SIGNALS & NOISE (Letters to Editor) May. 1983

Magnificent Obsession

Dear Editor:

I feel I have an incurable disease, and maybe you can help. Several years ago, I began reading Audio, and it has lead to an addiction to your magazine and to a constant equipment up grading. I wonder how many readers are, like me, never satisfied. In 1976 I started out with a Marantz 22206 20-watt receiver. Now, thanks to you, I own Klipsch LaScalas (with custom cane grilles) stained in walnut, a Yamaha CT-810 tuner, Yamaha CA-810 amp, Bang & Olufsen turntable, B & 0 MMC3 cartridge, TEAC cassette deck, dbx expander, Mitsubishi DA-720 stand, Monster Cables, and Sennheiser phones.

After reading your last few issues, you have convinced me I need a Sony compact digital disc player, a Nakamichi Dragon cassette deck, a Carver tuner, Polk speakers--the list goes on.

When will it stop? Will I ever be satisfied? I often wonder--does Len Feldman upgrade his equipment monthly? Please send help or money!

-Vernon Neal Arlington, Tex.

Tonearm Geometry

Dear Editor:

The article "Tonearm Geometry and Setup Demystified," by Martin D. Kessler and B. V. Pisha (Jan. 1980), should be understood as a historical survey as well as a survey of tonearm geometry.

During the past decades, several important contributions toward the optimization of tonearm geometry have been published. The earliest known use of the application of offset and overhang principles of which I'm aware was by Percy Wilson [1]. However, Wilson's design minimized tracking error alone, and not the tracking error weighted with the inverse of the groove radius. Wilson also published the de sign of an alignment protractor [2] based on the principles of [1].

The work of Lofgren [3] is the earliest paper known to me which aims at minimizing tracking distortion by minimizing the weighted tracking error. Lofgren showed that distortion due to lateral tracking error, which results from the use of a pivoted tonearm, can be minimized by using optimum geometry. The required offset angle and over hang equations for optimum geometry are given in that paper. These solutions are later referred to as the "ex act" solutions, and produce the three point, equal-weighted tracking-error curve.

Lofgren also considered an alternative approach. He believed that the annoyance factor of tracking distortion was cumulative with time. He considered altering the offset angle and over hang values to lower the maximum distortion between the null radii, and accepting the higher distortion thereby created (for a short period of the playing time) at the beginning and end of the record playing surface. Using the method of least squares applied to the distortion function, Lofgren derived a different formula to calculate the over hang, based on his alternate concept. No change was made to the offset angle.

Although Lofgren considered two different approaches toward minimizing the annoyance factor of tracking distortion, his derivation of the "exact" optimum offset angle and overhang equations was a most important achievement.

All one need do is select values for the effective arm length, and the inner and outer groove radii. Given these parameters, the offset angle and over hang may then be calculated using Lofgren's optimum design equations.

When these figures are employed in the setting up of a turntable and tonearm, tracking distortion is minimized across the selected playing surface of a record. What has been done is to minimize the tracking error per unit of radius, and not simply tracking error, because tracking distortion is directly proportional to the tracking error and inversely proportional to the radius.

Works by Baerwald, Bauer, Seagrave and Stevenson later followed [4, 5, 6, 7 respectively], where offset angle and overhang equations were also derived.

So far as I am aware, no attempt has been made to compare the equations derived by these authors, with the aim of determining the differences be tween them and assessing the "best" design equations. I did such a com parison, and found the results to be quite significant.

The design equations for optimum offset angle and overhang given by Baerwald, Seagrave and Stevenson are mathematically identical to those given by Lofgren, differing only in notation and arrangement. I have enclosed a copy of my analysis, which shows the mathematical equivalence of the various works, and it also contains a comparison and a summary of the results.

Stevenson also considered two different approaches toward the reduction of the effects of tracking distortion.

His secondary approach is identical to Lofgren's main approach (the three point, equal-weighted concept). Stevenson's primary approach considered that the annoyance factor of tracking distortion was basically de pendent upon the amplitude of such distortion, a concept opposite to Lofgren's alternate approach. Stevenson placed the inner null radius at the inner groove radius. While the overall distortion across the playing surface may now be slightly higher, the probability of high distortion (of all types) at the inner grooves is reduced.

