> I am not disagreeing with you but I still do not see why.  In a series
> resonant circuit, the the capacitance dominates the imedance below
> resonance and the inductor dominates above resonance.  In a parallel
> resonant circuit the opposite is true so one might expect the shape of
> the resonant curve to be different for these two cases.  But they can't
> be otherwise the geometric mean would not be able to describe the
> centre frequency in both cases.

But that's the point, it's *geometric* relationship, not a linear one.
The response of a resonant circuit is symmetric between 1/2 and 2x the
center frequency, 1/3 and 3x, 1/10 and 10x, etc.  The response will
therefore look symmetric on a logarithmic plot of frequency but not a
linear one.  This is also why the geometric mean works, but a regular
average (think of a linear mean) doesn't.


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