The spherical stylus (also called "conical") is the oldest stylus design for LP play. It is used extensively and it was the only shape available until the elliptical was invented and manufactured.
The spherical stylus is simply ball-pointed shaped at the tip end. Thus it is a sphere of typical radius= 18 micron (uM) or 0.7mil.
Example of a real spherical - Stanton DJ stylus

Spherical sometimes come in different radii, typically less than 18uM. In this way the stylus can trace the unworn parts of the vinyl groove. A good idea.
The 25uM stylus is made for mono records play. 65uM for 78RPM records.
So, what is the problem with the spherical? It is perfectly explained in this excellent web page by Jim Lesurf:
http://www.audiomisc.co.uk/HFN/LP3/aroundthebend.html
But i will hijack some of the pictures to summarize what is explained on that page.
The problem with the spherical is this:
Left blue spot - 12uM spherical
Right one - 8x18uM elliptical
The diagram shows a 20KHz 0dB groove at the start of the LP side. A very high frequency at a very loud level. The modulation is horizontal (mono).

So, as you can see, the spherical stylus is too big to trace the 20KHz tone correctly. What will happen? The spherical will "jump" or ride the wave "vertically" and thus give "tracing distortion". Specifically we are showing what is called "the pinch effect".
Also note that the stylus on this diagram is of 12uM radius; usually they are bigger - 18uM being a typical value. But also note that 0dB is a very high (loud) recording level for a 20KHz tone!
The stylus at the right, 8x18uM (.3x.7mil) elliptical, fits much better and is not showing that problem. Thus you can see how the elliptical traces better.
In practice this problem does not appear (or it is not significant) at the beginning of the groove. It becomes a problem [mainly for sphericals] at the end of the groove, since the groove angular speed is much smaller and thus things are tighter!!
Here is a 20KHz 0dB at the end of the groove. Again, this is an extreme case; no sane cutting engineer would cut, at the end of the groove, such high levels at such high frequencies, though!!

As you can see, the pinch effect would be extreme with a spherical and would even show with the elliptical, unless we use a narrower (smaller "r" radius) elliptical. Or a smaller spherical [not a good idea], or a more advanced stylus shape...
So what can be done to diminish this problem?? Alternatives for the cutting engineer:
(a) Tracing predistortion/ tracing compensation - while cutting the disk, a "tracing simulator" predicts the tracing distortion that will appear when the record is played, and adds, to the audio signal, the same distortion but in an inverse way so, when playing it with a spherical stylus of a specific radius , it will "cancel out".
Google "dynagroove". Tracing predistortion has been used in many records. If you have a clean, unworn record that sounds notoriously distorted with an elliptical, but sounds very well (undistorted) with a spherical stylus, you can bet it was cut with predistortion/tracing compensation. It will only sound good with a 0.7mil conical. Thus the importance of always having a spherical/conical stylus at hand.
(b) Introduce a strong cut-off (attenuation) of the high frequencies when approaching the end of the record and/or lower the cutting level significantly.
(c) Assume the listener will have a great tracking cartridge with an advanced stylus shape and be happy.
(d) I don't know. I'm not a mastering engineer.
However, again, this distortion will be much more evident:
- At the end of the record (inner grooves)
and
- At loud cutting levels
Returning to Jim Lesurf's article; he uses an estimate of the typical/max groove accelerations found on records (read his articles!) and makes the following graph:

The curves shows what the maximum tip radius can be to safely "read" groove accelerations of a certain "g" (gravities), at the end of the record (red curve) and at the beginning of the record (blue curve).
As you can see, the problem -as i said before- is at the end of the record. But what about gravities? Jim Lesurf writes:
So he marks around 1200g with a green dotted line. That would be loudest level on a typical record. For 1200g at the end of the record you need 5uM (0.2mil) of side radius (r). And, coincidentally, the smallest profiled ellipticals sold are 0.2x0.7 mil!! But those narrow ellipticals also are the styli with the smallest contact areas (not a good thing); narrow profile and great contact area belong to... advanced stylus shapes.Looking back at the results in last month’s article we found that the largest peak accelerations observed were around 1000g. By using these results we can now assess what the demands may be on a replay stylus.
Remember, a typical conical/spherical stylus is 18uM/0.7mil... Check out the graph and you will see that the typical conical will usually have a problem tracing the loudest parts at the end of the record, while performing fine at the beginning of the record.
That's why stylus comparisons should better be done using loud cuts at the end of the record!!
Again, this problem will be more or less noticeable depending on the cutting engineer choices at cutting the record. I have some records (usually from the start of the 60s) that perfectly OK at the inner grooves -- obviously because the cutting engineer knew everybody used spherical stylus (was there other choice before Grado's patent? :wink: ), and thus took care to significantly reduce cutting levels and high frequencies at the inner grooves.
Now, all this analysis has been with horizontal modulation (mono only). In stereo reproduction we have vertical and horizontal components, and things get more complex!













