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Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long)

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Posted on January 12, 2015 at 00:07:11
John Elison
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 Magnetic phono cartridges are velocity responsive electromagnetic generators. As the stylus follows the groove, it travels back-and-forth a certain distance every second depending on the amplitude of the groove. The distance it travels divided by time is known as its velocity.

The reference 0-dB level for vinyl corresponds to a lateral stylus-tip velocity of 5-cm/s RMS or a 45-degree velocity of 3.54-cm/s RMS. This velocity can be produced by a 1000-Hz groove with lateral amplitude of 11.25-microns or it can also be produce by a 100-Hz groove with lateral amplitude of 112.5-microns. Stylus-tip velocity is proportional to groove amplitude multiplied by frequency; therefore, as frequency decreases, groove amplitude must increase in order to maintain a constant voltage output from the phono cartridge. The following equation describes how groove amplitude is related to RMS stylus-tip velocity:


.

When we look at the diagram of a sinusoidal groove in the picture below, we can see that the stylus must travel four groove amplitudes for every frequency cycle. If the groove amplitude is 11.25-microns, the stylus travels 45.0-microns every complete cycle. At 1000-Hz, the stylus travels an average distance of 45000-microns every second. This is the average groove velocity, which can be expressed in centimeters per second by dividing microns by 10,000. Consequently, a 1000-Hz groove with amplitude of 11.25-microns produces an average stylus tip velocity of 4.50-cm/s


.

Normally, we are more concerned with RMS velocity or even peak velocity rather than with average velocity. The following equations can be used to convert average velocity into RMS and peak velocity for a sinusoidal groove.


.

Consequently, an average velocity of 4.5-cm/s is equivalent to an RMS velocity of 5.0-cm/s. Peak velocity can be found by multiplying RMS velocity by the square root of two. These are the reference 0-dB stylus tip velocity levels for vinyl.

Now let's bring RIAA equalization into the picture. RIAA recording equalization is absolutely necessary because phono cartridges cannot negotiate the large groove amplitudes that would be required for low frequencies on vinyl. Additionally, these large groove amplitudes would widen groove spacing and significantly shorten the time on each side of a vinyl record. Another important advantage of RIAA equalization is to increase signal-to-noise ratio by increasing groove amplitude at frequencies above 1000-Hz. In other words, RIAA recording equalization reduces groove amplitude in low-frequency grooves below 1000-Hz and increases groove amplitude in high-frequency grooves above 1000-Hz as the following diagram shows.


.

The purpose of this lengthy discussion will become clear in my next installment when I discuss the groove amplitudes of the 300-Hz test tones on the Hi-Fi News and Record Review Test Record.

Best regards,
John Elison

 

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RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on January 12, 2015 at 01:12:44
flood2
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Posts: 2558
Joined: January 11, 2011
 ...and remember who corrected your original figures and provided you with the amplitudes off the HFNRR disc!
Have you worked out the signal amplitude reference yet?
Regards Anthony

"Beauty is Truth, Truth Beauty.." Keats

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on January 12, 2015 at 03:28:24
Analog Bob
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 This is excellent information. Thanks John.

I wish there was a repository on this site where reference material could be placed, like on Vinyl Engine. Or would that create a duplicate source?

 

Very nice, John. I will be waiting for the next article! nt, posted on January 12, 2015 at 05:45:11
Dman
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 nt

Dman
Analog Junkie

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on January 12, 2015 at 14:31:51
Picklesnapper
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 Questions: Why are there two RIAA curves, why does the RIAA 2 have a rolloff in the upper frequencies and which one is typically used in phono preamps these days?

Indeed, when did the RIAA 2 even come about?

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on January 12, 2015 at 18:35:41
John Elison
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 The real RIAA curve is the blue line. The red line is something I found somewhere called an enhanced RIAA curve. They added a fourth time constant to roll off frequencies above 20-kHz. It might not be a valid equalization curve; I can't remember where I found it. Check out Wikipedia at the link below. It talks about it.

Best regards,
John Elison

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on January 15, 2015 at 18:35:59
John Elison
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 > I wish there was a repository on this site where reference material could be placed

I bookmark all the posts that I think I might want to refer to later. But, if you need any of this information at any time, feel free to ask. ;-)

Thanks,
John Elison

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on January 16, 2015 at 15:19:32
rditmars
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 It would be interesting to see this type of analysis used to compare 33 vs 45 rpm pressings.
*
"We are as gods and might as well get good at it." - Stewart Brand

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on January 16, 2015 at 16:35:22
John Elison
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 Nothing would be different at 45-rpm because nothing in this analysis is based on the rotational speed of the record or the linear speed of the groove relative to the stylus. As the title describes, this analysis is one of stylus-tip velocity relative to groove amplitude and RIAA equalization. All of this would be identical at 45-rpm.

