The Arm/Cartridge Matching Myth

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 :_/

I've been a victim of ignoring this issue. I had a very heavy cartridge for a short while, paired with my medium mass arm. The math did not work for this pairing.

I experienced a rumble that I just could not get rid of. To the point of considering building a subsonic rumble filter to cut off the problem. The better solution was to try a different cartridge, which resolved the issue perfectly.

Yes, it does matter.

Even though there's normally no musical content below 20Hz, there is a variety of noise caused by friction, and the mechanical reality of tracking.
What's the amplitude peak of undamped low frequency resonance? What exactly is it that's resonating, your cantilever perhaps? Ever hear of intermodulation distortion?

This is all well documented for decades now. Imperfect equipment and set-up can allow acoustic and mechanical feedback to wreck havoc that is absent with digital.

If low frequency resonance is near the audio band, say 18Hz, then 2nd harmonic intermodulation is 36Hz.
This is from The Audio Dictionary:
http://books.google.com/books?id=L38MrvScG3gC&pg=PA38&lpg=PA38&dq=low+frequency+resonant+peak+amplitude+in+tonearms&source=bl&ots=L7kNpNUcIL&sig=ux4FxgVPIC1wpe3-WPA3QYKSiYM&hl=en&sa=X&ei=aAQ8VNitOOzbsATX7YLACw&ved=0CDEQ6AEwAw#v=onepage&q=low%20frequency%20resonant%20peak%20amplitude%20in%20tonearms&f=false

Regards,

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.

Hi Halcro . . . I think the main conceptual problem here is that the resonant frequency is only one parameter that's descriptive of the tonearm/cartridge resonance envelope. Keep in mind that the tonearm/cartridge combination is a mechanical high-pass filter, and if there is a resonant peak . . . mathematically it must be a multi-pole system. This means that affecting any element changes not only the resonant frequency, but the width and height of the peak (Q), the transition-band slope, and the amount and periodicity of any pass-band ripple.

The difference between 8 and 12 Hz really is very little in the frequency domain - at 1/3-octave it's the same as two adjacent bands on a 31-band EQ. And while the tonearm/cartridge system is indeed multi-order, its filter slope isn't anywhere near steep enough to make much difference in LF response or warp-immunity simply with a change of frequency. Rather, the effect of raising the tonearm mass for a given cartridge usually increases the Q of the filter in addition to lowering the resonant frequency; that is, the resonant peak becomes higher and narrower.

The trade-offs of raising the system Q are the same as for any electrical filter: the "benefits" are that the transition-band (immediately below the resonant frequency) becomes sharper and more selective, and the pass-band (area above the resonant frequency) becomes overall "flatter". The "drawbacks" are that the system becomes dramatically more sensitive to energy imparted at the resonant frequency, the pass-band ripple increases, and increased ringing in the time-domain (impulse) response.

Pragmatically, the main issue will be the extent to which your turntable and environment conduct energy into the tonearm/cartridge system, and at what frequencies. If you're using non-suspended turntables, on sturdy furniture, in a concrete building, then you're probably going to have fewer issues with subsonic resonances, but your system will be more prone to acoustic energy conducted back into the tonearm . . . and a heavier, more rigid tonearm definitely helps to control and dampen this.

But for suspended turntables, springy wooden building structures, heavy support furniture sitting on carpet etc. etc. . . . indeterminately increasing the Q of the tonearm/cartridge system is playing with fire. Each of these additional spring/mass systems can potentially combine to create a condition where the system is extremely sensitive to subsonic and low-bass energy. Many view this as a reason to universally condemn suspended turntables . . . but it's simply a different type of energy to which the system is susceptible, and the trade-off for better immunity to conducted energy within the audio range.

But regardless of the type of turntable design, domicile construction, or support furniture . . . I seem to see fairly regular inquiries on these fora for help to solve the issue of woofer-pumping while playing records. Much of the time the owner has already followed this sort of advice . . .

The best match for ANY cartridge ever made….is simply the very best tonearm you can afford…whatever its Effective Mass

Given that the prime mechanism determining susceptibility to this phenomenon is the tonearm/cartridge resonance envelope . . . the notion that this issue could be avoided simply by spending more money on a "better" tonearm seems a bit unreasonable to me. It's simply far more effective to change to a lower-compliance cartridge, thereby creating a system with a lower-Q resonance envelope at a slightly higher frequency.

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