What is the appeal of the Denon 103 cartridges?

I know they have been around years. However, I see many music -gear reviewers with super expensive turntables running the Denon 103/103r. I'm thinking of trying one myself, possibly one of the ZU adaptations. 
I think many owners of the super expensive turntable can actually find/use reasonably priced cartridges instead of the multi-thousand dollar items promoted in high-end community by the manufacturers and reviewers. 

The problem is that most of them (unlike Denon) have been discontinued in the 80's, but Denon is still in production since the late 60's and the price is very low. 

Some other amazing cartridges from the 70s/80s era are rare and not easy to find for majority of audiophiles that also don't like to take a risk of buying used vintage cartridges, so the Denon for them is a chance to use a vintage cartridge made today for under $300. 

For others it is a business to offer their tweaks/mods for the same cheap cartridge to make it actually expensive (like Zu versions) and a little bit better. Or those companies that can offer same Denon with exotic cantilevers (instead of cheap aluminum) and better profiles. Almost everyone agree that tweaked is much better than the original, so i believe the result of different body, different stylus, different cantilever is a proof that original Denon is nothing special.  

Another example is Ortofon SPU, but the company produce so many versions by themselves instead of giving that option to others. 

Both are classic, old school low compliance monsters for heavy tonearms, originally designed for radio broadcast (like Denon). 

What i don't understand is the reason to invest in cheap Denon for all that special tweaks if man more (much better cartridges) available in its original form with superior cantilevers, diamonds and overall superior sound without any tweaks (just like designers made them from the start). Even some other old low compliance monsters with aluminum cantilevers are much better than Denon , for example Fidelity-Research FR-7f and fz. Also some MM/MI cartridges are better than Denon 103 at the same price category. 

But the Denon and Ortofon have a reputation, some others from the 70s era are just unknown for majority of people today, because they are rare.

Anyway for the price of $250 for 103 it is easy to try without big loss. 

But my advice is to learn a bit more about Conical stylus profile utilized in Denon, because this is the worst profile ever.   


- they are inexpensive (for a moving coil)
- pretty darn good at what they do - very musical
- and easily modified.

I started with the 103 and found it very nice. The price made it attractive for my first foray into the world of moving coil

I had used several other MM/MI cartridges from Rega and Nagoka, but preferred the sound of the stock 103

Like you I read many articles and decided to look at the various mod’s made by different people, Zu being one of them

I now have a Soundsmith modified 103 that I purchased directly from Soundsmith.

It allowed me to see just how good the basic design can function with a little "help"

The model I have has a ruby cantilever and an Optimized Contour Contact Line stylus, which provides much more detail and crisper dynamics, without affecting the overall tone and musicality attributed to the original 103 cartridge.

There is a guy in Italy that goes to extreme lengths by nuding the cartridge, rewinding the coils and replacing the cantilever/stylus to make it a top performing cartridge for a fraction of the cost of it’s competition.

My cartridge did require some additional mass to match the Rega Style arm on my TT, so I epoxied a brass plate to the cartridge, which really made the cartridge shine.

Here’s a little more detail on my Brass Plate tweak

@chakster is correct about the conical stylus being a poor profile, however, if you play lots of old albums, the conical stylus being less detailed than more modern profiles, can make for a more enjoyable listening experience.

Is it the best cartridge for the price? - I stopped looking for Cart’s when I heard the improvements of the Soundsmith mod’s

- it’s an affordable and musical first cartridge for "Moving Coil Virgins"
- the "engine" is very good - neutral but musical
- you can use VTA to fine tune the overall sound
- it’s very easy to setup/align
- lot’s a companies provide excellent mod’s
- it can be made to perform to the levels of much more expensive brands
- a lot is known about this cartridge

- It requires carful matching to the Arm - but most cart’s do
- Conical Stylus - elliptical would have been a better choice
- aluminum cantilever impacts the full abilities of the "engine"
- the plastic housing of the cartridge needs to be stiffer - like the ZU

When you delve into the ZU version of this cartridge, they basically
- use the best standard 103 cartridges from Denon
- add more mass to the cartridge with the aluminum shell
- the aluminum shell also ens the mount for the "engine".
- BUT - they DO NOT address the cantilever issue or the stylus profile
- For the Zu price - I believe  the Soundsmith options would be better and more affordable

If the mass of regular 103 or 103R is suited to the arm on your turntable, then I would recommend opting for a standard cartridge and getting Soundsmith (or similar company) to replace the cantilever/stylus with a better option.
Soundsmith used to offer other tweaks specifically for Denon Carts - so drop them an email to see what’s currently on offer

One thing to consider - as you progress to the more advanced stylus profiles you will need to exercise extreme precision when aligning the cartridge - you will require some kind of mirrored protractor, like the Mint Best Protractor - the paper variety will not be good enough.

