C256 is purely for scientific reasons, it divides by 2 neatly and repeatedly, so doubling up lengths for a monochord gives whole- numbers to the second. It's a full 9.5Hz flat (half a semitone) at A compared to A440.

There was (and is) a pseudoscientific movement to press for the adoption of A432, the reasoning being that it is an integral submultiple of the number of seconds in a day, and therefore somehow "naturally" correct. It ignores tha fact that the "natural" second, the heartbeat, varies wildly both between people and in any person from time to time, and furthermore ignores the fact that dividing time by frequency is nonsense.

As an aside, It's an interesting but apt coincidence that the SI unit of frequency, the Hertz (Hz), named after the German physicist Heinrich Hertz, is also German for "heart", and 1Hz is approximately the human heartbeat rate.