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.

 The for loop syntax is a way to loop through the array elements in order. By iterating, multiple files can be generated in sequence. This can be used to generate multiple single-cycle waveforms.

The above code loops through the numbers 1 through 5. When executed, it generates five sine waves from the base note to the fifth overtone in sequential numbers.

I will show you how to create a Wavetable in Octave, a numerical calculation software. The waveforms you create can be used with Serum, Ableton Wavetable, or any other audio-importable wavetable synth or sampler.

GNU Octave

• https://www.gnu.org/software/octave/index
  

Octave Programiming Tutorial

• https://en.wikibooks.org/wiki/Octave_Programming_Tutorial
  
• https://en.wikibooks.org/wiki/Octave_Programming_Tutorial/Vectors_and_matrices

Advice

• Octave is compatible with Matlab, so if there is a function you are not sure about, the Matlab web page is also a good reference.
• In Octave, if you don't put " ;" at the end of a line, the result of the calculation will be output to the command window. When looping, if you do not put a " ;" at the end of a line, the result of the calculation will be output to the command window endlessly, so be careful.

This section shows how to resize wavetables in Audacity. As an example, a wavetable with a length of 256samples per single cycle waveform is converted to a length of 1024 samples.

By multiplying the speed by 0.25, the length of the waveform is increased by a factor of 4.
256 x 4 = 1024 samples

Now you can use wavetables you created in WaveEdit in Ableton Wavetable.