Guides, Overview, Thoughts, Tonearms, Turntables

Tonearm resonance theory – or how I learned to stop worrying and love the heavy Japanese arms.

Measuring tonearm resonance frequency with the Ortofon Pickup Test Record

So you have a turntable with a tonearm and a cartridge and you are wondering if the combination of tonearm and cartridge are performing as they should. You might be able to enjoy your music, but you wonder if there an option to tweak the system by either upgrading the cartridge, tonearm or the entire turntable system. You’ maybe started researching and stumbled on the phrase Tonearm Resonance frequency and calculators that can tell you if it works or doesn’t. But cartridges are listed from the manufacturer with a lot of numbers and data, the same goes for your tonearm. Maybe the producer of your tonearm and system doesn’t list any data and stats for your tonearm, in which case you are even harder pressed. What should you buy?

You could go out and buy that expensive Moving Coil cartridge and step-up, and fingers crossed it might be the upgrade you want it to be. There is a lot of different cartridges out there and you might want to invest a lot of money in your hobby. But how do we actually use the specified data to make a decision into what should be the best combination? Even more important, how do we use the data we know to tell if it would be a problem?

A good place to start is by looking at the final combination of cartridge and tonearm. That is specifically tonearm/cartridge resonance frequency. This article will highlight all the relevant theory of tonearm resonance, and with this article you’ll be better suited for making a good decision. I will not be making a calculator or quick-fix tool, but instead explain the theory involved and the math behind a usable and precise method. But please note: as with a lot of theory, there is a gap between theory and practice when it comes to applying your findings to your real-world system. That is just the nature of audio-systems. What you think sounds good in the end IS a subjective matter and a lot of different aspects factor in to the listening experience. Tonearm resonance is just one part of a good analog system.

What is tonearm resonance?

When you are playing a record, the cantilever on your cartridge is both responsible for moving the cantilever in accordance to the grooves in the record producing sound and at the same time moving the entire arm across the record surface. This means your cartridge is doing two things at the same time:

1. being stationary enough for the cantilever to move freely on 2 axis producing sound. Since the signal is generated in the cartridge from the cantilever movement relative to the cartridge body.

2. Being able to move freely so as when the record grooves are moving across the record surface towards the spindle the while tonearm follows, positioning itself relative to the groove.

This is quite the task to ask for from a mechanical system, but it works and it is the exact task our cartridges and tonearms are designed to do. To allow this to happen a cartridge has a “springiness” to it – it has a totally rigid body, but the cantilever can move in 2 axis. How easily this movement is done, ie. the springiness of the cartridge is called the compliance. Different cartridges have different values for compliance, as the suspension, holding the cantilever has different stiffness.

The resonance of the tonearm and cartridge combination is describing both the frequency and the amplitude, where vibrations starting at the cantilever will propagate throughout the cartridge and tonearm. The frequency denotes when and the amplitude denotes how much.

It is important to separate the two terms frequency and amplitude here. look at the illustration below, the red arrow highlights the amplitude – measured in voltage and experienced as increased or decreased volume. The green arrow highlights one cycle of a tone, how many of these cycles in a second is the frequency. it is measured in cycles per second or hertz and experienced as pitch (a high note will have a high frequency and a low note a low frequency).

The resonance frequency is a direct product of the cartridge compliance and the effective weight of the tonearm – ie, how much force the needle “sees” in order to move the tonearm around the spindle. The amplitude of the resonance is a product of the tonearm dampening. IE dampening an arm-tube, using an oil-damper and so on will not affect the resonance frequency, but could dampen the severity of the resonance and the impact on playback.

How do we measure tonearm resonance?

The Ortofon Test-record on the turntable

Using a test record providing a tonearm resonance test, you can hear or see or measure the resonance frequency. I usually use an Ortofon Test record, but a lot of test-records are available, and they would provide you with the same result. I use the lateral test, as my cartridge Compliance is provided from the manufacturer as a dynamic lateral value.

The way the test works, is that the frequency in the track is also cut with a 1000hz tone, and when the cartridge starts to resonate the fluctuations are clearly audible in the playback of the record. The Ortofon test record goes from 20hz to 5hz in 1hz steps, and at the resonance frequency I can clearly hear the fluctuations in the test-tone, but also see that the entire cartridge is visibly vibrating.

