(sitting on my PC now, I will review this for more understanding)
Since I am working full time with these kind of stuff (loudspeaker nonlinearities), maybe I can shed some light on this mysterious parameter:
See, a loudspeaker is a highly nonlinear device. Just like mentioned before, trying to push the speaker "inside", you will see that you need more and more force as you pushing it in. The same is true for the opposite direction, but obviously, it's easier to verify if you push it in
The term for this effect is "
stiff", since, you need more force to get the same displacement, depending on the position of the speaker. "
Stiffness" represents the inverse of compliance - the less compliance you have, the stiffer is the speaker. And, as seen from the stuff I've written before, this depends on displacement.
So what's the deal with this effect?
See, an impedance just simply states a relation between voltage and current. So, as current drives the mechanical parts of the speaker, a voltage is induced back (called "
back EMF") because of the speaker movement. In other words, the compliant mechanical load also affects the electrical side. This will result in a dynamic impedance change, which will change the behavior of a current coming from a power amplifier. Mind this depends on displacement, a mechanical parameter. Thus, to model the interaction on the power amp side correctly, you have also to model the behavior of the (dominant) mechanics. Apart from that, a change in compliance will also dynamically shift the resonance frequency of the loudspeaker, since resonance frequency depends on the compliance.
Hence, even on a guitar speaker, you can leave this parameter on, since a guitar amplifier would have to work with the same changing load.
Note: since this nonlinearity depends on displacement, you will have this effect more pronounced on notes giving you more displacement. However, displacement will drop by 12dB/octave above the (linear) resonance frequency of the loudspeaker (see the mechanical lumped parameter model on this, it's a second order system).
I suspect you won't hear any effect on higher frequency notes, but it gets more pronounced on the lower notes. You shall hear it as a dynamic increase in perceived bass, from a spectral point of view (at least this is the effect on the speaker side).
Compliance isn't the only nonlinearity, but one of the most pronounced with a high impact.
(Edit: Just added a little bit more about the relation of the mechanics to the electrical side - I was just implying to much)