## ToneArm Geometry

During the many years I have been investigating and designing turntables and tonearms, I have asked many serious audiophiles this question many times: “What kind of distortion is caused by tonearm tracking angle error?” Nobody, not a single audiophile or any other person, has given me the correct answer. Many look at me with a puzzled expression, as though they have never thought about this problem before. Others, don’t know why they use a particular geometry or how much overhang they use. I knew the answer because I had read about this subject in *The Radiotron Designer’s Handbook*, Fourth Edition, 1953 pages 723 to 727. The subject of tonearm tracking is intensively covered in References 52 and 226. The English reference book *Audio Frequency Engineering*, 1961 by E.H. Jones, pages 204 to 209, also gives an excellent mathematical explanation of the tonearm tracking error. These references clearly present the answer to “What kind of distortion is caused by tracking angle error”: an increase in 2^{nd} harmonic musical content.

I struggled through the mathematics of these references and many times had to refer back to my college mathematics books to understand the equations and the author’s explanations. I decided to develop a different way of looking at this problem and yet come to the same conclusion. I have used a graphical technique with excellent results. The tracking angle error used for this analysis is 20° to make the results easy to see.

Consider the Figure 1 of a sine wave and consider that this sine wave is on a phono record. The line O-A (blue) is the cartridge stylus excursion path of a parallel tracking tonearm aligned for zero tracking angle error. The line O-B (red) is the cartridge stylus excursion path of a tonearm with a tracking angle error of Θ. Notice that line O-B is longer that line O-A. Using a strictly graphical approach, repeat these lines several times and then plot the differences of the excursion paths as shown. The result is a clearly defined even harmonic waveform, predominantly 2^{nd} harmonic.

In addition to the graphical approach, I wrote a program for the TI-84 graphing hand calculator and this program yields the same results. This program permits the tracking angle error to be varied over a considerable range and clearly shows the relation between tracking angle error and the amount of even harmonic musical content. Figure 2 shows the percent of even harmonic caused by tracking angle error. Notice that a tracking angle error of 5 degrees yields even harmonic content less that 0.2% and this amount of error is not considered to be small. Most experts agree that an increase of the even harmonic of musical content is not injurious of musical quality but rather, makes for a richer and more enjoyable musical experience. However, it is doubtful that our hearing is able to discern an increase of even harmonic musical content of this level.

After my investigations, I decided to relieve users of Amadeus of the issue of setting tonearm geometry and to use a fixed geometry. Based on the comprehensive analysis of J.K. Stevenson in the May and June 1966 article *Pickup Arm Design* and based on the dimensions of several phono cartridges in my inventory, I designed the tonearm for Amadeus to have a fixed tracking angle of 19 degrees and an overhang of 0.5”.

In a future edition of this blog ,I will describe how to make a low-cost tracking angle analyzer. This device will permit the user to determine the tracking angle error caused by cartridges different dimensions.

Please see this link for the Well Tempered Lab Headshell Alignment Guide for all Well Tempered turntable models.

William Firebaugh