Carlo,
Interesting thoughts and observation. Perhaps it's better to introduce distortion at the source, and keep the rest of the listening chain relatively linear so that the interaction between components is well-controlled and predictable, so you can dial in the kind of sound you want. If every element of your chain were non-linear, they'd interact in basically factorial combination --- each element of the chain would have its own set of interactions with every other element of the chain.
Mathematically, if something has 2nd order distortion, its transfer function looks something like:
t(x) = A1*x + B1*x^2
A1 is the gain of your system
B1 is the amount of 2nd harmonic distortion
Let's say you have another component downstream that has the same transfer function, and let's call it u(x) instead. Using both components in series (perhaps t(x) is your preamp, and u(x) is your power amp), you basically perform the following operation:
u(t(x)) = A2*t(x) + B2*t(x)^2 (A2 and B2 are similar in function to A1 and B1)
Expanding this out, you get a much more complicated equation:
u(t(x)) = A2*A1*x + A2*B1*x^2 + B2*A1*A1*x^2 + 2*B2*A1*B1*x^3 + B2*B1*B1*x^4
Rewriting all the constants to simplify the expression, you get:
u(t(x)) = A*x + B*x^2 + C*x^3 + D*x^4
A is the overall gain of the two components
B is the amount of 2nd order harmonic
C is the amount of 3rd order harmonic
D is the amount of 4th order harmonic
Some interesting things to note:
1. We now have harmonics that weren't there before: the general rule is that components cascaded together will make harmonics whose order is the sum of the highest harmonics of each component separately. So if one of the components had 3rd order distortion, and the other 2nd order distortion, we would have 5th order distortion when those components are used together.
BTW, feedback and cascaded stages will compound harmonics within a component, which is why Kevin Gilmore in his
Rules of Proper Audio Design says that individual stages within an amplifier must already have linear behavior without feedback, and why many designers like Nelson Pass prefer amps with fewer stages.
2. For simplicity's sake, my calculation assumed our components have only 2nd order components. In reality, real components have higher order components, as you can see in any Stereophile review with measurements. So the situation is way more complicated than my simple example.
3. Also for simplicity's sake, I only used two components. A real system often has more, and the complexity compounds.
4. Why does an nth order polynomial term imply an nth order distortion? The easiest way to see this is to assume x = sin(t), and expand out the terms. You'll see that one of the terms will have sin(n*t), which is an nth order harmonic.
So if we have one non-linear component, we can control fairly well what euphonic distortion we want. When you start using a bunch of them, they interact in very complicated and wide-ranging ways.
--Andre