A little mind experiment about the coil - core - inductance relationship.

Q - What is the "Q" of a coil?
A - The quality of the coil.
Q - OK? Plain English please.
A - The reactance and the resistance divide the energy. A pure reactance has no loses. A pure resistance has a power factor of 1.
Q - OK? So what is the power factor?
A - Pure reactance PF = 0. Pure resistance PF = 1.
Q - How do we determine the PF?
A - We would use vectors or phasers or trig factors.
    The simple math for Q is X / R. So if R = 0 Q is infinity. This is why the wire size, wire type and core material matter.
    
    
    Now on to the mind experiment part 1:
    Assume we wind an air core coil for my oscillator. It would have a Q determined as any other air core coil. Assume we set the circuit to oscillate at 4 MHz. All is well but it is fixed frequency. Now I want to lower the frequency by inserting a ferrite core. As I insert the core the frequency lowers. Assume the frequency changes to 3 MHz. This would be a small change from 30uh to 15uh with a 100pfd cap. What happens to the Q? Remember Q = X / R. The wire has not changed so R remains the same. The core causes the X to increase so Q increases.
    
 
    Now on to mind experiment part 2:
    Here is the real question to consider.
    The air core coil is 15uh.
    The core raises it to 30uh.
    I place a magnet against the core and it saturates, what happens?
    The relative speed at which the field expands or contracts is the variable.
    Consider the speed of sound in air and in water.
    Consider the speed of light in air and in water.
    When we place a straw in a glass of water it appears to bend, why?
    The basic laws for motors and generators tell us the field strength and relative motion determine the motor input requirements or generator output.
    
    Mind experiment final:
    The air core core has a Q of some value.
    The metal core has a higher Q.
    Assuming the air core Q is high enough for our circuit inserting the core should be ok.
    Saturating the core makes the core become "invisable" or in other words it will make the coil to act the same as the air core version.
    
    So in theory can I adjust the oscillator frequency by adjusting the bias on the core.