Tonearm Setup: Effective Mass, Inertia, and Sound

I have been experimenting with adjusting my tonearm's counterweight. I can add or remove extra weights and slide the counterweight mechanism toward or away from the pivot point of my arm. One can see from the three photographs below how the extra weights change the size of the counterweight, lower its center of gravity, and alters its position relative to the arm's pivot point.

I am curious how these changes may or may not affect the overall effective mass of the arm and the moment of inertia of the system. I would think these properties would interact with the cartridges compliance to change the sound. I assume that the added weight near the pivot also loads the arm's bearing to a greater extent which may affect the way resonances travel through and escape from the arm into the arm base.

Has anyone else done such experiments with his arm? Do you hear any differences? Is there a theoretical advantage to one position or another? As with the recent cartridge loading thread, it was fascinating to learn about the theory of cartridge loading, but in the end, final settings are often done by listening. I suspect that this may also be the case with these adjustments because of their interaction with the cartridge.

I do hear slight differences, but I'd like to start a discussion about this topic before describing what I hear.

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Comments

bazelio

Active Member
Sep 27, 2016
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#2
Peter, I think the short of it is that you are changing the moment of inertia, and in turn, the effective mass. Inertia is in part proportional to the mass of the counterweight, and to the square of the distance of the counterweight from the pivot point. You can therefore figure if you are increasing or decreasing total effective mass by comparing the delta mass to the delta distance of that mass (squared) from the pivot. Now, all that said, the majority of the contribution to effective mass is going to come from the cartridge end of the tonearm as it is much further from the pivot point than is the counterweight. So, while you are affecting effective mass to some degree with these experiments, it is a rather small degree. Likewise, small variances to your tracking force based on the (in)accuracy of your scale also contribute in some small way to differences you're hearing from one configuration to the next. :)
 

Vienna

Active Member
Oct 14, 2018
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#3
Once Harry Weisfeld of VPI, had written me in response to my question about this matter '...
Usually, all things being equal, the closer to the pivot the better as it lowers the effective mass, in theory.
In actual use there is very little difference but I think better nearer the pivot as it is easier on the cartridge cantilever to move the arm as the effective mass is lower.
Why beat the cantilever up if you don't have to so the answer is more mass nearer the pivot is better....'


Since then I am using counter weights of higher mass, thus nearer pivot
 

PeterA

Well-Known Member
Dec 7, 2011
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#4
I thought about this but lower effective mass is not necessarily better. It depends on the relationship with the cartridge's compliance. Image a tonearm with zero effective mass. Then the system would only depend on the effective mass of the cartridge body. Every effort of the cantilever to trace the modulations in the record groove would result in the tonearm moving along with the cantilever and there would be much less signal generated by the cartridge's motor. At least, this is what I think would happen.

Ideally, the cartridge should not move while the cantilever is moving freely tracing the groove. In reality this is not the case as the arm and cartridge body do move.

I actually think it has little to do with the theoretical advantages of effective mass and/or inertia, and much more to do with what is happening with the loading of the bearing and the movement of the cantilever relative to the cartridge body. Lowering VTF too much results in poor tracking. Lowering the inertia of the arm might result in lessening the movement of the cantilever relative to the cartridge, affecting the signal strength and frequency range.

I'm only speculating because I really don't know, but it seems to me to be about the effect at the cartridge motor and what is happening to generate the signal. And I do think there may be an audible effect with different loading of the arm's bearings depending on the design of the bearing mechanism.
 

bazelio

Active Member
Sep 27, 2016
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#5
Yes, I don't agree with Harry's take either. Too simplistic, as is his opinion that anti-skate isn't needed.

Maybe what we ought to do is calculate tonearm+cartridge resonance and attempt to zero in on a narrow range of 9-11 Hz - thought by some to be the ideal range. So, for e.g. if we're at 12Hz (which is still good), then per my recollection, an increase in effective mass should result in a slight decrease in resonant frequency which is probably desirable, albeit slightly. Likewise if we're at 8 Hz, then a decrease in effective mass should result in a slight increase in resonant frequency which is possibly slightly desirable as well....
 

mountainjoe

Industry Expert
Mar 25, 2015
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eigenaudio.com
#6
Yes, I don't agree with Harry's take either. Too simplistic, as is his opinion that anti-skate isn't needed.

Maybe what we ought to do is calculate tonearm+cartridge resonance and attempt to zero in on a narrow range of 9-11 Hz - thought by some to be the ideal range. So, for e.g. if we're at 12Hz (which is still good), then per my recollection, an increase in effective mass should result in a slight decrease in resonant frequency which is probably desirable, albeit slightly. Likewise if we're at 8 Hz, then a decrease in effective mass should result in a slight increase in resonant frequency which is possibly slightly desirable as well....
Agreed about getting to 9-11Hz resonance range. I use this handy resonance calculator - Vinylengine resonance calculator.

