How to actually use FM synthesis — A practical guide

One of the most pernicious lies in the synth world is that ethnosynthesis is difficult to understand. That's not true; it's really not difficult to understand. It’s very specific, you know? The problem is that nobody really teaches you exactly what you can do with it, and there simply aren't that many resources available.

In fact, there are not many straightforward tutorials on how to actually implement FM synthesis. When I was trying to learn FM synthesis, the overwhelming majority of the videos I saw on YouTube were just basic explanations of what it is. And really, that's a very easy thing to understand. I think that most content creators make an FM synthesis video because it's easy content and it makes them feel smart. What I wanted to do is create a video where I skip over all of the basic stuff, such as using a slow LFO and then speeding it up until it sounds like a timbre instead of a siren.

So, if you don't understand that this is the premise of FM synthesis, then I would suggest finding one of the numerous videos online that explain it. Instead, I wanted to create a video showing you how to actually use FM synthesis, along with some practical advice on how to make patches and more. This video is aimed at beginners, but it should be the second video on FM synthesis you watch, rather than the first. It's really not much more difficult than subtractive synthesis. You have the VCO, VCA, and VCF, and you can get a lot of mileage out of those three simple components.

And FM synthesis really isn't more difficult than that in its basic form. It gets more complex, but when you know what to do and how to start, it's really not that difficult. I have formulated in my mind that the best way to teach and learn FM synthesis is to understand the two-operator structure very thoroughly. You may have the impression that two-operator FM is lame, I guess, because it goes much deeper than that—it's more than just the two-operator structure. Two-operator FM is the purest form of FM. The reason why they had six operators in the original Yamaha FM synths is because, with all that flexibility, you can create emulations of real-world sounds.

And you can do that fairly easily by creating uncanny trumpets and similar sounds with a DX7. However, with two-operator FM, it can only ever sound like FM. I really like two-operator because I appreciate how FM sounds. Once you understand how two-operator works, everything else will become much easier. I would imagine that 80% of understanding FM lies in comprehending the two-operator structure.

So that's what I'm going to try to teach today. I know I said that I wasn't going to go over the basic premise of FM synthesis, but I will dive a little bit into FM theory because it's necessary. FM synthesis is often referred to as a form of additive synthesis, but I don't think that's accurate. I find it confusing to label it as a form of additive synthesis, even though you are generating more harmonics instead of taking them away.

But the point of frequency modulation (FM) is to generate sidebands around the fundamental frequency that you're starting with. Those sidebands are just peaks in the spectrum. Each one of them is a sine wave that gets added on top of the fundamental frequency. I just wanted to clarify here that it's not literally adding sine waves on top of the fundamental, which would, in fact, be additive synthesis. Instead, the harmonic frequencies are generated by altering the phase of the waveform, so it's calculated from the time domain, not the frequency domain. That’s how you get the more harmonically rich sounds. Those sidebands aren't necessarily in the harmonic series, but when your modulator is an integer multiple of the fundamental frequency, then all of your sidebands will be in the harmonic series. This will give you a more harmonically coherent sound and won't confuse the pitch of the patch. Okay, so I have here a two-operator Max patch with just one modulator and one carrier. I just wanted to demonstrate two really important principles that pretty much boil down to modulation amplitude and the ratio of the modulator to the carrier. As you increase amplitude, that generates more harmonics. As you increase the ratio, that spreads those harmonics out from each other.

So, between those two parameters, you have pretty much all the timbral variation that you can achieve in FM synthesis. It's quite simple, right? Let me demonstrate it quickly. I have a one-to-one ratio, and I'm going to increase the amplitude. You saw on the spectroscope that more peaks in the spectrum are being generated. Now, I'm going to increase the ratio with the amplitude high and see what that sounds like. You can see in the spectroscope that the same number of harmonics is present, but they are just spread out more. Higher ratio settings are how you get those bell tones, while lower ratio settings are your bread and butter FM sounds. So, you can think of amplitude as comparable to subtractive synthesis.

The amplitude is kind of like your filter cutoff frequency. The higher the setting is, the more harmonics you're going to have. Conversely, the lower the setting, the fewer harmonics you'll encounter. It's somewhat akin to turning a filter knob, but of course, it sounds nothing like a filter. So, I wanted to show you that, and then I have something else to share really quickly.

I have this parameter set up, and it's the exact same as the ratio, except it doesn't move in integer multiples. It just goes from 1 to 16 freely. So let's listen to that. It sounds really quick, so it might not sound great, but it is basically the same thing as a ratio. It just might be a little clearer what's going on.

