Tonearm/Cartridge Matching

Whenever I read articles or questions on this topic….the answer always seems to rest solely on finding the Resonant Frequency of the particular tonearm/cartridge in question?
As long as it lies between 8-12 Hz… have a good match.

RF= 159 / sqrt ((eff. mass + cart weight + fastener weight) x (compliance))
RF: resonant frequency in hz
eff. mass: rated by tonearm manufacturer
cart weight: rated by cartridge manufacturer, but if accurate scales
exist, an actual weight value could be used
fastener weight: screws, nuts, spacers, washers, shims. They have
weight and add to the mass over the stylus
compliance: rated by cartridge manufacturer
But there are many problems with applying this formula…and there are questions whether the Resonant Frequency gives any guarantees
regarding good sounding combinations?

Firstly….to apply the formula, one needs to know the Effective Mass of the Tonearm.
Many tonearm manufacturers neglect to give this information….and it is very difficult to measure oneself?
The reason for this omission by manufacturers…is that the true Effective Mass is a moving target.
It changes with the mass of the counterweight used and its relationship to the pivot (closer or further away) whilst arms with removable headshells are simply unknown quantities so that obtaining a reliable figure for a particular tonearm is difficult.
Cartridge Compliance is also problematic.
What the manufacturer states….is a ‘designed for’ figure. Each individually produced example is likely to vary (however slightly) from this figure except perhaps in the case of hand-built low-production models whilst the figure changes with temperature, humidity, age and use.
The question of re-builds and re-tips muddies the waters further.

With these significant problems….it is no wonder that the ‘calculated’ figures for Resonant Frequency always differ from the ‘measured’ ones in any of the studies I’ve read?

But the importance of the ‘Resonant Frequency’ itself….I have never seen questioned?
As far as I can tell…..the only reason to keep the ‘Resonant Frequency’ between 8-12 Hz….is that record warps produce frequency output below 8 Hz so whenever warps are experienced…..the frequencies produced will not excite the resonant arm/cartridge frequency and produce tracking problems and/or distortion?
If the ‘Resonant Frequency’ is much higher than 12 Hz…it could possibly become excited by deep low frequency information in the vinyl grooves.

But what if warps are not encounted?
What if most (or all) of your records are ‘warp-free’….or you have a vacuum hold-down turntable or employ a heavy clamp/weight and/or peripheral ring?
The ‘Arm/Cartridge Resonant Frequency’ then becomes an irrelevant figure?

Having experienced many tonearm/cartridge combinations….and tested many for ‘actual’ ‘Resonant Frequency’ using the Shure V15 TypeV Audio Obstacle Course Test Record….I have no evidence that the ‘Tonearm/Cartridge Resonant Frequency’ tells you whether a particular cartridge will sound well in a particular tonearm?

I'm certainly open to other's views on this?
I was in the high-end business for 25 years and my forte,
(speciality) was turntable set-up. I have set-up literally
hundreds and hundreds and hundreds of tables, arms and

Not once did I even think about the "Tonearm/Cartridge
Resonant Frequency". I can count on one hand the
number of combos that didn't quite sound right. Of course,
there is/was no damage to anything and it will always work,
but the sound might not be "locked in" as perfect
as could be.

So my thoughts on the subject are go ahead and try it!
Nothing to lose and you might find a combo that, on paper,
shouldn't sound good, but does.
IMO, there is much more to how a cartridge sounds in a particular arm than getting the Arm/cartridge resonance in the acceptable range.

The quality of the bearings, the type of gimbal/pivot used, the arm dampening and the resonance of the arm wand all have an impact on how good a particular cartridge sounds in a particular arm.
Totally agree with Mofimadness and for all the same reasons. So long as the cartridge tare weight is within the arm's range, set-up (alignment, azimuth, VTA, VTF, capacitance (MM), impedance (MC)) and general compatibility with your speakers is the most important issue.

In short, you may have to experiment a bit, but once you find a combination that sounds good to you, stick with it.

Happy listening!
Regards, Halcro: A question from analog hell, Devil Henry!

