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Basics of creating  wavetables in Octave Vol.3[FM]

6/4/2021

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Picture

Creating FM wavetables

FM synthesis is a synthesis method used in many synthesizers such as Yamaha DX series, Ableton Operator, Elektron Digitone, etc.
The FM tone is created by modulating the carrier oscillator with a modulation oscillator.
FM stands for frequency modulation, but it is actually phase modulation.

FM formula

FM(t) = A * sin(2pi*Fc*t + B*sin(2pi*Fm*t) )

A =
Carrier amplitude,  Fc = Carrier frequency
B = Modulation index  Fm = Modulator frequency

https://ja.wikipedia.org/wiki/FM%E9%9F%B3%E6%BA%90
You can see that this formula is almost identical to the formula for how to change the phase of a waveform described in Tutorial vol.1.
FM Synthesis

    
From this equation we understand that FM is a phase modulation.

Creating FM wavetable

FM with a 1:1 frequency ratio
Download
FM Synthesis 1-1

    
Picture

Examples of how to combine carriers and modulators

The timbre of the FM synthesis is determined by the way the carrier and modulator are combined. Here are some useful combinations.

Series

Picture
FM Synthesis(series)

    

Parallel

Picture
FM Synthesis(parallel)

    

The difference between FM Wavetable and FM Synth

The FM Wavetable requires that the frequency ratio of the modulator to the carrier be an integer. This is because the Wavetable has a fixed waveform length. So if you want to create a sound with a frequency ratio of 1 : 3.5, such as a bell, you will have to convert it to 2 : 7.

Next time: Modulation envelopes
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