Dear @cleeds : In reality the issue is not " dogmatic theorists " but common sense founded in the Löfgren theory where he proved through scientific equation calculations what for many years are the Standard for tonearm/cartridge alignment, it’s not that we accepted it’s the Standard in the industry just like the RIAA eq.
VIV Labs is telling you to come back to before 1924 because its " sounds better " and he gaves you no single factible evidence/fact/measure/theory that that could be true. As I said the overall issue is common sense that I know you have in very good shape.
Here part of the history of the Löfgren Standard that VIV LAbs " want it " to forget:
"""" During the recent decades, several important contributions on the optimisation of
tonearm alignment geometry have been published. The pioneering work of Percy
Wilson [1] in 1924 is the earliest paper known to this author in which offset angle and
overhang principles were discussed and applied in the mounting of the pivoted
tonearm, for the purpose of minimising the consequential record wear..................................................................................
Wilson minimised the change in tracking angle by applying offset angle and
overhang principles, and developed equations to achieve this, as published in his
pioneering 1924 paper.
In 1925, Wilson published the design of an alignment protractor [2] based on [1].
In 1929, a Wireless World article [3] (author unknown) included this statement: "It is
well known that to obtain the best reproduction, coupled with minimum wear on the
record, the needle should lie in a plane tangential to the record groove at the point of
contact, and should be free to move at right angles to the groove.". It seems that it
was understood by that time that tracking error not only produces record wear, but
also distorts the sound.
The first discerning statement on the origin of tracking distortion was made in 1937
by Bird and Chorpening [4]. In the presence of tracking error, and "... since the
needle point must vibrate about an axis at an angle to the groove tangent, sinusoidal
modulation of the groove will not produce sinusoidal vibration of the needle point even
when close contact is maintained, and therefore a certain amount of waveform
distortion occurs with a large tracking error.".
This was followed later in 1937 by Olney [5], who developed a model for tracking
distortion, and postulated that tracking distortion would be related to the ratio of the
recorded amplitude of the groove modulation to the recorded wavelength of the
groove modulation. It would later be shown by Löfgren that tracking distortion is
indeed proportional to this ratio. ....................................................................
The formal relationships between tracking error and tracking distortion remained
hidden until the publishing in 1938 of the historic paper by Professor Erik Löfgren [6]
of the Royal Institute of Technology in Stockholm, Sweden, and is the earliest work
known to the author which gives an analytical treatment of tracking distortion and
develops a new optimum alignment method to minimise it. Löfgren provided
mathematical equations to the distortion model developed by Olney, and undertook a
Fourier analysis on them. The results confirm the relationship postulated by Olney,
which translates into the distortion being proportional to the tracking error and
inversely proportional to the groove radius. The tracking error divided by the radius
has become known as the Weighted Tracking Error (WTE). Löfgren then sought to
minimise the tracking distortion by minimising the WTE.
Löfgren developed an optimisation method which involved applying the minimax
principle (as used by Wilson) to the WTE. The maximum level of the distortion is then
represented by the slope of the tracking error graph rather than by the level of the
tracking error. This method results in less tracking error at the inner grooves where
the wavelengths are shorter.
The introduction of this inverse radius weighting complicates the analytical solution,
and Löfgren uses an approximation method which relies on the error angle being
small. This is a reasonable mathematical approach, and incurs very little error. An
interesting feature of the optimisation method is that the null radii will later be shown
to be the same as those provided by the later authors.
The optimum solution from Löfgren provides for an offset angle and overhang which
minimises and equalises the three resulting WTE peaks across the record playing
surface. This three-point, equal-WTE solution has continued to be applied to the
present day, and I refer to this as the ’Löfgren A’ solution. .................
Löfgren’s paper was followed by papers from Baerwald [7] in 1941, Bauer [8] in 1945,
Seagrave [10] in 1956, Stevenson [11] in 1966, and Kessler and Pisha [12] in 1980. ..................................................................""""""
It’s not easy for me to post ( I’m not good with computers. ) the Löfgren equations and here a summary of it but exist several calculators in the internet where we can see all those equations.:
QUICK AND NOVEL ’LÖFGREN A’ ALIGNMENT CALCULATIONS The following equations provide a quick and novel (but reasonably accurate) method of calculating the optimum alignment parameters for the ’Löfgren A’ alignment, certainly good enough for practical alignment calculations. Using these equations, the optimum offset angle, the optimum overhang, and the resulting maximum |WTE| (at the three WTE peaks) may be easily calculated. The only input required is the arm length in mm. The equations utilise three numbers which remain essentially constant over the range of alignment values likely to be encountered in practice. Also included for comparison purposes are the results for the ’perfect Löfgren A’ solution. You may be surprised at the accuracy of these equations! The equations are based on an inner groove radius of 60.325 mm, and an outer groove radius of 146.05 mm. Notation: L = arm length, = optimum offset angle, d = optimum overhang, WTE = weighted tracking error. 1. Quick calculation of Offset Angle: L.sin ≈ 93.516 mm (Löfgren’s Linear Offset) so sin = 93.516 / L so = arcsin(93.516 / L) For L = 250 mm, sin = 0.374064: = 21.966 degrees The ’perfect Löfgren A’ result? = 21.963 degrees! 