So I guess you (may I say we?) should distinguish between FR related ringing and other ringing problems.

Hi! Most of us know you from some other place, but kindly write a word or two here.

I believe ringing here means time domain ringing, which correlates to aberrations in the FR as well. I also think it's easier to visualize ringing using a CSD's frequency/time resolution approach, than IR and FR alone.

Great explanation!  I think the second order analogy works well, but I don't quite see how it relates to PLL. 

LOL! Well ... maybe not so great. I saw the relationship to PLLs because most are second order and exhibit under, over, or critically damped behavior which can be visualized using their time domain step response "ringing".

PLLs are effectively low pass filters. If I remember correctly underdamped exhibit a peak (Q factor > 1/2) at the corner frequency, and overdamped don't (though bandwidth is narrower).

Also, would it be fair to say that an underdamped system would manifest itself as a long lived, high Q resonance, while an overdamped system would be a broader resonance at it's respective Fc? Or does an overdamped system kind of just blend in with the rest of the decay when you're looking at CSDs?

I think that would be fair to say, but I'm not certain of it, so take it with a grain of salt. I think that if a headphone is viewed as a set of cascaded second order systems, some elements might be low pass, others high pass, and other all-pass with a pair of complex poles and/or zeros at a particular frequency. Some of these sub-systems might have a high and narrow Q at different sets of frequencies which may result in ringing at said frequencies.

Even if the above is accurate, it doesn't say much about how these issues will be perceived. I believe the correlation between the measurements and subjective evaluation holds it's ground regardless of the accuracy of my reasoning. I also think Marv has covered that very well using very accessible terms and I believe it is the main objective of this thread.

One more question. So when we see ringing that's an octave apart like in the K601, what we're actually seeing is the non-linear effects of the resonance at that first F, correct? With any given resonance, is there a good way to predict whether we'll see ringing an octave above? Could high THD generally lead to these Octave Penetrators, or does it have to do with the nature of the resonance more so?

Thanks 

I think ringing is due to linear distortion. The K601 long lasting ringing at 15 kHz maybe is due to an abrupt discontinuity (null) 15 kHz. The one not so long lasting at 4 kHz probably due to the wide but shallow null from ~2.5 kHz to 5 kHz. The smaller one at 8 kHz perhaps due to the gentle peak from 5 kHz to 9 kHz.

The big differences between your measurements and theory is for example that ringing at two different but very close to each other frequencies will combine into ringing at approx. the center of those frequencies. With perfectly linear devices there should be two distinct ridges all the way down.

IMO measurements trade off frequency and time resolution, which I think can't be helped.