Hey, @glooms, exploring blindly can be fun too ^^
This said, FM synthesis is not that hard, despite being very deep.
Reading the “Tao of FM synthesis” 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:
-
FM is a composition of “operators”. Simplest is two, start from here and expand.
-
an operator in FM language is an oscillator (usually together with its own volume envelope). Most basic oscillator is a sine wave.
-
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 (what’s wrong with simple?). The term “algorithm” 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.
-
let’s 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 don’t here much anymore).
-
because we hear it, we’ll call it “carrier”, in FM synthesis improper appellation. “Carrier” somehow means “the one that receives modulation”, but in reality it only means “an oscillator that outputs sound”. Calling it “output” would have made it more understandable. That’s why we call it “carrier”.
-
Most basic FM is one oscillator (let’s 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 it’s going so quickly its frequency enters audio rates, we’re in FM territory.
-
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.
-
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). It’s 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, you’ll observe the same timbre for a modulator of 200 Hz on an A at 880 Hz.
The “ratio” is the modulator’s frequency divided by the carrier’s frequency. Keep it constant, and the timbre is constant. -
To get interesting timbres, though, you may 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 I’m out:
- when you synthesize a kick, you’ll 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 you’ll choose a configuration (aka an “algorithm”) with 3 outputs (aka “carriers”). On the body, you’ll want a decreasing exponential envelope on the pitch of a simple sine wave for instance.
To get noise, an operator that modulates itself (“feedback”) at a high level is perfect. You can add a decreasing sharper envelope on this feedback. Or on this operator’s 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 don’t 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. It’s a shame, cause it might be the most powerful synthesis, as in “do crazy sounds with very little”.
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 you’re 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 you’re doing, then add small things and go forensics on interesting patches…
If the modulator is acting on the volume of the carrier instead of its pitch, it’s 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 “basic” FM on M8 or DN will get you busy for a long time already.