Cartridge Loading and Compliance Laws

After reading into various threads concerning cartridge/arm compatibility, then gathering information from various cartridge manufacturers I am left feeling confused with head spinning a bit.... Ok, cart compliance I get, arm and total mass I get, arm/cart compatibility and the whole 8-12 Hz ideal res. freq. range I get. But why on earth then do some phono cartridge mfgs claim their carts are ok to use with med. mass common modern arms when they are in the highish 20-35cu compliance range? Am I missing something??

Ie. Soundsmith, VanDenHul, Ortofon and who knows, maybe more??

From what I gather, below 8Hz is bad and above 12Hz is bad. If one is less ideal than the other, which is worse I wonder, too low res. freq. or too high?
One more twist to the plot is that the cartridge specs may not be accurate to real world application. eg. the compliance of the cartridge may be given at a high frequency point and could be much different at low frequency. My SME tonearm conveniently lists the mass and compliance in the manual. So I can use the website calculators to determine my total system resonance frequency. I had a Denon cartridge at one time. It made my system Fn equal about 16Hz because my SME arm has low effective mass. It sounded good, but even the slightest warp in the record would cause the needle to skip. The stylus and tonearm were very animated when observing it closely while playing a record. I solved the issue by adding a 4 gram mass from England made for the Denon/SME combo. (It had threaded holes to fit the SME headshell and was designed to be glued to the cartridge. It also raised the tonearm making it easier to get the right VTA.) The 4 gram mass made Fn about 10Hz as I recall. The tracking was much more stable. A low system Fn such as 5-6Hz can make your turntable more susceptible to footfalls or other low frequency vibrations, including warps in the record. In the end, the calculation is only as good as the data supplied by the tonearm and cartridge manufacturers, but test records are available that can be used to determine actual system Fn.
So then in your case, you were able to fix things with a low compliance cart and lightish med mass arm by adding mass to the arm...hmmmm good thinking!

But how about this - what if the tables were turned and someone was dealing with a highish compliance cart and an arm that was a little too heavy for that cart? You can't take away mass from the arm and you wouldn't want to add mass to the headshell either like in your case....maybe a person could find lighter headshell screws for the cart or something....geesh what a ordeal this whole turntable business can be.
Correct, if the tables are turned, then you are out of luck. The only choice is a new tonearm or cartridge. Some might say dampening the tonearm would help, and it might. Only thing is, dampening is masking the underlying problem. There still might be consequences or undesireable attributes with dampening. That is different from isolation. Isolating the turntable and tonearm from airborne and mechanical vibrations is always beneficial.
Correct, if the tables are turned, then you are out of luck.

This is not entirely true. 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.
Good point. When talking about effective mass, we are really talking about inertia and the moment of inertia is proportional to square of the distance from the axis of rotation. So, yes, more counterweight mass closer to the pivot will reduce effective mass.
Dear Jeremy72: Laws?, IMHO there are no laws about but only theory about: that sometimes works and sometimes does not it depends on cartridge overall characteristics and tonearm it self.

IMHO it is not easy to take as a rule/laws a " generalization " like the resonance frequency range: 8hz to 12 hz. In this subject I think we can do better if we know what in specific we/you are talking about: which cartridge and which tonearm as which problems you are experienced with or what you don't like or want to improve at quality performance level.

I think that if you bring here that information some of us could help you with out be speculating on something we really can't even imagine.

regards and enjoy the music,
So from what you guys are saying if an arm had an eff. mass of say 14g then if you somehow made the counterweight heavier then you would automatically be reducing that number? Not sure I understand... if you have an arm that is 14g eff. mass, then how is that number able to be changed by increasing the weight on the end? Isn't it is what it is by design? Maybe you are just kind of manipulating things is what you are saying, to increase the res. freq. of the two.
So many times have I read about the 8-12Hz cart/arm res freq guideline its just like it seems to be a law to me because these numbers are the ones always brought up. Now people some times claim 9 or 10 is soem magic number even. I am no analog wiz or do I understand all of this stuff I am just wanting to understand what the hecks going on so I don't wind up putting together something that does not go together and sounds awful or has some weirdproblem.
"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.


