# Dictionary Definition

lunisolar adj : relating to or attributed to the
moon and the sun or their mutual relations

# User Contributed Dictionary

# Extensive Definition

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 months.

## Examples

The Buddhist, Hebrew, Hindu lunisolar, Tibetan calendars, Chinese calendar used alone until 1912 (and then used along with the Gregorian calendar) and Korean calendar (used alone until 1894 and since used along with the Gregorian calendar) are all lunisolar, as was the Japanese calendar until 1873, the pre-Islamic calendar, the republican Roman calendar until 45 BC (in fact earlier, because the synchronization to the moon was lost as well as the synchronization to the sun), the first century Gaulish Coligny calendar and the second millennium BC Babylonian calendar. 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 English also used a lunisolar calendar before their conversion to Christianity . The Islamic calendar is a lunar, but not lunisolar calendar because its date is not related to the sun. The Julian and Gregorian Calendars are solar, not lunisolar, because their dates do not indicate the moon phase — however, without realizing it, most Christians do use a lunisolar calendar in the determination of Easter.## 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.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 (in principle), 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:

12 / 1 = 12 (error = -0.368266... synodic
months/year) 25 / 2 = 12.5 (error = 0.131734... synodic
months/year) 37 / 3 = 12.333333... (error = 0.034933... synodic
months/year) 99 / 8 = 12.375 (error = 0.006734... synodic
months/year) 136 / 11 = 12.363636... (error = -0.004630... synodic
months/year) 235 / 19 = 12.368421... (error = 0.000155... synodic
months/year) 4131 / 334 = 12.368263... (error = -0.000003...
synodic months/year)

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 (99 synodic months, including 3
embolismic months) was used in the ancient Athenian calendar. The
8-year cycle was also used in early third-century Easter
calculations (or old Computus) in Rome and Alexandria.

The 19-year cycle (235 synodic months, including
7 embolismic months) 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 has built up to a full day, a
cycle can be truncated to 8 or 11 years, after which 19-year cycles
can start anew. 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 (used in the Easter calculations of the Julian
calendar).

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 (including 4×7
embolismic months) plus an 8-year cycle (including 3 embolismic
months) and so has a total of 1039 months (including 31 embolismic
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 (arising from continued
fractions) after the Metonic cycle (such as a 334-year cycle) is
very sensitive to the values one adopts for the lunation (synodic
month) and the year, especially the year. There are different
possible definitions of the year so other approximations may be
more accurate. For example (4366/353) is more accurate for a
tropical
year whereas (1979/160) is more accurate 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 − 1 = 1.7 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, 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.

## Notes

## References

- Introduction to Calendars, US Naval Observatory, Astronomical Applications Department.

## See also

## External links

- Panchangam for your city Panchangam for your city based on High Precision Drika Ganita.
- Perpetual Chinese Lunar Program The Chinese calendar is one of the oldest lunisolar calendars.
- Lunisolar Calendar Page contains a useful description of the difference between lunar calendars and lunisolar calendars.
- Calendar studies A general discussion of calendar systems including two examples of lunisolar calendars.
- Chinese Lunar Calendar with 'Yellow Calendar'

lunisolar in Min Nan:
Goe̍h-niû-ji̍t-thaû-le̍k

lunisolar in Catalan: Any embolismal

lunisolar in Czech: Lunisolární kalendář

lunisolar in Danish: Lunisolarkalender

lunisolar in German: Lunisolarkalender

lunisolar in Spanish: Calendario lunisolar

lunisolar in French: Calendrier
luni-solaire

lunisolar in Western Frisian:
Sinnemoannekalinder

lunisolar in Korean: 태음태양력

lunisolar in Indonesian: Kalender
lunisolar

lunisolar in Georgian: ლუნისოლარული
კალენდარი

lunisolar in Hungarian: Szolunáris naptár

lunisolar in Japanese: 太陰太陽暦

lunisolar in Norwegian: Lunisolarkalender

lunisolar in Polish: Kalendarz
księżycowo-słoneczny

lunisolar in Slovak: Lunisolárny kalendár

lunisolar in Swedish: Lunisolarkalender

lunisolar in Thai: ปฏิทินสุริยจันทรคติ

lunisolar in Chinese: 阴阳历