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The linear components between the nonlinear stages influence the nonlinear stages. For example, even in a relatively simple amp like, say, a Fender Princeton, the tone stack influences the behavior of the stages preceding and following it. It influences the preceding stage by changing the load and influences the following stage by changing the source impedance.Is this entirely true, though? Not a rhetorical question at all - I genuinely don't know and would like to. If modeling/ capturing components "that don't have user controllable knobs in between" and simply running them in series is sufficiently accurate to the original system (e.g. guitar amplifier) then we already have most or all of the tools needed at our disposal. But does this accurately model interactions between each of those systems resulting from input/ output impedances, etc.?
(Asking for a friend with one of those god-awful Quad Cortexes.)
IOW, you can't treat a tube amp as a cascade of isolated nonlinear and linear transfer functions.