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# The Korf Blog

The inside story: our research,
development and opinions

14 January 2020
Tonearm and Cartridge Matching, Part I
One subject keeps reappearing over and over again. On social networks and fora, in your emails, in magazines, in personal discussions. It goes like this:
Oh, I'd love to try a Shure V15V, but I don't have a very light tonearm, and it wouldn't work in anything else
You just can't put a Moving Coil cartridge on your light SME Series III tonearm, it's a terrible match!
You're thinking of buying an SPU? But you need a really heavy tonearm, or it will mistrack!
People still believe that the cartridge's compliance should be precisely matched with the tonearm's effective mass.

We have explored that subject before. We've found the source of that idea in the 1954 publication, and re-examined the assumptions behind it. What we have found out made us think that the simple formula is no longer applicable. But the people were just not ready to let that idea go.
Why is this idea so resilient? Perhaps it satisfies the inner explorer in all of us
Why is it so resilient? Perhaps it satisfies the inner explorer in all of us. You change the tonearm setup by using a heavier/lighter headshell, you put on the "Hi-Fi News and Record Review" test LP, and hearing that reassuring voice read out the frequency, you confirm that something has changed. It feels nice to be in control, to change things and observe the effect of change.

So I thought: we could also give every analogue enthusiast's inner scientist some food for thought. We should just show the measurements! And with this in mind, we went to work.

The Setup
Our test rig for low frequency measurements starts with a Micro Seiki RX-1500G turntable. It's reassuringly hefty, and we know it doesn't introduce any low frequency disturbances.

Then the Jelco SA-750DB tonearm that we've measured and used many times. Jelco publishes its effective mass (13.5g), so that should make our calculations easier. We've decided to use our own ceramic headshell to minimize the headshell influence and to be conservative. Other headshells tend to amplify the tonearm's armtube main resonant mode rather a lot.
And we'll start with the Ortofon SL-15E cartridge (thank you Jam!). Its vertical and horizontal compliance are also well-known: $$15 \cdot 10^{-6}$$ and $$25 \cdot 10^{-6}$$ cm/dyne respectively.

We'll be taking the horizontal and vertical acceleration simultaneously. The Picomin 22 accelerometers go down to 3 Hz, and that should be enough to capture our compliance resonances.

We are using the DAQ that is precise down to DC (0 Hz). Definitely not consumer-grade.

And it's probably the only device in our lab that's still in its factory calibration.
Why can't we just measure the cartridge output through the preamp?

There are pass-through capacitors inside most preamps. These capacitors act as high-pass filters.
We'll see a false "resonant peak" at 5-7 Hz, but in reality it's just 1/f noise shaped by the presence of the capacitor.

The Plan
1
Make sure our test rig is working fine and is picking up both high and low frequency resonances. We'll measure the low frequency set with it, and superimpose it over the usual 20Hz-20kHz sweep.
2
Change the cartridge to the one with different compliance, and see what the effect on the low frequency resonance would be.
3
See what the low frequency content of the usual LPs looks like. We'll use some nearly unplayable LPs from our collection to try and get the effects of warps and excentricity.
4
Do the analysis of the data and see if there are some recommendations to be made on matching tonearms and cartridges.

The Measurements
First, let's do the low-frequency (compliance) resonance calculation according to the well-known formula:

$$f={1\over{2\pi\sqrt{m \cdot c}}}$$

This would give us 8 Hz vertical and 6 Hz horizontal compliance resonance frequencies for the Ortofon SL-15E/Jelco combination. What would the actual measurements show?

The green trace is track 3, side 2 of HFNRR test LP—the narrated vertically cut low frequencies. It isn't a sweep, so you get this comb of separate frequencies. The blue trace is Clearaudio CA-TRS-1007 track 4, vertical 20Hz-20kHz sweep. They are, of course, not level-matched. The Clearaudio test LP represents the fairly normal recording level of an actual recording.

Isn't it interesting? We have not just one, but four low frequency resonance peaks! Two are centered around 10 Hz, and two larger ones around 20 Hz. And the peaks of this resonance, caused by specially devised exaggerated signal, are at about the same level as the armtube and headshell/cartridge modes.
The green trace is track 2, side 2 of HFNRR test LP—the narrated lateral cut of low frequencies. The blue trace is Clearaudio CA-TRS-1007 track 3, lateral 20Hz-20kHz sweep.

This is even more curious. Again, we have 2 peaks centered around 10 Hz, but there's also a strong gently declining response as we go higher, all the way to 25 Hz cutoff.
The charts are different from what we usually do. To achieve acceptable resolution in the low frequency range, we had to increase the FFT size significantly. And also, because most of 1/f noise is in the low frequencies, we subtracted the noise at idle from our measurements. This explains the negative numbers on the charts.

So what is going on?
We'll leave most of the conclusions till the last post in the series. But what we have seen so far suggests that either the resonance formula isn't too precise, or the content of those HFNRR test LP tracks isn't well calibrated. It feels like the signals around 10 Hz are recorded at higher level.

How can we check this? By doing the test using normal recordings to see if there's any LF content there. But first, let's see what results we'll get with a different cartridge.