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.
No. Because your model does not hold true in real life. In real life, the tonearm must permit the cartridge to trace the groove from outside to inside, and so it cannot be fixed in space, which is where your model falls short. In real life, the cantilever has to move the effective mass of the cartridge body and the arm wand up to the pivot point. The cantilever of a high compliance cartridge would be more prone to flex in response to the need to move this mass in addition to its need to flex in response to groove modulations, with a high mass tonearm vs a low mass one. This could produce a low level signal that is not part of the music signal, i.e., distortion. The best simple analogy I know is to think of a high mass arm as a truck and a low mass arm as a sports car. Have you ever seen a truck with bad shocks (high compliance/low damping) when it travels over a bump? It will be set into harmonic motion by the bump more easily than will a sports car with much smaller, higher compliance shocks, because the latter has so much less mass. Conversely, really hard shocks (low compliance) on a sports car will knock your teeth out. Even this model has flaws, I admit, but I hope I made my point.
I wonder would using lighter cartridge screws help if your arm were a little heavy and cart a little light compliance wise? Or would that make things even worse or with cart screws does it even matter really?

I have seen these really light aluminum and plastic cartrdge screws before and of course steel or stainless steel ones. Someone told me before that these little screws can affect the sound, how though I am not really sure.
Lighter screws are definitely better because that mass is at the farthest point from the pivot. So that affects the inertia of the tonearm. Aluminum screws are preferred for both less weight and the non-magnetic properties. Don't use plastic screws. Plastic creeps, ie. stretches, and you won't be able to maintain the torque with plastic screws.
To use your truck/sports car analogy however, a truck would be less likely to be knocked off its straight path than a sports car hitting the same bump. I dont know that the analogy works because the tonearm is not moving, and therefore has no momentum inertia of its own, only its fixed inertia as an impediment to motion. But since I dont want the tonearm to move relative to the stylus, why wouldnt that be better. Dont we want to keep the headshell/cartridge/stylus relationship fixed except for those movement in the stylus that correspond to the vinyl groove. Why would we want the tonearm to move? And if it did at the same rate as the stylus, which of course it can't, wouldnt that result in no sound at all. Isnt it the movement of the stylus and coil assembly relative to a fixed magnet what produces the sound. And if that fixed magnet moved the same as the stylus/coil, no sound would be reproduced.
Picture the stylus like a wheel on a car. The stylus has micromotion as it tracks the groove on a record and that motion is absorbed by the suspension. Just like the wheel on a car moves over small bumps in the road but the car remains fixed. In both cases in regards to the micromotion and inertia of the stylus and the wheel, they are very small compared to the mass of the tonearm or mass of the vehicle. So that micromotion causes little or no motion in their relatively massive counterparts. But when the stylus moves over a warp in the record, for example, now the entire tonearm must move in response to that warp. Consider that a macro-motion. In this case, if the tonearm has too much interia, the tonearm raises up to ride over the warp but takes too long to come back down resulting in a skip. Similar sitation in a car- a dip in the road or bump in the road causes the car to move up/down, but if the car has too much inertia, then it leaves the road surface. In both cases, a car or a tonearm, the spring rate and the effective mass affect how they respond to those macro-motions.
Manitunc, You wrote, "To use your truck/sports car analogy however, a truck would be less likely to be knocked off its straight path than a sports car hitting the same bump. I dont know that the analogy works because the tonearm is not moving, and therefore has no momentum inertia of its own, only its fixed inertia as an impediment to motion."

I don't really see what you are getting at. The tonearm most certainly does move, in the lateral plane it has to move in order for the stylus to trace the groove, in the vertical plane we don't want it to move (up and down), but it will to a degree that is directly dependent upon the compliance of the cartridge (the springiness of the cantilever) and the mass of the whole ensemble of the tonearm/cartridge. Obviously, the less vertical motion of the tonearm wand, the better.

As an aside, "momentum" and "moment of inertia" are two different things. Don't know what "momentum inertia" is. Finally, for both a truck and a sports car, the correct shock absorber damping will result in the least reaction to a "bump". (I don't really like my own sports car/truck analogy so much, either.)
I accept your analogy with respect to record warps. I was more referring to the stylus/arm relationship in the normal condition of tracing a flat record groove.