2. Quick Calculation of Overhang: 2.L.d - d 2 ≈ 7987 mm2 (Löfgren’s Ra 2 term) so d = L – SQRT(L2 - 7987) mm For L = 250 mm: d = 16.5180 mm The ’perfect Lofgren A’ result? d = 16.5198 mm! 3. Quick Calculation of Maximum |WTE| value at the three peaks: L.cos * max. |WTE| ≈ 2.709 degrees so max. |WTE| = 2.709 / (L.cos ) degrees per mm For L = 250 mm and = 21.966 degrees: max. |WTE| = 0.01168 degrees per mm The ’perfect Löfgren A’ result? = 0.01168 degrees per mm! CALCULATING TRACKING DISTORTION Tracking Distortion Löfgren showed that at lower distortion levels, tracking distortion is principally second harmonic in nature. He developed an expression which approximates this distortion, and presents it as the product of two factors in his EQN (22). This is an historically significant expression, as Löfgren was the first to show the relationship between the four variables involved in the generation of tracking distortion. A summary of Löfgren’s derivation of this expression is included in Section S10 of this analysis. Löfgren’s EQN (22) is: ≈ 𝑉 . 𝑅 This shows that the tracking distortion is proportional to the recorded velocity (𝑉) and tracking error (), and inversely proportional to the angular velocity of the record () and the radius (𝑅). As Löfgren notes, the first factor is independent of the position of the needle on the record, while the second factor changes continuously during play. We also must ensure the units are consistent. For example, if 𝑉 is in mm per sec, then R has to be in mm, and if is in radians per second, then has to be in radians. For the LP record with a typical peak recorded velocity of 100 mm per second and a speed of 33 1/3 RPM, the angular velocity of the record equals 360 (degrees per revolution) * 33 1/3 (RPM), or 12,000 degrees per minute, or 200 degrees per second. For consistency of the units, tracking error is then in degrees and groove radius is in mm. So the maximum distortion is: = 100 / 200 * tracking error / radius For example, with a tracking error of 2 degrees at a radius of 130 mm, the maximum distortion = 100 / 200 * 2 / 130 = 0.0077, ie, the second harmonic level is 0.0077 of the fundamental or 0.77%. We refer to the tracking error divided by the radius as the weighted tracking error or WTE, which means the tracking error weighted by the inverse of the groove radius. Thus, the maximum distortion is: = (100 / 200) * WTE = 0.5 * WTE (WTE in degrees per mm) RIAA De-emphasis. An added factor which Löfgren did not include, and which needs to be included, is the effect on the distortion of the RIAA frequency de-emphasis in the phono playback preamplifier. In accordance with the RIAA playback response curve, over the frequency range from 20Hz to 20KHz, which is about 10 octaves, the gain changes by about - 40dB. This averages at -4dB per octave, as Stevenson states. For the harmonic distortion components, this has the effect of attenuating the second harmonic by 4dB with respect to the fundamental, which means the distortion is lowered by this amount. This is a gain change of 10-4/20 , so we must allow for this by multiplying the distortion in EQN (22) by 10-4/20 . Thus, distortion = 0.5 * 10-4/20 * WTE (WTE in degrees per mm) In summary, the constant 0.5 * 10-4/20 converts the WTE figure in degrees per mm to a second harmonic distortion figure 30. At any playing moment, the actual level of distortion being produced is proportional to the recorded velocity (𝑉) at that moment. Thus, the distortion factor is the maximum expected distortion level. As a brief aside, we can convert the distortion constant = 0.5 * 10-4/20, which is approximately 0.3155, to the constant 1.76 used by Stevenson on page 215 of his paper. Stevenson used 100 mm/sec RMS (not peak) recorded velocity, so we must multiply the distortion constant by the square root of 2. He also used radius values in inches (not mm), so we must divide the distortion constant by 25.4. Stevenson also calculated percentage distortion, so we must multiply the distortion by 100. Thus, the distortion constant becomes 0.3155 * SQRT (2) * 100 / 25.4 = 1.7566, or 1.76, per Stevenson’s article. Thus, the maximum percentage distortion = 1.76 * WTE, where WTE is in degrees per inch. The RMS Value Löfgren based his ’Löfgren B’ alignment solution on the minimisation of the RMS distortion caused by tracking error. We’ll now investigate how we determine the RMS distortion. The RMS value of a varying quantity is a single figure which is a statistical measure of the magnitude of the varying quantity. In this application, the varying quantity is the distortion level occurring at each radius point across the record surface. The RMS distortion level is the single figure representing all these distortion levels. The %RMS distortion is simply the RMS distortion multiplied by 100. Procedure to Determine RMS Distortion To determine the RMS distortion, we perform two fundamental steps: 1. Define a distortion indicator or distortion factor, which is an expression indicating the level of distortion being produced at any point. 2. Apply the necessary mathematical procedure to the distortion factor. Löfgren’s EQN (22), described above, is a suitable distortion factor, as it indicates the level of second harmonic distortion caused by tracking error. As noted, it consists of two parts - a fixed part and a changing part. The fixed part, 𝑉 , is comprised of the peak recorded velocity on the record, divided by the angular velocity of the record. This is considered a constant, with a value of 100 / 200 or 0.5, as described. The changing part, 𝑅 , is comprised of the tracking error divided by the radius R, and it continuously changes during the play of the record. We refer to this part of EQN (22) as the weighted tracking error or WTE. The calculation of the tracking error is based on the inverse sine trigonometric function. The WTE is calculated using EQN J on page S9-6. Of course, the RIAA correction still needs to be applied to EQN (22) as discussed. In summary, the underlying method to calculate an RMS value includes the integration of the square of some function. In this case, the function is Löfgren’s EQN (22), where the WTE part is given by EQN J .
Cleeds, you said you read all the thread then I suppose between all posts you already did it with mines and especially the 3-4 latests ones that describes why I’m talking of common sense.
Look, the VIV Labs is not the first and not the last Stampede in audio where audiophiles " runs " with out really know why are inside the Stampede that arrives nowhere, that impedes to stay nearer to the recording. Yes, its develops a sound that they like it but that is far away from what it’s in LP groove modulation .
Each one of us have our specific targets, the VIV followers has only one: I like it no matter what, good for them.
R.
