Tonearm mass, high/med/low compliance- I need a tutorial

Alright, it's time for me to learn something. Corbin's cartridge query thread makes me want to understand the effect that tonearm mass has on... well... anything. Also, what does the compliance term describe? Is compliance about the arm or the cart.? What about ideal arm-cart. matching?

Looking for explanations from you guys, not links.

:headscrat I am more than mildly dazed. :headscrat

Yours in confusion,
Tyler

The compliance is the inverse spring constant that the needle suspension has.
The mass is the effective mass that the stylus sees, when it wants to move the tonearm.

Together they are forming a resonant system with a resonance frequency that should be around 10Hz, plus/minus something.
If the arm has a higher mass, the resonance freq. will be lower, and vice versa.
If the compliance is higher the resonance freq. will also be lower.
gusten

Thanks gusten. I still do not understand some of it.

I would assume that one wants a lower, inaudible resonant frequency- correct?

Also, is compliance listed in specs since it is a manufacturing constant?

What is considered a high mass arm? Look at my sig- are those stock arms considered high, med, or low mass?

Does this "constant" change over time with use and breakdown of the rubber compounds around the cantilever- it this what one hears change during the break-in period of a new cart.?

The mass seen by the needle would involve the lateral inertia of the arm, right? The effective vertical is variable via the counterweight, yes?

How mathematical do you want the explanation to get? If you've had physics with calculus, it's easy to understand how this resonance arises. If not, it's much less intuitive.

The rule of thumb for matching cartridge compliance to arm effective mass is that the resonant frequency should ideally fall between 8 and 12 Hz. Record warps can excite it if it's lower, and low bass in the record grooves can excite it if it's higher.

Most cartridge manufacturers specify compliance. It should not vary significantly over the useful life of the cartridge. Hardening of the suspension elastomers after many years of use can reduce compliance below spec. I doubt that break-in causes much change in compliance, but then I'm skeptical about break-in anyway; I believe that most of what audiophiles describe as "break-in" results from their becoming accustomed to the sound of a component rather than any real change in the component's sound.

Thanks Dr. I am a physics w/calculus instructor so give it to me. I would assume it's the harmonic oscillator derivation for a spring-mass system.

If I follow gusten's spring-mass info, resonant freq ought to be 1/sqrt(k•m)

tybrad said:

Thanks gusten. I still do not understand some of it.

I would assume that one wants a lower, inaudible resonant frequency- correct?

Also, is compliance listed in specs since it is a manufacturing constant?

What is considered a high mass arm? Look at my sig- are those stock arms considered high, med, or low mass?

Does this "constant" change over time with use and breakdown of the rubber compounds around the cantilever- it this what one hears change during the break-in period of a new cart.?

The mass seen by the needle would involve the lateral inertia of the arm, right? The effective vertical is variable via the counterweight, yes?

Click to expand...

Yes the resonance should be so low not interfering with recorded frequencies. But not so low that footfalls or other low freq. should have an output.

I would say that normally right figures are very difficult to find, that is why calculating is a hit and miss really.
I don´t know if the spring constant changes over a short playing time, if I should guess I would say probably for some cartridges.

The lateral and vertical eff. mass are in most cases very close, it doesn´t matter if the arm moves lateral or vertical, the counterweight is there in both cases.
gusten

tybrad said:

Thanks Dr. I am a physics w/calculus instructor so give it to me. I would assume it's the harmonic oscillator derivation for a spring-mass system.

If I follow gusten's spring-mass info, resonant freq ought to be 1/sqrt(k•m)

Click to expand...

Go to the head of the class. That's exactly what it is -- an undamped second-order system whose resonant frequency in radians/second is given by the formula you provided.

I'm not familiar with the arm models in your sig, but you might be able to get effective masses for them from the Vinyl Engine site. You'll need to register if you want to download any manuals. Registration is quick and free. Here's the URL: http://www.vinylengine.com.

There are also several reasons for the "magic" 10Hz number...

1) the damping influence of the cantilever suspension tends to be at its best around this frequency (varies a bit depending on design and materials though) - but it has been noted that frequently (ie with many cartridges) the amplitude increases as it gets further from 10Hz.

2) The bell curve of the amplitude boost caused by the resonance tends to extend around an octave up and down... so if it is 10Hz, it tends to extend up to 20Hz and down to 5Hz (roughly).

