Cartridge Loading and Compliance Laws

"Some arms have multiple weight systems, so if you can use a heavier counterbalance weight closer to the arm bearings that will get you lower effective mass as opposed to lighter weights further out."

What is the theory behind this? The heavier counterweight increases the effective arm mass. Also having the counterweight closer to the bearing gives a more stable tracking. This is what I did with my 11g tone arm and now the low compliance Koetsu grooves fine.

When we talk about tonearm effective mass, we are really talking about inertia. And when we talk about cartridge compliance, we are really talking about spring rate. Not to sound confusing, but high compliance is low spring rate and low compliance is high spring rate. So the resonance frequency of the tonearm/cartridge system is simply the square root of the cartridge’s spring rate over the sum of the masses. It is the classic spring/mass equation. The system will become very excited at its resonance or natural frequency meaning it will mistrack or even skip.
The moment of inertia of the tonearm about its pivot is I=mr2. So moving the counterweight further from the pivot point increases the inertia (effective mass) by the square of the distance whereas keeping the counterweight at the same distance and increasing the mass is a one to one change in inertia. That’s why using a heavier counterweight closer to the pivot reduces the tonearm effective mass.
The tonearm is on a pivot bearing with as little friction as possible, so it is important to have a tuned system that does not get excited by vibrations from the record/platter or vibrations external to the turntable. The stylus is connected to a suspension which gives it its spring rate. As the stylus moves up/down and left/right on the record it is pushing against the tonearm. As long as those motions or vibrations are not near the tonearm’s resonance point, the tonearm remains stable.
When you pluck a spring, it resonates at its natural frequency. A string nearby tuned to the same frequency will vibrate on its own because it is excited by the other string’s vibrations. That is called sympathetic vibration. The same holds true for the tonearm/cartridge system. The 10Hz +/-2Hz natural frequency is a rule because it works. Music ranges from 20Hz- 20kHz. So if the tonearm/cartridge system is tuned too closely to 20Hz, then the arm could become excited when playing music on the record that is close to 20 Hz. 10Hz being half of 20 keeps the tonearm/cartridge system safely away from the range of the music. Now at the other extreme, footfalls and other low frequency sources in the 5-6 Hz range will excite the tonearm if it is tuned too low. So again, 10Hz being double of 5 helps reduce the tonearm’s sensitivity to footfalls and such.
I hope this all makes sense.

Hi Toni,

I agree about compliance and cartridge suspension.

The questions are:

1. Does a heavier c/weight increase the eff. arm mass?
2. Is the tracking better with the c/weight closer to the pivot?

The above is my experience and I'd like to read other users' opinion.

Thanks,

Emil

Question 1: The eff. mass is a product of the counterweight mass (plus the overall arm mass)and distance squared from the pivot point. So increasing the counterweight mass increases eff mass, yes. Increasing the counterweight mass and then moving it closer to the pivot in order to maintain the same VTF will reduce the eff mass.
Question 2: The tracking is affected by a number of factors, but just considering the natural frequency of the cartridge/tonearm system the location of the counterweight is only a part of the final result. The ideal range remains around 10Hz.

I understand the need to keep the system resonance out of the audible frequency band and footfall band. But why would a low mass arm be useful in doing that. I would have thought that the idea was to keep the arm from moving in sympathy with the stylus, and a higher inertial would accomplish that. In fact, if we could maintain a ridgid mount of the cartridge body, and only allowed the stylus to move in response to the groove modulations, wouldnt that be the perfect set up, no losses due to the arm moving in the same direction as the stylus or gains for that matter when the arm moves opposite to the stylus. So wouldnt a high mass arm accomplish that goal better than a low mass arm, even with a high compliance cartridge.