The test will highlight the resonance frequency of the combination, but if you record the signal digitally you can also pinpoint the resonance-frequency by looking at an increase in amplitude on the waveform.

By measuring my tonearm and cartridge combination – the Fidelity Research FR-64S with FR-S3 headshell and Ortofon Quintet Black S cartridge i measure the resonance to somewhere between 6 and 7hz, those two tests are easily the most severe, and it is had to tell them apart in terms of severity.

How do we calculate tonearm resonance?

Resonance of a tonearm is given by the below formula:

where Meff is the effective mass and Compliance is the compliance of the cartridge

In order to calculate tonearm resonance we need to know the compliance of the cartridge and the effective mass of the tonearm. As mentioned before the compliance is a value denoting the “springiness” of the cantilever. The effective arm mass is the mass in relation to the spindle that the cartridge sees.

There is a lot of online tools and quick formulas for calculating tonearm resonance1, unfortunately these are mostly not correct – or they are correct enough, as they are based on estimates and approximations. The reason for this, is that effective mass is not one number, and you can’t simply add the weight of the cartridge and screws to the manufacturers given number.

Effective mass is the moment of inertia divided with distance to spindle (or Effective Length) to the power of 2:

EM = MI / EL2

Where MI is Moment of Inertia and EL is effective length. ie. distance between needle tip and spindle axis.

The moment of inertia of a compound shape as a tonearm is the same as the moment of inertia of all the parts of the tonearm. so for ease of calculation i’ve broken my tonearm into 4 shapes that i can more easily calculate. What i need is the mass of the part and the parts center of gravity distance to the spindle. A straight tonearm here is much easier that an S-shaped arm, and if your tonearm has a taper like the SME 309 or V tonearms, it makes it a lot harder.

So while you can’t add the individual parts mass together, you can add the individual moment of inertia. as mentioned above the moment of Enertia is the relation between mass and distance between spindle and center of gravity, and the total moment of inertia of the combination is the sum of all parts individual moment of inertia.

MI = M * L2

where M is mass and L is between the center of gravity and spindle axis.

Let’s take my Fidelity Research FR-64s with the FR-S3 headshell and an Ortofon Quintet Black S cartridge – all measurements of distance is made as the tonearm is setup with the cartridge having 2gr of tracking force.

Fidelity Research FR-64S with Quintet Black S in FR-S3 headshell
The test subject Fidelity Research FR-64S with Quintet Black S in FR-S3 headshell
accurately setting the tracking force is important!


M = 244gr, L = 3,6cm, MI = 3162,24 gr*cm2

Armtube between spindle and headshell:

M = 23,07gr, L = 12,5cm, MI =3604,69 gr*cm2

Armtube behind the spindle:

M = 5gr, L = 2,65cm, MI = 35,11 gr*cm2

headshell with mounted cartridge:

M = 29,37gr, L = 24,9 cm, MI = 18209 gr*cm2

The total MI (ie. the sum of all the moment of inertia) is 25011,7 gr*cm2 and the effective length is 24,9 cm so the total effective mass of this combination is 40,34gr.

By using this value in the formula for calculating resonance frequency, well get a resonance frequency at 6,46hz which is well below the optimal range

The consequences

From the measurements and the calcuation we reach the same conclusion – a resonance frequency at around 6 to 7hz. This is not an ideal or optimal situation. an ideal range would be between 8 and 12 hz, where someone even limits this to between 9 and 11. But what does an out-of-interval measurement actually mean in terms of your turntable performance?

Whatever the resonance frequency is, it would mean your system is susceptible to resonate if exposed to those frequencies. For high resonance combinations this could happen by the music you play, ie. bass-notes in the recording could be affected and it could even make your cartridge skip. However for low resonance frequencies, the system is susceptible to footsteps or rumble or vibrations in your record player.

I am lucky, that my turntable setup is very well isolated from any outside noise, as well as very good tonearm dampening meaning the a very low risk of external forces, making the system resonate. But another effect could be unwanted dampening of the high-end.

As you can read, suddenly you have to take your system and room into account as well.

Should I care?