What I meant is that the tonearm is not moving in relation to itself, while a car or truck is moving, thereby creating what I referred to as momentum inertia. You know, an object in motion tends to stay in motion. Knocking a moving vehicle off its line requires a force that increases with the speed of the vehicle. You dont have that issue with a tonearm, which is relatively fixed as compared to theh speed of the record groove. Sure, it has to travel across the record, and up and down over warps, but not at anything close to the speed of the wiggles in the groove, which at the outer groove is traveling around 1.74 ft per second. A 20 minute record requires the arm to move horizontally about .001375 ft/sec assuming a 4" playing surface. Hardly a meaningful comparison. That makes me believe that holding the cartridge steady and just allowing the stylus to move is the more accurate method. Again, I am not addressing warps. I do see, however, that once the arm does move, a heavier arm will tend to overshoot and be slower to react and return to the neutral position.

Doesnt the Townshend fluid damper trough at the headshell end essentially create a condition that the stylus would see as a more massive tonearm. I can tell you from experience that the Townshend system works very well, and cleans up the bass tremendously as compared to the same cartridge/tonearm without the damping trough.
Dear Manitunc, My point is that you cannot make the general statement that a heavy tonearm is "better" than a light one, or vice versa, because there are other factors involved and for sure there are conditions within which either proposition is the correct one. And the model of a cartridge held static in space is a bad one to start from, I still say.

"An object in motion tends to stay in motion". Yes, that is inertia.
"Momentum" is a quantity applicable to a body in motion. Momentum is equal to mass X velocity. Inertia also says that a body at rest will tend to stay at rest. A body at rest has no momentum.
This comment really makes me think, as I had no idea.

"Increasing the counterweight mass and then moving it closer to the pivot in order to maintain the same VTF will reduce the eff mass."

This could really help someone I think, in some cases at least. I wonder though how to judge how much the eff mass is reduced when the heavier weight is added and slid forward...would this be figured by somehow reducing or subtracting the actual amount of weight added to the counterweight to begin with from the starting eff mass without the extra weight??
I wasnt making a general statement that a heavy arm is better. I was just trying to think through the variables and it seemed that a heavier arm would do the things an arm is supposed to do better than a lighter arm. I dont know if that is true, however, since I havent been able to hear and compare the universe of arms out there. My thoughts were just that I seem to hear a mantra of heavy arm = low compliance cartridge, light arm = high compliance cartridge and was questioning whether that is true. Again, I dont know and only seek to understand and learn.
"heavy arm = low compliance cartridge, light arm = high compliance cartridge"
Yes, that is a mantra of the internet that I read very often, too. As I am sure you know, that formula is meant to set the low frequency resonance at a frequency between 8 Hz (so as not to excite resonance via footfalls and other very low frequency sources) and 12 Hz (so as to stay away from the audio bandwidth). The formula for that resonant frequency can be found on Vinyl Asylum and in other places, but tonearm effective mass and cartridge compliance are its principle determinants. So this is why the gurus tell us, "heavy arm = low compliance, etc". However, there are guys on this discussion group, most notably Raul, who point out that there are many other factors that determine the overall "goodness" of a match between tonearm and cartridge and that sometimes one can and should overlook the mantra in search of good sound. One example is that several owners of the Fidelity Research FR66, a 12-inch arm with very very high effective mass, claim it sounds fantastic with MM and MI cartridges that have very high compliance. Conversely, some others who own very light tonearms like the ADC and the Black Widow like to use them with MC cartridges that have low compliance. To all this I say, "go figure". The take home lesson I think is if you have a tonearm you like a lot, don't stop using it just because it might technically be a mismatch with your new cartridge, on the basis of its effective mass vs the cartridge compliance. All bets are off.

Why this is true is worthy of another separate discussion, but I have my ideas.
Another thing, I have often wondered about is - does it really matter if you use washers under the cartridge screws? I know it adds a little weight but is it a bad idea from a sonic perspective? Thoughts anyone??
Depends on the washer... a nylon washer should probably be avoided- the coupling between the cartridge and arm should be as tight as possible, and nylon will squish.
Ideas why cartridge/tonearm mating may defy the predictions:
(1) The compliance of the actual cartridge sample could vary significantly from what the manufacturer has published, especially if the cartridge has aged.
(2) Many systems cannot reproduce much bass below 30-40Hz and so a resonant peak above 12 Hz is not much of a problem and/or the turntable is well isolated and in a very stable environment, so resonance below 8 Hz is also not a problem.
(3) Little tricks used in certain tonearms to dampen resonance and/or to reduce effective mass, such as moving the counter-wt very close to the pivot point.
(4) Inaccurate data on tonearm effective mass.
(5) When one spends a lot of money for a tonearm and cartridge, one is predisposed to like the result.
Great responses everyone, I really thought this thread might help to simplify things for those of us who are not gurus. But boy what a can of worms I have opened, it just keeps getting more and more complicated! Oh well, thats analog and audiophiles for you.
What about this:

