This is a great and (relatively) concise video explaining what saturation means, different types of saturation and their relation to harmonics. Some really big insights there that will clear the process up for you. Big recommend.
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Glad it helped! I think we as producers tend to forget sometimes that behind every plugin we use there are hundreds of different algorithms doing different things with waveforms and digital representation of sound, since we only care about what we see and hear and that seems intuitive to us. Sound is physics and psychology and building incredibly complex things is only possible when you understand everything that goes on behind the scenes. Though you do have to pratice too… which is often more difficult than the theory, lol