I also created some headshell weights in order to dial this in on tonearms that might be light in mass compared to the compliance of a given cartridge. The weight is made of copper and I had a mind to try austenitic stainless steel and titanium but never did. The weights are designed to come in 2g, 3g, and 4g while maintaining a constant thickness so that you don’t have to re-adjust VTA when changing weights.

565E93A5-9CB3-45AE-AB68-A70900AD695F.jpeg
 
Likes: bazelio

Vienna

Active Member
Oct 14, 2018
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#7
After 40 years on turntables and tonearms manufacturing, i think that Harry has enough of experience to simplify things
 
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PeterA

Well-Known Member
Dec 7, 2011
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#9
I found this tonearm/cartridge resonance calculator from Wally Malewicz on line: http://www.resfreq.com/resonancecalculator.html

The effective mass of my SME V-12 arm is specified as 12g. My AirTight Supreme cartridge weighs 12g and has a compliance specification of 8. Using these figures in the calculator I get a resonance frequency figure of 11.486 Hz. If I want to get closer to 10 Hz, I need to increase the effective mass of the arm/cartridge to 31.7g.

I don't know if this calculator takes into account that the arm is 12" long, so the cartridge weight 3" further out from the pivot may change the calculations. It is hard to say without knowing how the calculator works. I also do not know how moving the counterweight closer to the pivot but also adding weight to it changes the effective mass of the system, so at this point, I'm not sure how useful this calculator is if one does not know how accurate his specifications are or how the calculator accounts for these differences.

In any case, adding extra weight to the counterweight allowing it to move closer to the pivot point does indeed alter the sound. In my system, I hear a more incisive sound, more defined image outlines, a tighter, and a more precise bass sound. There was also a slight hardening of high frequencies like cymbals. Vocals also got a bit closed in. Everything seems more vivid and saturated, more defined. My perception is one of more detail. I was actually a bit surprised how noticeable the difference is. However, the more I listened, the less engaged I was with the music. Observing details in the sound is not the same as being emotionally engaged with the music.

I removed one extra weight from the counterweight assembly and moved the mechanism further back. The sound became less defined, tonality less hard, images less etched in space. Music flowed more, it filled the room more, it became more organic. Dynamics seemed to even improve a bit. The sound went from more hifi to more natural sounding. It was more relaxing and engaging at the same time.

I then removed one more extra weight and moved the counterweight even further back from the pivot point. The sound changed again. Now it became softer and a bit dull. Less engaging again. The best position was in the middle. That combination of weight and distance from the pivot produced the most natural sound with this cartridge. It is the middle photo in the OP.

Is this all due to slight changes in the resonance frequency of the arm/cartridge system? Was I lowering the resonance frequency from 11+ closer to 10 by increasing the effective mass of the tonearm seen at the stylus? Was this when I moved it closer or further away from the pivot and changing the weights? Can it really matter that much? Apparently so. It is hard to say without knowing more about the actual math involved, but there is definitely a difference in sound between the three combinations.

I think the important thing is to experiment to see which sounds best in a particular system. It also helps if the arm design allows for multiple weights and a range of positions from the arm's pivot point. I have been told by an SME dealer that different materials for the extra weights can also affect the sound, but I have not tried that.

I had thought that concentrating the most weight closest to the pivot point would always produce the best sound. I learned that the sound can vary and that one should experiment to see what sounds best to him. My results are specific to my tastes and my arm/cartridge combination in my system/room context. Others may have completely different results, but I encourage people to experiment if they are so inclined and if their arms allow them to do so. I was surprised by what I heard.
 
May 30, 2010
15,506
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Portugal
#10
I found this tonearm/cartridge resonance calculator from Wally Malewicz on line: http://www.resfreq.com/resonancecalculator.html

The effective mass of my SME V-12 arm is specified as 12g. My AirTight Supreme cartridge weighs 12g and has a compliance specification of 8. Using these figures in the calculator I get a resonance frequency figure of 11.486 Hz. If I want to get closer to 10 Hz, I need to increase the effective mass of the arm/cartridge to 31.7g.
(...)
Peter,

As far as I remember the main objective is keeping the tonearm/cartridge fundamental resonance away from the turntable and vinyl resonances and outside the audio band, so the aimed frequency is dependent on the turntable characteristics.

Also consider that we have static and dynamic compliance and we usually do not know what is specified in the specifications, unless clearly stated. Besides the compliance value is usually measured at 100 Hz and is useless for the tonearm/cartridge resonance. IMHO the proper way of checking it is measuring with a test LP - we should use the track with a low frequency sweep, the resonance is easily seen.

