Lunisolar calendar

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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.


The Hebrew, Jain, Buddhist, Hindu, Kurdish and Bengali calendars, as well as the traditional Chinese, Tibetan, Japanese, Vietnamese, Mongolian and Korean calendars (in the east Asian 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.[1] The Chinese, Coligny and Hebrew[2] 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 Hindu calendars. The Germanic peoples also used a lunisolar calendar before their conversion to Christianity.

The Islamic calendar is lunar, but not a lunisolar calendar because its date is not related to the sun. 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[edit]

A rough idea of the frequency of the intercalary or leap month in all lunisolar calendars can be obtained by the following calculation, using approximate lengths of months and years in days:

  • Tropical year: 365.2422 (Y), Synodic month: 29.5306 (M)
  • Y/M = 12.36826: 12 months per common year or 13 months per leap year
  • Y - (M × 12) = 10.875 days per year (the epact)
  • 1/0.36826 = M/10.875 = 2.7155 (L): 1 leap month per 3 or 2 years, ccL or cL (average interval (in years) between intercalations).
  • 1L = 2.7155: 1(st) leap month in 3 years or in year 3 ccL
  • 2L = 5.4309: 2 leap months in 6 years ccLccL
  • 3L = 8.1464: 3 leap months in 9 years ccLccLccL
  • 4L = 10.8618: 4 leap months in 11 years ccLccLccLcL
  • 5L = 13.5772: 5 leap months in 14 years ccLccLccLcLccL
  • 6L = 16.2927: 6 leap months in 17 years ccLccLccLcLccLccL
  • 7L = 19.0082: 7 leap months in 19 years ccLccLccLcLccLccLcL
  • 19-year cycle: ccLccLccLcLccLccLcL (3 + 3 + 3 + 2) + (3 + 3 + 2) = 11 + 8 = 19 = 8 + 11 = (3 + 3 + 2) + (3 + 3 + 3 + 2) ccLccLcLccLccLccLcL
  • The year 2017 is a leap year in the traditional Chinese calendar: 2017 mod 19 = 3, ccLccLccLcLccLccLcL

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 every nineteen years. 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 goes above 29 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.

Lunisolar calendars with uncounted time[edit]

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.[3]

Gregorian lunisolar calendar[edit]

The Gregorian calendar has a lunisolar calendar, which is used to determine the date of Easter. The rules are in the Computus.

See also[edit]


  1. ^ F.C. De Blois, "TAʾRĪKH": I.1.iv. "Pre-Islamic and agricultural calendars of the Arabian peninsula", The Encyclopaedia of Islam, 2nd edition, X:260.
  2. ^ The modern Hebrew calendar, since it is based on rules rather than observations, does not exactly track the tropical year, and in fact the average Hebrew year of ~365.2468 days is intermediate between the tropical year (~365.2422 days) and the sidereal year (~365.2564 days).
  3. ^ Suttles, Wayne P. Musqueam Reference Grammar, UBC Press, 2004, p. 517.


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