Why is the price of new tonearms so high

Well - to get as plain as you: I think your model is incomplete.
The resonance frequency of a given cartridge/tonearm combination can be altered by moving a fairly heavy cylinder further away or closer towards the pivot.
The total mass of the moving body stays the same - of course.
But - I guess neither of us has any problems if we do not agree about the model at all.

Axelwahl

Your suppositions are correct and the figures are reasonable.

If we model a 100 g counterweight positioned 50mm behind the pivot, its contribution to the effective mass of a 225mm arm is 4.94 g*. If this is the position for VTF of 20mN, it needs to be moved 4.6 mm to come into neutral balance. The new position will indeed make a higher contribution to effective mass, it becomes 5.89 g an increase of 0.95g.

This would increase the maximal tracking force deviation quoted above from 6.2 mN to about 6.4 mN, about a 3% increase.

* this ignores the moment of inertia of the counterwight about its own centre of mass but since this doesn't change with position it isn't important so I left it out.

Mark Kelly

Dertonarm

That is completely wrong (again). The resonant frequency changes because the moment of inertia changes. The effective mass is simply the moment of inertia divided by the square of the effective length.

The total mass is irrelevant to the argument.

As far as I can see my model is complete according to D'Alembert principle. If you can show me something I have left out and provide a reasonable basis for the claim I'm listening.

Mark Kelly

Axelwahl your last point is where things get interesting.

Like everything else it is a matter of compromise. As you have noted, a low inertia arm reduces the maximal VTF variation. The compliance required to keep the resonant frequency in the right range changes at the same time, so the effect of a given warp in terms of displacement of the cantilever suspension depends on the resonant frequency: the higher the resonant frequency the smaller the effect.

Unfortunately we're not free to move here. As previously noted the product of inertia and (rotational) compliance forms a low pass filter. As the equation previously given shows, the attenuation and phase response of this filter depends on the ratio of f/f0, so as the resonant frequency moves towards the audio band the effects of these become more and more pronounced. That is why resonant frequency is optimised over such a narrow range.

Mark Kelly

FWIW, what Quiddity is saying makes sense to me.

IS it accurate to state that the combo of cartridge/compliance and tone arm together matters greatly? A great or expensive tonearm with mismatched cartridge/compliance still won't work well, right?