The Arm/Cartridge Matching Myth

I hope that I can clarify a few things for everyone. Resonance is a phenomena where a small amount of energy in results in near infinite energy out. It can occur in either mechanical or electrical systems. Static forces and dynamic frequency response are independent of each other. ie. Tracking force does not affect the natural frequency of the cartridge/tonearm system- unless you have so much tracking force that the cartridge suspension is bottomed out. You'll know that is the case if you see a thin ribbon of vinyl curling up behind the needle while playing a record.
Effective Mass is a shortcut for calculating the tonearm/cartridge system natural frequency. Effective mass is really the inertia of the tonearm expressed in grams. That's because the tonearm is resting on a fulcrum (pivot). The tonearm and counterweight weigh much more than just a few grams. Additionally, the effective mass can vary depending on the position of the counterweight. So a lower mass cartridge will lower the effective mass of the tonearm since the counter weight will be closer to the pivot. I guess the tonearm manufactures provide us with a nominal value. Don't forget to add the mass of the cartridge, not just the spring rate to the natural frequency calculation.
The only magic about 10Hz +/-2 Hz is that this is the "quiet" area. Below 8 Hz is the range of record warps and footfalls. Above 16 Hz is getting into the range of the music. The tonearm/cartridge system is still responding at 10Hz. Any energy input will make it respond at that frequency. The key is not to have input at 10Hz. This is so the inherent damping of the stylus suspension and any tonearm pivot bearing friction can be effective at keeping the tonearm/cartridge calm. That small amount of damping keeps things under control. If the tonearm system has a response at say 3-5Hz then the resonance- infinite energy out will overwhelm the damping properties and the tonearm will be greatly excited when rising over a record warp. You could certainly not have a problem with a tonearm system response of 5Hz as long as the records are perfectly flat, hole dead center and the turntable well isolated from footfalls.
I had a cartridge/tonearm system at 16 Hz once. It sounded ok but when I looked closely, the stylus was constanltly moving up and down. I rectified the problem by adding a 4 gram mass to the headshell. That dropped the natural frequency to about 10Hz. Everything was steady then.
The danger is that being outside the quiet zone (10Hz +/-) can result in excessive wear or even damage to your cartridge and records- even if it sounds fine.

Many arm manufacturers provide a dubious figure for their arm's Effective Mass whilst a large number provide no figures whatsoever....😷
The cartridge manufacturers simply provide a 'design target' for their compliance figures which can vary significantly from unit to unit....and also possibly changes over time...

'Effective mass' is the combination of the cartridge and arm, as seen in the post from Tonywinsc. As a result an arm manufacturer can't really publish an actual figure, unless they know the mass, compliance and tracking force of the cartridge (since the position of the counterweight will have an effect).

Harry, I don't think you need any more numbers. Take the grills off of your loudspeakers and see how much woofer excursion you are getting. If its a problem- for example if that is how the amplifier power is being gobbled up, you have a problem. If not- maybe you're in the right window.

If the cartridge can track through anything without breakup then you're fine. If not this is something to look at. Some torture tracks:

'Paranoid' by Black Sabbath - Vertigo white label LP (bass energy brings many systems to their knees in a heartbeat)

Village Music of Bulgaria - Nonesuch LP (massed females voices should sound clear)

Verdi Requiem side 1 track 2 - RCA Soria series LP (wide daynamic range with big bass drum whacks)

'Garden of Worm', side two of 'In the Wake of Poseidon' by King Crimson, pink Island LP (heavy Mellotron tracks tend to break up)

All of these recordings should sound really clean and undistorted in any way.

If you can track these without breakup you are in the window.

Bravo Tony `Ö´

Can´t agree more on everything you say.
It is exactly the same what I have experienced over the
decades.
The magic of 10 Hz +/-2.
We must aim exactly there. Everything else is superstition.

The SME III and all series have 2 options to increase mass
on headshell: 2.2 g and 4.4 g metal ballast weights,
very simple method to move the peak area. My SME provides
6.6 g of total extra mass.
http://www.ebay.co.uk/itm/SME-SERIES-309-SERIES-IV-SERIES-V-
4-4-GRAM-METAL-BALLAST-WEIGHT-BRAND-NEW-/141436953524?
hash=item20ee4ca3b4

Additionally, the super rigid titanium-nitride wand has 4
teak ribbons inside wand & is fluid damped outside. SME arms
have very informative sheet for effective mass & frequency
resonance values. SME III is Classic Beauty with fine lines
& gorgeous curves...
like Sophia Loren ~ :^)
Never underestimate damping, it´s the essence.

Generalizations, half truths, and oversimplification lead to erroneous conclusions even if they work. Rules are made to be broken and it's results that matter. You want to know the resonant frequency of your arm/cart? Buy a test record.

How is it that Halcro can track almost anything with a resonant frequency below the recommended range, magic? It's because his set-up isn't easily excited by acoustic/mechanical impulses and he probably doesn't play severely warped records. They sound like crap anyway, so why?

Resonance doesn't result in near infinite energy out. Even an atomic bomb is finite and we're not converting matter to energy, but the propagation of resonance can be a problem, mimicking oscillation.
Ever see the original Origin Live mod of the Rega arm? They cut two slots along the bottom of the armtube to prevent increased vibration/resonance propagation. The armtube can be sort of like an echo chamber for vibrations.

There are two basic ways to deal with any resonance and vibrations, and the cart will put vibrations into the headshell regardless of resonance. They are damping and dissipation. Over-damping compromises transient response and makes it sound dead, but judiciously applied will mitigate amplitude of resonance and aid tracking. What's the difference between damping and bearing friction? Not much methinks.
Dissipation is channeling energy down the armtube and out, hopefully. The trick is not to have mechanical vibrations go the other way. That's where high quality equipment and set-up comes into play. A well designed table will do this for you if it's set-up right.
Regards,

^^ the above seems to read as if there is confusion between the resonance of the arm tube with the mechanical resonance of the arm mass combined with the cartridge and its compliance. The two are different.

The adage that rules are made to be broken is in itself a generalization.

The reason the 10Hz target is desirable is not a rule- its a recommendation for best results. If you spend a lot of money on an arm and a cartridge only to have it mistrack by ignoring this recommendation, it is money poorly spent.