The intercalary month or epagomenal days of the ancient Egyptian, Coptic, and Ethiopian calendars are a period of five days in common years and six days in leap years in addition to those calendars' 12 standard months, sometimes reckoned as their thirteenth month. They originated as a periodic measure to ensure that the heliacal rising of Sirius would occur in the 12th month of the Egyptian lunar calendar but became a regular feature of the civil calendar and its descendants. Coptic and Ethiopian leap days occur in the year preceding Julian and Gregorian leap years.
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Egyptian intercalary month in the context of Egyptian calendar
The ancient Egyptian calendar – a civil calendar – was a solar calendar with a 365-day year. The year consisted of three seasons of 120 days each, plus an intercalary month of five epagomenal days treated as outside of the year proper. Each season was divided into four months of 30 days. These twelve months were initially numbered within each season but came to also be known by the names of their principal festivals. Each month was divided into three 10-day periods known as decans or decades. It has been suggested that during the Nineteenth Dynasty and the Twentieth Dynasty the last two days of each decan were usually treated as a kind of weekend for the royal craftsmen, with royal artisans free from work.
Because this calendrical year was nearly a quarter of a day shorter than the solar year, the Egyptian calendar lost about one day every four years relative to the Julian calendar. It is therefore sometimes referred to as the wandering year (Latin: annus vagus), as its months rotated about one day through the solar year every four years. Ptolemy III's Canopus Decree attempted to correct this through the introduction of a sixth epagomenal day every four years but the proposal was resisted by the Egyptian priests and people and abandoned until the decree by Augustus in 25 BC that established the Alexandrian or Coptic calendar. The introduction of a leap day to the Egyptian calendar made it equivalent to the Julian calendar, although (like the latter) it continues to diverge from the Gregorian calendar at the turn of most centuries.
Egyptian intercalary month in the context of Season of the Inundation
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).