Hickory, the thing is that if you are looking for a load anywhere from 0 ohms to say 2000 ohms, you can do fine by just inserting a loading resistor of the desired value -- since having a 47,000 ohm resistor in parallel with it won't reduce its value by any significant amount, as your calculation illustrates. BTW, the formula you give only works for 2 resistors in parallel -- there is a more general formula for multiple resistors in parallel.
I have often stated that a good place to start loading a given cartridge (getting into the ballpark) is to multiply 25x the cartridge's internal resistance/impedance. The optimum will vary, but not more than +/- 50% of the 25 multiple. Raul and I agree that the best procedure for discovering the optimum load is to listen to the bass while starting at the low end of the loading range and working up to higher resistances. If you do it this way, the bass will go from looser to tighter and then as you go too high (in load) the bass will begin to weaken (thin out and lose strength) the mid/high won't change (except in relative terms, to the bass) that much throughout the procedure.
If the load exceeds a cartridge's optimum by even a small amount (say running a cartridge at 800 ohms where it should be optimum around 100 +/- ohms) it will be hard to detect because it will sound pretty much the same (bright) from 800 all the way up to 47,000!
I have often stated that a good place to start loading a given cartridge (getting into the ballpark) is to multiply 25x the cartridge's internal resistance/impedance. The optimum will vary, but not more than +/- 50% of the 25 multiple. Raul and I agree that the best procedure for discovering the optimum load is to listen to the bass while starting at the low end of the loading range and working up to higher resistances. If you do it this way, the bass will go from looser to tighter and then as you go too high (in load) the bass will begin to weaken (thin out and lose strength) the mid/high won't change (except in relative terms, to the bass) that much throughout the procedure.
If the load exceeds a cartridge's optimum by even a small amount (say running a cartridge at 800 ohms where it should be optimum around 100 +/- ohms) it will be hard to detect because it will sound pretty much the same (bright) from 800 all the way up to 47,000!