The advantage of a faster rotational speed would be improved performance and lower tracing distortion, especially noticeable on inner grooves. Since records turn at a constant rotational speed, the linear speed of the groove traveling underneath the stylus gets slower and slower as groove radius decreases. Because the playback stylus shape is different from the cutting stylus shape, distortion increases as the linear speed of the groove slows down. The innermost groove radius of 60-mm would have a linear speed of 60-mm x 2π x 33⅓-rpm ÷ 60-sec/min = 209.4-mm/sec. The linear speed of the same 60-mm groove traveling under the stylus at 45-rpm is 60-mm x 2π x 45-rpm ÷ 60-sec/min = 282.7-mm/sec. The groove speed is 35% faster at 45-rpm and the length of the groove traveling underneath the stylus each second is 35% longer. In other words, a 60-mm inner groove at 45-rpm would be equivalent to a middle groove radius of 81-cm on a 33⅓-rpm record. This means that 45-rpm records produce lower stylus tracing distortion than 33⅓-rpm records.

Best regards,
John Elison

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 5, 2015 at 06:57:37
safesphere
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 It appears from your diagram that 4.5 cm/s is not the average, but the maximum groove velocity. The stylus does not actually travel four groove amplitudes every cycle, as this is physically impossible. Instead, the stylus would have traveled four amplitudes, if it were moving at the maximum groove velocity all the time (but it does not). Could you please clarify?

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 5, 2015 at 08:18:15
John Elison
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 Distance and velocity are independent of each other. If you walk across the street and back twice, you have traveled the distance across the street four times. It doesn't matter whether you run or walk, the distance you traveled does not change. Therefore, if you can't see that a stylus travels four groove amplitudes every cycle, then it would be impossible for me to clarify anything for you. Such is life!

Good luck,
John Elison

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 5, 2015 at 09:22:23
safesphere
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 I see now what you mean, thank you. One more question, could you please provide a link to the reference that "0-dB level for vinyl corresponds to a lateral stylus-tip velocity of 5-cm/s"? I would appreciate it. Thanks!

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 5, 2015 at 10:05:01
John Elison
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 I'll leave that one to you. If you find a link, let me know.

Thanks!

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 6, 2015 at 07:01:41
safesphere
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 According to this http://www.audiomisc.co.uk/HFN/LP1/KeepInContact.html, even after the RIAA equalization, to achieve the same 0 dB level, the groove velocity at the high end of the spectrum must be an order of magnitude higher than at 1 kHz. Do you agree?

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 6, 2015 at 11:01:21
John Elison
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 I'm not sure why you said "even" after RIAA equalization. You should have said "only" after RIAA equalization.

The electrical output from the phono cartridge is directly proportional to its stylus tip velocity. Therefore, in order for cartridge electrical output to follow the RIAA recording equalization curve, stylus tip velocity must also follow the RIAA recording equalization curve. For a constant electrical amplitude signal sent to the cutting head, RIAA equalization increases stylus tip velocity as frequency increases. The playback RIAA curve takes the electrical output from the phono cartridge and returns it to a flat frequency response.



 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 6, 2015 at 11:52:44
safesphere
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 Sorry for my wording, please disregard "even". My point is that one of the objectives of the RIAA equalization is to decrease the low frequency amplitude and increase the high frequency amplitude in order to even them out for all the good reasons. Since the stylus is sensitive to velocity rather than amplitude, one could assume that the RIAA equalization should even out the velocity across the whole spectrum. This however does not hold true and I wonder why. For example, is this because real life high frequency levels are naturally lower, so that after the [over]-equalization by the RIAA the real live levels are actually about the same in every frequency range? Or is this a wrong conclusion?

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 6, 2015 at 14:16:26
John Elison
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 > My point is that one of the objectives of the RIAA equalization is to decrease the low frequency
> amplitude and increase the high frequency amplitude in order to even them out for all the good reasons.

RIAA recording equalization has two primary objectives, maximizing playing time and increasing signal-to-noise ratio. There is a possible third objective of allowing the record to be more easily playable by reducing stylus displacement. These objectives are accomplished by reducing groove amplitude in the low frequencies and increasing groove amplitude in the high frequencies. Therefore, when you use the term "amplitude" in your statement above, I interpret this to mean "groove amplitude."