Here’s the text reformatted with correct capitalization and spelling: "How as you bring up the modulator frequency, it's going to spread out the harmonics. So yeah, I just wanted to demonstrate that really quick. Those two parameters are pretty much where all of FM synthesis lies. And it's pretty simple, right? Once you learn how it changes the sound when you alter these two settings, then you basically understand FM synthesis. So now let's dive deeper into this two-operator structure and show you what to do with it."

Okay, so now we understand the basic principles of what amplitude and ratio do, which is generate harmonics and then spread those harmonics apart. Now, let's learn a little bit more about what you can expect with certain ratio settings and how to achieve specific sounds that you want. I have FM8 for this, primarily because it has a nice oscilloscope and spectrum analyzer, and it's also a great synthesizer. However, it can be quite complicated for someone who is new to FM synthesis. On the bright side, you can often find it at a very reasonable price, which is why I got it. Okay, so again, I am using a one-to-one ratio, and I now know that as I increase the amplitude level, it generates more harmonics. Pay attention to the waveform and how it looks as I raise the amplitude a little bit. It starts to resemble a saw wave, and that's important because if you understand the basic wave shapes in analog synthesis, you know that saw waves produce both even and odd harmonics, while square waves yield only odd harmonics. You probably already understand the difference in timbre between these two waveforms.

Square waves are often described as sounding somewhat hollow, and the same can be said for triangle waves. Sawtooth waves contain both even and odd harmonics, while square waves and triangle waves only have odd harmonics. So, what can you surmise from the appearance of these waves and the way they sound? Well, the first thing to notice is that square waves and triangle waves are symmetrical waveforms, whereas sawtooth waves are not; they are asymmetrical. Sawtooth waves rise sharply on one side and then drop down to the other side with each cycle.

So that's an important point, because as we saw, with a 1:1 ratio, you get an asymmetrical waveform. Let's see what it sounds like when you have a 2:1 ratio; you get a symmetrical waveform, kind of like a square wave. So, yes, that's another important principle: when you use even ratios, you're only going to get odd harmonics, similar to a square wave, kind of counterintuitively.

And when you use odd ratios, you're going to get even harmonics, kind of like a subwave. So that might be kind of difficult to remember because it's somewhat reversed. With even ratios, you get odd harmonics. I guess maybe that can be your mnemonic device: it's counterintuitive. Therefore, even ratios equal odd harmonics. You can see that if I go up to a ratio of three, the waveform is asymmetrical.

And when I go up to a ratio of four, the waveform again is symmetrical. So, in order to learn FM, what you need to do is test out what these different configurations sound like with different ratios and different modulation levels or amplitudes. Just see, for example, if I do it just a little bit, how does it sound? If I do it a lot, how does it sound? If I do it at a really high ratio, how does that sound? You’ll get a sense of how to use these different settings in certain applications.

So, for instance, if I'm making a bass sound, I'm pretty much always going to be using a low ratio, like 2 to 1 or 1 to 1. Let me do this. It sounds like it would be good for a bass, right? Because you're retaining more definition in the low end. If you want to create a bell sound for whatever reason, even though I don't support it, you should just increase the ratio to 10 or something. But what you should do now is test out these different configurations and see what sounds good. What would sound good for what purpose?

Stuff like that. You only need to think about two operators for now. I really like a ratio of two to one for bass sounds. Yeah, a ratio of two to one makes a good bass sound too. Three to one? Not really. I guess that's not bad.

But these lower ratios are good for things like bass, basically. So, if it helps you, you can think about level as your filter cutoff frequency. The higher it is, the more harmonics you're going to hear, similar to opening up the cutoff frequency of a filter. So just between these two parameters—ratio and modulation amplitude—this is where most of the synthesis happens in FM synthesis. Understanding what settings between these two parameters produce different sounds will help you grasp how FM synthesis works on a larger scale.

Once you start moving into more operators, all of those rules and principles still apply, but you'll have more flexibility in how you can implement them in different ways. Okay, so now let's talk about feedback. Feedback is an extremely important parameter in FM synthesis, and I hate it when FM synths don't have feedback because there's just so much you can do with it. It's probably my favorite parameter in FM synthesis. So let's listen to how it sounds when I just have one sine wave, and I'm feeding it back into itself, into its own phase. You saw it kind of starts to look even more like a saw wave, right? It's not perfect, though.

It has these curves, and that's actually really important for phase modulation, because that makes a huge difference in phase modulation, whereas it wouldn't necessarily in frequency modulation. You should never, ever use an actual saw wave in a phase modulation synth, and every FM synth is phase modulation. Never use a saw wave. There's no point to it. But I think I want to do a video talking about the difference between phase modulation and frequency modulation, because there's some information to be explored that I don't think anybody has explored yet on YouTube.

