Tone arm resonance and cartridge compliance: How do they interact??

I read many years ago about the importance of tonearm resonance. How does that affect sound quality, and also cartridge compliance  How do you determine tonearm /cartridge compatibility??



The short answer is you determine by seeing if the screws fit. They usually do.

The long answer: Been running analog since the 70’s. Know all about just what you’re talking about. Its never been a factor.

Main reason it matters, audiophiles are all over the place trying all kinds of goofball stuff instead of just going with what works. So every once in a while some guy matches one oddball arm with one quirky cart, it sounds funny, some wise guy says yes compliant this with low mass that, and everyone succumbs to the tech talk. When in reality that’s not it, as invariably is proven ten minutes later when some other guy says hey I run that same cart, on that same arm, it sounds the bomb. They then technobabble back and forth, never getting anywhere.

So what I do instead, look at output, read listening impressions, go for what sound best matches my preferences. Never failed me yet.
Years ago I had a high compliance cartridge matched with a high mass tonearm. I was always blowing woofers. Yes it does matter to match the arm and cartridge. This chart from the Vinyl Engine will give you an idea if the cartridge and arm will work together!!
After so many years of posting this link people still asking the same question. There is an answer. 

The most common mistake is to make a wrong calculation using a compliance figure printed in the cartridge manual if this compliance measured at 100Hz, because for correct calculation we must know a compliance measured at 10Hz. 

If you see dynamic compliance measured at 100Hz first you have to do is to convert it to 10Hz using x1.7 formula. 

Then follow instruction in this link.  

To measure actual resonance of your particular cartridge and tonearm you need a Hi-Fi News Test LP, this is the only was to see what is the resonance and what's going on with a cartridge and tonearm in this situation: 

"Tracks 2 & 3: Cartridge & Arm, Lateral & Vertical Resonance Test
These two tracks are used to test the resonant frequency or your tonearm and cartridge combination in both the vertical and horizontal domains. These tracks offer both a visual and auditory indication of the resonant frequency; the stylus will “wobble” and the test tone will warble. A resonant frequency between 8 - 15Hz is ideal." 

Thanks to everyone who responded with valuable links and explanations

However, "jjss49"   noted: ..." this is the internet...and search is your friend"   Well bully for you!!!. 

Maybe, we should abandon these forums and just crawl into our internet cave, and let our fingers do the walking( searching)  Audiogon is a membership, and also a fraternity of people interested to high end audio and quality sound.

 It seems that member " jjss49"  does not agree or just wants to eliminate the human element altogether.   His comment seems unfriendly and not in the spirit of the Audiogon's forum option 

i just don’t appreciate laziness and entitlement

forum is here to help folks, but they should try to help themselves a little first

just a little
Another interesting link.
there are 4 posts on cartridge matching in the blog and a calculator, read the blog posts first.

I have the test record mentioned by Chakster, it was thrown in when I bought my last cartridge, an SPU Royal N. Before fitting the SPU to my arm (Schröder) I ran my Proteus through the resonance tracks. Arm eff mass 13g, compliance 13, cartridge weight 7.8g, 0.9g for the screws (I weighed them). The Vinylengine calculator gives a resonance frequency of 9Hz for this combination, on the test record there was warble from 14Hz down but visible wobble only at 7Hz. Fitting the SPU involved changing an aluminium cartridge mounting plate for a brass one, this raises the arm’s effective mass to ~18g plus whatever effect moving the counterweight half an inch further back has but I’ll ignore that. So for the SPU eff mass is 18g, cartridge and the adaptor that comes with it 15.9g,screws and nuts 1.5g and the compliance 8. This gives a resonance from the calculator of between 9 to 10 Hz, on the test record I initially didn’t see any wobble with the setting roughed in but after a couple of weeks of fine tuning by ear I ran the test again and this time it wobbled at 7Hz. The Korf calculator, which I hadn’t found until later, offers an explanation for what is going on.
10+ chakster. Forget about equations. Use the darn record!
 It is always best to start with a light tonearm. It is easy to add mass, much harder to take it away. You want to get your resonance point between 8 and 10 Hz for the best bass. When the cartridge gets to the resonance frequency you will see it start to bounce. You simply add mass until you get the resonance frequency down where you want it. There are head shell weights and Soundsmith sells a set of graduated head shell screws that are brilliant.
Effect. If the resonance frequency is too low the tonearm can bounce into the air when it hits a warp. Too high and your bass performance declines and you invite acoustic feedback. When you turn the volume up the system starts to howl. 
Dear @mijostyn : "  Use the darn record! "

Really, because exist no perfect recorded LP and in that so imperfect medium with so many different parameters involved and full of resonances/vibrations/noises/distortions developed how can you trust in what is supposed to be measured ! ! 

