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The Arm/Cartridge Matching Myth

When I began my journey in high-end audio 36 years ago….no-one ever wrote about arm and cartridge matching nor tonearm resonant frequency…?
Over the last 10 years or so…this topic has become not only ubiquitous, but has mutated beyond its definition, to THE guiding principle of matching cartridge to tonearm….❓❗️😵
The Resonant Frequency can be calculated using a complex formula relating Tonearm Effective Mass to the cartridge’s Compliance….or it can be simply measured using a Test record of various frequency sweeps.
The RECOMMENDED Resonant Frequency of any tonearm/cartridge combination is between 8-12Hz.
But WHY is this the recommended frequency and WHAT does it really mean…?

The raison d’etre of this Resonant Frequency…is to avoid WARPED records inducing ‘resonance’ into the tonearm…..
Say what…❓😵
WARPED records….❓❗️
Yes…..ONLY warped records❗️😎
But doesn’t it have any meaning for NORMAL records…❓
None whatsoever…..😊👍
Let me explain….🎼

A badly warped record induces the tonearm to rise and fall rapidly on the ‘sprung’ cantilever of the cartridge.
Depending on the severity and frequency of this warping…..a subsonic frequency between 2-5Hz is induced so if your tonearm/cartridge Resonant Frequency dips into this frequency range….it will begin resonating and thus miss-track and/or induce hum through your system.🎤
Keeping the lower limits of your tonearm/cartridge Resonant Frequency to 8Hz simply insures against this possibility.🎶

So what about the 12Hz upper limit…❓
This simply insures against the possibility of any ultra low-level frequency information which MAY be on the record, also inducing this same miss-tracking or hum. For instance if your tonearm/cartridge Resonant Frequency was 18Hz and you had an organ record or one containing synthesised bass going down to 16Hz…..your tonearm may miss-track or you MAY develop a hum❓😢

So how many badly WARPED record do you possess…❓
I have three out of a thousand or so……and have NEVER experienced miss-tracking or hum even on these three…❗️😍

Yet these days….everyone (without exception it seems)…even tonearm and cartridge designers….happily follow the dictum of this Arm/Cartridge MATCH as if it affected sound quality…..❓
This Resonant Frequency has ZERO affect on the sound quality of a particular tonearm/cartridge combination and I have proved it hundreds of times with a dozen different arms and over 40 cartridges.

The best match for ANY cartridge ever made….is simply the very best tonearm you can afford…whatever its Effective Mass…😘
128x128halcro
atmasphere's avatar
atmasphere
11,633 posts
 
^^ the above seems to read as if there is confusion between the resonance of the arm tube with the mechanical resonance of the arm mass combined with the cartridge and its compliance. The two are different.

The adage that rules are made to be broken is in itself a generalization.

The reason the 10Hz target is desirable is not a rule- its a recommendation for best results. If you spend a lot of money on an arm and a cartridge only to have it mistrack by ignoring this recommendation, it is money poorly spent.
harold-not-the-barrel
895 posts
 
Tony, I re-read you statement more closely but don´t agree
about "near infinite energy out", I assume this is a
typing error ? It´s annoying that one can´t edit own posts
shortly afterwards, we all make typing errors occasionally.
Anyway, the Equation is well known for ages and refers only
for the effective mass of wand + cart because the fulcrum
kinda splits the whole moving part (inertia mass) in two
parts. There is another equation for the whole system ? I´m
very curious to study it. Agree otherwise as I wrote.
tonywinsc
583 posts
 
The point that I was trying to make is that when an input frequency dwells on the resonance point of a mechanical system, the output amplitude tries to go to infinity. Of course, there are limitations but usually the limitation is failure of the system- something breaks. Picture Ella Fitzgerald focusing her voice on a crystal goblet. She finds the resonance frequency of the goblet and then sings holding that frequency steady. The glass responds to that input. The goblet starts to ring and the amplitude builds until the glass shatters. All with the relatively small energy input of her voice.
tonywinsc
583 posts
 
Harold, there is no single equation that I am aware of for determining the effective mass of the tonearm in grams. It is an involved calculation based on the mass of the tonearm and the moment of inertia of the tonearm assembly which, as you said must be broken down for both sides of the fulcrum. Also, the effective mass is not likely to be the same value in the lateral direction (unless the tonearm and counterweight are straight cylinders), just like the cartridge compliance will not be the same value in the lateral direction. That just means the dynamic response laterally will be different from the vertical dynamic response. And there again, the static forces should be the same in both the horizontal and vertical planes. I can't think of a reason why they wouldn't be.
lewm
12,554 posts
 
Some calculate the effective mass of the tonearm/cartridge system backwards, starting with the compliance of the cartridge and the observed resonant frequency, using a test LP. But that depends upon the accuracy of the manufacturer of the cartridge in stating compliance. Also, Mark Kelly has developed a rather simple method to estimate effective mass; the problem is that I have forgotten it. However, search the archives on the Vinyl Asylum or try Vinyl Engine.
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