My approach to FM synthesis.
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Hey, @glooms, exploring blindly can be fun too ^^
This said, FM synthesis is not that hard, despite being very rich.
Reading the âTao of FM synthesisâ is fun and gave me some basis to retain some knowledge and know more and more / learn from what I was doing.
FM vocabulary is often improper, as if someone had tried to obfuscate the knowledge. Just get the vocabulary right and you start understanding.
A few tricks:
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FM is a composition of âoperatorsâ. Simplest is two, start from here and expand.
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an operator in FM language is an oscillator (usually together with its own volume envelope). Most basic oscillator is a sine wave.
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a composition of FM operators is called an algorithm. No clue why, it has nothing to do with what an algorithm really is in mathematics or computer science. It could/should have been called a directional graph. Or a tree, or composition, or simply disposition or configuration. The term âalgorithmâ just makes it more complicated than it really is. One of the artificial mysteries of FM. Some people have a problem with democratizing knowledge I guess.
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letâs take a single operator. It has a basic waveform, that goes to the output. To hear it, it must go at audio rates (20 oscillation per second = 20 Hz is where we humans start perceiving sound, above 20 kHz we donât here much anymore).
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because we hear it, weâll call it âcarrierâ, in FM synthesis improper appellation. âCarrierâ somehow means âthe one that receives modulationâ, but in reality it only means âan oscillator that outputs soundâ. Calling it âoutputâ would have made it more understandable. Thatâs why we call it âcarrierâ.
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Most basic FM is one oscillator (letâs call it modulator) that acts on the pitch of another (the output/carrier). If the modulator is very slow, the modulator is called a Low Frequency Oscillator, aka LFO. If itâs going so quickly itâs frequency enters audio rates, weâre in FM territory.
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a modulator that runs at audio rates introduces new harmonics/timbres. If you want to keep the timbre characteristics for different pitches of the output note, the ratio/relationship between the operators must stay constant.
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ratio are not that hard to understand: I told you we hear sounds from 20 Hz to 20 kHz.
The lowest bass makes the speaker vibrate at 20 vibrations each second. Highest note would make it vibrate at 20000 vibrations a second. Standard A note runs at a frequency of 440 vibrations/second (or Hertz, = Hz). Itâs octave above is twice higher, at 880Hz. An octave bellow is half its frequency, 220 Hz.
If you like the timbre of a modulator at 100Hz on your carrier that outputs an A at 440 Hz, youâll observe the same timbre for a modulator of 200 Hz on an A at 880 Hz.
The ratio is the modulatorâs frequency devided by the carrierâs frequency. Keep it constant, and the timbre is constant. -
To get interesting timbres, though, youâll want the modulator effect to disappear with time. To do so, you use a decreasing envelope on the volume of the modulator.
A few more tricks and Iâm out:
- when you synthesize a kick, youâll most likely want a sharp transient, maybe even some slightly longer noise, and a body the pitch of which decreases. That makes 3 different sounds, so youâll choose a configuration (aka an âalgorithmâ) with 3 outputs (aka âcarriersâ). On the body, youâll want a decreasing exponential envelope on the pitch of a simple sine wave for instance.
To get noise, an operator that modulates itself (âfeedbackâ) at a high level is perfect. You can add a decreasing sharper envelope on this feedback. Or on this operatorâs volume if you simply want to shut it down.
The transient will be similar but even sharper. On M8 we have a click waveform, very well suited. In FM synthesis you donât always have to use clever ratios, nor use modulators. A simple composition of waveforms might be all you need for a sound. - to create a saw wave from two sine waves, get a ratio of 1 between the modulator and the carrier
- to create a square wave, choose a ratio of 2
What makes FM harder is IMO the improper vocabulary used to describe it. Itâs a shame, cause it might be the most powerful synthesis, as in âdo crazy sounds with very littleâ.
Which brings me to the second thing that makes it hard: the number of controls.
On DX7 or PreenFM2, you have 6 operators with a shitload of parameters, that feels like youâre operating a nuclear plant.
M8 or Digitone are good examples of simplified UIs that retain only the necessary to dive in the sea of FM and harvest complex timbres in no time.
Start simple, with 2 operators, until it makes sense what youâre doing, then add small things and go forensics on interesting patchesâŚ
If the modulator is acting on the volume of the carrier instead of its pitch, itâs called amplitude modulation (AM), btw. You can apply the principles of FM on any parameter, indeed. A4 LFOs are cool for this. Or Eurorack ^^.