Okay, I need to add a caveat to this because there are ways to make a saw wave sound good in FM. But in short, you can't just use a straight-up saw wave because it won't sound good. It has to do with the difference between phase modulation and frequency modulation. This further motivates me to create a video on it, so I'll probably do that. You can use a really dull saw wave with very limited harmonics, and you can make it sound pretty cool that way.

But just a straight-up saw wave, don't do it. If you're ever going to program your own FM synth, just avoid that. Anyway, it does kind of look like a saw wave, right? What's happening is that as the output of the operator you're listening to feeds back into itself, it pulls its own phase backwards and sharpens it. The feedback feature is essentially the important part. If you dial it in a little, as you adjust it more, it just becomes noise, which is a really important tool to have when you're designing sounds.

But something to note with that is that it doesn't sound like white noise. It's kind of like a dynamic noise that's really sharp in the high end. But again, it's really, really nice to have when you're making sounds. So, with this idea of sharpening the waveform in mind, and also with the idea of how to generate odd versus even harmonics in FM synthesis, we can now make a really convincing square wave and saw wave. Let's do the saw wave first. So, I have the modulator.

I'll set it to one, and I'll start bringing that up like that. In FM synthesis, you can route anything anywhere, basically. So I'm going to route the output of the carrier back into itself in a feedback loop. That looks like a pretty nice saw wave. I mean, it's not perfect, but it is better than just feeding back one operator.

When you have two operators, it kind of helps straighten things out a bit more. So there's a pretty convincing saw wave. This is an actual filter, not just a pretend filter. But yeah, if you're using FM in a subtractive... Hold on, can I just say, it's funny how Germans always say "subtractive"? Did you notice that? Like, they never say "subtractive"; they always say "subtractive."

And now I'm starting to say it because I watch so many German synth people on YouTube. But if you're using FM in a subtractive context, that's how you can make a saw wave. So now let's do the same exact thing, but make a square wave. To do that, we know that we need an even ratio, so let's increase it to a ratio of two to one.

And look at what that sounds like. So that's a pretty damn good square wave, to be honest. It's obviously not perfect; it has these little inconsistencies, but it's definitely a square wave, and we can listen to that filtered as well. So yeah, that's why it's important to understand this idea of different ratios giving you different kinds of harmonics. Whenever you would reach for a square wave instead of a saw wave, or vice versa, you could do the same thing here with a ratio of one to one versus two to one.

You can almost achieve a resonant filter-type sound with feedback by adjusting the amplitude. I don’t know; it definitely doesn’t sound like a traditional filter. Actually, I think my favorite ratio setting is a 1:2 ratio. We can achieve this by setting the modulator to 0.5. So, you could think of it as 0.5 to 1—the frequency of the modulator is half that of the carrier.

So let's listen to what that sounds like. It's super good for basses, really thick, and you can hear it decay into a higher frequency. It sounds really good with some feedback, so you can almost achieve some resonant filter-type sounds with that. I just love the way that sounds. That's really good for basses. You could also go even lower, like 0.25, but in my opinion, that's a little too low.

Yeah, definitely too low for this. Let me put this up. You kind of almost get some form of sounds out of that. I really like the way that sounds. It almost resembles an uncanny valley resonant filter. So we're not looking at the scope, but you can kind of hear how, with the feedback higher, it has this sharper high-end timbre to it, as if you were turning up the resonance on a filter sweep.

So yeah, that's feedback—a very important tool in your toolbox. It's probably just the third tool you need. You really only need three: ratio, amplitude, and feedback. With those three elements, that's pretty much where all of FM synthesis is performed. That's where all the sound designing happens.

And then, of course, envelopes, which control LFOs and other parameters, manage the amplitude level over time. But once you have explored these three concepts, you'll be well on your way to understanding FM synthesis. Once you can predict what changes will produce various sounds, that's when you can start making executive decisions in your sound design with FM, rather than feeling like you're wandering aimlessly. So, yes, that's feedback—my favorite parameter. Now that you understand the two-operator structure, I’m going to give you some advice on how to approach algorithms.

I had this whole idea of what to do with this section. I was going to use one of my hardware synths, but it just was way too complicated. I think that the best way to teach this is to just give some examples. But first, I'm going to go over the basics of it. Really, it's just more of the same stuff.

So you're more than halfway there to understanding it. First, I'm going to talk about three plus operator stacks. As you can see, the algorithm we have selected here in the operator is just a stack of four. The last two are the regular two-operator structure that we're used to, and then we're going to add a third one on top of that.