Regards and enjoy the MUSIC NOT DISTORTIONS,
I am surprised no one has mentioned yet that the tonearm has no intrinsic resonance, because the only resonance it has that you care about is the resonance  with the cartridge bolted onto it. The effective mass of the tonearm is equal to the basic effective mass plus contributions from the cartridge, the head shell, the cartridge screws, and where the counterweight is located. That’s why in the end few of us really know exactly what is the effective mass to which we are coupling our cartridges. Finally, the resonant frequency is a product of the effective mass multiplied by the compliance of the cartridge after you take the square root of that product and invert it.So, high mass and high compliance both have a tendency to reduce the resonant frequency. There is an inverse relationship.

Plus, the effective mass of an arm varies depending on how far from the bearings is the counterweight. Some arms incorporate a counterweight that affords adjustable mass, the Zeta being one such.

In addition, while the arm and cartridge interaction does create a resonance, most (all?) armtubes have a resonant signature independent of that. Brooks Berdan used to (RIP) fill arm tubes with expandable foam to reduce armtube resonances, and the designer/maker of the excellent Audiomods arm installs braces inside his armtubes (just like the braces inside well-made loudspeaker enclosures) to raise the resonance in frequency.

Increasing arm mass lowers resonance frequency
@roberjerman, that's simply not true. It's a common misconception because resonance charts calculate frequency based on total arm weight. But resonance is a function of other factors besides weight; including stiffness, flexibility and damping. Putting a weight on the headshell will help to damp the headshell but not the arm tube. And weighting the headshell may actually result in worse performance. Probably not unacceptably worse but often measurable worse.

The tonearm is a level balanced on a fulcrum. If you take a counterbalanced lever of, let's say, 10 feet long, and increase the weight on both the headshell (effort arm) and the move the counterweight away from the fulcrum, will the resonance increase, stary the same or decrease (amplitude AND frequency stabilize or shift)? The correct answer is that amplitude will increase and frequency will shift. The same thing happens with a tonearm, but on a much smaller scale. 😁

br3098, You are confusing two different things.  roberjermain is correct, and I wrote the same thing, a few posts above yours.  BOTH increasing tonearm effective mass and increasing cartridge compliance will decrease the resonant frequency of the system.  If you will look at the equation, you will see that the product of the two quantities is inversely proportional to Fres.  Now, what bdp and you are talking about does not per se alter the resonant frequency, as long as you don't change effective mass and compliance. What damping and choice of materials does, if done smartly, is take the energy of the resonance that will occur at the calculated frequency and spread out or broaden the resonant peak, the range of frequencies at which the energy of resonance is dissipated, which is usually a good thing that can mitigate an otherwise bad pairing of cartridge and tonearm.  And yes, the (distance from the pivot to the center of mass of the CW)-squared times the mass of the CW, adds to effective mass.  That's why, if you want to minimize effective mass, you want a heavy CW that can be moved as close as possible to the pivot. (Because the em will vary as the distance-squared but only in direct proportion to CW mass.)
The beauty of the adjustable-mass counterweight of the Zeta arm (accomplished via removable steel discs in the hollow counterweight) is that if one wants to use the arm in it's lowest effective mass guise, more discs are placed in the counterweight and that cw is placed as close as possible to the arm's bearings. For higher em, fewer discs and the cw further away. Counter-intuitive, but true.
My Triplanar and I suppose several other tonearms achieve the same end by supplying a set of CWs that vary in mass. You can slide them on or off the rear end of the arm. Further the Triplanar CW is physically decoupled from the pivot by a nonrigid damped joint.
Dear @lewm : obviously that a tonearm as a cartridge in static way has no intrinsec resonances but in the very first moment that the TT spins even with the tonearm in rest that tonearms has " resonances/vibrations " at micro levels. So @bdp24 is rigth about.

