Frequency Modulation Synthesis

FM is frequency modulation. It's the most well-known modulation and it is not just one technique. There are many different types. We'll look at the Max/MSP patches and try them. 

Basic FM

First, let's make an oscillator.
We want to modulate the frequency. Say, we want to modulate the frequency 680 to 1080 every second. Then, how to modulate that? First of all, set the carrier frequency as 880hz. Secondly, set the modulator frequency as 1 because we want to modulate the frequency every second. Thirdly, set the modulation depth(modulator amplitude) as 200 to produces a sine wave -200 to 200. Lastly, add those. Now, we can see the frequency modulation.
It sounds like a huge vibrato. But what if we modulate the frequency more often? Like 200 times a second? Let's do it.
At first, it sounds like a vibrato, and when it modulates fast, we can't recognize the vibrato and we get some partials. This is the Basic FM.

Simple FM 1

From now on, we'll use the index. Because we want to get partials but if we control the depth, the modulator amplitude, we have to use a huge number. Therefore, multiply the index by modulator frequency is the modulator amplitude. Let's see.
This is more simple than the Basic FM. Because modulator frequency 200hz and modulator amplitude 200 is equal to modulator frequency 200hz and index 1.

So we can control three parameters; Carrier Frequency, Modulator Frequency, and Modulator Index. This is Simple FM 1.

Simple FM 2

Let's think about the Index. And also, let's think about Additive Synthesis. In additive synthesis, we controlled the amplitude of partials by envelope. What if we control the index by envelope? Let's do it. And from now on, it'll get a bit complicated. So open the max and copy me is the best.

Carrier frequency is 400hz, modulator frequency is 200hz.
The index is 5 and the duration of sound which will produce by FM synthesis is two seconds (2000ms). 
Is it too fast? Let's change the duration by 8 seconds.
We controlled the modulator's index and carrier oscillator's amplitude using envelopes. This is Simple FM 2. 

Multiple FM

Let's throwback Additive Synthesis again. And what if, we add FM synthesized sounds that are controlled by envelopes? First, let's make one FM synthesis oscillator. And this time, we'll control the modulator frequency using a ratio. If the frequency is 440hz and the ratio is 1:3.6, the carrier frequency will be 440hz, modulator frequency will be 1584hz.
And also, we can control the carrier oscillator's amplitude using an envelope and add carrier oscillators like additive synthesis. 

Multiple Carrier FM 

What if we connect one modulator to carrier oscillators? We can get three fundamentals.

Parallel Multiple Modulator FM

We can also connect two modulators in parallel to one carrier oscillator.
This is FM Violin using Parallel Multiple Carrier FM.

Series Multiple Modulator FM

We can connect modulators in series, not in parallel. We can get more partials with low modulator frequency.

One Oscillator Feedback FM

We can also use a carrier oscillator as the feedback. And also we have a feedback index. But in Max/MSP, if we connect it directly by a cord, we can't hear anything. So we should use 'send~' and 'receive~'.

Two Oscillator Feedback FM

We can also make Two Oscillators Feedback FM.

Thank you for reading. You can download all patches on my GitHub.

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