Tone arm resonance and cartridge compliance: How do they interact??

Increasing arm mass lowers resonance frequency

@roberjerman, that's simply not true. It's a common misconception because resonance charts calculate frequency based on total arm weight. But resonance is a function of other factors besides weight; including stiffness, flexibility and damping. Putting a weight on the headshell will help to damp the headshell but not the arm tube. And weighting the headshell may actually result in worse performance. Probably not unacceptably worse but often measurable worse.

The tonearm is a level balanced on a fulcrum. If you take a counterbalanced lever of, let's say, 10 feet long, and increase the weight on both the headshell (effort arm) and the move the counterweight away from the fulcrum, will the resonance increase, stary the same or decrease (amplitude AND frequency stabilize or shift)? The correct answer is that amplitude will increase and frequency will shift. The same thing happens with a tonearm, but on a much smaller scale. 😁

br3098, You are confusing two different things.  roberjermain is correct, and I wrote the same thing, a few posts above yours.  BOTH increasing tonearm effective mass and increasing cartridge compliance will decrease the resonant frequency of the system.  If you will look at the equation, you will see that the product of the two quantities is inversely proportional to Fres.  Now, what bdp and you are talking about does not per se alter the resonant frequency, as long as you don't change effective mass and compliance. What damping and choice of materials does, if done smartly, is take the energy of the resonance that will occur at the calculated frequency and spread out or broaden the resonant peak, the range of frequencies at which the energy of resonance is dissipated, which is usually a good thing that can mitigate an otherwise bad pairing of cartridge and tonearm.  And yes, the (distance from the pivot to the center of mass of the CW)-squared times the mass of the CW, adds to effective mass.  That's why, if you want to minimize effective mass, you want a heavy CW that can be moved as close as possible to the pivot. (Because the em will vary as the distance-squared but only in direct proportion to CW mass.)

The beauty of the adjustable-mass counterweight of the Zeta arm (accomplished via removable steel discs in the hollow counterweight) is that if one wants to use the arm in it's lowest effective mass guise, more discs are placed in the counterweight and that cw is placed as close as possible to the arm's bearings. For higher em, fewer discs and the cw further away. Counter-intuitive, but true.

My Triplanar and I suppose several other tonearms achieve the same end by supplying a set of CWs that vary in mass. You can slide them on or off the rear end of the arm. Further the Triplanar CW is physically decoupled from the pivot by a nonrigid damped joint.

Dear @lewm : obviously that a tonearm as a cartridge in static way has no intrinsec resonances but in the very first moment that the TT spins even with the tonearm in rest that tonearms has " resonances/vibrations " at micro levels. So @bdp24 is rigth about.

The overall subject always been a little controversial because the formula calculates the resonance frequency of a cartridge/tonearm at static/rest way. The numbers are the ones from those combinations of tonearm-cartridge and it’s a good place to start with the subject but those numbers will change during playback because exist additional parameters that affects it.

Yes, the formula says what you posted but you have experiences where that not really happens during playback because you love that very heavy FR tonearm with a cartridge boarding in the 40-50 cu and you love that combination.

So, some one out there needs to model what in reality happens taking in count all those multiple factors/parameters around this controversial subject.

Even those always is convenient try to achieve the ideal frequency range in our tonearm/cartridge combinations because the quality performance will be better than if we don’t care about. Problem is that several times we like what is wrong and dislike what is rigth !

Btw, """ supplying a set of CWs that vary in mass . "" this was posted too by @bdp24 with his Zeta tonearm but is not critical inside the resonance formula because the CW is near the fulcrum and contributes very low for the total mass.
What is important for place/position the CW the nearest we can to the tonearm bearing is to gives to the tonearm a better overall " displacement/operation " during playback, give an additional facility to the tonearm work.


Regards and enjoy the MUSIC NOT DISTORTIONS,
R.