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?