I have a Lyra Delos cart (Approx. 12 x 10 cm/dyne at 100Hz; 7.3g) on a Pro-Ject 9cc arm (8.5g effective mass). For the most part it tracks well, but I occasionally get sibilance distortion in the right channel (even with too much anti-skate). Yes, my anti-skate is correct, along with alignment, VTA, VTF, etc. Would the brass weight help track the hottest sibilant grooves by adding mass to my arm? Any suggestions would be great. Thanks.
Wow, a 28gram brass headshell weight and 100gram counterweight add on?! Someone correct me if I am wrong but I think that is an extreme concept and probably not the best one. Instead maybe you could add a couple of stainless steel washers under your headshell screws atop the tonearm end where the cart mounts. If I had to guess I'd say you would be much better off going this direction over adding 128g of solid brass to your arm!

I could be wrong though so maybe someone with more knowledge can share their thoughts also.
To experiment with variations in vertical inertial mass I added dual counterweights to the wand of a Trans-Fi linear tonearm. This is the high-mass version for medium-to-low compliance cartridges:

I also made a low-mass version for medium- and high- compliance cartridges. This version uses 7-20 gm counterweights.

The optimal adjustment resolves tracking problems such as edginess and sibilance. Too much inertial mass takes the life out of the music. My experience suggests that the Mapleshade weights would be too heavy-- particularly on a long moment arm.

It's great to be done with the math and to resolve each situation empirically.
Those Mapleshade weights may indeed damp resonances but the overall mass of the tonearm combo now might be a bit much for those microscopic movements of a tiny needle in a groove. And you have to "bond" that weight to your headshell - meaning it is destroyed if you don't like it after all.

They way the show it configured the heavy weights are at the ends of the forward and back ends of the arm. Typically you want to have heavy weight closest to the pivot point so up and down movements of the arm are more easily made by that fragile cantilever and stylus.

I'll wait until someone here reports on it.
While daydreaming about carts I'd buy if money were no object, I looked at the spec for a low output mc VDH Colibri and found something which is baffling to me -

Weight (metal body) - 7g

Compliance - 35/mn

"Colibri metal body. Total cartridge weight is 7 gram. Suitable for arms with an effective tone arm mass of 10 gram to 14 gram." According to VDH website.

Now, what I am trying to figure out is how in the world a cart with that soft of a suspension go good with anything but a super super low mass arm.

From what you guys are saying exceptions exist but i am sorry this ones specs just appear too extreme not to be curious about. Excuse my ignorance and far be it from me to second guess mr. VDH but the specs imo beg the question.
Another thing about that VDH cart which is odd is that its the only low output mc I've seen around with a super soft suspension compliance. The others around are almost the complete opposite - low output mc's with low to med. compliance. 5-15mn weird....eccentric designer maybe? If I am mistaken here please excuse my ignorance and lack of experience. Just trying to get a grip on this stuff.
Hi Jeremy,
From VDH - Static Compliance: 35 Micron/mN

To estimate arm/cart res use dynamic cu @ 10Hz.
Static compliance is always higher than dynamic. It's dynamic compliance that is used to estimate arm/cart resonance. The standard used in these calculations is measured at 10Hz. Some Japanese cart manufacturers measure dynamic at 100Hz. Those figures are not directly comparable to 10Hz figures.
So, what you are saying is that most mfg.'s (Lyra, Shelter, Ortofon ect.) use dynamic compliance numbers on their spec sheets but for some reason VDH is using static compliance figures. Correct me if I am wrong here..

Is there a conversion calculator for converting static compliance to dynamic compliance?
Is this formula correct? If so, it would indicate that both are identical measurements only stated in different units.