So this blue one, periwinkle, I think. I don't know. Yeah, I think it's like periwinkle. Okay, anyway, let's start dialing in some modulation. Okay, that’s fine. So, like I said, it's pretty much just more of the same thing. It sounds pretty much like how you would expect it to sound when you modulate a modulator. So, let's just start dialing this in a little bit. So yeah, it starts to bring in more harmonics, more high end. You can do it like this just for more harmonics, but I don't find that very useful. What I find stacks of operators like this useful for is basically varying the amount of modulation that these operators are doing over time. So it’s basically just using the envelopes. That's really mostly what FM synthesis is now that you understand the basics.

It's just about understanding how you can use the envelopes to your advantage. So first, let's give the good old modulator a little bit of attack. All I've done is just give the first modulator a little bit of attack, so it kind of swells in. I'll demonstrate how it sounds when I have a sharp attack on this one. This modulator is going to modulate the modulator quickly, and this one is going to modulate the carrier slowly. So let's just listen to how that sounds.

What's nice about operator stacks like this is that if you use a high ratio for the first modulator, let's say, eight, and then use an operator with a low ratio to modulate the one with a high ratio, it can create interesting effects. I don’t know; these examples aren't sounding very good because I'm not really in the mood to do all this. But the basic idea is to generate different types of harmonics with these different operators and do it at various times. For instance, I can use an LFO on this one, let's say.

Let's try to turn this into a chord, actually. Yeah, so basically what I have going on is very simple. The first modulator is set at a ratio of 0.5 to 1, which gives it a richer bass. Then, on this operator, which is modulating the modulator, I have the envelope set to full blast, and I'm just using the LFO to bring it in and out. I thought it might need some echo. Essentially, the idea is to vary the amount of modulation from each of these operators at different times.

And that's basically how it works in any algorithm, no matter what the configuration is or what is modulating what. All you're dealing with when you look at algorithms, after you understand the basics of FM synthesis, is trying to put those into the puzzle and see what you can do with each of these operators to change the timbre over time. I feel like that's the most obvious thing. I don't even know if I'm doing this very well. It will be better when I get into the examples.

But anyway, it's very simple. Once you understand the two operators, it begins to become more intuitive what you can do with each of these operators in a stack. So, let's talk about parallel operator stacks. I really like this kind of algorithm, where there are just two stacks of two. You have one set of two operators and then another set of two operators.

So, let's reset all this. According to this algorithm, we have B modulating A and then separately D modulating C. I'll make this group do something interesting, and then I'll have this stack do something different. We can listen to the first stack like this: a really simple two-to-one ratio gives us a sharp attack. Then we can mute that one and listen to the other stack. We have one side that's producing this sound and the other side that's producing this sound.

And then put it together. The way you should approach these kinds of algorithms, where there are multiple carriers, is to think of them as two different layers to your sound. I believe that is the most important thing to consider when you're looking for an algorithm to use: look at how many carriers there are. For example, in this case, there are three carriers, but for two of them, there is no frequency modulation happening at all. There's just one stack of two operators, and for those two operators, there’s no frequency modulation; it's just going to be sine waves. This might not be particularly useful for what you’re trying to achieve, so you need to consider what you are going to use those two straight-up sine waves for. Therefore, I wouldn’t get too hung up on choosing which algorithm to use.

Just check and see how many carriers there are, and then think about what kind of sound you want to make. I would say that this algorithm is the most versatile. It's simple, and you can wrap your head around it pretty easily, and you can get a lot of cool sounds out of it. When you get into the algorithms that have multiple modulators in one carrier, those are for pretty specific applications. For instance, if I have an algorithm like this with one operator modulating three carriers, I can create kind of formant sounds. So, yeah, you get that "ya-ya" sound. Basically, what's happening is that the lone modulator has a ratio of 0.5, which is really low, and that's kind of giving you the bass pitch of the voice in formant terms. Then you have these three operators: two of them are at high ratios, so those represent the formant peaks and the formant frequencies in the spectrum, and then this one gives it a little bit more body. So, this is providing the modulator, while the carrier A is also responsible for the bass pitch of the formant. The other two operators represent the formant frequencies. You can experiment with some really high frequencies; when you go above around 15, it still kind of sounds like a formant, but it sounds—well, I was going to say it sounds more unnatural, but all of this sounds quite unnatural. Anyway, what I wanted to show is that this is a very specific kind of use case, which is why I would use an algorithm like this.

But for general purposes, you might just want to start out with a simple algorithm like this and then see, okay, what do I want to do here that I can't do with this algorithm? Then look and see if, you know, maybe this one makes more sense or whatever. Something like this, where it's just for carriers, I never use something like that. I don't find it useful at all, really. Some people say, "Oh, well, you can do additive synthesis with that because it's literally just adding sine waves together." I think that I have too much respect for actual additive synthesis to disgrace the name of additive synthesis by using this for it.

