In this tutorial, using a Syntronik Minimoog as an example for comparison, I will explain
fundamentals of FM synthesis using a 4 operator FM synth, FM4.
Let's look at how you create a sound using subtractive/ analog synthesizer using Syntronik
Minimoog.
Typically, you start with VCOs to select harmonic rich waveforms including sawtooth and square
waves.
It's main purpose is to generate a harmonic rich tone.
In this example, we have a sawtooth wave.
Then you set VCF or filter to cut down certain harmonics and set an envelope to control harmonic
contents over a time.
At the end, you set VCA or amplitude envelope to control the overall volume of a sound.
So it's quite simple using VCO, VCF and VCA.
So what's like to make a sound on a FM synthesizer?
I will show you similarities and differences between 4 Operator FM synthesis and Subtractive
(e.g., analog) synthesis from VCO, VCF and VCA.
Let's start with VCO.
VCOs generate harmonic rich sounds, so you don't need to create harmonic rich sounds
from scratch.
For FM synthesis, instead of VCOs, we have operators which are different to VCOs.
Key differences are,
They only generate either a sine wave or harmonic poor waveforms.
They have an individual envelope to control either volume like VCA or harmonic content
like VCF, depending on how they are used.
They have an individual Level control so as to control either volume like VCA, or harmonic
content like VCF depending on how they are used.
They have an individual velocity setting so as to control either volume like VCA, or harmonic
content VCF depending on how they are used.
So this is visualisaiton of what operator is all about.
You have a pitch control with an envelope, tracking, velocity and level.
On its own, it generates either a sine wave or harmonic poor waveforms.
Although FM4 or other FM synths such as TX81z can have selectable sine wave derived harmonic
poor waveforms, the DX7 only has a sine wave.
So why do we only use a sine wave or less harmonic waveforms for FM synthesis?
The answer is that FM synthesis is one of the most efficient synthesis method to generate
a wide range of harmonics and inharmonics, simply from a sine wave.
Let's look at an example of making the famous DX7 Tube Bells on FM4.
If you haven't made the DX7 Tube Bells using FM4, you can do so by pausing this video and
watch another FM4 Sound Design Tutorial for Tube Bells, appearing at the top of screen
now.
Using only operators 1 and 2 with a sine wave, you can generate the bell's main metallic
inharmonic tone.
That means that if you start to use more harmonic rich waveforms, you can end up with producing
too much unwanted harmonics/ inharmonics with FM synthesis.
So with FM synthesis, you create your own harmonic/ inharmonic rich tones without a
sawtooth or square wave found in VCO.
So, for analog synth users, this is backward thinking!!!
This is so counter-intuitive to analog synth users, because harmonic rich waveforms are
already in VCO and you just select one.
FM synthesis, like additive synthesis, you need to create harmonic rich tones from scratch.
This is the first step to learn about FM synthesis.
You need to create harmonic rich waveforms.
Let's try creating a sawtooth wave from scratch using FM4.
Select any sounds, but change algorithm to 5.
Turn only operators 3 and 4.
We will set feedback to 10.
The feedback loop on operator 4 puts its output signal back in to itself, allowing to generate
a harmonic rich wave forms, instead of a sine wave.
We will change Pitch for both operators 3 and 4 to 1.00 and select a sine wave.
We will set operator 3 ADSR envelope to a bit slow attack to 5.0, no decay, maximum
sustain and slow release to 5.0.
We will set operator 4 ADSR envelope to a bit fast attack to 0.0, no decay, maximum
sustain and release.
Adjust Level for operator 3 to maximum.
Set operator 4 Level to around 6.4.
Put other parameters like LFO and Velocity to 0.
And make sure to turn off unison or arpeggiator.
Also set Model to I, so you get minimum noise.
You can also turn off track by setting it to 0.
Let's press a key.
Now you hear a sawtooth wave.
What we've done is to using FM synthesis to generate a sawtooth wave from a sine wave.
Note that we have operator 4 with a feedback loop.
It allows to generate a sawtooth wave.
Let's turn of feedback by setting it to 0.
Now we don't have a sawtooth wave.
So by now, you understand how FM synthesis using sine wave operators can be set up like
VCO to generate a sawtooth wave.
We can look at VCF.
Let's look at subtractive synthesis, in this case Minimoog on Syntronik.
Once you selected a harmonic rich waveform, like a sawtooth wave, you can use VCF to control
the harmonic content of a sound.
VCF or filter allows you to cut down harmonics, or enhance particular harmonics using resonance.
It's quite easy to do this, as you only need to play around with a filter.
Let's see how VCF is used for subtractive synth, like Minimoog.
As You can see, I'm reducing cut off frequency by turning Cutoff nobe.
I increase resosnance, and adjust cutoff again.
Now we have mid harmonic rich saw pad.
I will change VCF envelope.
I increased decay with less sustain.
Now we have a shorter saw pad.
But for FM synthesis, you have to control the harmonic contents of a sound without a
filter.
Let's look at the FM4 example with a sawtooth wave.
You will notice that Operator 4 with a feedback loop is connected to operator 3.
