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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…..you 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?
128x128halcro
halcro's avatar
halcro OP
2,664 posts
 
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 know....so 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 :-)

Regards
Henry
nandric's avatar
nandric
4,086 posts
 
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.
timeltel
830 posts
 
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?

Peace,
Post removed 
syntax's avatar
syntax
2,193 posts
 
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.
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