Let's just say that. But yeah, I wouldn't put too much stock into what algorithm you're going to use before you start. Just pick a simple one and see where it goes from there. It's always fine to try out another algorithm randomly in the middle of a patch and see what it sounds like. That's pretty much how you learn to pick an algorithm—by experimenting.

But yeah, the most important takeaway, I think, is how many carriers the algorithm has. Okay, so now I have some drum sounds in a drum rack made entirely out of operator voices. Let's just listen to how it sounds. It might not be what you'd expect from FM drums; it sounds kind of like a 909, almost with samples, reminiscent of a 707 sample.

I think this one was it. Yeah. Anyway, let's just go through these individual drum sounds. All of them are made with very basic FM synthesis, using only sine waves and pretty standard bread-and-butter methods. First, this is my favorite algorithm for bass drums. As I said, it's super versatile because you get two layers: one for the body and one for the transient. Let's listen to the body first. It's a three-to-one ratio, so let's hear the carrier first. It's just a sine wave with a pitch envelope. To give it more body, I used a ratio of three. It's really subtle; it sounds a little bit like overdrive. Actually, a ratio of two to one is really good for overdrive-like sounds. As we learned before, it transforms the output waveform into a kind of soft square wave, which emulates the sound you get from soft clipping in a distortion circuit. Let’s listen to how that sounds. If you close your eyes, it kind of sounds like it’s overdriving, you know what I mean? So that's really nice. Also, the ratio of three to one is good for retaining definition in the low end. When you want to maintain that clarity, use lower ratio settings. So, that’s the body of the kick.

Now let's listen to the transient. So that's literally all this side is doing. And that, plus the body, sounds like this. Without the transient, it sounds like this. So, it's very, very simple. The way I created this transient-type section is by using this carrier with a really short decay.

And then I have the modulator pretty high, and the feedback is turned all the way up. So that's what it sounds like when the carrier has a longer decay. All I'm using this sound for is just the very beginning of the kick drum to give it some more snap. This is a very simple configuration, and it produces a pretty good kick drum. Now let's move on to this clap. This one's a bit more complicated because I have some external modulation going on, but you can usually do something similar in an FM synth, like the Digitone or something similar.

So again, I have this double stack of two operators. Let's just listen to this first section first, and that would again be like the body of the clap. So that makes up the bass for the clap, and the section up here, again, makes up the noisy part of it. So let's listen to that. And all this is, well, you usually can't go up to a ratio of 41 in most FM synths because that's just kind of ridiculous.

I'm surprised that they let you do that in the operator. But again, it's a similar thing where I have the modulator. The feedback is set to 100, so it gives you a really noisy sound. You really don't need this. Let me see what it sounds like. Yeah, so literally, okay, it didn't even matter.

Basically, it's just the same thing. I have the modulator, the feedback is set really high, and that's just giving you noise, pretty much. It's giving you FM noise. To make it sound like a clap, I have this MIDI shaper, which I just drew in a ratchet because I didn't know how else I would do that in Ableton. I'm still pretty new to Live. But without that, it sounds like this.

It produces a nice ratcheting sound, and when combined, it creates a clap. You can achieve this quite easily using LFOs. For instance, the Digitone has an exponential envelope LFO. If you repeat that, it generates a really good ratchet sound.

So that's how you make clap sounds. You always need a ratcheting envelope for claps, just because that's the nature of it. That's what gives it its characteristic sound. But, you know, you can apply this same logic to a snare drum. I don't really like using snares, but it would just be the same thing. You would have the body with these two operators, and you would give it a pitch envelope, and then you would have a noise portion of it.

And I've done all of this with just sine waves again. I created all of this with a very simple and basic FM setup, so let's listen to the hi-hats. For these hi-hats, I have a stack of four operators because the more operators you have in a stack, the more metallic high-end and atonal sounds you can get. I have this first operator; let's just listen to that. It's essentially the bedrock for all of this modulation to happen because the modulation is what's giving this sound. In fact, I'm not even using this last operator; it's just a three-operator patch. So, let's listen to the first operator. That kind of gives the shape of the cymbal. You can think of it as indicating what kind of cymbal it is. Instead of being a ratio of the MIDI note that you tell it to play, it plays whatever frequency you dictate it to play without changing up the keyboard. That might sound a little confusing, but really, all you should take away from this is that this is not a pure ratio. It's free-running, so the sidebands it generates aren't going to be harmonic, and that's important for a lot of percussive sounds, especially cymbals. And then, I have this one.

So I guess I actually lied. I did use a waveform that wasn't a sine wave. But let's listen to how it sounds with a sine wave. Yeah, the 16 harmonic saw wave sounds a little bit brighter, but we can just do the same thing with a sine wave. It sounds fine.