Any higher than 10Hz, and this effect starts to impact on audible frequencies, at 10Hz a standard subsonic filter (as used to be mounted on most phono stages and integrated amps/receivers) will filter out the excess low frequencies, stop the woofers pumping and sucking up all the amps power, without have a bad effect on the audible music range.
At the lower end, 2 to 4 Hz tends to be footfall, and natural external vibration frequencies, if the resonance extends down this far, many turntables start to badly suffer from footfall issues etc... (also warp issues).
This series of potential problems can however be handled by improving turntable isolation... with some effort! - But there is still the issue of Warp related and record centering related flaws.

The result of all the above is a "rule of thumb" that best results are achiever with Res F of around 10Hz.

With regards to working out what works best with which, I find the VE tool/chart to be very useful http://www.vinylengine.com/cartridge_resonance_evaluator.php

The other key tool is Luckydogs EMC spreadsheet with which one can easily calculated the true effective mass of ones arm...http://www.luckydog.demon.co.uk/images/EMC.xls

Final tricky bit:
The compliance measurements come in 3 common forms:

1) Static compliance
2) Dynamic compliance measured @ 10Hz (common for European and North American manufacturers)
3) Dynamic compliance measured @ 100Hz (common for Japanese manufacturers)

Of all these, only the 2nd (Dynamic compliance measured @ 10Hz) is useful for the calculation of resonant frequency.

There is a VERY crude/rough estimate that can be used, which converts from static to Dynamic10Hz by dividing by 2, from from Dynamic100Hz to Dynamic10Hz by multiplying by 1.75 - there are however quite a few examples that do not in fact comply with this rule of thumb.

Another thing to watch out for, some combinations have a Res F that should be too high or too low for a good match, yet work well together - this is usually the case for cantilevers that are heavily damped. (eg: ortofon 2M series)

However there are a number of audible downsides to heavy damping, the damping affects frequency/phase performance, and leads to slower rise time and responsiveness of the needle.
Balanced against this is the additional stability provided by the extra damping.
Highly damped cantilevers are a tradeoff - they tend to sound better on the "average" setup, but tend not to sound as good as the lesser damped versions of the same cantilever when on a "perfect" setup.
Good for marketing, good for ease of use, not so good for perfectionists... c'est la vie.

An alternative to damping at the cantilever is damping (fluid, servo or magnetic) of the arm itself either at the pivot, or at the headshell (as per "The Rock") - this allows the use of more "ideal" low damping cantilever setups, while still having the arm stability benefits of damping.
Excess damping of this sort can however lead to "scrubbing" issues resulting in intermodulation distortion - so in this particular case, and this particular way it is possible to "overdamp".
(as opposed to plinths, racks and mounting systems where infinite damping is the ideal!)

In my opinion categorising should be roughly as follows:

Low Mass arms = less than 8g
Mid Mass arms = 11g to 20g
High Mass arms = greater than 25g

Yes I have left gray areas between the categories!

Note that true ultra low mass arms like the Revox Linatrack, Moerch and SME arms are all well below 6g (with the best ones being around 4g)

Marketing materials from Technics in the 80's was claiming the SL1200mk2 as a "low mass arm" - at the time everyone was aiming to be "low mass" - and the 12g of the SL1200mk2 was lower than the average S-arm which was between 16g and 20g in many cases...
But by no stretch of the imagination can a 12g arm be called low mass - and certainly not compared to the Revox, Moerch, or SME low mass arms!!!

With regards to compliance...

High Compliance = over 20cu - match with low mass arm
(in the heyday of high compliance the ADC's came in at 50cu, Ortofon's early OM series were at 35cu - current Ortofon OM's are a mere 25cu... )
Mid compliance = 16cu to 12cu - match with mid mass arm
Low compliance = below 10cu - match with high mass arm

I hope this all helps without getting too mathematical about it all!

bye for now

David

The only thing I can add to David's excellent explanation is a note on the units of compliance. 1 compliance unit (cu) = 10^-6 cm/dyne.

There's so much solid info in the first page of this thread that it should be a Sticky on the forum. Compliance/arm mass/resonance confuses a lot of people and I think it would be useful to have a ready reference for it on the front page. Or somewhere.

