Lunisolar Calendar

Lunisolar calendar is the combination of solar calendar and lunar calendar. This calendar is more successful in indicating the season than the lunar cycle. If the solar year is taken as a sidereal year then the calendar will predict the constellation near which the full moon may occur.

Given below are some examples of the Lunisolar calendar:

• The Hindu, Buddhist, Tibetan, Chinese and the Hebrew calendars are all lunisolar calendars. The Hindu and the Buddhist calendars track the sidereal year (the orbital period of earth) whereas the Hebrew, Chinese and the Gaulish Coligny calendars track the tropical year in which indication of the seasons is given.
• The Tibetan calendar was influenced by both the Hindu and Chinese calendars.
• Some Christians use lunisolar calendar to determine their Easter festival.

A Lunisolar Calendar can be divided into two forms:

• One is the Hermetic Lunar Week Calendar which consists of 12 lunar months and a leap month after every 2 or 3 years.
• Second is the Simple Lunisolar Calendar in which the year begins between Gregorian December 3 and January 1.

Determining the Lunisolar Calendar
An arithmetical Lunisolar calendar consists of an integral number of synodic months which are fitted into the years by a fixed rule. A synodic month is the mean interval between conjunctions of the Moon and Sun corresponding to the cycle of lunar phases.

Calculation of the Calendar
Divide the average length of the tropical year by the average length of the synodic month. This results in giving the average number of synodic months in a year. It comes out to be as given below:

12.368266....(fractional value)

The 8-year cycle including 99 synodic months and 3 embolismic months (an intercalary month) was earlier used by the Athenians. It was also used in early third century Easter calculations in Rome and Alexandria.

The 19-year cycle is the classic Metonic cycle. It is used in most arithmetical lunisolar calendars. It is a combination of the 8- and 11-year period. In case, any error occurs in the 19-year cycle then it can be shortened to the 8 or 11-year cycle. By doing this the 19-year cycle can be started again. The Metonic cycle does not have an integer number of days, but it was adapted to a mean year of 365.25 days by means of the 419 year Callipic cycle.

An 84-year cycle was used by the Rome from the late third century until 457. Similarly, Christians in Britain and Ireland also used an 84-year cycle until the Synod of Whitby (7th century Whitby in Northumbria).

There are different possible approximations to the year. For example (4366/353) is more accurate for a vernal equinox tropical year and (1979/160) is more accurate for a sidereal year than the last listed approximation with the 334 years cycle.

Calculation of a Leap month
The frequency of the intercalary or the leap month can be derived from the following calculation, using approximate length of months and years in days:

Year: 365.25, Month: 29.53
365.25/(12 29.53) = 1.0307
1/0.0307 = 32.57 common months between leap months
32.57/12 - 1 = 1.7 common years between leap years

The Hebrew and Buddhist calendars restrict the leap month to a single month of the year. Thus, the number common moths between leap months is usually 36 months. On the other hand, the true motion of the sun is used by the Chinese and the Hindu calendars. This increases the usual number of common months between leap months to an approximate 34 months when there is a doublet of common years and reduces the number to 29 when there only a common singleton occurs.