So again, I have this operator at a fixed frequency, not a ratio. Then I have it going really high. With a frequency that high on this modulator, it serves the purpose of making it noisier. This modulator gives it a metallic bass, and then this one imposes noise on top of that. The most important part of this sound is that we have a high-pass filter.

And this is: I'm kind of a purist when it comes to FM. I don't like to use filters. I don't really like the idea of making a harmonically rich sound and then just filtering it out. I like the sound that FM makes when you use it on its own terms, in terms of taking away harmonics by reducing the modulation level. However, filters are really helpful when you're making drums, especially hi-hats and cymbals.

So, let's listen to how it sounds without this high-pass filter. It still has that classic FM metallic sound, but filtering out all the unnecessary low end is really important for drum synthesis when it comes to FM. Most FM synthesizers nowadays come with filters for each voice. Back in the '80s, you might have needed to use a mixer board to remove the lower frequencies. However, for this synthesizer, we just have a built-in filter. It retains that metallic signature, but being able to filter out the unnecessary lower parts of the sound makes it really good for hi-hats specifically.

If you're using a crash cymbal or a ride, you might want some of the low end. But hi-hats, in my opinion, need to be pretty high-passed. And this weird 707, it's like a 707. Yeah, it sounds like one of those Latin drum samples. I don't really think we need to go into it. It's just random, but these ones are kind of like toms, I think.

I'm not going to go super deep into the specifics of both of these sounds, but basically, you can kind of see the pattern. I have these operators running at fixed frequencies, so the sidebands are not going to be in the harmonic series. Instead, they're going to be spread out in a different way, which lends itself well to percussive sound design. I also have a pitch envelope applied. Creating nonspecific drum sounds like this with FM synthesis allows you to experiment freely—throwing everything at the wall and seeing what sticks. Generally speaking, fixed frequencies are effective for this type of sound design, or at least ratios that are off and not perfectly multiples of the fundamental frequency.

And as you can see with this one, I only have one carrier, and these are just three random frequencies that are modulating this carrier. So it creates three bumps in the spectrum, and with the amount of modulation, it generates even more bumps above those. FM drums are really fun to experiment with because you can just do random things like that. This one sounds kind of like an FM version of a 909 drum or a 909 tom. It's the same concept: you have fixed frequencies, and you just dial it in to see what kind of sounds you can make and what fits the drum track.

So I'll put together again; it goes like this. Yeah, it's fun! Okay, for my final example of how to use algorithms, I'm going to show some dub chords that I tried to create. So, let’s listen to this one. On this patch, I've given the carrier a little bit of attack, so it's not super poignant. A really small amount of attack, just so it’s not as snappy. Then, I have this other element at a ratio of two, coming in kind of gently, and that remains consistent throughout every iteration, I think. So, that forms the basis of this patch. Additionally, this operator is also modulating the carrier separately from the other one.

And it shows that I have... Let me see. Yeah, I had this one turned on, but it's pretty subtle. Yeah, it just gives it kind of a gentle overhang. This one is where the movement comes in, though. So for this, I have a sharp attack and a pretty fast decay. It's at a ratio of six, so it's going to bring in a good amount of high end.

But importantly, I have the LFO modulating the volume of it, so the overall level. It's a really slow LFO, so it comes in kind of sparsely, and that's important for dub techno chords to give this continually evolving sound. Most of the time, it's going to have a slow attack, and the chord comes in gently. Sometimes, it will give you more of a stab, so when you send that to a delay, it adds some interest every once in a while. So, there's number one. This one has the same basic idea; you have a kind of base amount of modulation, which is these two.

And then this one, as you can see, the LFO is modulating this, and it just kind of brings in more high-end periodically. So, yeah, it brings that high end in and out. And then this one has a ratio of 0.5, which is going to give it a lot more bass. As you can see, this one is directly modulating the carrier, so you have these two modulating the carrier separately, and then this one modulating the carrier. This is also kind of being brought in and out of intensity. So, yeah, there's a bit too much going on in this FM patch for dub techno, but you get the idea. Approaching algorithms pretty much boils down to using your envelopes well and seeing how many carriers the algorithm has so you can determine how you want to use these different stacks. If you want to layer them up, like in this one, or if you want to have a lot of modulation going on at the same time. Having multiple modulators on the same carrier also gives it a kind of layering, but it just gives you less control over each of the layers because you're limited to one carrier. However, it can produce some cool sounds. Lastly, I just wanted to show a couple of tips and tidbits that you might find interesting regarding FM. So we learned how to make a square wave and a saw wave in FM, and now I'm going to show you how to create a triangle wave. This is a bit more rare because it requires negative amplitude and negative modulation, and most FM synths don't have that because it complicates things.