Let's proceed from the premise that response is the sum of mechanical and electrical properties. With an electro-magnetic generator current is proportionate to stimulus, in this case provided by groove modulation, and, that the frequency of a recorded signal is inversely proportionate to its length along the groove.

Response limits are reached when a state of excessive electromotive force exists, resulting in saturation of the coils in which condition current actually decreases. Or, when due to either extreme acceleration or magnitude of groove modulation the stylus is no longer able to track accurately. The consequence is either distortion or damage to the groove walls.

A 1kHz signal recorded to vinyl represents a displacement of 80 microns and at 20 dBl a peak acceleration (according to a study by St. Andrews College) of 3km/s/s, "the equivlent of acceleration 320 times that of the earth's gravity". These forces are exerted on the stylus which in turn drives the cantilever (we're moving right along here) ;)

View the cantilever variously as a rod, tube or beam, it will none-the-less tend to resonate at certain frequencies. A cartridge's suspension functions as both a bearing and damping mechanism, the lower the compliance the greater the damping properties, a constrained beam is less prone to sustain vibration. The down side of this is if the cantilever is overly damped it tends to flex and scope of excursion is diminished. If compliance is too little, damping factors are reduced and cantilever recovery times are reduced. Neither of these conditions are a particularly good thing.

Let's consider the cartridge suspension as both a spring and dynamic vibration absorber. Cool, but it takes a tonearm to make it all come together and the damm thing has mass which must be accounted for. All the above conditions tell me so.

In a paper presented to the AES, Shure technician C. A. Anderson states:

"resonance exists because the arm and pickup assembly behaves like an effective mass that is coupled to the record groove by means of a stylus assembly with its own mass, compliance, and mechanical resistance". Sounds like a team?

Ideally, frequencies below the natural resonance produced by warps, eccentric groves or surface imperfections will not disturb the signal because the tonearm and cartridge move as a unit. This occurs when compliance and mass allow the tonearm and cartridge to remain centered above the groove. Modulations are read by the stylus (tracing), the stylus reads both sides of the grove equally (tracking). When cartridge and tonearm remain centered, the assembly floats with surface anomalies and the signal is unaffected.

Resonances can be considered as being constructive or destructive. When a recorded signal matches the natural resonance of our tonearm/cartridge, Mr. Anderson states the recorded signal can be enhanced by 6 to 20 dBl. He doesn't state such but in the instance of destructive resonances a diminution of signal at specific frequencies might be anticipated. Under certain system related conditions this may (or may not) be heard as beneficial.

At resonant frequencies the stylus tends to "scrub" in the groove, in the instance of a gross compliance/mass mismatch the entire tonearm can be seem moving laterally. Wow, flutter and warbling might be observed. This is because as the stylus scrubs in the groove it describes an arc, effectively adding or subtracting from desired groove speed. Floor and air-borne vibrations also tend to excite resonances in a tonearm, this due to cantilever resonance, damping inadequacies (of some description) and consequently a complimentary spring/mass relationship become a consideration.

Passive damping techniques such as isolators, vibration absorbing materials or viscous dampers, active damping mechanisms incorporated through electronic means, or simply ensuring an optimal compliance/mass ratio exists are means of addressing these unwanted resonances.

Hope this answers your question regarding the desirability of matching compliance/arm eff. mass?

My thoughts exactly Mofimadness and Effischer.
For years I have been puzzled by the almost universal adoption of the Tonearm/Cartridge Resonant Frequency school of compatibility?
I have over 30 cartridges which have been played across a dozen arms....and I have heard only a few combinations which sounded poorly enough to be avoided. And most of those involved only one tonearm which no longer resides chez moi.