The overall subject always been a little controversial because the formula calculates the resonance frequency of a cartridge/tonearm at static/rest way. The numbers are the ones from those combinations of tonearm-cartridge and it’s a good place to start with the subject but those numbers will change during playback because exist additional parameters that affects it.

Yes, the formula says what you posted but you have experiences where that not really happens during playback because you love that very heavy FR tonearm with a cartridge boarding in the 40-50 cu and you love that combination.

So, some one out there needs to model what in reality happens taking in count all those multiple factors/parameters around this controversial subject.

Even those always is convenient try to achieve the ideal frequency range in our tonearm/cartridge combinations because the quality performance will be better than if we don’t care about. Problem is that several times we like what is wrong and dislike what is rigth !

Btw, """ supplying a set of CWs that vary in mass . "" this was posted too by @bdp24 with his Zeta tonearm but is not critical inside the resonance formula because the CW is near the fulcrum and contributes very low for the total mass.
What is important for place/position the CW the nearest we can to the tonearm bearing is to gives to the tonearm a better overall " displacement/operation " during playback, give an additional facility to the tonearm work.

Regards and enjoy the MUSIC NOT DISTORTIONS,

I’ve seen low effective mass referred to as low moment of inertia. It is logical to conclude that a low moment of inertia arm requires and benefits from a low friction bearing.

Geoffrey Owen offers his Helius Omega Silver arm (used by Tim de Paravicini on his excellent EAR-Yoshino table) with the choice of Ruby or Silicon Nitride (Si 3N 4) ball bearings, both of which possess a hard, very smooth surface and therefore low friction, perfect for an arm’s bearings.

Dear Raul, I have to differ with you only on what you wrote in your first paragraph. The effective mass of the tonearm and the compliance of the cartridge determine the resonant frequency according to the formula that you know and I know too. You are probably right that in the real world resonance  is not so easy to figure out just from numbers. The first of all problem is that we really usually don’t know the effective mass of the tonearm/cartridge we’re using. For example, the Fidelity research has a very high effective mass when used with its factory supplied head shell, which in itself is heavy. And head shells have an inordinate affect on effective mass, because they are out there at the end of the tonearm. I use the Fidelity research tonearm with a high compliance cartridge, but I use a very lightweight head shell when I do that. And yes, from a listener standpoint the combination is very successful. But I have to freely admit that I really don’t know exactly what is the effective mass of the tone arm and cartridge combination that I ended up with. The Acutex cartridge that I used with the Fidelity research tonearm is also an extremely lightweight cartridge body in and of itself. Probably many grams lighter than a typical fidelity research cartridge of the vintage era. I can only tell you there is no audible sense that the resonant  frequency is interfering with bass response or anything else. The best way to work out what is going on with the tonearm and cartridge and resonance  is probably to figure out the resonant frequency by using a test LP or a very novel test that I read about on vinyl asylum. So then you would hopefully know the compliance of the cartridge and the resonant frequency and from that you can work backwards to get some idea of effective mass.
lewm, I agree and disagree with different parts of your statement. Rather than cut and paste a text on mechanical amplifiers and resonance, please tell me how adding weight at the headshell is beneficial to the resonance of the lever?

I agree that increasing the mass of the lever (arm tube) will dampen a mechanical amplifier. But increasing the resistant load will have the opposite effect, decreasing stability and increasing secondary effects (hysteresis, etc.) Ideally, you would change the mass of the tonearm buy using arm tubes of differing weight and matched headshells. Some manufacturers used to do this.