The vinyl engine site also has several calculators and information on this subject: https://www.vinylengine.com/cartridge_database_tools.php
 

ack

VIP/Donor & WBF Founding Member
May 6, 2010
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#11
One of the reasons I added those copper shields on my armwand that you have seen, Peter, is so that I could increase its effective mass and move the counterweight further back. All of that have improved the sound in here, and it's one of those mods that I have not actually talked about. Glad you did.
 

PeterA

Well-Known Member
Dec 7, 2011
5,632
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North Shore of Boston
#12
Thanks Ack. What you did surely increased the effective mass of your arm and I'm glad you like the results. I changed both the weight of my counterweight and changed its distance relative to my arm's pivot point. According to an on-line calculator, increasing the weight and moving it towards the pivot decreased the effective mass of the arm and its moment of inertia, and decreasing the weight and moving it away from the pivot increased the effective mass of the arm. I don't know exactly how these changes altered the resonant frequency of the arm/cartridge system or what value I ended up preferring. What I do know is that my adjustments altered the sound of my system and that if one's arm allows for such experimentation, it may be worth playing around with it.
 
Last edited:
Jan 26, 2014
84
9
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Milano Italy
#13
The effective mass of my SME V-12 arm is specified as 12g. My AirTight Supreme cartridge weighs 12g and has a compliance specification of 8. Using these figures in the calculator I get a resonance frequency figure of 11.486 Hz. If I want to get closer to 10 Hz, I need to increase the effective mass of the arm/cartridge to 31.7g.
Pay attention to declared compliance. 8Cu at which frequency? Usually Japanese producer declare their compliance at 100 Hertz, so at 10 Hertz real compliance could be much higher (around 15/16 cu).
So the RF of the system could be around 8/8.2 Hertz.
To verify i think could be helpful a test record.
:)
 

PeterA

Well-Known Member
Dec 7, 2011
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#14
Pay attention to declared compliance. 8Cu at which frequency? Usually Japanese producer declare their compliance at 100 Hertz, so at 10 Hertz real compliance could be much higher (around 15/16 cu).
So the RF of the system could be around 8/8.2 Hertz.
To verify i think could be helpful a test record.
:)
Thank you Pepe. I appreciate the information. If I use 15/16 cu, the resonant frequency is 8Hz. If I use 8 cu, it is 11 Hz according to the calculator on Vinyl Engine. Somewhere in between seems pretty close to 10. I do prefer the sound if I increase the effective mass of the arm slightly by removing a weight and sliding the counterweight aft. I may also try heavier mounting screws to increase the effective mass of the cartridge by 1.0 gram.

I'm currently listening to the much lighter vdHull Colibri in my system and will revisit the AirTight Supreme this Summer along with my MSL Sig. Gold.
 

andyr

New Member
Oct 6, 2010
6
1
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#15
Once Harry Weisfeld of VPI, had written me in response to my question about this matter '...
Usually, all things being equal, the closer to the pivot the better as it lowers the effective mass, in theory.


Since then I am using counter weights of higher mass, thus nearer pivot
My understanding allies with Harry's - so I also have the c'weight as close as possible to the inner end of the c'weight stub (ie. as near to the pivot point as possible).

My maths is not good enough to understand how a lighter c'weight further away from the pivot point changes an arm's eff mass - compared to a heavier c'weight closer to the pivot point. However, it seems to me to be straightforward if you think in terms of inertia.

If you hold one end of, say, a 4' stick which has a 2lb weight attached to the other end and start waving the stick around ... you will find it difficult to control the movement of the weight. But if you move your hand to be next to the weight ... you will be able to control the weight's movement much more easily - even if you change the weight to 5lbs.

So reducing the inertia of the c'weight ... allows the stylus to track the groove better.

Andy
 

PeterA

Well-Known Member
Dec 7, 2011
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#16
My understanding allies with Harry's - so I also have the c'weight as close as possible to the inner end of the c'weight stub (ie. as near to the pivot point as possible).

My maths is not good enough to understand how a lighter c'weight further away from the pivot point changes an arm's eff mass - compared to a heavier c'weight closer to the pivot point. However, it seems to me to be straightforward if you think in terms of inertia.

If you hold one end of, say, a 4' stick which has a 2lb weight attached to the other end and start waving the stick around ... you will find it difficult to control the movement of the weight. But if you move your hand to be next to the weight ... you will be able to control the weight's movement much more easily - even if you change the weight to 5lbs.

So reducing the inertia of the c'weight ... allows the stylus to track the groove better.

Andy
Hi Andy, I too had thought this about getting the weight as close to the pivot as possible to reduce inertia. However, after much experimentation, I no longer think that one can generalize about this. I think it has much to do with the compliance of the cartridge and its relationship to the inertia of the arm. I have three cartridges and have spent much time adjusting and trying to optimize each of their performance levels in my SME V-12 arm.