FYI - I still keep my first 103 (with brass plate) around - for when I have to send my existing cart back for "re-tipping"

Hope that helps - Steve
If you like the beauty and soul of real music then the stock 103 is the real deal.  A little more Hi Fi then 103r.  If you want alot more Hi Fi this forum will give you all kinds of reasons to buy something else.

This is the one industry that took a bunch of wrong turns for profit and graph results.  Another great product from the good old days Quad 57.  Of course not cheap.  And those shitty dht tubes and transformers etc...

I would suggest reading up on the reviews and notice how many people would state, " Well it was not the most detailed but it was musical and enjoyable".  

Enjoy the ride
The Denon 103 series are a proven and reliable signal source that will give you 90% of what is in those vinyl grooves! And for that last 10% be prepared to pay around 10X the cost of a 103!
Plus the fact that they are still available factory-fresh (unlike other mc cartridges of yore) makes them very appealing to the budget-concious audiophile!
My favorite version is the 103D - higher compliance with an elliptical stylus and tan body. I have one along with a gold body anniversary edition, plus a new 103R and several 103's.
The appeal is they provide rock solid  sound for reasonable cost in the right setup.

I’m reminded of that every time I fire up my 103R mounted on Linn Basik tonearm on Linn Axis table.   
Post removed 
I have the 103R on the Pioneer PLX1000 TT. I use it with a Denon SUT into the Robert Grodinsky Research RGR 4 preamp. Noise-free wide dynamic range sound quality!
I think that a major factor in the quality of this cartridge is that it is very consistent and repeatable. No variation in the manufacturing process means you know what to expect. This is not true of some of the very expensive cartridges. A very good value, but I wouldnt say 90% of the best, but then again I hate these type of statements.
The predecessor of DL-103 MC was DL-107 MM designed for NHK broadcast. I bought NOS for about $250 and it was also impressive, but only until i bought much better cartridges for a little higher price.

When someone telling me this is "real music not a high-end" it is always sounds like "yeah i want to hear real music and to be closer to the soul of music". Unfortunately it has nothing to do with reality. I believe the rolled-off sound of Denon and its conical tip can be ok in some super high resolution (or harsh) horn based speakers or something like that, when the owner trying to avoid high resolution cartridges because of some personal preferences (to get rid of detailed airy highs and deep bass etc).

It’s like telling people to stick to the 78rpm and a gramophone, for some of them this is the heart of music, not a high-end. Not for me.

I bought conical Ortofon SPU because i expected i will get something special, i already had a very expensive modern high-end cartridge at that time in my ex tube based system and full range high efficient speakers from Zu Audio (upgraded Druid mk4).

I was very disappointed in sound of Ortofon SPU with conical tip. Compared to my ex ZYX Premium 4D it was such a downgrade and i could not stand it, it was extremely boring to listen any old record with Ortofon SPU, but i expected it could be better (no it’s not better).

Ortofon is better and more expensive cartridge than Denon, but still nothing special. I’ve been using them on Thomas Schick tonearm designed for those cartridges and a phono stage for MC with bult-in SUTs. Later i tried to return to the SPU and discovered Royal G mkII with Replicant 100 stylus - this was the best SPU i have ever heard. Prior to that i tried SPU Spirit (limited edition) and it was also so much better than conical SPU.

I think my ex Denons and Ortofons are on the lower side while the ZYX is definitely on the higher side in everything including the astronomical price.

But after years of my own research i prefer something in the middle and when we’re talking about low compliance MC cartridges at moderate price there are many of them in $500-1000 range, all of them are from the 70’s era. I think this is where the musicality really is, but with correct reproduction due to many advantages in cartridge design, better cantilever and superb stylus tip.

The superiority of Denon 103 or 103r is the biggest myth in audio (imo).
They are so easy to find new and this is the reason people are talking about it.