Well perhaps you should – it is a good idea to have a rough knowledge of the limitations of your system and in what direction is should be improved. Take my experience, the Quintet Black S performs fine despite the very low resonance frequency, but that is also due to my entire setup being as isolated as it is. However I have plans for purchasing a Fidelity Research headshell that weighs considerably less for sporting this cartridge. I have also fitted another tonearm to my turntable, the SAEC WE-407/23, which is lighter while still being a heavy tonearm.

The thing is – I love my FR-64S tonearm. It is beautiful and a very good sounding tonearm – despite being so heavy that it shouldn’t sound good. So in my system, with my gear i’ve found that I really don’t care because it sounds amazing when it plays, and as soon as the needle drops I forgot al about it not being optimal, and just listens to music.

If however I want to try another tonearm or another cartridge, i would go for a lighter arm and a lower compliance cartridge to have the flexibility in my system to match cartridges and tonearms in other ways and go up in resonance frequency instead of down. If you own a vintage system, note that the market for low-mass vs high-mass tonearms shifted in the 80’s with low-mass arms and high-compliance cartridges being popular but today’s high-end cartridges are better suited in medium to high-mass tonearms.

See the SME Series-3000 article for an overview of the evolution of that tonearm

The best thing I can tell you to do is to listen, borrow and test equipment before you buy it – you’ll need to try tonearms and catridges out on your own system before you purchase them – get social with other audiophiles and hifi-enthusiasts, and share experiences.

  1. A list of tools on VinylEngine:

(8) Comments

  1. Units of the frequency are Hz=1/sec.
    In your formula frequency has the units of seconds:

    1. Thank you for your feedback, it is much appreciated – I will edit the content to reflect your input!

  2. Sascha Zeptner says:

    Thank you for your article! Nice and comprehensive information with an conclusion I really like – listen to the music, trust your ears but keep in mind that there might be room for improvement because of physical principles.

    1. Thank you very much Sascha!
      I hope that you enjoy reading future content, and sorry for not replying to your comment earlier!
      We audio-enthusiasts are all on a journey that is mainly subjective, but reproduction is based on physical principles and limitations.

      Thank you again!

  3. Flee41 says:

    Thanks for a great article! Can you please explain how exactly do you use the 315 Hz lateral test from the Ortofon LP to determine the resonance frequency? Either I just don’t get it or the figures just don’t seem to match

    1. Hi Flee41
      First off – sorry for the wait!

      I am not using the 315hz lateral test to check the resonance frequency.
      The 315hz test is used for tracking ability, and is used to determine the tracking error and is very useful to examine if your alignment of your tonearm was made correctly. Specifically you’ll find mis-aligned antiskating, which is otherwise hard to set correctly.
      The next test on the record is a tonearm resonance test, which test from 25 to 4hz, with a superimposed frequency of 2,349 and 2,960hz – the idea here is that the resonance will be both audible and visible to the naked eye.

      The “issue” here is that it is not a sweep, but in 1hz increments so you’ll find resonance is worse at 1 frequency more than another, and I use that to determine that the resonance is somewhere between two points, as I can see and hear that the resonance increases and decreases around these points.

      Hope that helps 🙂

  4. Lex Kroese says:

    Hello Soren,
    This is a very good article you’ve wrote, but i have a few questions about the measurements. The length of the counter weight is 3,6 cm and the length of the armtube behind the spindle is 2,65 cm. This means that the conter weight is longer than the armtube behind the spindle. But when I look at your tonearm I see that is a lot longer than the counter weight. So how did you measure these lengths?
    I am also curious how you’ve establised the weight of the armtube behind the spindle.
    What also seems strange to me is that the length of the armtube between spindle and headshell is 12,5cm while this distance seems a lot longer to me. Would you be so kind to explain this to me?
    Kind regards,
    Lex Kroese

    1. Hi Lex
      I think the confusing factor here is that L denotes the spinde to center of Mass distance – so basically, each L value of an object is the distance between the spindle center (pivot point) and the middle center of mass of the moving object.
      As the entire moving mass is a sum of its parts, I’ve tried to assume the weight of each part.
      Getting the weight has been by measuring and weighting parts of the arm, so the weight of the arm tube behind the spindle was a calculated value based on the effect of the weight on the balance of the system; isolate the weight and infer the mass of the spindle rod.

      This is not exact, but this piece attributes only a little to the entire system mass; so you would find success in assuming it was either a solid piece of stainless steel or a rod filled with aluminium.

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