To get a flat frequency response, you need to balance the natural resonance of the cantilever (depending on design and materials anywhere from 10kHz to 75kHz - comes up as a bell curve of amplitude boost extending 1 octave either side with a peak of around 6db to 12db depending on the damping in the suspension of the cantilever), with the electrical resonance generated by the combination of inductance, resistance and capacitance.
If you have a really really really good stylus with a super light cantilever (like on the Technics EPC100mk4 as an example) - the resonance out at 75kHz, means that the bell curve finishes at around 35kHz - so you want to keep things as neutral and flat as possible - low inductance, and low capacitance is the way to go.... avoid any resonance, and minimise high frequency drop off.
If on the other hand you have a standard aluminium cantilever, with a resonance somewhere between 10kHz and 16kHz -then you need to carefully balance the parameters to reduce the mechanical resonance while keeping as much of the highs as possible - usual result if you manage to get it flat to 15kHz is a dramatic dropoff after that.
Another thing is that most (almost ALL !) cantilevers have losses in the upper midrange / lower high end (probably caused by flexing of the cantilever - appears as increase in THD) - depending on design this can be balanced out by selecting R/C/Z values that have a slight boost in that zone (electrical resonance!) - followed by a steep drop (to balance out the cantilever mechanical resonance)
If you think this is a tricky balancing act - you are spot on - and well nigh impossible to get right without measurement !
Varying the C or Z will shift the "knee" of the electrical response curve either up or down the frequency spectrum, raising R will make the knee more pronounced and boost the amplitude at that knee frequency by generating a resonance at that point.
Calculators like the hagerman only provide information on the electrical resonance - they don't tell you about the mechanical resonance.
Only way to work out the mechanical resonance is to measure it - preferably with a very low C & Z ( to keep electrical resonance out of the picture - even if in operation you will be running with higher C & Z to balance things out) - that way you keep things electrically "flat" and expose the mechanical behaviour of the cantilever.
Then you calculate what C/Z/R will be required to balance out the measured mechanical resonance - and that will get you on the way to an objectively improved configuration.
Through the 60's, 70's and early 80's the holy grail was flat frequency response.
Around the time CD came out, things went very strange - Ortofon did a series of listening tests with "Golden eared" experts, and concluded that audiophiles preferred a rising top end - all their designs after that had that type of voicing.
Shure on the other hand concluded that audiophiles preferred a drooping top end and released their new series of cartridges (the "x" versions V15VxMR and M97xE) with an accordingly droopy top end.
I think around this same period (and presumably associated to it) was the blooming of the subjectivist school of audiophiles - adjust it till you like it, if you like it then it must be perfect....
To put it really simply - getting flat frequency response from such an imperfect medium as vinyl by using a vibrating needle on a mechanical cantilever attached to a magnetic generator is an incredible feat of advanced engineering.... and very very few setups will every achieve it.
The best setups get close though! and can sound wonderful. They will also sound different with every differing recording played - whereas setups that have frequency anomalies will impose those colourations on every recording - giving them an artificial similarity that they should not have. (but that the listener may enjoy....)
just my 2 or 3c ....
bye for now
David