P.S. My favorite low compliance LOMC cartridges are: Miyajima Kansui, Miyabi MCA and Miyabi Standard, Fidelity-Research FR-7fz i also enjoyed Klipsch MCZ-10 Ruby and Victor MC-L10 just to name a few.

Actually, i have had many LOMC cartridges that disappointed me, but fascinated some other people for some reason. So we’re all different and it’s a matter of taste and sometime a lack of experience with something special.

On MM/MI side you know my preferences: AT-ML180 OCC, Grado Signature XTZ, Grave LEVEL II, Grace F14, Garrott p77, Glanz MFG-61, Victor X-1II and many others.

After buying and try one out I have to agree with chakster on this it’s ok for the money but imo not worth spending more money to make it better when you can spend the same total and get better yet still with another cart . It’s just a great entry level mc cart that’s been around for a long time because it’s good for that price point. 
glennewdick -- yeah, like it is with many others, my Denon 103 is long-departed.  First and foremost, I could never get it to track, especially through the inner grooves.  It drove me nuts, too, that even when the Denon did track the inner grooves it lost fidelity on 'em.  Actually, the only place it sounded prime was in the middle of a side.

My first replacement for the 103 was one of their newer models, I can't remember which.  It tracked better if not superbly.  It also didn't have quite the magic.  Later, in a fit of madness, I got myself a Shure V15 with the dynamic stabilizer. Not the highest of fidelities but, man, it feared no lp side, no matter how edge-warped.  It flawlessly tracked every 45 in my three foot long collection of 'em. 

Anyway, cut to the present.  I'm now eminently satisfied with my Lyra Delos.  It tracks everything with ease and class...though I admit to be super-paranoid about using it on anything truly whiplash-warped.
I had one for years.  It was warm, and enjoyable, much in the way that Grado's can be.  Like most cartridges, setup is the most critical - and probably means more than what one starts with as a hunk of diamond, metal and who-knows-what.
And, int he grand scheme of things, cheap.
I could listen for long periods and enjoy it. But more i wont say since it was many years ago.
Don't under-estimate a Grado Black or Green either.
Oh yeah.  I remember my Grado!  Could've easily have lived with it for the rest of my days. I even met Grado at a hifi show.
By audition, the Hana EL (at about the same price level) is better. You may wish to learn more about this amazing cartridge. 
Don’t under-estimate a Grado Black or Green either.

Comparing cheap Grado Black (or Green) to expensive Grado Signature XTZ anyone can understand why the cantilever and stylus profile make so much difference in sound. The difference between lower and upper range of Grado cartridges is huge. When a cartridge designer is making his top model it must be (and it really is) superior to the entry level models. But those models looks almost identical and even styli are interchangeable.

For the same reason anyone who paid a lot for an expensive cantilever (to replace Denon stock DL-103 cantilever and stylus tip) are all claimed the upgrade in sound quality is obvious.

Don’t forget that Joseph Grado invented first Stereo MC cartridge and patented it. But he’s making an MI cartridges simply because they are better almost in every aspect. His top Signature XTZ was $750 in the 80's. 

I had a Hana EL. Nice sound though far less dynamic than a modded 103. My favorite 103 recieved a new JVC aluminum cantilever with nude shibata and Stanley Engineering closed Cocobolo body. Just lovely sound. 

My all time favorite carts however are as follows 

1. Audio Technica ART9
2. Klipsch MCZ-7 (retipped with ruby cantilever + micro scanner II tip)
3. Phillips GP922 (FGS special retip
4. Supex SD900 Super (shibata retip)
5. Grace F9 (boron cantilever,  micro ridge tip)
6. Fidelity Research FR-7
7. Fidelity Research FR-1 Mk3F
Thanks. Currently I'm enjoying my AT VM540ML. Tracks nice and a good general "all arounder". I play everything from 40's 50's Jazz-Big Band, Classical and 50's-90's classic rock. Vintage records that are not in perfect shape play great. 

I have been thinking for a while to upgrade to the ART 9 and keep the 540 for less than stellar recordings. I have a Technics 1200GR so switching headshells and adjusting tonearm would be a breeze. 

