I know that in organ building a similar effect is actually sought out: when a 16' D and 10 2/3' D (sounding an A) are properly tuned and played together, a resultant pitch, an octave lower, a 32' D is heard. In organs this is handy because not many buildings can house a veritable forest of huge pipes that a proper 32' rank would require.
Kind of odd that it should be the fundamental A you're hearing and not the D. Kind of a neat effect, though! Does it only happen with that combination? Or do C/G, E/B and F/C produce similar effects? What happens when you slightly untune one of the strings just a bit?