Since stylus tip velocity is proportional to the product of groove amplitude and frequency, low frequency modulations would be too large for reasonable groove spacing and high frequency groove noise would overpower musical harmonic content. The reason RIAA equalization can work is because the energy in music is significantly reduced in the higher frequencies. High frequencies consist mainly of harmonics, which are much lower in level than fundamentals. Everything above 4100-Hz consists of harmonics and probably much of everything above 2000-Hz consists of harmonics.

> Since the stylus is sensitive to velocity rather than amplitude, one could assume that the RIAA equalization
> should even out the velocity across the whole spectrum.

I don't understand how you can come to that conclusion when you already stated above that "the objectives of the RIAA equalization is to decrease the low frequency amplitude and increase the high frequency amplitude." Again, I interpret this to mean "groove" amplitude since that is the subject of this thread.

Good luck,
John Elison

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 6, 2015 at 15:42:47
safesphere
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 I see, my guess was on target: naturally lower real life levels at higher frequencies even out the groove velocity throughout the spectrum while the RIAA equalization is concerned specifically with the groove amplitude. Thanks John, this is very helpful. I am working on a paper for the tonearm alignment formulas to minimize tracking distortions. I know this horse has been beaten for nearly a century since Loefgren in 1938 and before, but it is not dead yet :) Alex

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 6, 2015 at 19:46:20
John Elison
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 I don't think RIAA equalization necessarily "evens out" groove velocity as much as it balances the disparity between groove velocity and groove amplitude that would otherwise occur. With RIAA equalization, maximum groove velocities are heavily weighted toward higher frequencies, but without it groove amplitude would completely dominate lower frequencies to the extent that playing time would be cut in half and cartridges would not be able to track the grooves. Have you ever seen Shure's measurements for peak groove velocities on vinyl? I've included Shure's graph below.

I'll be curious to hear your thinking on tonearm alignment formulas to minimize tracking error distortion. As far as I know there is nothing new under the sun in this area. Loefgren figured everything out in 1938, but it will be interesting to see what you come up with. I've included a link to my tonearm alignment geometry spreadsheet if you don't already have it.

Good luck,
John Elison


.
.

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 6, 2015 at 20:21:11
safesphere
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 Makes sense. Thanks! On the the tonearm geometry, Loefgren did a great job defining the A and B solutions. However, the problem with A is that it emphasizes lowering distortions at the inner radius at the expense of increasing them elsewhere (although not as bad as Stevenson). Yet a rare record extends all the way to the inner radius statistically resulting in increased distortions for no benefit. In turn, the problem with the B method is that Loefgren did not find the exact solution, but used one of the formulas from A for B. Close, but only approximate.

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 7, 2015 at 00:08:41
John Elison
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 I think you have a misunderstanding of Loefgren's mathematical methods. If you want to nit-pick, you are correct that some of his equations represent approximations, but the difference between the exact solution and his approximations are negligible unless you believe his method of approximating tracking error distortion is less than desirable.

Both of his alignment methods are based on approximating second harmonic distortion from tracking error at a stylus tip velocity of 10-cm/sec by dividing actual tracking error by groove radius and multiplying by a constant. Do you have a different approach? If so, I can assure you that tracking error distortion is a function of tracking error, groove radius, and stylus tip velocity. Therefore, any approach you develop will be an approximation since stylus tip velocity is a dynamic variable and not a constant.

Let me know what you're thinking and I will show you that anything you can come up with is only an approximation. Actually, the pivotal tonearm is the most egregious approximation. Consequently, the only way to eliminate an approximation for tracking error distortion is to eliminate tracking error. This requires a tonearm design solution, not a tonearm alignment solution.

> the problem with [Loefgren] A is that it emphasizes lowering distortions at the inner radius at the expense of increasing them elsewhere

There can be only two points within the playing area where tracking error distortion is zero. Everywhere else there will be tracking error and tracking error distortion. If you look at the tracking error distortion curve for Loefgren A, you will see it has the same amount of distortion at the inner radius as at the outer radius and also at the maximum distortion point in-between the null-points. That's what Loefgren A does. It minimizes and equalizes the three distortion maximums within the modulated groove envelope.