I think each cartridge must be good or bad in its original form, each time someone changing a cantilever from one to another the result is a different cartridge and the sound is not as expected by the designer of the original cartridge. Some people think they are always smarter than cartridge designers or they think their re-tippers are smarter than people who actually design cartridges. The problem is that a cartridge is not good enough, simply not the best model or does not sound as expected. 

Many cartridge designers explained why it can be a disaster, refirbishing is very bad idea for almost any high class cartridge. For a low class cartridge it can work, but If a cartridge is not good then it can be replaced by a much better cartridge, no need for frankenstein that retippers are offering. 

Stick to the original cartridge and if you don't like it buy another original cartridge. This process can take entire life, because hundreds of great cartridges are on the market (lomc, mm, mi, moving flux, strain gauge etc) and you never know what you like until you will buy it! Some carts like IKEDA or Decca does not have a cantilever at all. 


Had a 103D and a Zu modified 103 and honestly, while I could certainly enjoy music with either, neither one was anything special and the Zu definitely wasn’t so much better than the standard 103D to be worth the additional price.

For the same money there are Audio-Technica cartridges that sound more enjoyable (to me), and though many would love to believe that there is some special inexpensive cartridge that is equal to or better than the multi-thousand dollar cartridges that’s pretty much a wishful thinking myth, in my experience.

Good to consider articles at this link: https://www.stereophile.com/content/denon-dl-103-phono-cartridge
From years past. 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. 

Denon 103 and 103 R can sound best in wooden bodies, with appropriate tonearm mass.  Set-up is important, but value for money is very well rewarded.
The compulsion of language and grammar. The ''S is P'' sentence form. Aka ascribing properties to specific objects. But we
can't say anything about any cart without comparison with other
carts. This however imply relationship between objects. For
relations however the ''S is P'' sentence form is not suitable.
''Brother'' for example does not describe any object or subject
but refer to an family place in a  family ordening. Or, to put
this otherwise:  ''better than...'' relationship assume comparison. 
IMHO it takes a heavy arm for that low compliance (I use a Jelco 750 for them).  Proper use of a step-up transformer really helps as well, and there is a lot of disinformation around.  Some hints:

 1) a transformer has no set impedance; it reflects the load impedance back to the source as a function of turns ratio.  There are calculators on line. 

2) You lower the load impedance from the MM's typical 47k by adding resistors in parallel.  Some people solder resistors across RCA plugs and insert them into Ts at the preamp's MM In.  Others find or make a switchbox for this purpose.

3)The thumbrule for desired reflected impedance at the cart is to start at 2x the DC resistance and go up.

4) For a DL-103 (40 ohms) you want to start around 80 ohms.  A common turns ratio for use with DL-103s (and others) is 1x10.  A 47k MM input would reflect as 470 ohms; we need 8k, to reflect as 80.  A standard E96 1% value of 9.76k in pararallel will give you 80.1.  I usually wind up at about 100 ohms (Denon says >100); 12.7k yields 99.98 ohms.  15.8k yields 118 ohms...

A caveat:

The reflected impedances only work that neatly (factors of 10) for 1x10 transformers - there are square roots in the formula.

All vintage Denon SUTs are 1x10 or have that option via switch.
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.

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


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. 

Denon square cut spherical is different to conical. DL103R paper spec that come with cartridge describe as 0.2mm square solid diamond.  Specs for conical styli are around 0.4 to 0.6. And the specs for a common elliptical cartridge are 0.3 x 0.7.  The Denon diamond cut is their own. This contributes to cartridge good sound on 103 and 103R.  This is not conical diamond they use. 
If you want to look at the proper diamonds then check this.
This is what the most important.

If you think the Denon is a bit closer to Elliptical (while everywhere in documentation it is still described as Conical, not Elliptical) then i want to remind that Elliptical profile is also nothing special and can’t compete with accuracy and life span of the Shibata, LineContact, MicroLine, Micro Ridge, Stereohedron, Replicant-100, Gyger and VdH.

Compared to all of them an Elliptical tip is just an entry level (Conical is the worst).

Denon 103 was invented in 1968, before some of the best profiles appeared on the market.

At that time all carts were Conical/Spherical, not even Elliptical as far as i know.

Quadraphonic records and Shibata profile changed everything, but it was in the 70’s, not in the 60’s.

A high compliance MM cartridges changed everything in the industry in the 70’s.

And you will never find any audiophile cartridge even with elliptical profile today. All the best carts comes with best profiles, not with the worst profiles.

