I think you need to read more. A lot more. …
… a truckload more, as they say. Nope, my original question was, if there was measurement data that confirms the general superiority of certain stylus shapes. After a bit of back and forth I personally concluded, that the ‚library‘ on this board would only tell: the excellent cartridges are all equipped with parabolic shapes, but such a shape would not even statistically grant a better performance. That‘s a subtle take on the observation, and it is valid.
I would sort the measurements in three clusters. No non-parabolic stylus is better than mediocre, with the exception of VM95 elliptical, nearly all parabolic are mediocre, There are only two that shine, Shure V15 and AT VM95. Sidenote: there is no MC that I found to be right out excellent.
All the reading on theories is inconclusive. It lacks analytical depth by far, even if combined. Despite the marketing fuss no real data is available.
Then we came to the ‚fricatives‘ test with a certain test record. Again, thanks for publishing it. What you accuse me of is exactly what I said. None of the cartridges performed as if a problem was resolved.
It is not illogical to scrutinize the nature of the remaining problem. It is not about regular overtones aka harmonic distortion as it is predicted by the ‚ball following a wave‘ model. Instead, most of the distortion product seems to be located below(!!) the driving frequency (10kHz bandwidth limited random noise in my case). That‘s typical for chaotic systems. And what else would one expect from a system of multi-dimensional composition, having internal feedback loops in parameters influencing each other, and shows 10% HD ++ to begin with.
My hypothesis was then, only to say something, that a wider conical stylus would, due to pinching, be forced harder to vast accelerations, which it might not follow. But it partly leaves the groove. It may lean on one side only, jumping over the modulation on the other side of the groove for a little. That would explain the subharmonic nature of the byproducts.
On first glance the parabolics appear to be favorable, because those avoid the pinching by a bigger margin. But it also tells, that it‘s not directly the shape, but insufficient tracking force. Low compliance of the cantilever, higher tracking force, combined with low effective mass of the needle, combined with a heavy tonearm might help.
Fun fact: even Noble laudats like Einstein, Klein, Sommerfeld failed miserably when they tried to explain how a bicycle works— really. We are not that dumb, right?