But âbasicâ FM on M8 or DN will get you busy for a long time already.
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What a beautiful response!
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What you would do to avoid accounting 
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Itâs a bit tricky to find the next installment in the âTao of FM synthesisâ blog linked above. Hereâs another view into the same material which groups the separate parts together for convenience.
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Weâre all going to be FM champions now ! I knew some of these just from using it for years !
Now time for the FM advance class !
Virt is a legendary tracker (chiptune) artist ahaha havenât watched this in a long time donât know how useful it relates to all FM probably a lot!
You rule
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I used to own an MnM, and tried quite hard to make sense out of all the explanations about FM but could not really - although the algorithms are clearly explained in the manual.
@LyingDalaiâs explanations would have been helpful then!
Itâs only when using the Twisted Electrons Blastbeats that FM started to make sense to me.
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My one rule for FM that has served me well in other synths and has held so far as Iâve been learning the Digitone:
Always try a small adjustment before a big adjustment.
In analog synthesis, a big adjustment is just covering the distance from A to B. You know whatâs between those points. In FM, the space between those points is the exact opposite: there could be anything in between.
Itâs like driving a mile through farmland versus driving a mile through the city. With analog, everythingâs wide open and you just need to go in the direction of your destination. With FM, sometimes you have to pull over, park, and discover that hidden gem on foot.
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Good point and excellent analogy!
An example is adding an operator: you would usually choose a different âalgorithmâ/configuration, but if there is a non-null level envelope amount on the new operator (= you add it already found itâs thing) the change can be drastic.
Itâs better IMO to start with a 0 amount and raise it slowly, unless you already know what youâre doing from experience.
FM is both incredibly complex and shockingly simple.
Complex because itâs the literal opposite of the subtractive synthesis weâre used to. Instead of starting with harmonically dense waveforms and removing harmonics with filters, FM takes the most harmonically simple wave form (sine), and adds harmonics to it with modulation. If we try to look at it from the subtractive standpoint of the waveforms generated (AKA: the time domain, AKA: with an oscilloscope), it looks crazy!
But if we look at FM the way it wants to be looked at, from a harmonic perspective (AKA: the frequency domain, AKA: with a spectrograph), itâs shockingly simple. We can learn all there is to know about with three examples:
A sine wave is heard (at audio rates) as a single frequency:
This is a C4:
If we modulate the frequency of a sine wave with another sine wave, we add harmonics.
The level of those harmonics are determined by the depth of the modulation, and the placement of those harmonics are determined by the ratio of the modulator to the carrier.
A 1:1 ratio adds every harmonic in the series. With a fundamental of C4, we see harmonics for C5, G5, C6, E6, and G6:
A 2:1 ratio adds every second harmonic in the series. With a fundamental of C4, we see harmonics for G5, E6, A#6, and D7:
A 3:1 ratio adds every third â C6, A#6, E7, G#7, etc.
What about those slightly smaller peaks between every third??
These are aliasing-like âreflectionsâ of higher harmonics â C5 in addition to C6, E6 in addition to E7, etc. These get more pronounced as we reach higher into the harmonic series with higher ratios. And the higher into the harmonic series we go, the more weird intervals we find. So itâs usually not worth going above a ratio of 5:1 unless weâre looking to make some crazy sounds.
These rules are recursive.
We can modulate modulators. What happens when we do? The exact same thing as when we modulate a carrier â it adds harmonics depending on its ratio and depth. But instead of adding them to the fundamental of the carrier, it adds them around the harmonics the the modulator is adding to the carrier, essentially filling in gaps.
So we can take our 3:1 modulator and modulate it with a 2:1 modulator. The result will be like adding every 2nd harmonic around every third harmonic:
Here, the green is a 3:1 mod of the carrier sine wave. The orange outline is a 2:1 mod of 3:1 mod of the carrier sine wave. We can see that every third harmonic has had a second harmonic added around it.
Thatâs it. Thatâs all there is to FM. Of course, by chaining modulators in different combinations and sweeping mod depth over time with envelopes we can make infinite soundscapes. But all follow these simple rules. So now, when looking at an FM patch, you ought to be able to close your eyes and picture exactly what its spectrogram looks like.
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Cool, I knew there was more to know about FM synthesis but ignored that. Got to dig deeper it seems.