It's not really a point in most cases, but something really cool that you can do with it is make a triangle wave. So let's see how that works. I'm starting out with a sine wave, of course, and you can see that I have these controls set to bipolar. This is the modulation amplitude and the feedback. I'm going to bring the amplitude down a little bit, just so you can see what it looks like.

So, this is a ratio of two to one, and the amplitude is negative. I'm going to go back and pause for a second to see what it looks like. You can see we get that classic soft square that you get with a two-to-one ratio, but if you go negative, you get a soft triangle. That's kind of strange, right? I don't know, maybe you wouldn't expect it. Now, I'm going to show you just positive modulation and I'll go with feedback, both positive and negative, so you can see what that looks like. It sounds similar, but there are some slight differences in the spectrum. As you can see, the positive feedback kind of squares off the top, while the negative one brings the top inward a little bit, almost like a triangle. So, let's apply that to this little soft triangle thing that we have going on. This is just a tiny bit of negative modulation, and then I’ll take a tiny bit of negative feedback. You get a pretty decent triangle wave.

And again, this is very, very rare in FM synths. I think that one of the old Yamaha synths, I believe it's the SG-77 or something like that, can do negative modulation and feedback. However, one interesting newer one is JEM from Forz. This is part of a Max for Live device called Opal, which is a drum synthesizer that has four different synth tracks, and an FM synth is one of them. It features a two-operator FM synth. Interestingly, it has negative modulation and negative feedback, so let's just try to recreate it here. I'm not going to play the audio, but I'll just show you what it looks like.

So, yeah, just a little random fun thing. If you ever venture to program your own FM synth, this might be something to consider. You know, making it more complicated isn't necessarily a good idea, but you can do interesting things within limited control ranges. Actually, the Model Cycles has a little bit of this too on its kick engine. So, just a fun little tidbit: you can make a triangle wave with FM, and you can also use pulse-width modulation. However, I'm not going to show that now because it's more complicated. Now, I'll give a little advice on using non-sine waveforms. I think people have the impression that sine waves were so simple back in the '80s, and now we've moved on from that, so we can use any waveform we want for FM. In my opinion, that's not a very good mentality. I think it's because people think that FM is frequency modulation instead of actually being phase modulation.

But there's no reason why you can't use non-sine waveforms. It's just that the best results come from waveforms with very limited harmonics. So, additive synthesis is a really good complement to FM. When you look at an FM plug-in like FM8, you'll see it has these other waveforms. Let's look at this triangle. If we examine the spectroscope, you can see it only has 1, 2, 3, 4, 5, 6, and 7 harmonics.

So, it's not a full triangle wave; it's very limited. Let's also look at the sawtooth wave. You can see it only has 16 harmonics. Real sawtooth waves and real triangle waves have a lot more harmonics than that.

This waveform, while not having as high of a resolution, shows a lot of curvature in the phase. In fact, there is a saw wave with three harmonics, which actually resembles modulation at a one-to-one ratio with just a little bit of amplitude. This waveform is very curved, and this type of sound is best if you're planning to explore beyond sine waves with frequency modulation (FM).

And you can see there are these other ones with harmonics that are at specific intervals, harmonic intervals. It also has the TX81Z waveforms, which are kind of fun. Should I explain in detail? I don't know. Basically, with how FM works in those old Yamaha synthesizers, it made sense to implement this kind of waveform because the sine lookup tables they used were a quarter wave.

And then, instead of repeating it in the same pattern—like a quarter wave this way, this way, and then the negative portion—they could just read it back in a different way, like this. Yeah, it just gave you a little bit more variation. So you could generate higher harmonics without using multiple stacks of operators. That's not as flexible as using stacks of operators because, again, you can do different things with those with the envelopes. It doesn't have to be just a static level of higher-order harmonics.

But as you can see, these still have very limited harmonic content. So, these kinds of things are best for when you're not using sine waves. In FM synthesis, the Digitone has a really good implementation of this because it is essentially additive synthesis. I think the maximum number of harmonics they used was 16, and these harmonics were parameterized, allowing you to sweep through them. I'm pretty sure it used a wavetable composed with additive synthesis, as this would be more computationally efficient. You can sweep through the different harmonics, which is nice. I always prefer when things are parameterized instead of being selectable, if that makes sense. I think that was good design. I don't know if there are any other FM synths that stand out to me in this regard. So, that's a brief overview of non-sine waveforms in FM synthesis. Now, I'm going to recommend some good FM synths. FM8 is a good plugin.

It's very flexible. You can route things in a lot of different ways, so it's fun. However, it's quite complicated for a beginner. But I think it's a good implementation of FM.

