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20 December 2025
The Answer to THD Puzzle
Thank you for the letters with the answers to the linear tracker versus pivoting tonearm puzzle in the previous blog post! This is probably the most letters I have ever received following a blog post, not counting the hate mail after our "compliance matching" series.
Curiously, practically every single person got the answer wrong! Here's the correct legend:
Curiously, practically every single person got the answer wrong! Here's the correct legend:
For the linear tracker, the TDH is rising as a function of linear groove speed. And for the pivoting arm, there's something that keeps the THD quite high up until the last few centimeters of LP's radius. What can that be?
There's a green line on the chart that may help us solve this riddle. It's also a pivoting tonearm, in fact that's our own TA-SF11R. And it's THD chart is uncannily close to the linear tracker's.
What is going on here?
We have already established that the tracking error is blameless. Were it not, the THD would have converged at null points. There is something else at play here, and I think I know what it is.
There's a green line on the chart that may help us solve this riddle. It's also a pivoting tonearm, in fact that's our own TA-SF11R. And it's THD chart is uncannily close to the linear tracker's.
What is going on here?
We have already established that the tracking error is blameless. Were it not, the THD would have converged at null points. There is something else at play here, and I think I know what it is.
Offset Angle and THD
To check my hypothesis, we have mounted the same cartridge with the offset angle of zero, and ran a THD measurement of the same test LP.
But wait, what's that green line? Is it another linear tracker?
No. It's our TA-SF11R pivoting tonearm.
No. It's our TA-SF11R pivoting tonearm.
Stylus Dimensions--The Only Thing That Matters?
In our previous post, we have shown the THD chart for a bonded spherical stylus. And, of course, everybody went "come on, this is spherical, it's pinched out of the groove, what would you expect?"
Well, what about a nude spherical of exactly the same size? Should be broadly similar, right?
What you see here is the THD of the same bonded stylus in green, versus JICO Morita nude spherical stylus in red.
Well, what about a nude spherical of exactly the same size? Should be broadly similar, right?
What you see here is the THD of the same bonded stylus in green, versus JICO Morita nude spherical stylus in red.
Interesting, isn't it? Not only is the THD performance of the JICO spherical stylus vastly superior to the noname bonded stylus of the same size. It is superior to bonded elliptical, and to some lesser nude elliptical styli too (not shown). Bravo, JICO.
Limits to THD Measurements
In the meantime, let me show you some more data that we extracted from THD measurements. In general, those are not a practical solution for cartridge alignment and diagnostics purposes because of very low repeatability. First of all, there's dust and dirt. Even a tiny speck on the diamond stylus can worsen the THD performance by a factor of 2-3. Another thing that surprised me was cellular phone influence. Having a cell phone ring, or having a phone conversation near the playback rig ruins the measurement completely. I haven't done any experiments to prove it, but it feels like the THD recorded in the presence of a cell phone is heavily modulated by its radiation power.
Below is the THD measurement of Ortofon SPU GM E cartridge, completely ruined by the mobile phone call in the next room. The phone starts ringing when the stylus is at 125 mm radius, then there's a short conversation that is over by the time the stylus passes 110 mm. Red is the right channel, left is blue.
Below is the THD measurement of Ortofon SPU GM E cartridge, completely ruined by the mobile phone call in the next room. The phone starts ringing when the stylus is at 125 mm radius, then there's a short conversation that is over by the time the stylus passes 110 mm. Red is the right channel, left is blue.
In the meantime, let me show you some more data that we extracted from THD measurements. In general, those are not a practical solution for cartridge alignment and diagnostics purposes because of very low repeatability. First of all, there's dust and dirt. Even a tiny speck on the diamond stylus can worsen the THD performance by a factor of 2-3. Another thing that surprised me was cellular phone influence. Having a cell phone ring, or having a phone conversation near the playback rig ruins the measurement completely. I haven't done any experiments to prove it, but it feels like the THD recorded in the presence of a cell phone is heavily modulated by its radiation power.