> the problem with the [Loefgren] B method is that Loefgren did not find the exact solution

Loefgren did find the exact solution, but he found an approximation that was much simpler and produced results with well under 1% error from the exact solution. They didn't have computers when Loefgren developed his equations. Here is an example of Loefgren's error for a 230-mm tonearm.

Here are Loefgren's approximated null-points applicable to any length tonearm:

70.3-mm
116.6-mm

Here are the true null-points for a 230-mm effective length tonearm rounded to one decimal place:

70.0-mm
115.9-mm

The error is 0.43% for the inner null-point and 0.60% for the outer null-point. This error becomes smaller for longer tonearms.

I'll be very interested to see what you come up with that you believe is better than Loefgren's approach.

Good luck,
John Elison

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 7, 2015 at 05:33:20
safesphere
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 Yes, I am very familiar with this matter and repeated the math in different ways even before Loefgren's paper went to the public domain. When you state that he found the exact solution and approximation for the B method, what are you referring to? I do not see the exact solution in his paper. He did not perform the variation of the distortions integral by the linear offset, but only by the overhang. So when you give the numbers for the exact solution, what are you referring to? I may be wrong, of course, but as far as I am aware the exact variation solution has been never published.

The math involved assumes the tracking error to be small to simplify the formulation of the distortions integral. Otherwise the integral would not be solvable other than numerically while the difference would be negligible indeed. However, once the integral is defined, it represents an alignment problem that deserves the exact solution after nearly a century of its formulation regardless of how close the exact solution may be to the approximation. I agree that the difference may not be audible, but if it is tangible, such as providing measurably different null points, then people paying big bucks for their tables might appreciate the extra precision :) Plus this is fun and better than solving word puzzles :)

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 7, 2015 at 10:22:33
John Elison
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 > When you state that he found the exact solution and approximation for the B method,
> what are you referring to? I do not see the exact solution in his paper.

You're right! I apologize! You obviously have a better understanding of the math than I. The null-points for the exact solution that I presented were calculated from my own Excel spreadsheet model using Excel Solver in conjunction with numerical integration to find the weighted tracking error curve with the lowest RMS distortion in-between the inner and outer modulated groove radii.

About 20-years ago I developed my own mathematical model to evaluate the pivot/stylus/spindle triangle while solving for the the angle at the stylus using the law of cosines. The complement of this angle represents the offset angle to the groove tangent at the stylus. Tracking error is determined by subtracting the cartridge offset angle from the groove tangent offset angle. Using my spreadsheet model I discovered that the null-points actually changed very slightly with the length of the tonearm. The longer the tonearm, the closer they came to Loefgren's solutions. I concluded that the reason for this was because Loefgren must have approximated the sine or tangent of an angle, such as tracking error, by the angle itself. In other words, sine(a) = a or tangent(a) = a, which are valid approximations for very small angles.

My mathematical ability is more in tune with algebra than calculus. I like to crunch numbers with calculators and spreadsheets. Therefore, I'll be very interested in seeing how you approach the problem of an exact solution. I have found the differences to be very small to point of being insignificant, though.

Again, I apologize for misleading you.

Best regards,
John Elison

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 9, 2015 at 00:24:44
safesphere
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 > Here are Loefgren's approximated null-points applicable to any length tonearm:

> 70.3-mm
> 116.6-mm

> Here are the true null-points for a 230-mm effective length tonearm rounded to one decimal place:

> 70.0-mm
> 115.9-mm

Interesting. I have so far a work-in-progress analytical model that is not yet exact, but seems to be a step forward. It gives:

70.16 mm
116.14 mm

These numbers are closer to your "true" numerical model than the Loefgren B numbers are. I am also in the process of building a similar numerical model as a useful tool to verify the analytic results and build protractors.

There could be two different types of numerical models. A simple one would assume that distortions are reverse proportional to the groove radius. A much more complex model would take a PCM signal of some actual recording, integrate it to obtain the stylus displacement, apply the tracking error, differentiate the result to obtain the stylus velocity, and compare to the original signal to find the total distortions.

If you are crazy enough to try coding this, you would need a formula for tracking distortions of an arbitrary signal. To get this formula, you simply need to replace A*sin(2*Pi/L*x) with arbitrary y(x) in Loefgren's (7). The result is:

z(x)=y(x-z(x)*sin(d))/cos(d)

where
y(x) is the integrated source signal
z(x) is the distorted signal
d (delta) is the tracking error (angle)
x is the space coordinate along the groove

This formula cannot be handled analytically, but can numerically. I bet the result would be virtually the same as of the simple method. Way too much trouble for practically no gain :)

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 9, 2015 at 12:10:34
John Elison
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 Have you done anything to find the true values for Loefgren A? I found there to be a slight error in Loefgren A formulas, too. The approximated null-points are:

Inner null = 66.00-mm
Outer null = 120.89-mm
Linear offset = 93.445-mm.

