So in the Julian/Gregorian (no leap year on centuries i.e. 1900, 2000) The reason why Sept – Dec doesn’t match is because of Julius and Augustus Cesar so all the months got shifted back two.
sept = 7 (month 9)
oct = 8 (month 10)
non = 9 (month 11)
dec = 10 (month 12)
Since this is the month of Heracles it is now Herc. Inspired by Darkblood1.