Rccc,
For clarity, I don't think its helpful to consider resonances in a tonearm in this context. Stray energies leaking from a cartridge can cause problems whether the arm resonates or not. Intra-arm resonances would indeed be a problem, but lets manage one disaster at a time.
The primary deleterious sonic effects of energies leaking from a cartridge occur when those energies are reflected back into the cartridge, causing it to generate spurious, time-delayed or phase-shifted echoes. It's the sonic equivalent of glare reflected off a windshield, with a similar cause.
I wish I could offer a broadly useful method to determine, measure or quantify, but all I can say is that we hear and identify those time-shifted echoes. We've heard enough arm/cartridge combinations to recognize them when they occur, and also to recognize when something else occurs that sounds like them but isn't. My partner's remarkable ears, science expertise and ever-questioning mind often play a role. Consider two cases:
#1
Before a recent cartridge trial Paul specifically predicted it would have these issues. He said so based certain design elements, which he expected would make such behaviors inevitable.
He was right, though the sub-cycle echoes were much worse than even he expected. Paul left the room after a few minutes in pain. (Our audio buddies would recognize the behavior. He has a vanishingly low pain threshhold for time-domain distortions. Problems that take me hours to identify give him a splitting headache in mere minutes.) I struggled with the cartridge for 2-3 sides but the longer I listened the more obviously annoying it got.
This $8K cartridge actually sounded excellent in every other respect, yet those reflected energies were clearly audible and - thanks to a uniquely misguided design - untameable by any tonearm. Prediction sadly confirmed.
#2
In a more recent trial a much humbler cartridge started off okay, but I began noticing anomalies after half a side or so. There was a trail of diminishing echoes off the back end of every note (not soundspace echoes, artificial ones). I commented to Paul that it sounded *somewhat* like the echoes from that $8K disaster, though not nearly so bad. That was the limit of my diagnosis.
Paul listened for a few seconds and said, "I hear what you're hearing but they aren't mechanical echoes. It's probably electrical. This doesn't sound quite like a moving coil nor a moving magnet. How does this cartridge generate a signal?"
I was impressed, not for the first time. Anyone else would have been stunned speechless... Quite unprompted, Paul had correctly deduced that this was neither an MM nor an MC. It was a MI!
He knew nothing about this cartridge. He'd never looked at it. He didn't know what brand it was. Yet after hearing it for a few moments from the dinner table, a room away from the system, he identified its electro-magnetic functioning as something unusual. Measure that! ;-)
I read from the pamphlet about how this cartridge worked. Paul nodded and confirmed his suspicion that we were hearing hysteresis effects. Then he explained hysteresis. ;-)
Now if I could just bottle the ability to hear and identify hysteresis coming from a magnets the size of a pinhead ...
***
Regarding measurement and quantification, my sense is that arms, cartridges and setups present too many variables. Energy leakages from a cartridge vary with the tonearm its mounted on, the screws, nuts and washers, the tightening of the screws, etc. Once the energy gets into the tonearm, each arm varies in its ability to dissipate that energy rather than reflect it back into the cartridge. Further, each of these behaviors is a frequency dependent function. It seems to me that the applicability of any measurable "leakage factor" to a different setup would be questionable.
All fairly useless, but it's what I've got,
Doug