Stevenson's main approach and Lofgren's alternate approach are based upon factors totally different to the geo metrical optimization (minimization) of the weighted tracking error. Stevenson was concerned with the amplitude of the distortions at the inner groove area, while Lofgren believed the annoyance factor was time-cumulative. Stevenson's approach does not refute the work of Lofgren, Baerwald or Seagrave, as all four authors have produced the same design formulae, based on the same (unique) geometrical problem. What Stevenson does is to employ the same formulae in two different ways, based on two different concepts.

Lofgren's alternate approach and Stevenson's primary approach are in deed worthy of attention, but as they are in fact different in psychoacoustic terms, which "modification" should be employed? Is there any need to modify the basic approach? Some recent advertisements and conjectures argue that Stevenson's equations are more accurate than Baerwald's, which is "outdated." I would argue that the difference really lies in the criteria used for selecting the inner and outer recorded groove radii as design parameters (and hence the location of the inner null radius), and not in the mathematics of the papers discussed so far. Quite simply, the advertiser has chosen to use the (same) optimum design formulae, which were derived by Lofgren, in the manner pro posed by Stevenson's main approach, which placed the inner null radius at the inner groove radius. It should be noted that Stevenson's design equations are identical to Lofgren's.

The optimum design formulae de rived by Bauer [5] will result in a small increase in overall distortion compared to Lofgren's, as Bauer used two simplifying approximations in his analysis.

I will now attempt a summary of the various works discussed above:

1. Lofgren, Baerwald, Seagrave and Stevenson produced identical, and ex act, equations for optimum offset angle and optimum overhang.

2. Lofgren and Baerwald also produced identical, but approximate, equations for overhang.

3. Bauer's offset angle equation was an approximation.

4. Bauer's overhang equation is identical to item 2, above.

5. Seagrave also produced an approximation for overhang which is more accurate than item 2.

6. Lofgren's secondary approach and Stevenson's primary approach are simply modifications to the three-point, equal-weighted tracking-error concept, and aim at reducing the annoyance factor of tracking distortion. How ever, they are different in psychoacoustic terms.

My analysis shows this comparison in a much clearer way than I have described here. References [8, 9, 10] provide comprehensive summaries on the subject.

In conclusion, the equations derived by Lofgren in 1938 are not outdated.

The fact that Baerwald, Seagrave and Stevenson produced equations identical to Lofgren's certainly confirms the preciseness and validity of Lofgren's work. The contributions of Lofgren and Baerwald are the definitive references on the subject of tracking distortion and its reduction. However, it should be stated clearly that if Lofgren's paper had been the only paper ever published on the subject, we would still have the same optimum design equations to employ in the reduction of tracking distortion as we have today.

The real problem we have today is the selection of an acceptable inner recorded groove radius to use in Lofgren's optimum design formulae and not which design formulae to use. For that, we have the choice of Lofgren's, Baerwald's, Seagrave's or Stevenson's! Upon request, I will forward a copy of my complete analysis to any interested readers.

Graeme F. Dennes, Member A.E.S., Member I.E.E.E.

104 Whippoorwill Drive Warner Robins, Ga. 31093

References

1. Wilson, P., "Needle Track Alignment," The Gramophone, Sept. 1924, pg. 129.

2. Wilson, P., "Two Notes on Gramophone Adjustment," The Gramophone, March 1925, pg. 381.

3. Lofgren, E. G., "On the Non-Linear Distortion in the Reproduction of Phonograph Records Caused by Angular Deviation of the Pick-Up Arm," Akustische Zeitschrift, Nov. 1938, pg. 350.

4. Baerwald, H. G., "Analytic Treatment of Tracking Error and Notes on Optimal Pickup Design," Journal of the Society of Motion Picture Engineers, Dec. 1941, pg. 591.

5. Bauer, B. B., "Tracking Angle in Phonograph Pickups," Electronics, March 1945, pg. 110.

6. Seagrave, J. D., "Minimizing Pick up Tracking Error," Audiocraft Magazine, Part 1, Dec. 1956, pg. 19; Part 2, Jan. 1957, pg. 25; Part 3, Aug. 1957, pg. 22.

