How to measure tonearm effective mass

Some of us who use high or low compliance cartridges fret about mating them with tonearms of low or high effective mass, respectively. Most of us rely upon data supplied by some manufacturers to specify the effective mass of their tonearms, but many manufacturers do not even supply such data. Does anyone know a simple and relatively accurate method for determining effective mass? We know what "effective mass" is; we want to know how to measure it.
Most actually don't know what tonearm effective mass is. Tonearm effective mass can be expressed as the moment of inertia about the pivot divided by the effective length of the tonearm squared. Which makes it very hard to calculate mathematically as it is dependent on the distance of mass distribution from the pivot.

There is a simple practical method for determining the effecive mass of a tonearm and it is to put in a cartrige of known compliance and use a test record to determine the resonant frequency of the moving system, such as the HFN&RR Test Record and then you can work the math back from there to determine the exact effective mass of the arm.

Resonant interactions between arm and cartrige audibly swamp any and all contributions that are a result of the primary arm/cartridge resonance and are much less predictable. There is some common angst about primary resonance, but just being in the ball park is generally more than enough.
Oh and to work the maths backwards the resonant frequency is equal to 159 divided by the square root of the effective mass of the arm times the compliance of the cartridge. Even so, you will only come out approximately, because of variance in compliance with frequency and static vs. dynamic compliance to name just two of the reasons.
Google might make it easier if you find someone that explains it an easy way.[][]
I couldn't resist the second link because of the stylus picture.
Since I put the link to the stylus, I should add that they look more like a rock instead of a nice looking gem(in 1st pic) for those that haven't seen one under a good microscope. This link shows a real one, if you scroll down about halfway. The second shows others, click on pic for close up. Sorry for going off subject.[][]

Damn this stupid forum software.

Can't edit anything. The above post makes no sense without the original VA post which is here:

Mark Kelly

Aren't you glad you asked ........

Chuck, I AM glad that the question brought responses from some of the most knowledgeable people around this part of the hobby.
Viridian, The Catch-22 is the bit about needing a cartridge of "known" compliance. I guess one can figure that out by starting with another tonearm of "known" effective mass, or else one can start with manufacturer data, which I am not at all sure I trust. But thanks. As far as that goes, there was a neat idea from John Ellison on VA that is germaine to this issue. For a case where we know either the effective mass or the compliance of the cartridge, you simply drop the stylus onto an LP whilst recording the harmonic motion of the bouncing cantilever. For that he uses his computer and appropriate software. Once you freeze the decaying sine wave that describes the signal coming from the bouncing of the cantilever, you can make measurements that will get you back to the unknown parameter.
Mark, Did you make reference to the John Ellison method? I will take a look.
Mark, I see you had posted your own novel method on VA. Looks a bit cheaper to try, compared to John's which requires one to buy the requisite computer software. Thanks.

I was just being facetious ... You ask a simple question and get very complicated answers but you are right it is a very good question...
Hey Chuck. Are you THE Chuck, formerly of Northern Virginia, to whom I spoke at RMAF?

The confounding reports of apparent tonearm/cartridge mismatches that sound great have me thinking about the quality of the data for compliance and tonearm effective mass that we start with. Also, for some of the newer/newest tonearms, there are NO data coming from the maker. To wit, I asked a dealer about the effective mass of the Talea. Turns out an exact number is not available.

Of course also, Raul and others have correctly (probably) pointed out that the compliance/mass issue is not at all the sole determinant of a good tonearm/cartridge marriage. I suspect that is a very important truth.
Dear Lewm: +++++ " have correctly (probably) pointed out that the compliance/mass issue is not at all the sole determinant of a good tonearm/cartridge marriage. I suspect that is a very important truth. " +++++

why you have doubts about with so many testimonies not only on that MM thread but on other threads and even on proffesional reviews like that one that I pointed out in more than one ocassion review on Audio magazyne (1984) reviewed Ortofon MC 2000 cartridge. Well, maybe because you are " technical " oriented and like to know in precise way the why's, I would like to know it too.

Now, some way or the other we have to trust in the tonearm/cartridge manufacturer specs, yes maybe sometimes could be some errors but I think normaly are trusty numbers.

In other side, what I think we need is some one that take the task to " design " a mathematical/computer model that take in count any single factor/parameter/subject that has influence in the cartridge quality performance level and that could give us an " idea " of what to expect with a cartridge under " some/any " circumstances " where cartridge is surrounded.
Who say I take it?

