The old rhyme goes
Thirty days hath September,
April, June, and November.
When short February's done,
All the rest have thirty-one.
So there are five months that have 30 days or fewer:
February (28 days for three years in a row, then 29 days in the fourth year), April, June, September and November.
There are seven months that have 31 days:
January, March, May, July, August, October and December.
This means that there is almost a pattern of the months with 31 days alternating with the months with 30, but it doesn't hold up in the summer when you have two months in a row with 31 days: July and August. The story I heard is that August once had 30 days and a different name, but when it was renamed in honor of Caesar Augustus, it was given an extra day. I do not know where that day is stolen from. (February is my guess.) In any case, if August were not allowed an extra day, we would have two short months in a row because September has only 30 days.
Another calendrical custom handed down to us by the Romans--though more honored today in the breach rather than in the observance--is the "ides." The ides (the same whether singular or plural) is the approximate middle of the month. A lower case "i" is used when the month is not specified, but it is capitalized for a given month, especially in the case of the Ides of March, which remain memorable because Shakespeare made much ado about this ides in his play "The Tragedy of Julius Caesar," in which Caesar is murdered on the Ides of March. (Shakespeare also gave us--in "The Tragedy of Hamlet"--the otherwise now inscrutable phrase in the first sentence of this paragraph, "more honored in the breach than in the observance," which basically means that people usually don't observe it.)
For my purpose here, an interesting thing about the ides stems from its usually falling on the thirteenth of the month. The Ides of March, however, always falls on the fifteenth. In fact, in only four months does it fall on the fifteenth: March, May, July and October. You will note that all four are months with 31 days. This means that all of the short months celebrate--whether in the breach or the observance--their ides on the thirteenth. This leaves only January, August and December as months with 31 days but with the ides on the thirteenth instead of the fifteenth. Once we note that August originally had only 30 days, we might have an explanation for why its ides falls on the thirteenth, but I do not know why the ides of January and December fall on the thirteenth; although, it is true that these are the first and last months of our calendar. (The Romans did establish January 1 as New Year's Day, but other societies have celebrated the new year on other dates.)