Retip a Denon DL-103R or buy another one?

Nope, effective mass is not really an accurate description, it's the moment of inertia that we are trying to increase with a low compliance cartridge. That is what the stylus/cantilever is pushing/resisting against when modulating in the groove.
Adding 10 grams of weight certainly doesn't increase the effective mass (moment of inertia) by 10 grams, probably less than half of that.
The formula for calculating effective mass is very complicated. Intuitively you would think that adding 10 grams at the headshell would increase the effective mass by 10 grams but unfortunately it doesn't.
This has been discussed many times on other forums by some pretty smart folks and is very well established.
Here is one such discussion. As you can see, adding 10 grams at the cartridge end adds maybe 3 grams to the effective mass.
Special thanks to chakster over on Audiogon.

Here is detailed explanation of what is Effective Mass, someone posted all that before, i will just quote again:

"So effective mass in not mass - it's inertia! In fact, even the common measurement (in metric grams) is a misconception. This is brought to you here, by the tonearm manufacturers, as a curtsy to the layman. Effective mass, like any inertia, is measured in Kg/m/s2 (that is kilograms per meter per second squared). Since we're talking very small mass here - everything is divided by 1000 and so we're actually dealing with grams per millimeters per second squared. The general em formula relationships are manipulated such that we're left with grams only - but nevertheless it's Inertia!!!. Keeping that in mind it's easier to regard effective mass for what it is.

Another misconception is the relationship between 'effective mass' and mass. If you add 1 gram to the tip of the tonearm you do not add 1 gram of effective mass to the tonearm No way Jose!. You do not add a 1/3 or a half - none of it catches here. So, how much do you add? Well, that cannot be described in English, it can only be described in a math equation. This is what it looks like:

M(kg) = m(r²/L²) + (Z/3)

m is the counter weight mass
r is the counter weight distance from the pivot
L is the effective length (pivot to stylus tip)
Z is equal to twice the mass of the front end of the tonearm at the effective length. Your headshell mass is part of 'Z'.

M is the effective mass and the whole thing is in kilograms but it doesn't matter. This is just to demonstrate why the relationship between mass and effective mass is not as straight forward as one might think.

L (the leverage or effective length) will affect the importance of the real estate the most. In other words - the tip of the tonearm is the most strategic location where mass can affect inertia. Adding just a tiny amount of mass to that specific location might, just as well, be equivalent to the total effect the counterweight has on the effective mass of the tonearm. It's that important! This is where 'r' vs 'm' in the formula kicks in.

Having said that... movements of the counter weight back and forth across the back of the tonearm seldom changes effective mass by any significant amount. It's typically punched in and pre-calculated into the specs of the tonearm and it's a generic part of the given effective mass."

On Edit: the formula above is a very simplified version as it doesn't take into effect all of the components and mass measurements along the radius of the tonearm. The thing that really stands out on this dumbed down version of the formula is +(Z/3). So any change in mass at the end of the tonearm is divided by 3.

BillWojo

 

Here is a more comprehensive formula from Reed tonearms web page.

The main criteria for designing, producing and choosing to buy tonearm are often wiring (internal and external), connections, and effective mass and geometric dimensions of tonearm which is clearly very important. However, there are some other criteria, such as tonearm moment of inertia (It) and acoustic resonance characteristics, which are often left out while they should be considered as well.

It is the sum of cartridge moment of inertia (Ic) and counterweight moment of inertia (Iw).



It = Ic + Iw



Even with smallest LP twist or miscentering, It would affect VTA (Vertical Tracking Angle), SRA (Stylus Rake Angle) and VTF (Vertical Tracking Force) of tonearm. It influence on VTA, SRA and VTF causes distortions that are subjectively heard as detonation. The frequency of distortions varies from 0.5 Hz to 20 Hz and can be up to 0.5 %.

To reduce these distortions, usually damping systems are used. Both mechanical and magnetic damping systems are complicated and quite expensive. However we suggest reducing It, which is the main reason of distortions, first.

Moment of inertia depends on mass and square of distance formula.

Research shows that Iw can be reduced by increasing the mass of counterweight and pushing it towards the bearings. The mass of counterweight can not be highly increased because the bearings will get overloaded and that will cause friction problems. In order to minimize friction sapphire bearings with tungsten carbide points are used. These bearings rest sphere on sphere (both spheres having different radius). Clearance of bearings is not possible because it will cause azimuth and VTA errors and make additional distortions. For this reason constantly loaded bearings should be used.

Ic can be decreased by:

1) Reducing effective mass. Effective mass of tonearm can be reduced by changing the material of armtube. Tonearm should be matched with cartridge so that Tonearm Resonant Frequency is 10 +/- 2 Hz. Therefore, effective mass of tonearm must be within certain limits.

2) Reducing effective length of tonearm. Decreasing the length of tonearm to less than 9” increases tracking error distortions. On the other hand, if the length of tonearm is more than 12”, the distortions caused by It become more significant.

Statics of tonearm (static position) can be expressed by the following equations:







where

mc – cartridge weight,

mch – head shell weight,

mat – armtube weight,

lef – effective length,

lw – counterweight section length,

mw – counterweight weight,

mwh – counterweight holder weight.

Because Iw should be (and usually is) at least 10 times smaller than Ic, for approximate calculations we should examine only Ic:







where

mc – cartridge weight,

mef – effective mass,

lef – effective length,

Ic should be less than 20 000 g×cm2.

As you can see, it get fairly complex.

BillWojo

 

Agree fully that it is moment of inertia that we are talking about. But I'll agree with John
Elison on this one.

