Intercalary month in the context of "Leap week calendar"

The Roman calendar was the calendar used by the Roman Kingdom and Roman Republic. Although the term is primarily used for Rome's pre-Julian calendars, it is often used inclusively of the Julian calendar established by Julius Caesar in 46 BC.

According to most Roman accounts, their original calendar was established by their legendary first king Romulus. It consisted of ten months, beginning in spring with March and leaving winter as an unassigned span of days before the next year. These months each had 30 or 31 days and ran for 38 nundinal cycles, each forming a kind of eight-day week—nine days counted inclusively in the Roman manner—and ending with religious rituals and a public market. This fixed calendar bore traces of its origin as an observational lunar one. In particular, the most important days of each month—its kalends, nones, and ides—seem to have derived from the new moon, the first-quarter moon, and the full moon respectively. To a late date, the College of Pontiffs formally proclaimed each of these days on the Capitoline Hill and Roman dating counted down inclusively towards the next such day in any month. (For example, the year-end festival of Terminalia on 23 February was called VII. Kal. Mart., the 6th day before the March kalends.)

The Season of the Inundation or Flood (Akhet in Egyptian) (Ancient Egyptian: Ꜣḫt) was the first season of the lunar and civil Egyptian calendars. It fell after the intercalary month of Days over the Year (Ḥryw Rnpt) and before the Season of the Emergence (Prt). In the Coptic and Egyptian calendars this season begins at the start of the month of Thout (about 11 September), continues through the months of Paopi and Hathor, before concluding at the end of Koiak (about 8 January).