OK, let me weigh in here.
First, thanks to Chris, for not only doing all these tests, but taking the time to try to explain to the rest of us.
Now, I have two comments:
First, I believe all mics, AT831 or otherwise, will have *some* distortion if not powered correctly. By "correctly", I mean having some resistor between the source of the FET and ground. This could be 4.7k, 2.2k or whatever. If you look at any schematic of a high-end mic, you'll see this resistor. In fact, AT853x phantom adaptors (miniXLR to XLR) have a 5.1k resistor there (I've traced the circuit), so the 4.7k resistor that Chris found is pretty close. Now, whether we *hear* the distortion is another factor. That could depend on the sound level, low frequency content, or just how good our ears are.
Second, the so-called "plug-in-power" from recorders has two variables. One is the open circuit voltage (eg., 2.5v for Edirol and MD), but also there is a series resistor inside. If you want to measure, put a voltmeter on the (unloaded) jack and measure it. Next, put a small resistor, something like 1k, across the output, and meaure the voltage again. You can use ohms law to figure out what the internal resistor is. For Edirol it is 2.2k. For Minidisc it is 6.8k. The higher this internal resistor, the harder it is to get enough "juice" to power a set of external mics. I believe Guysonic did some nice measurements, but those were to power his specific mics, so not much help to us.
Oh yeah, choosing the resistors (2.2k or whatever) depends on both the mic and the plug-in-power circuit. I've had great luck with a 2.2k resistor and with Sennheiser MKE2 mics on the Edirol. I have not experimented with other setups. I did modify several pairs of AT853 mics with 2.2k, but did not test them extensively.
Richard