Turntable matching to MC or MM cart.

Practically it’s subjective, we have different systems and you have no idea who is a person who will answer your question (and his/her experience with different tonearms/cartridges).

Of course it’s subjective, I don’t try to reach some dogma or universal solution. The question is theoretical, no intention to solve an issue or make a decision here. Other people experience in this matter that exactly what interesting.

Well, I have tried more than 60 cartridges and probably over 10 different tonearm. I have no problem to use my cartridges correctly according to their compliance and my tonearm mass, I can fine-tune everything with different heardhells as it can add or deduct mass (or heavy mounting screws for tonearms with non removable headshell). 

Hi-Fi News Analog TEST LP is the only tool to measure vertical and lateral resonance (online calculators always off). 

I think it's nice to have 3 tonearms (light mass, mid mass, and very heavy).  

There is no need whatsoever to match turntable and cartridge.  Matching tonearms and cartridges is worth doing and requires experimentation, which is why some of us crazies own so many tonearms. Where the tonearm(s) use a detachable headshell, having a lot of different headshells, constructed of different materials and of different weights, is also handy for getting the most out of a cartridge.  This is not purely about achieving some magical resonant frequency, in fact that is a very secondary consideration in my experience.

Both Lewm and Chakster have valid points. Moving magnet, iron or coil is not an issue with tonearm matching. It is purely an issue of cartridge compliance and the effective mass of the tonearm. There is significant variability in both parameters so in reality the only way you can really know what is going on is to use a test record like the one chakster recommends. Having said this moving magnet cartridges tend towards higher compliance and lighter tonearms. The lowest compliance cartridges are moving coil. Moving irons have a foot in both puddles. Having seen some interesting test results I am favoring lighter tonearms and more compliant cartridges as they follow undulations (low frequency) in the vinyl surface better. Looking at an oscilloscope they produce less low frequency rubbish. Heavy arms can not move fast enough (more inertia) transferring the undulations to the cantilever. It is sort of like your woofer flapping at low frequencies. It is not making any sound but you can hear it in the higher frequencies due to Doppler distortion. It is hard to make a big car handle like a sports car for the same reasons. 

Matching of any cart applies to the phono stage with a few compliance outliers. Then you only have to pick an arm and find what works best.

I am a MM/MI guy and use a phono stage specific to MM/MI carts of the high output verity. If I decide to go MC low I will buy a SUT.

Gail 2 https://www.lejonklou.com/products/gaio-grammofonsteg-2/

matches well with all my Nagaoka MP Cart’s