Your Denon 103 today is just like the Denon from 1968, same stylus profile. This is oldschool cartridge.

But Denon designed much better cartridges with different styli, those carts are better than DL-103, but you can only buy them used or NOS, so people prefer not to talk about it, ignoring the fact that Denon made much better cartridges than earlier DL-103 which is probably the best seller. Remember DL-S1 or DL1000 ? 

But again, some people still listening to 78rpm on gramophones and enjoying it too.

Chakster  DHT tubes  go back to at least the 30's  transformers even further.  I am guessing  you are not a musician  who has played in bands and orchestra's.  My objective  is easy, I like the sound of real live music.  Black backgrounds, air around instruments,  super tight bass, sound stage, etc...  are audio file terms.  Attack, decay,  pitch, tone, vibrato, body are  musician terms.  Go to a live performance  which is not using amplification and close your eyes and listen to a bass play even electric bass.  How tight is it? Then listen to a drummer  does the cymbal  sound like wood/plastic hitting a piece of brass or some tilted up sound which hi fi people  seem to like.  Maybe a simple test is to sit near a grand piano and does it sound WARM  and inviting  or NEUTRAL  and detailed?

In regards to your total discuss  for denon 103's my question is how many arms did you try.  How many step up trans and loads did you try??? How many phono pre  amps???  Etc...

I bet my 16 inch silicone damped Brazillian  rosewood arm with my 103 / 103r/ 103 wood / alum body etc...  On a 50 pound platter with a 3 phase 50 watt motor / controller,  does not sound like a 78 on a gramophone. 

Enjoy the ride
Chakster DHT tubes go back to at least the 30’s transformers even further. I am guessing you are not a musician who has played in bands and orchestra’s.


Right, i am not a musician, but i have a piano on the left of my system and i can compare the sound coming from my real piano to the sound coming from recorded piano in my system. My system has tremendous dynamics (with 101db high efficient full range drivers). I’ve been there with very rare NOS tubes, and when i completely removed all the tube gear from my system it became superior with First Watt and Pass Labs amplification. Here is the latest image of my system. However, i must say i do not swap gear as much as i swap cartridges and tonearms.

Tubes are nice to look at, some killer First Watt amps does not looks so attractive as this system i put together for a friend or as good as my ex system. But everybody knows that First Watt amps are very special and each of his amp is unique, i am using current-source F2J for crossover-less speakers (full range drivers). All the rarest telefunken military 60s tubes in my ex triod push-pull amp blown away by First Wass F2J. I do love to experiment with better tubes with and some single ended tube arms if someone will give me $10k just for fun, the First Watt gear is cheaper and better, more convenient in the modern world, the sound and resolution is fantastic, if i will ever buy another amp it will be another First Watt, probably SIT-2 or something like that.

In regards to your total discuss for denon 103’s my question is how many arms did you try. How many step up trans and loads did you try??? How many phono pre amps??? Etc...

Way too many that i can even sell a half of them. For my favorite low compliance cartridges as the moment i have Ikeda IT-345, FR64s with B60, FR-64fx with n-60. I have enough SUTs, Headamps, Phono Stages, Turntables, Tonearms to properly match my cartridges, i tried over 50 samples in the last 5 years or so. I want to tell you that i love vintage cartridges, but not Denon 103 or 107 and not the similar conical SPU, because they are inferior to almost everything i have tried and i explained why. I have also mentioned my some of my favorite cartridges in earlier posts here and if you like to hear something special i will tell you just one that will blown away almost everything: Fidelity-Research FR-7fz from the 80’s (also low compliance monster, so it can be used on those heavy tonearms where you can use Denon 103). Last night i’ve been listening music with FR-7fz connected for the first time to my new 47 Labs Phonocube (also current injection phono stage) and i was blown away, it was better that all the SUTs and Phonostages i have been using before.

Maybe when i tried my SPU and Denon my system was not as good as today, but it was a great system anyway, i have much better cartridges today and i just don’t understand all the hype about Denon 103. it can be a good cheap cartridge, but even with the money people spending of DL-103 i would buy superior MM/MI cartridge instead. Some people are too lazy to learn and to try something different. Only comparing one cartridge to another we can say something about each of them.

