It's the combinaton of bullet diamter, length, weight, overall shape, intenal mass distribution, air density, air temperature, and bullet velocity which determine the spin rate needed for a bullet to stabiize. A computer program like McGyro can assist in determining a bulet's stability, but just shooting them is a more reliable test. It's hard to determine the internal density distribution of jacketed bullets.
Most bullets have the best stability at Mach 0.85 to 0.9 for subsoinic bullets, and at speeds above Mach 1.5 for supersonic bullets. Mach .95 to 1.1 are the least stable.
http://www.jbmballistics.com/cgi-bin/jbmdrag-5.0.cgi