If you are going to stabilizing mass to most conventional tonearms, adding it as close as possible to the pivot point will both increase stability and lower resonance.
I’ve used my Stanton 881s on my Ikeda 407 with a light headshell. And with the counterweight all the way in I can’t balance it with the dynamic balance off. When I add dynamic weight I can only add a half gram to be correct.   Even though this is wrong I agree with  @lewm  and really like how this cartridge sounds on the Ikeda than on my lighter  tonearm. My speakers do reach very low bass response and I do get some woofer pumping with this setup. My woofers face backwards so I didn’t notice at first. I don’t think this is very good for the speakers and no longer use this setup. Do you @lewm get this woofer action at all using your FR arm in this way. 
The different size counterweights are supplied so you can counterbalance different weight (mass) cartridges. You can not control resonance with different mass counterweights because once the cartridge is balanced you wind up with the same effective mass regardless of counter weight mass.
Now Raul, unless you are blind measuring resonance points with a test record is painfully easy. Your comment would leave me to believe that you have never set up a cartridge correctly.
The problem with calculations is that there is enough variation in tonearms and cartridges that the published specs may be off a little.
The record tells you what is really happening. But the resonance is not a sharp peak. It is a bell curve. The point where the cartridge starts bouncing is what you pay attention to. You know you are close when you hear the warble. Using the test record also gives you an idea of how severe the resonance point is. Some combinations barely move at the resonance point while with others the cartridge almost goes air born in which case it might have to be changed. I suspect it is a matter of damping.
Moment of inertia is different then effective mass. Longer heavier arms have higher moments of inertia. This really only creates issues following warps. If records are stored correctly very few should be significantly warped. Vacuum hold down and reflex clamping solve the problem under any circumstance. 
there is another moment - most of tonearms do have rubber gourmet or other means to isolate counterweight (s), so it has it's own resonance which can be measured.
 " Your comment would leave me to believe that you have never set up a cartridge correctly. "

You have no idea what you are talking about and this time as almost always your opinions comes from your imagination are what you figure about with no true foundations but your own experiences that could be some wrong because your misunderstanding on " something ". Do you think you own the audio Bible?

Sorry, no one has it and forgeret about that LP test and re-read what I posted to you because I think you are way wrong if think that even with vaccum hold down that LP test is PERFECT.

br3098, If you wanted to insult me, you could not have done a better job than to accuse me of cutting and pasting from a text. ( You wrote, "I agree and disagree with different parts of your statement. Rather than cut and paste a text on mechanical amplifiers and resonance,...")  Whatever I wrote anywhere on this thread came out of my own head, and I take full responsibility for it, right or wrong.  I also am happy and willing to be corrected, if wrong.
Now, as to the second part of your inquiry, "please tell me how adding weight at the headshell is beneficial to the resonance of the lever", I'd be happy to respond if I could figure out what you are talking about.  Where did I claim that adding weight to a headshell was "beneficial" to resonance?  What I did say in response to Raul is that exchanging a heavy headshell for a lightweight one (or for that matter exchanging a lightweight headshell for a heavy one) has an "inordinate" effect on effective mass. By using the word "inordinate", I mean the effect on effective mass is nearly 1:1, since the headshell is right over top of the cantilever.  Whereas, adding mass anywhere else on the arm going back to the pivot point is of lesser consequence due to its distribution on the lever.  Effective mass is a quantity related to the distribution of the mass of the tonearm, not merely to its weight if you put the whole shebang on a scale. Do you disagree with that?  If so, state your case.
Dear friends @lewm  : as I said to complicated to be really precise or to achieve/have numbers in the subject because exist several parameters to take in count during play and we have to remember that even if we can't see the cartridge bounce all happens at microscopic levels and no matters what numbers says we really don't know what is down there happening.

Cartridge has its own resonance frequency between the: cantilever/stylus and the fulcrum in the suspensiion where the cantilever is atached.

The next thread is interesting for the gentlemans that want to confirm what they already know or that want to learn a little more on the subject:,effective%20mass%20of%20the%20tonearm.

