Lunisolar calendar

From Free net encyclopedia

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 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 has a whole number of months, in which case most years have 12 months but every second or third year has 13 months.

1 Examples
2 Determining leap months
3 Calculating a "leap month"
4 See also
5 External links

[edit]

Examples

The Hebrew, Hindu lunar, Buddhist, Tibetan calendars, and Chinese calendar used alone until 1912 and then used along with the Gregorian Calendar are all lunisolar, as was the Japanese calendar until 1873, the pre-Islamic calendar, the first century Gaulish Coligny calendar and the second millennium BCE Babylonian calendar. The Hebrew, Chinese and Coligny 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 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 realising it, most Christians do use a lunisolar calendar in the determination of Easter.

[edit]

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 synodic 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 months in a 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, an integer number of tropical years as listed in the denominator have been completed:

The 8-year cycle was used in the ancient Athenian calendar.

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 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.

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 4×19 year Callipic cycle.

The 8-year cycle was also used in early third-century Easter calculations in Rome and Alexandria. Rome used an 84-year cycle from the late third century until 457. Early Christians in Britain and Ireland also used an 84-year cycle until the Synod of Whitby. The 84-year cycle is equivalent to a Callipic 76-year cycle plus an 8-year cycle and so has 1039 lunar months.

The last listed approximation (4131/334) is very sensitive to the adopted values for the lunation and year, especially the year. There are different possible definitions of the year, other approximations may be more accurate. For example (4366/353) is more accurate for a vernal equinox tropical year and (1979/160) is more accurate for a sidereal year.

[edit]

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 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.

[edit]