Koetsu compliance compatibility issues

No one is likely to have the breadth of experience described by Syntax. However, my Koetsu Urushi, which seems to be at least a bit higher in compliance than your Black, ran well in my Triplanar (effective mass = 11 gm) but is even better in the Kenwood L07D tonearm, with the stock 12-gm headshell. I could believe it would benefit from a higher effective mass tonearm like the FRs.

Geoch, You wrote, "So, don't bother. You simply can't trick the formula."
But in fact the formula itself is "tricky" and only gives you a ballpark estimate of the resonant frequency, even if your input data are accurate with respect to one's particular sample of a particular cartridge. So my approach would be to forget the formula but to try in a general way to match a low compliance cartridge with a medium to high mass tonearm, etc, etc.

I am one who does use ESLs and OTLs and who does very much like the Urushi that I own. I also have a Colibri and an Ortofon MC7500 and several tonearms and turntables. Many days, I prefer the Urushi over all. I don't think a 12" arm is necessary to enjoy the Urushi, but when I finally acquire one, I will try it.

Just to update, I'm enjoying greatly my Koetsu with my older phantom arm. Loving the musical combo!

I'm using a koetsu jade with a VPI JMW-10 on a TNT turntable.
On paper the JMW-10 is a poor match for the jade as it's a unipivot with effective mass is in the 10-11gm range. That being said it sounds awfully good to me. Would an arm with a higher effective mass sound better? Maybe and one day I plan on finding out but for now the combo sounds great regardless of the math formulas.
A few things to consider, the stone body koetsu by being heavier by around 4gms then their wood/urushi counterparts and thus increase the effective mass of the arm their used with.
The effective mass of an arm can be increased by adding a cartridge weight. I know that VPI sells a 3gm aluminum weight for this purpose and I've seen a 5gm brass head shell weighs available.
Additionally by using a LIGHTER counterweight further back on the arm as opposed to a heavier counterweight closer to the pivot point will also increase the effective mass.
Just my 2 cents.

Hi franks,

Additionally by using a LIGHTER counterweight further back on the arm as opposed to a heavier counterweight closer to the pivot point will also increase the effective mass.

This statement does not make sense.

The physics formula for levers is M=FxD (M = moment (effectice mass), F = force , and D is distance from the pivot).

From my understanding, the moment (i.e. effective mass) is the upward force by the lever, the downward force of the mass post fulcrum is dependent only on the mass of the counterweight (and a constant gravitational constant!) and its product with its distance from the fulcrum.
Cheers<

Bobby