Good explanation! I'm impressed! - John Elison - Vinyl Asylum

RE: DL-103R stuff - John Elison - Vinyl Asylum

Won't be exact, but it's going to be very close to what you add in a/the headshell weight.

 

Some strive for perfection, others,,,,,,,,,,,,,,,

 

That explanation is totally wrong. Sorry. Look at the formula for moment of inertia that I posted above. Use the simplified one, it's fine for this discussion.
Plug in the numbers fot your tonearm. All John is doing is a simple balance equation, we need to know the moment of inertia, it's what the stylus is resisting.

BillWojo

 

I just took a look again at the simplified equation Bill and you stated above that:

"The thing that really stands out on this dumbed down version of the formula is +(Z/3). So any change in mass at the end of the tonearm is divided by 3."

But the instructions given regarding the equation state that: "Z is equal to twice the mass of the front end of the tonearm at the effective length. Your headshell mass is part of 'Z'."

Therefore you're not taking a change (increase) in mass at the headshell and dividing by 3. You're doubling it first and then dividing by 3. That's a big difference. A 3 gram headshell weight if placed above the stylus should then result in an increase in effective mass of 2 grams on a 12 gram effective mass tonearm, not 1 gram.

The end result factoring in either a larger counterweight or one that is extended further to balance out the increased mass at the stylus point and the resulting increase in effective mass from that should take you much closer to a one to one ratio when it comes to mass added to the headshell vs increase in effective mass.

Maybe I'm missing something?

I'd guess that, in the end, there wouldn't be much difference between John's calculations and the one you posted.

 

I've been enjoying a few days with the VAS Ebony, a Denon 103 in a wooden body with an eliptical stylus. I felt a standard 103 in a wooden body could be a good compliment to my 103R in the metal body. The only problem is while it has a great tone as is, I'm curious as to how it would sound with the sapphire/micro ridge setup.

Note the cartridge is shown attached to an Ortofon LS-2000 headshell (15.5g), total effective mass was calculated by brazenly adding headshell weight to tonearm effective mass per manufacturer suggestions, flagrantly ignoring all math and science.

 

How does your DL-103R and wood bodied DL-103 compare? VAS does excellent work, I'm lucky enough to have him only an hour away.

BillWojo

 

I no longer used modified Denons but did use them for about 5 or 6 years. No experience with the stock 103 but rather with 103R's which are mainly purported to be mainly a bit more extended and less "rolled off" in stock form than stock 103R.

So over that time period I used:

1) Stock 103R
2) 103R in Ebony body
3) 103R in Clavellin body
2) 103R in Ebony body with Soundsmith level 2 ruby cantilever and line contact stylus
3) 103R in Ebony body with Soundsmith level 3 ruby cantilever and OCL stylus
4) 103R in aluminum body with Soundsmith level 2 ruby cantilever and line contact stylus

All of them used for about 800-1000 hours with the exception of the clavellin body, which I did not like that much. It sounded a bit lightweight and tipped up compared to the ebony body, which proved to me that all woods do not sound the same.

In comparing the ebony and aluminum bodies both with the same stylus and cantiliver, however, they were pretty similar and I honestly felt them to be pretty similar to each other; the ebony might have given a very slightly warmer presentation with the aluminum perhaps a touch more dynamic, but there was not much in it between the two and the beauty of the aluminum bodies is that they can be found very cheap and there is zero risk of stripping threads on them. So I still have an aluminum bodied 103R here as a spare/backup, although I haven't used it in about 4 years.

A good body will radically improve the cartridge-there is no doubt about it. But moving to a better cantilever (ruby, sapphire or boron are all substantially better than aluminum in my opinion) and a more sophisticated stylus profile will get you much, much more out of the cartridge as well. On a percentage basis, probably a bit more than the body change. So if I had to say that a rebodied, retipped 103R gave you a 100% improvement I'd say that about 40% of that improvement would come from a good body and about 60% from the improved cantilever/stylus combination.

I didn't use sapphire on my 103R's but have used it on another cartridge that I had retipped which also had an aluminum cantilever originally: namely an Ortofon MC 20 Super, and I've also used a boron cantilever with microridge on another MC 20 Super as well as an Accuphase AC2 that I've had rebuilt.

A better stylus (line contact or MR) on the Denon in a good system is going to dig out a whole bunch of detail and information in the midrange that the Denon conical simply misses. It's really surprising when you first hear it. Dense and complex musical passages, instruments, back up vocals that you just didn't realize were there with conical suddenly show up with a more sophisticated stylus profile. Bass and low frequency info is probably a bit better defined, but it's in the midrange and high frequencies that the better styli really show you what you've been missing. As well as the increased detail and info in the midband, the better styli will give you much better reproduction of high frequency info. High frequencies sound a bit crude, splashy and ill defined when you compare the Denon conical with a good line contact or microridge.

So if you like what the bodies have done, which I would expect that you would, a better stylus and cantilever will give you even more and really take the cartridge to the next level. But it is starting to get a bit pricey, unlike bodies which can be done on the cheap. When I was rebuilding my 103R's you could do a ruby with line contact for $250. Now it's up to $350 and $400 for the OCL and $450 for boron with a good stylus. Sapphire with LC or microridge is probably the sweet spot in terms of value anymore, but I prefer boron to either sapphire or ruby, finding that it's probably just a touch more neutral, a bit quieter in the groove and providing a mid hall kind of perspective as opposed to slightly more front of the hall or front row with
ruby and sapphire.