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1 September 2025
The Trap of Mental Experiments
It's been a while, hasn't it?
I haven't had time to write in the last few months. When a company grows quickly, it often incurs a lot of debts—organisational, engineering, compliance, etc. Many companies move forward while accruing more and more of those debts in the hope of achieving escape velocity before the reckoning. Maybe one in a hundred can pull this off. The alternatives for other 99 are, either collapse under load, or painstakingly go through monster checklists, making sure their operations can cope and grow.
We spent the past few month settling those debts. But, this means we now have a research and publishing debt! Fortunately, that's an enjoyable one to settle.
Where do I start anew? Easy! We get asked all the time: why don't you use the "scientifically correct" tonearm alignment like Löfgren or Bärwald, and instead stick with a crude one like Stevenson?
In spite of apparent simplicity of the question, there's a lot to unpack here.
I haven't had time to write in the last few months. When a company grows quickly, it often incurs a lot of debts—organisational, engineering, compliance, etc. Many companies move forward while accruing more and more of those debts in the hope of achieving escape velocity before the reckoning. Maybe one in a hundred can pull this off. The alternatives for other 99 are, either collapse under load, or painstakingly go through monster checklists, making sure their operations can cope and grow.
We spent the past few month settling those debts. But, this means we now have a research and publishing debt! Fortunately, that's an enjoyable one to settle.
Where do I start anew? Easy! We get asked all the time: why don't you use the "scientifically correct" tonearm alignment like Löfgren or Bärwald, and instead stick with a crude one like Stevenson?
In spite of apparent simplicity of the question, there's a lot to unpack here.
Where Do Tonearm Alignments Come From?
We all use the established alignment templates as if they are some sort of scripture. But where do they come from? How do we know if they are true?
Of the three main types of cartridge alignment, two are really ancient. Eric Löfgren published his paper in Stockholm in 1938. H.G.Baerwald presented his independently produced theory in New York in 1941. LP would not be introduced for 7 years, and then another 9 years would pass before the first stereo record is pressed in 1957. Both had 78 RPM mono shellac records in mind when they did their math.
Of the three main types of cartridge alignment, two are really ancient. Eric Löfgren published his paper in Stockholm in 1938. H.G.Baerwald presented his independently produced theory in New York in 1941. LP would not be introduced for 7 years, and then another 9 years would pass before the first stereo record is pressed in 1957. Both had 78 RPM mono shellac records in mind when they did their math.
Then, in 1966, a young (26 years at the time) J.K.Stevenson presented his theory in May and June issues of the "Wireless world" magazine. By then, stereo LP was dominant—and yet, Stevenson's alignment is usually condemned as the more primitive of the three!
All three papers are quite math heavy, the first two much more so. I will not bore you with it. If you want, the derivations in all three papers are there for you to follow.
All three papers posit that the angular tracking error directly translates into harmonic distortion, namely an increase in second harmonic. Harmonic distortion is bad, so to avoid or minimize it we need to very carefully minimize the angular error. And if we do so by employing an offset angle and an overhang, the THD plot will look like this. I've taken it from a 2022 AES publication, "New Analytical Results for Lofgren C Tonearm Alignment"
There's something else that unites all three papers. None of them offers anything in the way of experimental proof. Which is understandable given the vintage of the first two, and the tender age of the author of the third. Lab time was expensive in those days.
All three papers posit that the angular tracking error directly translates into harmonic distortion, namely an increase in second harmonic. Harmonic distortion is bad, so to avoid or minimize it we need to very carefully minimize the angular error. And if we do so by employing an offset angle and an overhang, the THD plot will look like this. I've taken it from a 2022 AES publication, "New Analytical Results for Lofgren C Tonearm Alignment"
There's something else that unites all three papers. None of them offers anything in the way of experimental proof. Which is understandable given the vintage of the first two, and the tender age of the author of the third. Lab time was expensive in those days.
No real world data is used as an input, and no physical experiment is ever performed to confirm the result.
All three papers are what is called a "mental experiment". A mathematical model of reality is built, and then further speculation is used to arrive at a result.
No real world data is used as an input, and no physical experiment is ever performed to confirm the result. This happens much more often than a layperson may expect. Entire fields of modern science are based on the flimsiest of actual data (and often on none at all).
No real world data is used as an input, and no physical experiment is ever performed to confirm the result. This happens much more often than a layperson may expect. Entire fields of modern science are based on the flimsiest of actual data (and often on none at all).
