Leap month in the context of "Leap week calendar"

A lunar calendar is a calendar based on the monthly cycles of the Moon's phases (synodic months, lunations), in contrast to solar calendars, whose annual cycles are based on the solar year, and lunisolar calendars, whose lunar months are brought into alignment with the solar year through some process of intercalation – such as by insertion of a leap month. The most widely observed lunar calendar is the Islamic calendar. The details of when months begin vary from calendar to calendar, with some using new, full, or crescent moons and others employing detailed calculations.

Since each lunation is approximately 29+1⁄2 days, it is common for the months of a lunar calendar to alternate between 29 and 30 days. Since the period of 12 such lunations, a lunar year, is 354 days, 8 hours, 48 minutes, 34 seconds (354.36707 days), lunar calendars are 11 to 12 days shorter than the solar year. In lunar calendars, which do not make use of lunisolar calendars' intercalation, the lunar months cycle through all the seasons of a solar year over the course of a 33–34 lunar-year cycle (see, e.g., list of Islamic years).

A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) compared to a common year. The 366th day (or 13th month) is added to keep the calendar year synchronised with the astronomical year or seasonal year. Since astronomical events and seasons do not repeat in a whole number of days, calendars having a constant number of days each year will unavoidably drift over time with respect to the event that the year is supposed to track, such as seasons. By inserting ("intercalating") an additional day—a leap day—or month—a leap month—into some years, the drift between a civilisation's dating system and the physical properties of the Solar System can be corrected.

An astronomical year lasts slightly less than 365⁠1/4⁠ days. The historic Julian calendar has three common years of 365 days followed by a leap year of 366 days, by extending February to 29 days rather than the common 28. The Gregorian calendar, the world's most widely used civil calendar, makes a further adjustment for the small error in the Julian algorithm; this extra leap day occurs in each year that is a multiple of 4, except for years evenly divisible by 100 but not by 400. Thus 1600, 2000 and 2400 are leap years, but not 1700, 1800, 1900, 2100, 2200, and 2300.