7. Stevenson, J. K., "Pickup Arm De sign," Wireless World, Part 1, May 1966, pg. 214; Part 2, June 1966, pg. 314.

8. Carlson, R. E., "Resonance, Tracking and Distortion: An Analysis of Phonograph Pickup Arms," Journal of the Audio Engineering Society, July 1954, pg. 151; also reprinted in Audio Engineering Society Anthology Series, Disk Recording, Vol. 2: Disk Playback and Testing, pg. 259.

9. The Audio Critic, Vol. 1, Nos. 1, 4, 5 and 6.

10. Kessler, M. D. and B. V. Pisha, "Tonearm Geometry and Setup Demystified," Audio, Jan. 1980, pg. 76; "Addenda," April 1980, pg. 26.

11. Randhawa, T. S., "Pickup Arm De sign Techniques," Wireless World, Part 1, March 1978, pg. 73; Part 2, April 1978, pg. 63.

12. Gilson, R. S., "The Cartridge Alignment Problem," Wireless World, Oct. 1981, pg. 59.

Author's Note:

After almost three years of searching, I have finally located the Lofgren paper of 1938 which was cited by Baerwald in his 1941 definitive analysis of tonearm geometry. It is now established that the derivation of the various optimum equations was originally done by Lofgren and not Baerwald. I did not cite the Lofgren work because I had not read it. After having read Mr. Dennes' treatise, "An Analysis of Six Major Articles on Tone Arm Alignment Optimization and A Summary of Optimum Design Equations," I was pleased to know that he, too, had found the Lofgren and Baerwald papers to be the most definitive analyses of tonearm geometry to date. The Lofgren work has certainly withstood the test of time. Martin Kessler's and my original intent in writing the 1980 article was to bring together, in a comprehensive manner, all the important contributions to tonearm geometry, including the world literature, that we had read, so that young engineers and students might have the information more readily available. We made no claim to any original work, and we regret that we were unable to cite the "first" contribution to tonearm geometry, the 1924 classic work of Percy Wilson. Like the Lofgren work, we knew that the paper existed but were unable to find it until a copy was located by the late Percy Wilson's son, Dr. Geoffrey Wilson, and sent to us after our article was published. Mr. Dennes' treatise was truly a labor of love, and it is hoped that many of our readers (engineers and very technically oriented audiophiles) will request a copy of this excellent mathematical analysis of the six major articles on tonearm geometry. With the advent of the compact digital audio disc and the laser beam stylus, all this, of course, becomes moot as it is relegated to the pages of history, but at least we now know the true historical facts.

-B. V. Pisha

Plug Those Ears

Dear Editor:

I write with reference to the article entitled "Ears" by Simeon Costa published in the December 1982 issue.

The impression engendered by this article is that sensor i-neural (S-N) hearing loss, in particular noise-induced loss, can be corrected or at least ameliorated by the proper type of hearing aid.

As a practicing acoustician and industrial hygienist, I feel that this is a misleading and dangerous statement, since it implies that all deterioration of the hearing mechanism can be re versed by means of a prosthesis. As a group, noise-exposed workers have the largest incidence of hearing dam age in North America, and therefore have the most to gain by protecting their hearing. Human nature embraces the idea of cure rather than prevention (this is nowhere more obvious than in the continuing automobile seat-belt debate in North America). Thus, if an authoritative magazine such as yours suggests the existence of an easy after-the-fact "fix" for S-N loss, it pro vides no incentive for noise-exposed workers to wear their hearing protection.

The article should have stressed that the only path to continued good hearing is assiduous use of hearing protection both at work and at play, when noise levels exceed about 80 dBA. The hearing-impaired person may well be helped by a hearing aid, but the degree of aural fidelity restored in this way will only be a pale shadow of the real thing, akin to viewing the Mona Lisa through a thick fog.

Good earplugs-one size fits all are available for about 250 at any industrial safety supply house. No audiophile should be without a supply of them if he is to retain the full audible frequency range and acuity with which Mother Nature endowed him.

-Michael R. Noble, Vancouver, B.C.

Editor's Note:

Mr. Noble is correct about the importance of prevention in as much as no hearing aid can fully compensate for hearing loss. I use E*A*R foam plugs which I obtained from the Cabot Corp., 7911 Zionsville Rd., Indianapolis, Ind. 46268.

-E.P.

(Source: Audio magazine, May 1983)

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