Lunisolar calendar

A lunisolar calendar is a calendar in many cultures whose date indicates both the Moon phase and the time of the solar year. If the solar year is defined as a tropical year, then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year, then the calendar will predict the constellation near which the full moon may occur. As with all calendars which divide the year into months there is an additional requirement that the year have a whole number of months. In this case ordinary years consist of twelve months but every second or third year is an embolismic year, which adds a thirteenth intercalary, embolismic, or leap month.
Their months are based on the regular cycle of the Moon's phases. So lunisolar calendars are lunar calendars with – in contrast to them – additional intercalation rules being used to bring them into a rough agreement with the solar year and thus with the seasons.
The main other type of calendar is a solar calendar.
Examples.
The Buddhist, Burmese, Assyrian,
Hebrew, Hindu, Jain and Kurdish as well as the traditional Chinese, Japanese, Korean, Mongolian, Tibetan, and Vietnamese calendars (in the East Asian Chinese cultural sphere), plus the ancient Hellenic, Coligny, and Babylonian calendars are all lunisolar. Also, some of the ancient pre-Islamic calendars in south Arabia followed a lunisolar system. The Chinese, Coligny and
Hebrew lunisolar calendars track more or less the tropical year whereas the Buddhist and Hindu lunisolar calendars track the sidereal year. Therefore, the first three give an idea of the seasons whereas the last two give an idea of the position among the constellations of the full moon. The Tibetan calendar was influenced by both the Chinese and Buddhist calendars. The Germanic peoples also used a lunisolar calendar before their conversion to Christianity.
The Islamic calendar is a lunar calendar of exactly 12 months, but not a lunisolar calendar because its date is not related to the Sun; Its solar counterpart is the Solar Hijri calendar, which is used in Iran and Afghanistan. The civil versions of the Julian and Gregorian calendars are solar, because their dates do not indicate the Moon phase – however, both the Gregorian and Julian calendars include undated lunar calendars that allow them to calculate the Christian celebration of Easter, so both are lunisolar calendars in that respect.
Determining leap months.
A tropical year is approximately 365.2422 days long and a synodic month is approximately 29.5306 days long, so a tropical year is approximately 365.2422 / 29.5306 ≈ 12.36826 months long. Because 0.36826 is between 1/3 and 1/2, a typical year of 12 months needs to be supplemented with one intercalary or leap month every 2 to 3 years. More precisely, 0.36826 is quite close to 7/19 ≈ 0.3684211 and several lunisolar calendars have 7 leap months in every cycle of 19 years.
Intercalation of leap months is frequently controlled by the "epact", which is the difference between the lunar and solar years (approximately 11 days). The Metonic cycle, used in the Hebrew calendar and the Julian and Gregorian ecclesiastical calendars, adds seven months during every nineteen-year period. The classic Metonic cycle can be reproduced by assigning an initial epact value of 1 to the last year of the cycle and incrementing by 11 each year. Between the last year of one cycle and the first year of the next the increment is 12. This adjustment, the "saltus lunae", causes the epacts to repeat every 19 years. When the epact reaches 30 or higher, an intercalary month is added and 30 is subtracted. The intercalary years are numbers 3, 6, 8, 11, 14, 17 and 19. Both the Hebrew calendar and the Julian calendar use this sequence.
The Buddhist and Hebrew calendars restrict the leap month to a single month of the year; the number of common months between leap months is, therefore, usually 36, but occasionally only 24 months. Because the Chinese and Hindu lunisolar calendars allow the leap month to occur after or before (respectively) any month but use the true motion of the Sun, their leap months do not usually occur within a couple of months of perihelion, when the apparent speed of the Sun along the ecliptic is fastest (now about 3 January). This increases the usual number of common months between leap months to roughly 34 months when a doublet of common years occurs, while reducing the number to about 29 months when only a common singleton occurs.
With uncounted time.
An alternative way of dealing with the fact that a solar year does not contain an integer number of months is by including uncounted time in the year that does not belong to any month. Some Coast Salish peoples used a calendar of this kind. For instance, the Chehalis began their count of lunar months from the arrival of spawning chinook salmon (in Gregorian calendar October), and counted 10 months, leaving an uncounted period until the next chinook salmon run.
Gregorian lunisolar calendar.
The Gregorian calendar has a lunisolar calendar, which is used to determine the date of Easter. The rules are in the Computus.
List of lunisolar calendars.
The following is a list of lunisolar calendars: