Fidelity Research FR64s Headshell dilemma

Bukanona, I am still not quite sure I understand your point.  Surely you would agree that Euclid, Pythagorus, and the rest have left us enough formulae to deal with any nuance of tonearm alignment.  If you consult the original papers by Baerwald and/or Lofgren, I am sure you would see they relied upon the geometry we learned in high school, albeit maybe not every high school student could solve their problem.  As to the LP with a 1 kHz test tone, are you saying that I can buy such a test LP or that I could have one made?  I chose the frequency of 1 kHz merely as an example of a pure tone that would be a reasonable place to start to measure distortion induced by tracking angle error; it is not a matter of right or wrong.  Cartridge specifications usually list stereo separation at 1 kHz and cartridge output is often measured at 1 kHz. In the event, one might want to make such measurements at 100 Hz, 1kHz, and 10 kHz, and any other frequency of interest in between, I suppose.  It's a matter of how much time and energy you would want to put into it.  It would also be good to interface a computer between the output of the cartridge and the distortion analyzer, so that one could obtain a plot of distortion vs time and translate that into distortion vs location on the surface of the test LP.

Lewm, tonearm isn't a geometrical object it's also a mechanical one.
Yes Logfren and Baeward relied on geometry as we do build models of real world - it's part of science. After making model we do measurement in real life if results are as predicted = we have made good model.

There is services which can do such single sided like this one
https://www.onecutvinyl.com/
As about frequency yes it's a matter of methodology of experiment. I do believe that it can be very interesting topic. 

I think @atmasphere could cut an acetate too :) 
Any pressing plant can do that. 

Dear @lohanimal  and friends: Till today seems to me that other than @dover , perhaps @lewm  and finally @nandric learning on the overall alignment subject all of you still have a different levels of misunderstood and I know that because what you are posted here.

Here we go. Please forgeret about Stevenson or Baerwald existence and be in focus with the Löfgren targets with the cartridge/tonearm subject:

the main tragets were and are to calculates the precise overhang and offset angle for any pivoted tonearm and determine both null points to make the accurated cartridge/tonearm alignment set up.
Those and nothing more were the targets and his alignment exist because of those.

Now, to achieve those targets Löfgren formulas calculations needs only 3 input parameters: EFFECTIVE LENGTH, MOST OUTER GROOVE RADIUS AND MOST INNER GROOVE RADIUS.

The overall alignment calculations needs no other parameter information even Löfgren does not gaves any formula to calculate P2S because it does not need it.
So please forgeret too about P2S, it's totally un-important for the alignment calculations.

Through those 3 input parameters the Löfgren calculations gives us: overhang, off set angle, both null points, linear offset, tracking error and tracking distortion levels.

So the critical in put parametr by the Löfgren calculation is the EL. I posted that the P2S distance is achieved by difference and Löfgren gaves it in this way: M=L-d , where L is the EL and d the overhang.

The null points calculated are a fuction of the inner/outer radius and can change if and only if the inner or outer radius are or is changed. 
Lófgren A and Löfgren B has its own and different null points that are the same ( inside the A or B choosed alignment. ) it does not matters the tonearm EL.

Here the Löfgren direct information:


"""  Using these equations, the
optimum offset angle, the optimum overhang, and the resulting maximum |WTE|
value (the |WTE| value 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 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. ( IEC standard. )
Notation: L = arm length, b = optimum offset angle, d = optimum overhang, WTE =
weighted tracking error.  ""



@chakster  in good shape you need to focus in the Löfgren information because all your misunderstood belongs that you are focus in other " things " maybe in what you read somewhere, maybe in what you suppose, maybe in your wrong supposition that Ikeda-san knowledge levels is to thigh ( that it's not in this subject. ) or maybe because the explanations came from me but it does not matters what you are totally wrong because that total misunderstood.

Now, the overall and main target of Löfgren calculartions is that through his formulas solution we can put the overall tracking error and tracking distortions at minimum for any pivoted tonearm cartridge set up.

Perhaps some of us can't detect those distortions levels but exist and are affecting the cartridge signal quality levels. We have to remember that in all the ling room/system are developed several kind of distortions/noises/colorations and the like, this is that exist an accumulative distortions levels. So if we can put at minimum the ones developed through the cartridge/tonearm alignm,ent set up this means we are in the rigth " road ".

Now, inside any of the alignments ( Löfgren, Baerwald or Stevenson. ) and for each tonearm EL exist one and only one P2S distance to achieve all those targets explained here.
If we change the EL in any alignment or if we change from one type of alignment to other then and always we must change to a new P2S as a result of the new calculations for the overhang and off set angle to take advantages to put at minimum those tracking error and tracking distortion levels.

If with the same tonearm we change from Löfgren alignment to Stevenson with out change the P2S then those tracking error and tracking distortions goes higher. Why?, because the P2S distance is the difference between the tonearm EL and overhang and the change of overall kind of alignment gives us a different overhang value.

So any one of us can make what we want it following the Löfgren targets or our wrong " targets. So ( @chakster  ) you can follow doing the same: does not change the P2S leaving the same no matters what but you achieve overall higher distortions levels even if you can't detect it.

 Stevenson and almost all japanese tonearm designers are wrong when they choosed Stevenson. Maybe they did it because never took the time to see a comparative chart/diagram/graphics where even a " blind " gentleman can see is totally wrong and useless as an tonearm/cartridge alignment. Here again a calculation sample where we can read in the tracking distortion chart that Stevenson has lower distortioons only in the last 3mm of the recorded LP surface and only if that LP has recorded information at that distance/radius, normally 95% of the LP's has not recorded signal at those very inner last 3mm grooves:


https://www.vinylengine.com/tonearm_alignment_calculator_pro.php?arm1=Arm+1&l1=el&a1lv=245&a1=la&oh1v=&oa1v=&arm2=Lofgren+A&l2=el&a2lv=245&a2=la&oh2v=&oa2v=&arm3=Lofgren+B&l3=el&a3lv=245&a3=lb&oh3v=&oa3v=&arm4=Stevenson&l4=el&a4lv=245&a4=st&oh4v=&oa4v=&rs=12&rsv=&og=iec1&ogv=&ig=iec&igv=&cal=y&submit=calculate


This comes from erudite alignment gentleman:


"  As a background note re the 'Stevenson A' alignment. Stevenson's goal was to
minimise (in fact to make zero) the weighted tracking error (WTE) and the resulting
distortion at the specified inner groove radius. However, under the 'Stevenson A'
alignment, the WTE (and the distortion) occurring over about 75 percent of the record
playing time is greater than that which occurs under the 'Löfgren A' alignment for the
same conditions (ie arm length and groove radii). Further, the 'Stevenson A'
alignment is only significantly better than the 'Löfgren A' alignment during the last 3-4
mm of the record playing surface (usually less than one minute of playing time).  """


@bukanona in that link are the measurements you are looking for.

Now that from some years now exist excel tool and several internet calculators where we can take the P2S distance as an input calculations ( like vinylengine. ) does not meaNS IS THE RIGTH WAY TO GO. aS WITH MATHEMATICS ANY ONE CAN MANIPUKLATES THE NUMBERS BUT THAT'S NOT THE WAY Löfgren did it and he is the " inventor " of where all alingnments comes.

One gentleman here posted that for he it sounds better with uni-din alignment using Stevenson. Well the main and critical subjet in the overall alignment subject is not what we like it but the way to make things rigth.

The other " thing " that the cartridge must be straigth in the headshell means nothing at all because the cartridge will be as the calculated parameters say.


Regards and enjoy the MUSIC NOT DISTORTIONS,
R.

I think the key here from Raul is that the P2S mounting distance is specific to the tonearm regardless of alignment choice.  This is what I thought all along.  
So when a knowledgeable person with experience with the FR-64s suggests 231.5 is correct and not 230.0 for P2S, what is this possibly based on?  Actually measuring the EL of his FR-64S arm?  I’m sure someone here remembers what the 231.5 suggestion was actually based upon.