There aren't many FM synths that have a modulation matrix for the operators. Another good one is Galanta by Force. In fact, everything by Force is very high quality and sounds great. They have good interfaces as well, so I would highly recommend their products. They're doing something new, and it's refreshing to see a company that isn't constantly reiterating past synth styles. I believe we should move on from remake culture.

I think that should be over with. Um, anyway, this is a two-operator FM synth, and it has some interesting quirks. It features cross-modulation between the operators, as well as both positive and negative feedback on each operator. Additionally, it has an intriguing stereo function that creates a unique sound. What I believe it's doing is duplicating the modulator and then offsetting the phase of one of the copies. This allows it to modulate the carrier on both the left and right channels.

So I think that's what's going on. But it's just a nice little stereo addition. And yeah, it's very simple and sounds really high quality. So I would recommend this one. Another one is this whole device, Opal, which I mentioned earlier when I was briefly showing you Gem.

This is also similar to Glunta, but it has negative modulation, which is nice. It's tailored for percussive sounds, which is cool. The phase actually starts at a quarter wave, so you always get this pop, which I really like the sound of, and it helps with percussive sound design. It also has this noise, which is cool. It is FM noise, but it's actual FM noise, not phase modulation feedback noise. It's noise modulating the frequency of the whole thing, so it sounds really cool.

It's nice to have noise that's not just feedback noise, serving as another layer that you can add on. You can use feedback in a different way at the same time if you want to. Everything in this device is really nice. I would certainly recommend it if you're into old school vintage lo-fi FM sounds. This company, Plogue, is really good for that. They have a Genesis/Mega Drive emulator and the Porta FM emulator, which is a lot of fun. What was it called? Yes, the Yamaha PortaSound, which I believe was a two-operator FM synth and is quite rare. You couldn't edit the parameters, I don't think; it just had preset sounds. But with this emulator, you can edit the parameters, and their stuff is very meticulously reverse-engineered, so they get everything pretty much accurate in terms of sound. They call it bit-accurate emulation. I think this one is nice because you get two layers, along with a drum synth. The Mega Drive emulator sounds really good, which is interesting because it’s emulating the Genesis/Mega Drive—known for being notoriously lo-fi. The quantization noise in it is really vivid. Even though I just said I wish we would stop constantly reiterating the past, it is nice to have these classic sounds. I actually do love remakes of things when it comes to synths and such, but I'm just tired of everything being that way these days. Anyway, this company is a good one, and they have non-FM stuff too if you're interested in that.

And of course, as I was making this video, the new Digitone 2 dropped. It looks really cool. I would still recommend the first Digitone if you're only interested in FM stuff because it's a really high-quality FM synth. The way that things are parameterized is nice; it takes a slightly different approach, but you still get that classic FM feel, which is cool. I also really like the way the old one looks with its different-colored keys. I know a lot of people didn't like that, but it's kind of sad to see the new one omit that feature. That said, the new one still looks really cool. So yeah, the old-school Digitone is a nice FM synth, even though the new one will have an FM drum machine—or an FM machine that's specifically for FM drums. The old one can produce really good drums, too.

You get the two LFOs, and there are a lot of really good drum patches already out there that you can download for it. My favorite drum machine of all time is the Model Cycles. I think it's just kind of perfect, to be honest. I love how simple it is, and I love the way it looks.

I love how light it is. Everything is parameterized really well, and it's truly one of a kind. You know, there’s nothing else like it; there is no other FM drum machine. It’s really nice that the parameters are narrowed down and zoomed in to certain kinds of ranges with FM.

They keep you in a sweet spot, and you still get a lot of flexibility with what you can get out of them. But it's cool—it's just nice to see something like this. I guess that this whole recommendation section is pretty much just a hagiography of S. Madison. I am really inspired by his work, so I have no problem with giving him some praise. Actually, something interesting is that these controls are usually macro controls, managing multiple parameters at once within the FM structure, under the hood. So I really like approaches like that.

I think it's inspiring. I believe that more synthesizers should be made like that. Every implementation of FM doesn't have to be this classic reinterpretation of the Yamaha approach, because that was just one interpretation, right? There is a lot that you can do with FM. There are many ways to implement it and make it easier for the user to get something going quickly with it.

So that's why I really like the Model Cycles, my favorite drum machine. So yeah, that's all I have for this video. I hope that it was informative for people. If you have any questions, let me know. If you have criticisms or if you think that I didn't explain something well, just let me know. I'm not planning on being a YouTuber, so I don't really care if this video gets shared or liked or whatever, but I guess it would be nice if more people were able to be exposed to it.

So, yeah, thank you guys for watching.