What is the appeal of the Denon 103 cartridges?

Sorry - one more:  That 2x impedance thumbrule only applies to stepup transformers.  If you are using an MC amp stage, it's 10x.  For the DL-103 that would be 400; some inexpensive phono preamps are fixed at 100 ohms or thereabouts.  You would need a soldering iron and a schematic to do anything about that.  My PS Audio Nuwave Phono Converter includes settings for 60, 100, 160, 600 and above.  The lower 3 don't sound good. - maybe "loose" and losing frequency extremes.  600 sounds best; I've lowered it to 400 with a switchbox but it didn't make much difference if any.  Above 1000 or so it started to "thin".

Also maybe unfair to describe Denon 103 and 103 R stylus as simply conical. It is special Denon cut diamond - described as naked square cut. Under microscope it looks like it has been cut to a pyramid with the sharp apex of the pyramid being slightly rounded to sit in the record grooves. Conical diamonds look different under microscope, more rounded and much blunter.

Not sure what you’re looking at, but according to the Denon specs it is 16.5 μm diamond spherical tip = conical.

Yes, it is nude and very well polished

Tubehead, you may have misspoke by accident. The formula relates the reflected impedance as inversely proportionate to the square of the turns ratio. (For a 47K resistor load, a 1:10 SUT will reflect 470 ohms to the cartridge, as you correctly stated. That’s 47K divided by 100.) There’s no need to worry about square roots. It’s been many years since I listened to a DL 103, but I don’t know why such a set up wouldn’t work just fine without any further messing around with the load resistance. Also, I have always wondered, and still cannot understand, why the goal for the load resistance should be any different when you are using an SUT, compared to when you are using a high gain phono stage. Perhaps someone else can enlighten me.

If

# of turns primary - Np
# of turns secondary - Ns
primary impedance - Zp
secondary impedance  - Zs

then

Np/Ns = square root of (Zp/Zs)

Zp = (Np/Ns) squared x Zs

Just Google "transformer impedance ratio" for the above formula.

for a 1x10 transformer, Zp/Zs = 0.1 so Zp = (.01)Zs

As you can see it is simple for 1x10.  You will want to use a scientific calculator app for any other values... it's still not THAT hard.

A coil (the MC) reacts differently to transformer loading.  For an RC  coupled amp we want the the input Z to be 10x (or more) the Z of the incoming signal to avoid distortion and losses due to the RC load that the amp input represents.  To put it very simply, if you matched the impedances you would drop (lose) half of the signal in the outputZ of the source.  Transformer action is not amplification, it is energy transfer and works differently.  A transformer would tranfer max power with a perfect Z match but this would lower the transformer's bandwidth (among other things).

Try it!

Variables and their values. Everybody seems to understand what
''best cart'' means. But is that a fact?  As I mentioned in my previous
post ''better than relation'' imply  comparison, say: x versus y''.
If the value for x is Denon 103 what is the value of y ? ( 3 +y= ?).
This may mean ''some other'' or ''all other''. ''All other'' nobody can
claim while with '''some other''  we can see by mjw 25 7 names 
as values for ''some''. So he is the only one ''logical correct'' 
user of the language of variables. To put this differently the
expressions ''all'' , ''some'' , etc . are not names with referring
function otherwise ''x + 3'' would name some number. 
Variables only mark the place where an name must be put to
make the whole expression understandable.