Regards and enjoy the MUSIC NOT DISTORTIONS,
Raul, I guess we are all guilty of what we call in English "talking past each other", which means not paying attention to what the other guy said.  I fully agree that no calculation based on pure physics will really predict how a given combo of tonearm and cartridge will behave in practice.  The numbers are only a starting point.  This is why I pay no attention to the notion that if your calculated resonant frequency is not between 8Hz and 12Hz, the match is poor.  It's well and good to use the numbers as a guide, but that's all they're good for.  So, I think we agree.
I AM kind of a math guy, so it is interesting to me to note that the resonant frequency depends upon the square root of the quantity M*C, where M = effective mass, and C= Cartridge compliance (at 10Hz).  Because of the dependence upon the square root, there are actually a very wide range of values for both quantities that will work to fulfill the 8 to 12Hz desired endpoint.  For fun, one can play with one of the on-line calculators to see what extremes you can get away with.  But the fact is that few of us really know what the effective mass of our tonearm plus cartridge plus hardware actually is, due to all that was already discussed, and even cartridge compliance probably varies from sample to sample and according to the age of the cartridge.
You can not control resonance with different mass counterweights because once the cartridge is balanced you wind up with the same effective mass regardless of counter weight mass.
No, that is completely mistaken, and is one of the reasons many pickup arms offer counterweights of different weights. That’s because a factor in effective mass is the distance between the counterweight (actually, the counterweight’s center of mass) and the pickup arm pivot.
@lewm I think you misunderstood my reply. I was not insulting you and was not implying that you pasted from a text. I was saying that I was trying to avoid doing that myself. I apologize if my meaning was not clear.

I will restate my point: adding mass to a tonearm can be beneficial. But adding mass at the headshell (farthest point from the fulcrum) is problematic, will result in increased instability at the point of contact (stylus) and will not significantly alter resonance issues to the entirety of the tonearm. Mass is best added distributed along the arm but will have the most effect closest to the fulcrum.
Mass is best added distributed along the arm ...
Perhaps ...
... but will have the most effect closest to the fulcrum.
No, the opposite is the case. The further from the fulcrum, the greater the effect of the mass. The pickup arm works as a lever.
Dear @cleeds  : Maybe @br3098 is refering that near the fulcrum makesthe tonearm has more operationsl stability but agree with you about modified the effective mass.

The pickup arm works as a lever
Exactly. And the further mass is added away from the fulcrum the more destabilizing the effect. Resonance (the original topic of this post) is increased. A pivoted tonearm is not just a lever, it's a mechanical amplifier.

I'm not saying that adding mass to the headshell does not have benefit. But there are also detrimental effects. From the perspective of decreasing resonance and other artifacts the best of all worlds is to increase total mass uniformly and proportionally across the entire length tonearm and headshell. Barring that, adding weight to the tonearm closest to the fulcrum will have the most damping effect and reduce resonance frequency change.

If curious, this paper on Tonearm Mechanics does a pretty good derivation of the resonance and the effects of mass.  
It's essentially a problem in integral calculus.I have and will continue to align myself with what Raul and cleeds have said, which is what I also have written, in response to BR3098.  Adding mass at the headshell has the largest possible relative effect on effective mass, compared to adding mass anywhere closer to the fulcrum or pivot.  The effect of added mass on total effective mass is lessened as one approaches the pivot.  As we have already noted, adding mass, because it increases effective mass and would have the tendency to reduce the resonant frequency in magnitude, but not necessarily in amplitude, which would depend more on damping, stiffness, materials used, etc.

BR3098, forgive me for being overly sensitive and for misinterpreting your earlier remark.  In any case, I was not in any way upset or angry, just confused.

@lewm @cleeds 

Gents, my diatribes were only in regard to the OPs question regarding resonance. Obviously adding mass further out from the fulcrum is the most effective use of mass, but (as I described) is problematic for mechanical reasons and is not the most effective method of reducing resonance amplitude. Calculating the change in resonance magnitude will require additional information not provided.

Now if, as lewm proposed, we are allowing the alteration of other factors including "damping, stiffness, materials used" then all bets are off. I hadn't realized that we were discussing a tonearm with an infinite k value. 😁

TL;DR ...

One point I’d make is that the numbers are a good staring point, but will take you only so far. I’d give serious credence to "tribal knowledge", trying the combination out, as well as the advice of a trusted dealer.

I took the compliance calculator off our website because I was seeing too many people treating it as gospel instead of as a guideline.

A customer brought over a Van den Hul cartridge to test with a Kuzma 4Point (11"). Frankly (from the compliance and tracking force recommendation), I didn’t think this would be a good match, but that’s why you try things.

I documented that session over here
I suspect the Kuzma’s phenomenally, low friction bearing plays a strong part in this, as it’s a wonderful combination.

... Thom @ Galibier Design






Haven't seen a telegram in maybe 50 years except while watching an old movie on TCM.

why are you screaming?

have you been hanging out with kimberly g?   :)