The damage done by this formulaic calculation is to convert it into a general 'rule of thumb' whereby heavy low-compliance cartridges (MC) should be used in heavy rigid tonearms whilst lightweight high-compliance cartridges (MM/MI) should be used in low-mass arms?
Yet I have found that a famously high-mass arm like the Fidelity Research FR-66S has consistently sounded wonderful with dozens of light-weight high-compliance MM cartridges....
And many audiophiles find this hard to believe?
So recently I have begun testing the ACTUAL tonearm/cartridge resonant frequency using the Shure V15 TypeV Audio Obstacle Course Test Record.....and it doesn't appear that difficult to meet the recommended criteria.
So far.....six out of six tonearm/cartridge combinations tested have been between 8Hz-12Hz.
Regards Professor (Timeltel),

Thank you for that easy to follow summation.
I can't argue with any of it.
Where I have a little difficulty is...
When a recorded signal matches the natural resonance of our tonearm/cartridge, Mr. Anderson states the recorded signal can be enhanced by 6 to 20 dBl.
There are no recorded signals below 15Hz on a vinyl disc as far as I as long as the tonearm/cartridge resonant frequency is not above 12Hz or thereabouts....there should be none of the problems you describe?
Floor and air-borne vibrations also tend to excite resonances in a tonearm, this due to cantilever resonance, damping inadequacies (of some description) and consequently a complimentary spring/mass relationship become a consideration.
This may be true.....but these same floor and air-borne vibrations are then affecting everything in the turntable chain including platter, spindle, motor, plinth, cartridge, stylus cantilever, armboard and even the vinyl disc itself?
In that situation.....'saving' the tonearm will be of little reward?

I hear what you say about 'damping' of the tonearm.....but all I can tell you is that I have had three unipivots which were damped by silicone fluid.....and all of them sounded better to me without the damping.
I also had a tonearm made out of wood.....yet many of my hollow-tube metal tonearms sound better?

Finally....I agree with you about the desirability of matching compliance/arm...but I don't believe it's a particularly difficult thing to achieve (see above). And if an arm/cartridge combination actually fell outside the recommended range, and I didn't play warped records.....I wouldn't lose any sleep :-)

Dear Henry, You was the first to call Herr Professor,uh,
Professor. How many lectures should he provide for free?
I intend to respond to this lecture as soon as I get my
degree in mechanics.
Regards, Halcro: Friend Henry, perhaps it's a matter of degree. It seems most A'goners are quite capable of determining "when good enough is good enough".

A Shure M-44E tested on a low LOW mass Infinity Black Widow TA produced extraordinary bass. Not sure if there was a 20 dBl exaggeration but hfs were objectionably recessed. On another arm the poor cart performed as expected.

One might wonder if, other than resonant behavior, there is reason for the difference heard when changing mats?

There is much focus on the primary resonance of the arm/cartridge system, but that falls below, or at the bottom of, the audible range.

What we should be concerned about are the secondary cartridge/arm resonances that fall completely within the audible range. If you have doubts, just tap your arm with a pen. You are not hearing a 9 cycle resonance, you are hearing the secondary resonances that will color the midrange and above, IMHO.
The general opinion is, that it is fine when the result is between 8-12.
It is overrated and I don't give much for it. Today you have different materials in the Arms (Steel, Aluminum, Wood, Titan etc. etc.)
These materials all have different resonances. Next, you have different kind of bearings (from construction and from design). these differences can be huge.
Back to life
I have (and had) combinations which have been between 9.7 -10.0- 10.4
Nearly super, but I was amazed that some carts performed MUCH better in Arms where the "calculation" showed different datas.
This calculation is more or less a help but I don't give a dime for it. A good designed tonearm is much more important.
I wrote several times about that when I made my comparisons with my Arms and Datas and the result was always the same, the best quality Arms worked best with a lot of cartridges at superior level. And other Arms only with a few ones.
Btw. Cartridge design does not stop with compliance, how they react with a tonearm can be totally different, but you never read something about that.
Lyra Titan / Olympos for example is superior in top Arms only (energy transfer via Headshell into the Arm), when used in Arms with cheap bearings or bad geometry you get an analytical sound which is not a pleasure to listen to. But all has go through a Phonostage and that one can change the results also.
It is quite interesting.
Whew! Thanks to those that agree with "try it and listen approach".

While there is much merit in the measurements, it all comes down to the instruments on either side of your head.