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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

Showing 6 responses by harold-not-the-barrel

harold-not-the-barrel
895 posts
 
Tony & Lewm, Don´t worry, The Calculation exists.
The question is who has the ability to find out the Equation
and solve the mystery ;)
We must call Stephen Hawking immediately !
My hat off to Mark Kelly as well.
Btw, one of my test records is 2 mm off-center, hardly can
measure anything that truly makes sense ? :/
harold-not-the-barrel
895 posts
 
Bravo Tony `Ö´

Can´t agree more on everything you say.
It is exactly the same what I have experienced over the
decades.
The magic of 10 Hz +/-2.
We must aim exactly there. Everything else is superstition.

The SME III and all series have 2 options to increase mass
on headshell: 2.2 g and 4.4 g metal ballast weights,
very simple method to move the peak area. My SME provides
6.6 g of total extra mass.
http://www.ebay.co.uk/itm/SME-SERIES-309-SERIES-IV-SERIES-V-
4-4-GRAM-METAL-BALLAST-WEIGHT-BRAND-NEW-/141436953524?
hash=item20ee4ca3b4

Additionally, the super rigid titanium-nitride wand has 4
teak ribbons inside wand & is fluid damped outside. SME arms
have very informative sheet for effective mass & frequency
resonance values. SME III is Classic Beauty with fine lines
& gorgeous curves...
like Sophia Loren ~ :^)
Never underestimate damping, it´s the essence.
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.
harold-not-the-barrel
895 posts
 
Good evening

The Equation for Resonant Frequency in a pivoting TA is quite simple.
It depends on the total mass of tonearm (tonearm wand + cartridge) M (g) & cart´s compliance C (just quantity of units alone)

F(Hz) = 1000 /(6.28x the square root of MxC) Hz.

The bigger both the M and C are the smaller the F is, the smaller both the bigger the F.

For example let´s use the SME III and its very low mass arm wand 5 g.

For a very compliant SHURE with M 11.6 g and C 30 cu the frequency is 8.5 Hz.
For a very stiff Entré-1 with M 10.8 g and C 10 cu the frequency is 15.3 Hz.

The "safe" value for F is 8-12 Hz.

Using a stiff LOMC on a very low mass arm smears sound just under 20 Hz if the vinyl actually contains music in these very low frequencies, of course, and thus doesn´t quite make sense :-/
Using a hyper compliant DENON DL-207 with 50 cu on a medium mass arm leads to tracking issues around 5.5 Hz where pressing faults are serious :_/
harold-not-the-barrel
895 posts
 
The previous equation seems insufficient to me because I can
´t add VTF anywhere, maybe my old computer can´t download
the whole thing ? And I can´t get the whole picture of the
situation :/

This explains better:
https://www.google.fi/url?
sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CB4
QFjAA&url=http%3A%2F%2Fwww.reed.lt%2Fresearch%2F53-
research&ei=tc1AVJjxG4PMyAOF_oCABQ&usg=AFQjCNEf9XrvTXFC6pusi
SMCBYgueJxhvA&sig2=_x5-iRRiVyPPyn0S9kI9hA

As we find out, for approximate calculations we need only
cart´s inertia Ic.

This explains the resonant frequency more closely but it´s
basically the same as the first equation I mentioned
earlier:
https://www.google.fi/url?
sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CCg
QFjAB&url=http%3A%2F%2Fwww.reed.lt%2Fabout&ei=tc1AVJjxG4PMyA
OF_oCABQ&usg=AFQjCNG6_QFNv0_fVjFLmtuMpe0A6lqUug&sig2=Ew7sZSC
PJIblULLCnN2fog

All this is simple basic mechanics. Approximate calculations
to start with.

But the mystery remains. We need to find out
The Calculation of Everything including all variables, VTF,
VTA, structures & materials inside the wand, magnetic fields
within etc.

I believe in natural sciences only. And Halcro´s
experimentations and observations as well, although they are
unorthodox.
I think we should ask Stephen Hawking.
harold-not-the-barrel
895 posts
 
Fleib, Great ! That link works.

Luckily our Luckydog is a scientist and listens vinyl. My hat off to him as well.
I have measured the effective mass of my SME III for SHURE´s topdog (excuse the clumsy expression) at 1.2 g VTF and yes, this formula gives 4.3-5.6 g depending on the weight of the counterweight ass´y (I can´t remember it precisely) but the value is as I was expecting. Increasing VTF to 1.5 g (with JICO/SAS stylus) it gives 4.2-5.5 g. Fine !

It would very interesting hear what Stephen Hawking would think of and this hobby of ours, wouldn´t it. I can´t email him ´cos I haven´t his address :/

I tought my URLs work as they generally have worked so far... Or maybe we live in paraller universes and the wormhole connecting our worlds is getting weaker...
This may very well be my last message. If so, I wish best of times and hope we will solve this mystery sooner or later.

The answer, however may be quite different for both of us because our universes have different laws of nature and thus our psychics are different, more or less ;_)
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