Output tube bias, transformer turns ratio, and wire sizes all affect the damping to some degree. Sometimes those flyback voltages from the voice coil we spoke of earlier can get quite large. If you ever see a schematic of a guitar amp and notice the designer has installed solid state diodes between the plates of the output tubes and ground, it is to help quench those flyback voltage spikes. The eddy current flows in opposite direction to the coil flux, which results in power loss and increased distortion. Eddy currents are negligible in a air cores because voltage isn't induced in a non-magnetic core.
Induction decreases when more power is applied.
The reason for this inverse relation is when all the magnetic lines of induction become full, or saturated, only a small additional amount of induction can be produced which leads to distortion. Iron cores often become saturated 2 or 3 times faster than air core inductors. Magnetism is induced in an iron core when voltage is applied to it, magnetizing the core in one direction. Additional power is needed to reverse the magnetic field, and the reversal may not be instantaneous resulting in unwanted distortion. Therefore, air cores have substantially reduced hystereses distortion due to the fact that they have no magnetic core.