I came up with slightly different numbers by adjusting the weighted tracking error curve for exactly the same distortion at all three maximums. The true numbers for a 230-mm effective length arm are:

Inner null = 65.97-mm
Outer null = 121.05-mm
Linear offset = 93.512


Loefgren's Approximation
.

.
.
True Loefgren values for a 230-mm effective length tonearm
.



 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 9, 2015 at 19:46:25
safesphere
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Posts: 11
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 Assuming your numerical calculations are precise, your numbers show the error of about 0.1%, give or take. I have looked at Loefgren's A and the only approximation he makes there is in (32) in the very beginning by setting:

cos(f-d)=cos(f)+d*sin(f)

where f is complimentary to the offset angle and d is the tracking error. With the offset angle of 23.97 degrees and the maximum tracking error of 1.89 degrees, the above formula gives the 0.75% precision. So it is very possible that it affects the result by 0.1% in the end. The difference you have is about 0.1 mm, which is about the best you can physically achieve with a protractor, so it doesn't seem a big deal, but is indeed interesting. There is no way to do the math without this formula, so, I guess, a precise numerical model is the only way to get the exact numbers, but even then this may depend on the actual musical content, as I described in the previous post (where I also forgot to mention the RIAA equalization).

My bigger issue with Loefgren A is that it makes no logical sense in the first place. A rare record extends all the way to the minimal standard radius, and minimizing distortions there at the expense of increasing them everywhere else just makes no sense to me, as statistically this substantially would increase real life distortions.

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 9, 2015 at 21:20:54
John Elison
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 > My bigger issue with Loefgren A is that it makes no logical sense in the first place.
> A rare record extends all the way to the minimal standard radius

In my opinion Loefgren B makes no logical sense. It is a rare person who would use the minimal standard radius as the innermost groove for Loefgren A or B when modulated grooves do not exist at that position.

Loefgren B is illogical because it minimizes the area underneath the squared weighted tracking error curve when it is the actual tracking error curve that should be minimized. Why do I want higher distortion in the inner and outer groove area so I can have lower distortion in-between the null-points? That seems illogical to me. I want the lowest possible distortion across the entire playing area and that requires Loefgren A as well as an accurate definition of the modulated groove envelope.



 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 9, 2015 at 21:57:02
safesphere
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Posts: 11
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 Sure, it is a matter of personal preference. The A method minimizes the maximum distortions; the B method minimizes the average distortions. The A method is better for the beginning and the end of the record; the B method is better for the middle of the record. This "middle" is longer by time than these "beginning" and "end" combined, so you get "the lowest possible distortion across the entire playing area" with the B method.

The way I look at this is that with the B method the distortions are larger than the largest distortions of the A method only so close to the end that most records never get there anyway. Statistically across your LP collection you would get a lot less distortions with the B method. However, again, this is a personal preference and exactly the reason why different methods exist. There is no wrong answer here.

The reason squared distortion are used for calculations is because distortions are voltage that you need to square to get the sound volume. In other words, what you actually hear is squared distortions, so it is logical to use them.

Good idea on using a larger than standard inner radius for personal setup calculations, but what "personal standard" would you choose, short of measuring all your LP collection and never getting new LPs? The lowest radius in my collection is 59 mm that is already lower than the RIAA standard. And then I have a few records with 61 mm. So it seems to me that I have little choice, but use the 2 3/8" (60.325 mm) RIAA standard anyway. In fact, choosing a wider standard for the B method only makes it closer to the A method with a more narrow standard :)

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 9, 2015 at 23:26:10
John Elison
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 Okay, you use 60.325-mm and 146.05-mm for your modulated groove envelope with Loefgren's "B" alignment. As for me, I'll use 65-mm and 135-mm groove limits with Loefgren "A" and we'll see which alignment sounds better. LOL!

BTW, if you need a good arc protractor that's free to download, check out the one at the link. It beats anything else out there for the price.

 

RE: Stylus-Tip Velocity relative to Groove Amplitude and RIAA Equalization (Long), posted on March 10, 2015 at 00:26:28
safesphere
Audiophile

Posts: 11
Joined: March 5, 2015
 They match :) Thanks for the link!

 

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