Onhwy -- it's not a hard and fast specification by any means, however it's based on (and borne out by) a few (unforunately very few!) cartridge makers who DO specify optimum load values for their cartridges. And also the concensus of a lot of audiophiles who report their results. I have compiled these anecdotal reports, and it's amazing how consistently the results work out to the 25x (the resistance of the cartridge in question.)
As for science, it's pretty simple, though again, not hard and fast, because of so many other variables like cable length and composition, phonostage design etc. However if you take an average gain of 50dB (most MC phono stages are between 40 dB and 60 dB I'd say) and an average output of 0.40 mV (most cartridges have outputs somewhere between .20 and .60 mV) you will come up with (again this is an average) an impedance matching differential that requires the driven impedance be (at least) 25x the impedance of the driver. Notice I said "at least". So why wouldn't say 47K ohms be even better since it's way above the "at least" minimum? That's a fair question. the answer has to do with the miniscule value of the driving voltage, as opposed for instance to the (usually) healthy voltage with which preamps drive amps. In the cases of both cartridge-to-phono preamp (always) and preamp-to-amp (sometimes, but often enough to cause problems), when the driving voltage falls to near the minimum input sensitivity of the driven device, it's important that the match be closer to the theoretical ideal (minimum) to insure flattest frequency response and best efficiency (input voltage to output voltage) for the driven device. If you need proof of that, think of the many discussions you've (probably) read where somebody is complaining that their magabuck preamp and their megabuck amp are producing thin, or glarey, or bass-shy sound and they can't figure out why. The problem lies not with the equipment, but with the combination. And why BTW, we have all these expensive ICs with network boxes (like MIT and Transparent) which allow better impedance matching (load adjustment) of preamp to amp. Personally, I don't think this would be necessary if the equipment were well matched to begin with. But I digress, sorry.
So this 25x factor is really a rule of thumb which is meant to get things to a point (ballpark) from which you can be pretty sure that an optimum value (obtained by listening) will be found within a range that's easy to work with, practically speaking. I usually recommend 50% +/_ This means for instance that if a cartridge had an internal resistance of say 30 ohms (sometimes spec'd. as "output impedance") and therefore (IMO) a theoretical ideal load of 750 ohms, that you would probably find your best sonics somewhere between 375 ohms and 1125 ohms. If you were to start out at 750, and depending on what you hear, it's not hard to tell if you should go up a little or down a little (and after you do, you may decide to stick with 750 ;~)) What you WILL avoid however, is sitting there for two weeks with a huge bag of resistors (and a soldering iron, if the person who designed your phono preamp thought you should only have to do this once!!) until you zero in on the optimum load for your setup.
I can say one thing for sure about any MC cartridge (not HO of course) without fear of being made to eat my phono cables: It's never going to be 47K, and it's never going to be equal to the internal resistance of the cartridge (like 6 to 30 ohms). I mention this because that's the range most @#^?*! cartridge manufacturers give you. Yeah, great! So where are you supposed to start?! Try 25x to start, it might not be absolute perfection, but it will save you a lot of time and aggravation getting there.