ETA: note that arm mass can be altered to some extent to improve resonance. Mass can be added to any light arm if a cart is to be used whose compliance is too low for the arm's original mass. Arms with removable headshells can be fitted with a lighter or heavier than stock headshell, changing the effective mass by +/- 4G or more.

Dr Tinear, David, and Gusten,

I really enjoyed your explanations of cartridge compliance, tonearm mass, and resonance. Very well presented and clear. You fellas know your stuff.

These discussions are the best part of AK, for my money.
Kudos.

waterjetguy said:

Dr Tinear, David, and Gusten,

I really enjoyed your explanations of cartridge compliance, tonearm mass, and resonance. Very well presented and clear. You fellas know your stuff.

These discussions are the best part of AK, for my money.
Kudos.

Click to expand...

Yes guys (and everyone)- many, many thanks. I will now unpack and re-assemble all of this info into something that I can own.

Yours in gratefulness,
Tyler

Sony PS-X5

Wow, and thank you!

How can I find out the arm mass of my Sony TT?

All I found are:
-VTA range: 0-3g
-Shell weight: 10.5g
-Cartridge weight range: 2.5 - 9.5g
-Cartridge weight range (with extra weight): 8 - 14.5g

Not sure where the arm mass is hidden.

Thanks

hrudu said:

Wow, and thank you!

How can I find out the arm mass of my Sony TT?

All I found are:
-VTA range: 0-3g
-Shell weight: 10.5g
-Cartridge weight range: 2.5 - 9.5g
-Cartridge weight range (with extra weight): 8 - 14.5g

Not sure where the arm mass is hidden.

Thanks

Click to expand...

You can find out if You use Luckydog´s EMC, a guess would be high mass.
gusten

Without adding any confusion, as I see it the resonance freq. is no big deal (if not totally wrong). If we have a span of 6-14Hz there is normally frequencies on the record to slightly excite a resonance. This will mean that we will an output at the resonance, never mind what freq. we have.

This is not so good, but what we can do about it is only really to apply a damping force at the tonearm pivot, to lower the amplitude. (or damp in other ways) But too much damping force will cause side forces on the needle, as the arm will need a higher force to move, which we should avoid.
gusten

gusten said:

Without adding any confusion, as I see it the resonance freq. is no big deal (if not totally wrong). If we have a span of 6-14Hz there is normally frequencies on the record to slightly excite a resonance. This will mean that we will [have] an output at the resonance, never mind what freq. we have.

Click to expand...

Because of that, you can actually just observe the real-world resonance frequency by recording the output and analyzing it, which I think is pretty cool.

I'm going to have to ask whether third party styli, such as Jico, complicate this picture. Isn't the stylus assembly what controls compliance?

And has anyone ever produced a simple graph showing the best match of compliance and effective mass?

Edit: I found this:

http://www.resfreq.com/resonancecalculator.html

So I entered 12 for the mass of the Technics 1220 tonearm and 22 for the compliance of a Shure V15-III, and got 9.8 for the resonant frequency. But what about the mass of the cartridge? Is it somehow taken out of the equation?

js1138 said:

And has anyone ever produced a simple graph showing the best match of compliance and effective mass?

Click to expand...

Yes, I've seen some around, but if you type in a mass to the vinylengine tool you get a customized one.

Bauhausler said:

There's so much solid info in the first page of this thread that it should be a Sticky on the forum. Compliance/arm mass/resonance confuses a lot of people and I think it would be useful to have a ready reference for it on the front page. Or somewhere.

ETA: note that arm mass can be altered to some extent to improve resonance. Mass can be added to any light arm if a cart is to be used whose compliance is too low for the arm's original mass. Arms with removable headshells can be fitted with a lighter or heavier than stock headshell, changing the effective mass by +/- 4G or more.

Click to expand...

I've experimentally determined resonance by digitally recording the stylus dropping onto the disc and measuring the wavelength in my recording software. It's often disturbingly different from the number I get using the stylus and arm manufacturers' supposed 'specs'. You usually don't get a clean sine wave because of the difference in vertical and lateral compliances but it's obvious if you're hitting near the magic 10 Hz target or not.

Instead of recording the drop, just record several minutes of playback and convert it to a spectral content graph. Unless the drop works better... I haven't tried it that way. I'll have to. Seems like it would be off, though.