I bet my 16 inch silicone damped Brazillian rosewood arm with my 103 / 103r/ 103 wood / alum body etc... On a 50 pound platter with a 3 phase 50 watt motor / controller, does not sound like a 78 on a gramophone.

I hope so, but the cartridge design significantly improved during the 70’s/80’s era, no doubt. I think i explained why? So if you like vintage sound you will find the best in this era, not in the 60’s when it comes to phono cartridges. I agree that old tubes are great, but cartridge is different. Learning a lot about cartridge design i do not see any single reason for use a Conical tip unless you like rolled-off sound.

Dear @aberyclark : Please do it a favor and let here the 103 gentlemans lovers and go for that ART-9 that's a very good quality performer.

You can't go wrong with it and I'm sure you never look back with it.


Regards and enjoy the MUSIC NOT DISTORTIONS,
Tubehead, The formula in the form you quoted is the same as mine, except you start with the end of my calculation.  It's just algebra.  But 99% of the time, one is going to use the formula starting with a known turns ratio in order to determine the reflected impedance across the transformer.  If you start with a known turns ratio, you square it (obviously), e.g., a 1:10 turns ratio will reflect an impedance which is equal to the resistance across the secondaries divided by 100 (10^2).  So, in that use of the formula, there is no need to take the square root of any number, albeit the square root is available rapidly with any decent calculator.  I agree that we really have no argument here.
Now, can you tell me why the "rule" for loading is 2X for a SUT and 10X for the pure resistive load of a high gain phono stage?  What's also odd to me: I have only ever seen this reasoning used among those who use the Denon DL103 series of cartridges.
Listening to my Denon DL-103S on a newly acquired JVC QL-A7 TT through a Denon AU-320 SUT and it sounds fantastic. Very musical is the best way to describe it. Lots of detail as well.
The DL-103S is described by Denon as a special elliptical but some say it's a micro line cut. Back than "micro line" was trade marked I believe. 
Anyway, it's a keeper.
Currently I'm enjoying my AT VM540ML. Tracks nice and a good general "all arounder"
@aberyclark I have a AT VM750SH and while a good all-rounder, my cheapest Decca (Grey Export) blows it away. You can pick one up for around $700-$800.
What does either of those two cartridges have to do with this discussion?
@billwojo If you were paying attention, I'm replying (and quoting) directly to the OP.
Different religions assume different beliefs. The same apply for
this question. The English saying is: ''I am not rich to buy cheap
stuff''. The other say: ''no better deal than bargain''. 
I think the 103 is a great cartridge.
I currently have 2 on a 2 armed Artisan Fidelity Lenco.
one is stock except for a Nasotec aluminum body. The body cuts down on extraneous resonance and most importantly makes mounting much easier (no nuts required). This cartridge is mounted on a Fidelity Research FR64S, which I have found to be the perfect arm for the very stiff Denon.
 The other is a fully kitted SoundSmith “Gold” , which has a wood body, brass top plate, ruby cantilever optimized line contact stylus.
 The suspension has also been modified to be higher compliance.
 It is mounted on a Analog Instruments Seggwan arm. This is a 12”cocobolo unipivot.
both are feeding SUTs: one is a Ypsilon MC16, the other is a DIY 15x Shure transformers. I swap SUTs and phono preamps from time to time.
cut to the chase:
i prefer the stock one.
 The stock lacks the detail of the Gold but it makes up in body and richness. I have found that correct azimuth makes as much difference with the spherical as it does with the LC. Once you achieve perfect phase angle the details are quite excellent and the body is superior.
 I still like the hot rod gold; on Ac cappella choral music it has a immediacy that is quite seductive. Smaller group pieces such as string quartets and lieder are sublime. 
consistent build - very good left right channel balance
good sound as standard - there's nothing offensive about it
good value
re-tipping transforms them
you don't have a heart-attack if you do damage it
you just don't obsess and simply listen instead of waiting for high end fireworks
The stock Denon is not calibrated for perfect channel balance, for this reason Zu Audio calibrate them to select and sell the best samples with perfect balance.

Re-tipping make no sense, because a brand new cartridge cost less than re-tip alone. 

At higher price better vintage MC cartridges available with better styli and better cantilevers, as a result much better sound. Investment in Denon make no sense for this reason, refurbishing make no sense too. Some people just love to mess around with them, in the end the overall price is way over some other nice MC cartridges that does not require any mods at all.