"The Egyptians produced the earliest calender on record, in 4241 B.C. It set up 12 months of 30 days each & added 5 days at the end of the year for a total of 365 days. Ancient Babylonian calenders had 13 months; so did some Greek calenders - each Greek city could set up its own. The Romans left calender keeping to a high priest, who seems to have neglected his chore; by Julius Caesar's time summer months were coming in spring! Caesar corrected this in 46 B.C. in the Julian calender with a 365 day year plus one day added every 4th or leap year. Even with all that , tho, the calender was longer than the year of the seasons. In 1582, Pope Gregory XIII remedied this - and gave us the calender we now use - by dropping ten days into limbo, making October 15, 1582, the day after October 4, and directing that the leap years should be omitted on century years not divisible by 400. The calender year still exceeds the solar year by 26 seconds."
January and October of the same year, always begin w/ the same day. So do April and July, September and December, as well as Feb, March, and November.
(Spinning Wheel magazine, Jan-Feb 1964)