, I’ll leave it here.
If you want to learn more about FM8, check out friend-of-the-family Tim Cant’s video for Native Instruments:
agArturia Synclavier V
The New England Digital Synclavier is somewhat of an enigma – everyone has heard of it (and heard it on various records) but few have used one, let alone seen one in real life.
Produced between about 1977 and 1980, similarly to its British cousin the Fairlight CMI, this combined the new technologies of sampling with additive synthesis and frequency modulation.
Not only would you have had to part with around $200,000 (far more by today’s rate accounting for inflation) but these were notoriously tricky to program.
Luckily for us, the good guys at Arturia have made a software version, retailing at a very reasonable €199 at the time on publishing.
Patches in the Synclavier are referred to as Timbres. Timbres can be made up to twelve component partials, which you can think of a little like oscillators. The original Synclavier only had four partials so the Arturia one is three times more powerful.
There are two windows for the Synclavier, the first is the timbre edit page (here, highlighted with a green box). Here we can make broad changes to all of our partials, changing their amplitude and FM envelopes, FM amount as well as voice information and we have a basic arpeggiator.
By clicking the button (white arrow) at the top we can expand the timbre edit page (white box). This allows careful and detailed control of each of our twelve partials including their pan position, tuning, FM amount, frame speed (more on this later), envelopes for amplitude and FM and two LFOs, one for pitch modulation and panning. Partials can be copied and pasted as well as solo’d and muted.
By click the SCR screen page we can access a more visual edit page for our partials. There are tabs (pinky/red) for each of the twelve partials amplitude and FM envelopes (which they refer to as harmonic envelopes). The envelopes are as to be expected, with time values for delay, attack, decay and release as well as peak and sustain portions. Partials can be shift-selected allowing for batch editing.
We also have a tab for assigning partials to key zones, a time slices page (detailed below), a basic mixer, MIDI modulation matrix, FX and global settings.
The time slices tab is where most of the engine room of this synth is. We have carrier and modulator operators each with control of of the amplitude and phase of up-to twenty-four harmonics(!). There are various edit controls such as templated geometric waves (sine, saw, pulse, triangle), drawing tools (pencil, eraser, straight line etc) and “coefficients restrictions”, which is nothing to do with the UEFA Champions League as far as I can tell. This means we can restrict the harmonics we’re selecting from ‘all’ to odd numbered, even numbered, octaves and fifths.
The sheer scope of potential sounds available here is huge – sitting somewhere between the simple yet powerful design of Ableton’s Operator and something more complex but slightly scary like Native Instruments Absynth.
Where it really comes into its own as a proper additive synth is the frames themselves. These are states that can be morphed between a little like the wavetable index of Serum or Massive. I’ve not found a limit to the number of frames you can have. Here just one partial with no frequency modulation – morphing between the basic partial and seven additional frames, each with a different harmonic makeup.
Really the best place to start with for learning the Synclavier is Arturia’s own sound design videos on their (excellent) YouTube channel. I’ve embedded part 2 of their look at the Synclavier as a lot of the content in part 1 is covered by me (albeit in slightly less detail) above. This goes deeper into what can be achieved combining the various synthesis engines in the Synclavier. Enjoy.
I wanted to finish off with an excellent Mylar Melodies video (please give him moines on Patreon). This is a video about the ALM Akemie’s Castle eurorack module – crazy 4 operator FM synth fully CV-able. What’s really interesting about it is that it focuses in on the sounds capable of (for want of a better phrase) dicking around with FM.
Something mylar melodies mentions is that while we all know and understand subtractive, there’s a sort of unknown quality about FM that still makes it interesting and possible to stumble across bizarre sounds.
The linear nature of the signal flow in a subtractive synth means that although we could all improve our understanding a little, it’s rare you’ll surprise yourself. FM on the other hand has oscillators interacting with each other at its core level, and the fragile nature of their interaction is fundamental to the scope of sounds that FM can produce.
I hope you’ve enjoyed this tutorial and have hopefully learnt something new; I had a lot of fun researching it. It’s actually been in my drafts for ages but I’ve been refining and tweaking it to ensure I do sufficient justice to the topic.
If there’s something I’ve missed out it might either be accidental (I am human) or deliberate (perhaps it’s too technical for these pages) – either way, please do let me know in the comments or get in contact. Have fun!