But I digress. If we are to believe AES, in the 87 years since Eric Löfgren's paper was published, nobody bothered to test his (or Baerwald's, or Stevenson's, or Bauer's) theories experimentally. Even in 2022, people writing about alignment stick to pure theoretical mathemathics.
But why? It's such a simple measurement!
In science, this usually means that many people have actually done the experiment. The result they got disproved the orthodoxy. So they thought it prudent not to publish it in any form, lest their careers or reputations suffer.
Fortunately, I have no such limitations. We will measure total harmonic distortion (THD) over the whole side of an LP, using different styli, and see how well the result matches the mental experiment.
But why? It's such a simple measurement!
In science, this usually means that many people have actually done the experiment. The result they got disproved the orthodoxy. So they thought it prudent not to publish it in any form, lest their careers or reputations suffer.
Fortunately, I have no such limitations. We will measure total harmonic distortion (THD) over the whole side of an LP, using different styli, and see how well the result matches the mental experiment.
THD Measured Over Tonearm Arc
To measure THD over the arc of the tonearm's travel, we need a test record with the same signal recorded over the whole side. Our dealer Mr Markus Wierl graciously provided us with such a record, a Sperling Testschallplatte TLP-1. It has a whole side of 1 kHz sinewave in both channels.
The problem with all test LPs is, all of them have a measure of harmonic distortion already cut into the grooves. As far as I know, none of the test LP manufacturers specify even the approximate extent of this distortion.
In the case of Sperling TLP-1, the pre-cut harmonics seem to be fairly benign and, what is more important, more or less equal through the side.
The problem with all test LPs is, all of them have a measure of harmonic distortion already cut into the grooves. As far as I know, none of the test LP manufacturers specify even the approximate extent of this distortion.
In the case of Sperling TLP-1, the pre-cut harmonics seem to be fairly benign and, what is more important, more or less equal through the side.
Another word of caution. We are taking the signal post RIAA decoding, while both Löfgren and Baerwald made no provision for it. Stevenson did. While RIAA decoding can certainly impact the absolute level of THD, for us it is important to know that relative THD between signal at different radii and between takes remains valid. Interestingly, 1 kHz is a zero decibel point on a RIAA curve—this frequency is neither boosted nor attenuated. In our case, this means that even the absolute THD level should be correct!
With that, let's look at the THD chart of a common elliptical stylus, 0.2 by 0.7 mil (5 by 18 micron):
With that, let's look at the THD chart of a common elliptical stylus, 0.2 by 0.7 mil (5 by 18 micron):
This is smoothed with 25 point moving average, and yet it is still quite jagged. Interestingly, the peaks are quite different on every playback. Why? Dirt and dust.
What we have is a more or less linear progression from low-ish THD in the outer grooves to 2% closer to the runout.
In light grey, I have added the theoretical distortion caclulated according to Stevenson's formula. Two zero distortion null points, and then the higher the error angle the higher the distortion. Righ?
Ouch. Nope. Nothing like it, in fact. What we have is a more or less linear progression from low-ish THD in the outer grooves to 2% closer to the runout.
Shall we see what a more advanced stylus plays like?
Ouch. Nope. Nothing like it, in fact. What we have is a more or less linear progression from low-ish THD in the outer grooves to 2% closer to the runout.
Shall we see what a more advanced stylus plays like?
This is even more interesting. The observed total harmonic distortion is lower than the calculated second harmonic percentage. In fact, in the outer grooves, the measured THD is exactly half of the theoretically predicted.
And again, the measured curve is more or less linear, save for a rise in the inner grooves.
Okay, let's go in a different direction. Let's take something much simpler—a conical stylus. Maybe it will match the theoretical predictions?
And again, the measured curve is more or less linear, save for a rise in the inner grooves.
Okay, let's go in a different direction. Let's take something much simpler—a conical stylus. Maybe it will match the theoretical predictions?
Here, we had to adjust the vertical scale to make a much higher distortion visible. Still, no trace (excuse the pun) of anything resembling the theoretical prediction. Just a slope, proportional to linear groove speed.
What Do We Make of This?
Looking at the measurements, the first thing that springs to mind is "all three theories, Löfgren's, Baerwald's and Stevenson's, are bunk". Their failure in predicting harmonic distortion is complete. Not only the relationship between THD and radius is wrong. The very scale of expected THD is also off.
It still makes sense to optimize for less tracking error
So, does this mean the calculations are completely useless and we all should just use straight tonearms from now on? I don't think so. The three authors got the tracking error calculation right; they just completely failed at understanding its implications. It still makes sense to optimize for less tracking error, just not because of harmonic distortion.
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