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.
Usually there is an additional requirement that the year have a whole number of months,
in which case most years have 12 months but every second or third year has 13.
Examples The Hebrew, Buddhist, Hindu, Burmese, Bengali,
and Tibetan calendars, as well as the traditional Chinese, Japanese, Vietnamese, Mongolian and
Korean calendars, 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 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 To determine when an embolismic month needs
to be inserted, some calendars rely on direct observations of the state of vegetation, while
others compare the ecliptic longitude of the sun and the phase of the moon.
The Hawaiians observe the movement of specific stars and insert months accordingly.
On the other hand, in arithmetical lunisolar calendars, an integral number of months is
fitted into some integral number of years by a fixed rule.
To construct such a calendar, the average length of the tropical year is divided by
the average length of the synodic month, which gives the number of average synodic months
in a tropical year as: 12.368266......
Continued fractions of this decimal value give optimal approximations for this value.
So in the list below, after the number of synodic months listed in the numerator, approximately
an integer number of tropical years as listed in the denominator have been completed:
Note however that in none of the arithmetic calendars is the average year length exactly
equal to a true tropical year.
Different calendars have different average year lengths and different average month lengths,
so the discrepancy between the calendar months and moon is not equal to the values given
above.
The 8-year cycle was used in the ancient Athenian calendar.
The 8-year cycle was also used in early third-century Easter calculations in Rome and Alexandria.
The 19-year cycle is the classic Metonic cycle, which is used in most arithmetical lunisolar
calendars.
It is a combination of the 8- and 11-year period, and whenever the error of the 19-year
approximation accumulates to 1⁄19 of a mean month, a cycle can be truncated to 11 years,
after which 19-year cycles can resume.
Meton's cycle had an integer number of days, although Metonic cycle often means its use
without an integer number of days.
It was adapted to a mean year of 365.25 days by means of the 4×19 year Callipic cycle.
Rome used an 84-year cycle for Easter calculations from the late third century until 457.
Early Christians in Britain and Ireland also used an 84-year cycle until the Synod of Whitby
in 664.
The 84-year cycle is equivalent to a Callipic 4×19-year cycle plus an 8-year cycle and
so has a total of 1039 months.
This gives an average of 12.3690476...
months per year.
One cycle was 30681 days, which is about 1.28 days short of 1039 synodic months, 0.66 days
more than 84 tropical years, and 0.53 days short of 84 sidereal years.
The next approximation after the Metonic cycle is very sensitive to the values one adopts
for the lunation and the year, especially the year.
There are different possible definitions of the year so other approximations may be more
accurate for specific purposes.
For example a 353-year cycle including 130 embolismic months for a total of 4366 months
is more accurate for a northern hemisphere spring equinox year, whereas a 611-year cycle
including 225 embolismic months for a total of 7557 months has good accuracy for a northern
hemisphere summer solstice year, and a 160-year cycle including 59 embolismic months for a
total of 1979 months has good accuracy for a sidereal year.
Calculating a leap month 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 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
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.
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 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, 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.
See also Hebrew calendar
Hindu Calendar Computus Easter rule for Julian and Gregorian
calendars.
Calendar reform Solunar theory
Notes
References Introduction to Calendars, US Naval Observatory,
Astronomical Applications Department.
External links Lunisolar calendar year 2014
Lunisolar Calendar Calendar studies
Acano by Professor Jose Barrios Garcia Acano: a lunar calendar from the Canary Islands
Model of lunisolar calendar based on observation of the sun and moon position