1 cm / dyne = 1 g ^-1.s^2 = 10^3 kg^-1.s^2

thus 10^-6 cm/ dyne = 10^-3 kg^-1.s^2

1 um = 10^-6m

1 mN= 10^-3 kg.m.s^-2

therefore 1 um / mN = 10^-3 kg^-1.s^2

the two units are thus identical.

From what I gather on the Colibri test measurement sheet their testing is conducted at roughly 100Hz. (Similar to how Lyra tests)
All this together would seem to indicate that the stated VDH 35 Micron/mN compliance is the same as saying 35 x 10-6 cm/dyn only in different terms. If testing was done @ 100Hz. I think...

Its kinda like saying .5" is the same as 1/2" Right?

My math could be flawed though, so if that is the case anyone please feel free to correct these statements above.
There is no formula to convert static compliance to dynamic. In fact dynamic cu can be different laterally than vertically. For resonance estimates vertical is normally used. Most specs are dynamic cu. For example, most Benz carts are 15cu (dynamic). VDH only gives static, but tells you eff mass range of arms for the cartridge.

The only examples of both static and dynamic I could find listed is AT. The 33EV has a static cu of 40. Dynamic is 10 @100Hz. That's equivalent to approx 17, 18 @10Hz. There is no reliable formula to convert 100Hz to 10Hz.

IMO it's better to find out what makes a good match from other users. Resonance estimates are often wrong and great sounding combos can be outside of the recommended range. If you want to find out exactly what res freq is, get a test record. You're more likely to get bad results with a low cu cart on a light arm. When res is near the audible band it can impact on the music.
Not that I disagree because to be honest I am not absolutely certain but maybe someone can check with a mfg. like VDH or Lyra about that conversion. There are others who believe those numbers can be compared with accuracy.

What on earth would make someone like VDH put a number like that for compliance spec if nobady can understand it?

I hear you though, maybe trial and error means everything but not all of us have the luxury of rolling dozens of arms and carts just to find out which ones work well together. Thats why specs are important to me imo so that I can try to put something together which I think might be close to being right combo the first time. Maybe thats why some people get sick and frustrated of analog before they get a taste of what it can really do. just my 2 cents here and thanks for the knowledgeable people (like Fleib) kind enough to provide their input.
I think what Fleib is saying is to read what others post here as workable combinations.
This will save you the task of testing dozens of cartridges yourself.
What Fleib is also saying (and I agree wholeheartedly) that there is enough doubt and inaccuracies in theory and printed data as to render them dubious in accurately providing correct indications?
Halcro said it more succinctly than I. That's what I mean. Resonance calculators are just an estimate. I've calculated combinations that should resonate at 8Hz, and they tested at 10Hz. Effective mass is will change with things like the distance of the counterweight from the pivot (moment of inertia). Cartridges might vary somewhat or age. If you're really interested in the math I suggest that you go to Vinyl Engine and do a search or ask in the forum.

Re: 100Hz conversion. There doesn't seem to be an exact formula for conversion. Carts in the 10cu range (100Hz) have 10Hz cu approx 1.75 x that. The AT-150MLX, 33EV (10cu @100)have cu = 18 approx. An AT-95 or Clearaudio MM has 6.5cu @100Hz and approx 15cu at 10Hz. The DL-103 has 5cu at 100, and seems much stiffer. An old Pioneer PC-401MC has static cu of 16 and 100Hz dynamic of 12cu. VTF range (1.7 - 2.3) would indicate a stiff suspension. None of this makes much sense for arm matching. 100Hz cu seems more like a measure of tracking ability at 100Hz (bass), than cu around res freq which is near 10Hz. The only correlation I can come up with is a sliding scale. Low 100Hz cu is more than doubled for conversion. Med - 10cu is x 1.75. Higher, around 12 to 16 @100 is closer to to that number.

There are other things to consider as well. Certain combinations will work better, in some cases, than others, even though compliance/mass would seem OK. That's why it's really more effective to ask or read what the best matches are.
Fleib and Halcro, your responses were both enlightening, thanks for the indulgence.

All is a bit confusing still, to me anyway.
So Fleib, if I am understanding what you stated above what this boils down to is being the vdh Colibri static compliance is 35 Micron/mn then we in all likely hood are looking at a dynamic compliance in the 20-22cu range. Numbers being approximate, I assume...tracking specs say 1.35-1.5 g on VDH website so this makes a bit more sense.