The Korf Blog

The inside story: our research, development and opinions

16 May 2017
Geometry Part I. Static geometric errors.
This is the first post in a series dedicated to tonearm geometry. I will try to avoid repeating the obvious and the well-researched, focusing on things that are often overlooked. Korf Audio has done extensive proprietary research into the relative importance and audibility of these errors, and I'll share some of the conclusions.

The tonearm's main task is to accurately position the stylus in the groove. It must do so in 3D space, tracking the groove and allowing for the eccentricity and warps in the disc being played. The three planes in which stylus is moving give us 3 possible types of static stylus placement error, assuming the stylus always remains in contact with the disc:

  • Horizontal angular alignment error
  • Stylus rake angle error
  • Stylus azimuth error
All three were studied extensively in the 1950-1980's, and the results are available from the AES. If you are designing anything that has to do with analog disc reproduction, these should be your table books. $200 or so buys you half a century of research worth many million dollars.

Voume 2 of the AES Disk Recording anthology
Horizontal angular alignment error α is known to introduce harmonic distortion (largely second harmonic). All pivoting tonearms and most linear tracking ("tangential") arms have this error.


The resulting harmonic distortion in % is often calculated according to formula 4.44 * tracking error angle / groove radius in cm (for modulation velocity 10cm/s). No-one really knows who came up with it (it is often falsely attributed to Baerwald), and no meaningful derivation of it is found anywhere. It isn't supported either by the measured 2nd harmonic distortion or by the audible effect of misalignment.

The measurements suggest that the distortion isn't related to angular error in a linear fashion. Up to a certain threshold there is very little change, but further increase in error leads to drastic increase in distortion. Such distortion also seems to be inversely proportional to linear speed of stylus versus the groove.

This error also creates a phase shift between channels.
Stylus rake angle (SRA) error β is often confusingly called "Vertical tracking angle (VTA) error". There is considerable controversy on how audible small SRA errors are. It is perhaps summed up best by Geoff Husband in his 2004 TNT-Audio article. Large SRA errors result in significant and measurable intermodulation distortion.

SRA is a result of interaction between the headshell angle (tonearm "height") and the cartridge's cantilever. Because the cantilever is attached to a cartridge by means of compliant suspension, SRA is dependent on the tracking force (downforce).
Stylus azimuth error γ is perhaps the least well-known of the three, probably because very few tonearms are adequately equipped to correct it. It is assumed by most that it largely impacts channel separation and cross-talk, but also causes significant intermodulation.

Cartridge manufacturing inaccuracies are the main source of azimuth and SRA errors.

In my experience, many "boutique" cartridge manufacturers do not have either the equipment or the set of procedures needed for consistent quality control. Even the hand-picked samples given to magazine reviewers sometimes have SRA and azimuth quite far away from what a consumer can reasonably expect.

In the next installment, we will explore the dynamic geometric errors resulting from stylus tracing the groove and following the disc's imperfections. Korf team is visiting High End 2017 in Munich, so the next blog post will be delayed by a week.
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