I'm not talking about anything EQ related. Anyone who has played around with high end analog equipment understands that it transforms the sound in ways that aren't possible with simple EQ. I was wondering if there was a mathematical explanation for what is occurring when this happens, such as, how certain frequencies are shifting and by how much, etc. Plenty of VSTs exist that attempt to replicate that analog warmth sound, but I'm interested in knowing what sound/math transformation is actually taking place here. Is there any useful sources which discuss this topic from a mathematic stand point? Or perhaps some sort of fundamental/basic type of transformation that is acting on the sound?
Background: Musician for 5+ years, programmer for 15+ years.