Another fun chart is the THD for 45 RPM.
In our previous post, we have shown the THD chart for a bonded spherical stylus. What about a nude spherical of the same size? Should be the same, right?
What you see here is the same bonded stylus versus JICO Morita nude one. Whose THD performance is on par with most nude elliptical styli.
Various alignments
Stereo
Show raw data, you can draw any curve you want with spot measurements
45 RPM
Mobile phone interference ruined many measurements
Some of the critics pointed out that the Baerwald second harmonic distortion is calculated for 10 cm/sec lateral velocity. Congratulations, you are now one step away from finding the error in the Löfgren/Baerwald calculation.
Linear tracker
Various alignments
Stereo
Show raw data, you can draw any curve you want with spot measurements
45 RPM
Mobile phone interference ruined many measurements
Another fun chart is the THD for 45 RPM.
In our previous post, we have shown the THD chart for a bonded spherical stylus. What about a nude spherical of the same size? Should be the same, right?
What you see here is the same bonded stylus versus JICO Morita nude one. Whose THD performance is on par with most nude elliptical styli.
Various alignments
Stereo
Show raw data, you can draw any curve you want with spot measurements
45 RPM
Mobile phone interference ruined many measurements
Some of the critics pointed out that the Baerwald second harmonic distortion is calculated for 10 cm/sec lateral velocity. Congratulations, you are now one step away from finding the error in the Löfgren/Baerwald calculation.
Linear tracker
Various alignments
Stereo
Show raw data, you can draw any curve you want with spot measurements
45 RPM
Mobile phone interference ruined many measurements
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 calculations of cartridge alignment, two are really ancient. Eric Löfgren published his paper in Stockholm in 1938. H.G.Baerwald presented his independently derived but broadly similar 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 Löfgren and Baerwald had 78 RPM mono shellac records in mind when they did their math.
Of the three main calculations of cartridge alignment, two are really ancient. Eric Löfgren published his paper in Stockholm in 1938. H.G.Baerwald presented his independently derived but broadly similar 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 Löfgren and Baerwald 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. And, while he came up with a different alignment, he relied on Baerwald's formula to calculate distortion as a function of tracking angle error.
All three papers are quite math heavy. 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, mostly an increase in second harmonic. Harmonic distortion is bad, so 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 illustration on the right. I've taken it from a contemporary 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, mostly an increase in second harmonic. Harmonic distortion is bad, so 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 illustration on the right. I've taken it from a contemporary 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 typically means one thing only. The experiments were done, and the results disproved the orthodoxy. The people running the show hate iconoclasts, and the results were buried.
Fortunately, we live in the internet age. And the internet is great for bypassing all sorts of gatekeepers. 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 typically means one thing only. The experiments were done, and the results disproved the orthodoxy. The people running the show hate iconoclasts, and the results were buried.
Fortunately, we live in the internet age. And the internet is great for bypassing all sorts of gatekeepers. 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 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 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 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 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. 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 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 added the theoretical distortion caclulated according to Baerwald'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 of 0.6 mil (15 micron). 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 of 0.6 mil (15 micron). Maybe it will match the theoretical predictions?
It's a crude bonded conical stylus, so I had to adjust the vertical scale to make the much higher distortion visible. Still, no trace (excuse the pun) of anything resembling the theoretical prediction. Just a slope, proportional to the groove's linear velocity.
What Do We Make of This?
Looking at the measurements, the first thing that springs to mind is "all the three theories, Löfgren's, Baerwald's and Stevenson's, are bunk". Their failure in predicting the measured harmonic distortion is complete. Not only the relationship between THD and radius is wrong. The very scale of expected THD is also off.
It might still make sense to optimize for less tracking error
So, does this mean the calculations are completely useless and we should all just use straight tonearms from now on? I don't think so. The three authors got the tracking error calculation right; they just failed at understanding its implications. It might still make sense to optimize for less tracking error, just not because of harmonic distortion.
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