Harmonious Triads is an excellent book about the standardisation of tuning (among many other musical topics). Change of tuning was sometimes used as a scam by 19th century military bandmasters to force the bandsmen to buy new instruments. They got a rake-off from the instrument makers.

431, 433, 439 and 443Hz would all be good choices for A as they are prime, which makes them magic. 439.823Hz is 140 time pi, and that's near enough 440 for folk, but 436.681Hz would be better as that's 139 times pi, and 139 is prime, making it a doubly magic frequency. I shall retune my kazoo forthwith.