Regards and enjoy the music,
Lew, All I can contribute on this subject is the result of modifying a linear arm to allow micro adjustments to effective vertical mass across a wide range of adjustment. This set-up separates observations related to changing effective mass from observations related to changes in wand composition or length. The effects are remarkable. So far in limited experience with a few cartridges, small changes in effective mass have more impact than VTF on taming subtle tracking problems and improving LF performance. The granularity and wide range of adjustment necessary to optimize each cartridge, suggest that the broad categories of light, medium, and heavy arms may be too coarse to consumate perfect marriage between arm and cartridge-- unless achieved by guess and by gosh.
Funny that only one pivoted tonearm I can think of actually has capacity to alter its effective mass, and that is the MA707 or the CF1 (or both) made by Micro Seiki. They used the simple device of a weight that slides fore and aft on the arm tube. You'd think that idea would have been widely adopted. Maybe they had a patent.

For some reason the first of my two posts hasn't turned up - I've had no end of problems with this forum lately. It referred to a post on another forum, maybe that's part of it.

Anyway, in it I posted a link to an improvement of my method by "markse", which involves using a rod of known inertia balanced at its midpoint in the place of the weights I used to calibrate the system. One end of the rod is attached to the speaker cone and the shift in resonance is plotted the normal way. This removes the inaccuracies generated by pushing the speaker's suspension off centre.

It does complicate the calculation somewhat, but a shorthand method is available - if the rod is uniform and thin in porportion to its weight, the "equivalent mass" seen by the speaker is 1/12th of its actual mass. Thus if you wanted a claibration range of say 10 to 20 g equivalent mass, choose rods around 120g and 240 g. Convert the frequency to a period (eg by inversion) and the result is a linear correlation of period shift to equivalent mass.

Mark Kelly
Correction to above post:

Where I said "convert the frequency to a period (eg by inversion) and the result is a linear correlation of period shift to equivalnet mass"

I should have said "convert the frequency to a period and square the result. The result is a linear correlation of this quantity and equivalent mass."

My apologies for the error.

Mark Kelly

where you say "This set-up separates observations related to changing effective mass from observations related to changes in wand composition or length.", there is a further complication.

One of the things affected by wand composition and length is the presence and amplitude of arm resonances. If you happen to clamp the sliding weight at a vibrational antinode you will substantially alter the resonant character of the arm tube. This shows that there is some interaction between the two sets of parameters.

I've been playing with an arm with deliberately split vertical and horizontal effective masses (an idea I stole from the Dynavector DV50X series) and am investigating making the vertical effective mass adjustable. My first method was a simple sliding weight on the arm tube and I came across the resonance interaction I described.

Next up is a method of tuning the counterweight(s) so that the VTF and effective mass are separately tuneable. This gives me a problem if a very light cartridge is used, reducing the distance between the centre of mass of the counterweight and the pivot and reducing the possible adjustment range for effective mass, so I may have to combine the two.

Mark Kelly

any arm that has split counter weights can have its effective mass adjusted. Triplanar, Talea, etc.
Mark, My tonearm has the front and rear counterweights riding on separate threaded rods going into the pivot and independent of the arm tube. Thus adjustment of counterweights does not affect the secondary resonance characteristic associated with wand composition or length. Also, its linear design allows separate manipulation of horizontal and vertical mass. Thus far I've found that the vertical mass is the more critical adjustment. Up to two-thirds of the assembly's total moving mass resides in the counterweights-- allowing a wide enough range of adjustment to characterize the tonearm as "universal."

Dan_ed, Indeed a split rear counterweight allows some adjustment. The question is whether the range of adjustment is sufficiently wide for a particular cartridge. In addition, with such an approach it is not possible to separately adjust horizontal and vertical mass; the adjustment of one affects the other.

I would add that with any long pivot arm, the rear counterweight(s) is in the final analysis the slave of the wand/cartridge lever. With a linear wand it is possible to unpack and play with each variable separately.

Thanks for the clarification. Now that you mention it I saw a phot of your mod to the Terminator (on VA?) and thought it was a very clever solution.

Mark Kelly
Dan_ed, Good point about the tonearms that can accommodate two counter-wts, but as Dave mentioned, the range of adjustment of effective mass afforded by that arrangement would seem to be quite limited.

Mark, Despite the setback you described, do you continue to pursue a Dynavector-like tonearm design where the vertical effective mass could be adjusted? I wonder whether your final solution to that problem would be retro-fittable to my DV505, eventually. Actually, what I do now is just change headshells as and when needed to change EM. That obvious ploy does not allow "on the fly" adjustment to max out the performance of a given cartridge, however.

I have no intention of making any of this available commercially. It's slowly dawning on me that whatever ability I have as a designer, it's more than compensated by my lack of ability as a business person.
Yes, thanks Lewm. I should have added, "adjusted to some degree", or some such. ;-)
Hi Mark,

I've been following this topic (motor controller) for a while now. There's obviously a great deal of interest from a growing number of turntable owners in finding a better way to extract the most music from their equipment. Is there any plan to share your design with a wider community by making it available to the DIYers in some fashion?
James, This is/was a thread about tonearm effective mass. I think you want to post on the thread about "Garrard" motor controllers. It's possible that Mark intends to sell his Garrard/Lenco controller.