My arm has additional weights which can be added or removed from the counterweight assembly. I have found that some of my cartridges prefer the counterweight actually being slightly further away from the pivot and some closer to it. With the removable weights, I can adjust this until the arm/cartridge combination sounds best.

This is how I think of it: Imagine an arm with zero bearing friction and extremely low inertia. As the stylus straces the groove modulations, the arm would simply follow because there is essentially no resistance. The cantilever would not move relative to the cartridge body, so no signal would be generated. There needs to be relative movement between the cantilever and the arm/cartridge body to generate a signal and I think that is where the cartridge compliance and the arm's effective mass and inertia come in.

Perhaps someone can explain this better than I can.
 
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tima

Industry Expert
Mar 4, 2014
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#17
This is how I think of it: Imagine an arm with zero bearing friction and extremely low inertia. As the stylus straces the groove modulations, the arm would simply follow because there is essentially no resistance. The cantilever would not move relative to the cartridge body, so no signal would be generated. There needs to be relative movement between the cantilever and the arm/cartridge body to generate a signal and I think that is where the cartridge compliance and the arm's effective mass and inertia come in.
This is interesting. I bet you've gone through a lot of effort checking different counterweight locations and resulting sonics.

Even with zero bearing friction and low inertia, wouldn't groove modulations still cause the cantilever to move? Are you suggesting the arm itself would micro-move with the modulations? I would think the arm with all its weight would need to be inertialess. Then I think of a car sitting on a road with zero friction between road and tires. (Some) friction is our friend.
 

PeterA

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Dec 7, 2011
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#18
Yes, Tim. If there is extremely low inertia and no friction, and a rather stiff cartridge suspension, I would think that the cartridge body/arm would then move along with the stylus/cantilever, resulting in less than appropriate relative movement between the two. The signal generated would then be adversely affected. Some amount of inertia or mass is needed so that there is relative movement between the stylus/cantilever and the cartridge/arm. This movement is what generates the signal. Finding the best balance is what enables one to extract the most natural sound from the grooves, or so I suspect. Ideally, I would think that the cartridge body/arm would be extremely stable and only move in one direction, steadily toward the spindle along with the grooves, while the stylus/cantilever would move with the groove modulations precisely.

I suppose the distance of the counterweight to the pivot may also matter depending on what type of bearing is used at the pivot. In other words, it is a very complex and dynamic system in which each part plays a role, so I think it is probably not good to assume that the best performance will necessarily result from a general rule like "keep the counterweight as close to the pivot point as possible" in every instance.

This is why I think the amount of inertia, if controllable by the design of the counterweight, can and should be experimented with for best performance and results. I do this by listening.
 

Mike Lavigne

Member Sponsor & WBF Founding Member
Apr 25, 2010
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#19
with my Durand Telos Sapphire tone arm it was always very important to use the largest weight close to the pivot as opposed to a smaller weight farther away.

the Telos used special 'unobtainium-metal' weights (denser and heavier for their size) which were a clear step up over the standard Telos weights. i now use those special Telos weights on my Tosca. (the standard Tosca weights are lighter for their size). these weights made a clear positive difference in the bass slam and energy projected. so maybe it's not just the weight and location, but also the density and focus of that weight that matter.

after i got my Clearaudio GFS (fairly heavy) Joel had a special longer weight made (not cheap) which took the place of using 2 weights. this could be a little closer to the pivot and also as a single weight was better. this longer weight works on the Telos, but not the Tosca.

i feel like more of an observer of cause and effect, than really understanding exactly why things happen. on some level i have some feel for the forces involved, but try to not just do things because i (think i) know they are better, but because i can hear that they sound better.
 
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PeterA

Well-Known Member
Dec 7, 2011
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#20
Mike, were these audible results always witht he same arm and cartridge? I ask, because I am guessing that a cartridge with higher compliance might favor lower inertia with the counterweight closer to the pivot, while a cartridge with lower compliance might favor an arm with greater inertia from having the weight further from the pivot. But, this is just a guess. I wonder what the cartridge manufacturers would say.

The amount of inertia of course also has to do with the weight of the cartridge, the effective mass of the arm, and perhaps type of bearing. I do appreciate the option of adding or removing weights while sliding the counterweight assembly toward or away from the arm. Flexibility is good if one likes to experiment toward optimizing the sound. And, I imagine the material properties of the weights can matter too.

I may look at whether or not a different weight location affects anti skate. I suspect that the greater the inertia and effective mass of the arm, the greater the skating force is on the deflection of the cantilever. I also imagine that the performance over warps should also be affected by the location of the counterweight.
 

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