This arrangement is called algorithm and it determines how each operator interacts with
each other.
In this example, Operator 4 is modulating Operator 3 with frequency modulation, and
it is called a modulator.
This means that by controlling operator 4, you can control the harmonic content of a
sound.
So, for FM synthesis, operator 4 is acting like VCF.
By controlling its pitch to generate different harmonic contents, envelope to change harmonic
contents over time and level to set the overall harmonic content, you have VCF with a filter
and an envelope.
Let's try changing the sawtooth tone with filter cut off using FM4.
Let's adjust Level to 6.0, 5.5 to 5.0, 4.0.
3.0 and so on.
What did it happen?
Like moving the filter cut off setting, the harmonic rich tone is getting softer and softer
to become more like a sine wave with no overtone.
So Level for operator 4 as a modulator determines the overall harmonic content.
Now put back Level for operator 4 to 6.4.
We will use operator 4 envelop.
Let's put decay around 5.0. and sustain to 0.
Now the harmonic content of the sound is changing by its envelope, like a VCF envelope.
So we now have VCF equivalent in FM4, called a modulator.
The modulator is any operators that sit on top of an operator that actually output a
sound.
We can look at each algorithm and how modulators are arranged in detail later.
Let's look at Syntronik Minimoog again.
Once you selected a waveform and set VCF, you can control the overall volume using VCA
or amplitude.
It has an envelope and you can control the overall volume over a time.
So is there a VCA equivalent in FM synthesis.
Yes, there is.
Now we know how FM4 operator 3 and 4 are arranged.
Operator 4 is a modulator, acting like VCF to control the harmonic content of a sound.
So what does operator 3 do.
It is called a carrier and it controls the volume of a sound over a time, just like VCA
in analog synth.
Let's try using operator 3.
Set Operator 4 envelope back to maximum decay, maximum sustain.
Now we have a sustained sawtooth sound.
We will use operator 3 envelope to control the overall volume of the sound over a time.
Set decay to about 5.0 and put sustain to 0.
Press a key and we have a carrier envelope controlling the volume of the sawtooth sound
over a time, just like VCA.
Now, we've covered VCO, VCF and VCA, and similarities and differences between subtractive
and FM synthesis.
Let's look at algorithm.
I mentioned briefly that algorithms are the arrangements of FM operators so as to generate
desired harmonics and inharmonics.
Instead of 32 algorithms found in the DX7, 4 operator FM synths have only 8 algorithms.
We can quickly go over 1 by 1.
Algorithm 1 has only 1 tower with all operators stacked on top of one another.
It has only 1 carrier and the rest is modulators.
That means that Operator 1 can acts like a VCA and the rest acts as VCF, generating harmonic
rich tones.
Algorithm 2 has only 1 carrier and 3 modulators.
Operator 1 controls the overall volume and the other operators act as VCF, controlling
overall harmonics.
Algorithm 3 has 1 carrier, as operator 1 , acting like VCA.
The rest is a modulator, controlling the overall harmonics, like VCF.
Algorithm 4 has only 1 carrier, as operator 1, acting like VCA.
The rest is a modulator, controlling the overall harmonics, like VCF.
Algorithm 5 has 2 independent towers.
Each tower acts as an independent VCO, VCF and VCA.
For tower 1, operator 1 is a carrier, acting like VCA, and operator 2 is a modulator, acting
like VCF.
For tower 2, operator 3 is a carrier, acting like VCA, and operator 4 is a modulator, acting
like VCF.
Algorithm 6 has 3 carriers, operators 1, 2 & 3 acting like 3 VCA, and it has 1 modulator,
operator 4, acting like VCF.
Algorithm 7 has 2 carrier only operators, 1 & 2, and unlike VCA, they generate their
own sine waves or other waveforms.
They are used as additive synthesis.
Their envelopes act like VCA envelopes, controlling the overall volume.
There is also an independent tower with a carrier operator 3, acting like VCA, and a
modulator operator 4, acting like VCF.
Algorithm 8 has only carrier operators 1, 2, 3 & 4.
There is no modulator, so each operator generates sine wave or other waveforms independently.
Each envelope acts as a VCA envelope, controlling the overall volume.
Using only sine waves, you have additive synthesis.
So how do you know which algorithm you need to use to create a particular sound.
You don't.
Algorithm is provided for sound design possibilities and expandabilities.
There is no rule to say this algorithm for this sound etc.
It's all up to your imagination.
Let's revise what we've learnt so far.
With analog synth, you select harmonic rich waveforms using VCO, VCF controls the harmonic
contents of a sound VCA controls the volume of a sound
for FM synthesis, you have an operator with a sine wave for less harmonic rich waveforms
and you create a harmonic rich waveform from scratch
for FM synthesis a modulator (an operator that sits on top of another operator) controls
the harmonic content of a sound.
for FM synthesis, a carrier (an operator that sits at the end and outputs a sound) controls
the volume of a sound.
Now you can save the patch you made so that we can use it in Part 2 of this FM synthesis
tutorial.
There will be more FM synthesis tutorial for 4 operator FM synth.
Part 2 will cover sound design of FM pads and advanced used of different waveforms.
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