# Lunisolar calendar

A lunisolar calendar is a calendar whose date indicates both the moon phase and the time of the solar year.

If the solar year is taken to be a tropical year then a lunisolar calendar will also give an indication of the season. If it is taken to be a sidereal year then it will give us an idea of the constellation near which the full moon may occur.

This is normally done by having a calendar year that corresponds to a solar year and a month which corresponds to a lunation so that the day of month indicates the moon phase. There is usually the additional requirement that the year has a whole number of months, in which case most years have 12 months but every second or third year has 13 months.

If the lunisolar calendar is defined to have a year that corresponds to the tropical year then the month of the year (which corresponds to a lunation) will roughly indicate the season, and the day of month will roughly indicate the moon phase.

The Hebrew, Chinese, Hindu lunar, Buddhist, and Tibetan calendars are all lunisolar. The Hebrew and Chinese lunisolar calendars track the tropical year whereas the Buddhist and Hindu lunisolar calendars track the sidereal year. Therefore the first two 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 Islamic calendar is not lunisolar because its date does not indicate the season or time of sidereal year and the Gregorian Calendar is not lunisolar because its date does not indicate the moon phase.

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:

• 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 = 2.7 common years between leap years

A representative sequence of common and leap years is ccLccLcLccLccLccLcL, which is the classic nineteen-year Metonic cycle. The Hebrew and Buddhist calendars restrict the leap month to a single month of the year, so the number of common months between leap months is usually 36 months but occasionally only 24 months elapse. 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, so 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.

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