I've been out of sorts and off schedule for a while now, and for the past three months (if we include this month) I haven't had the monthly reminders and thus have not talked about the months.
May was originally the 3rd month of a ten month year and had 31 days, when January and February were added it got kicked back to five but retained its 31 days. That makes it a long month so the ides are on the 15th. May was not changed in the Julian or Gregorian reforms to the calendar.
May is named after Maia which is kind of weird. Maia is a Greek goddess. It would be like if March had been named Aresy or something Ares-rooted instead of being named after Mars.
That said, Maia actually has a much richer tradition amoung the Romans and it is even possible that Roman Maia =/= Greek Maia. Anyway, she was about growth.
On the other hand, it might have been named not after Maia but the maiores (elders, ancestors, forefathers) who the Romans venerated in their private religion and held up as exemplars in public life.
June was originally the fourth month of 30 days. When January and February were added it became the sixth month and lost a day. Thus reduced, it was a short month meaning the ides fall on the 13th.
In the Julian reform gave it the thirtieth day back. So it has remained to this day.
The gods are in dispute over the origin of the name of this month. Juno claims it as here own. Youth (Juventas) claims it as hers and points out that when Junior for June is paired with Maiores for May the two form a nice thematic pair. Meanwhile Concordia claims it comes from the word meaning "to join" (jungo, junctus) and is in honor of the joining of the Romans and Sabines.
If the Trojan War has taught humnaity nothing else, it should have taught us that one should not get involved in a dispute between three goddesses.
Originally the fifth month of the year, July began it's existence with the uninspiring name "Fifth" (Quintilis.) It was thus the first of the number months that filled out the ten month year after the four named months.
It originally had 31 days and kept them throughout its history. That makes it a long month meaning the ides are on the 15th.
While various reforms would leave the month untouched, the name was changed after the death of Julius Caesar. It was changed to honor him, thus: July.
And those are the months we missed.