Lunisolar calendar
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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.
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[edit] 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 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 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.
There are some lunisolar calendar reform proposals: One is the Hermetic Lunar Week Calendar which normally consists of 12 lunar months and a leap month every 2 or 3 years, and with a year that always starts near the vernal equinox. Another is the Simple Lunisolar Calendar, whose year always begins between Gregorian December 3 and January 1. Also there is the Meyer-Palmen Solilunar Calendar whose year always begins near the vernal equinox by using a 2498258 days in 84599 months in a 6840-year-cycle rule.
[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 synodic 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:
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)
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 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 synodic months (including 31 embolismic months). This gives an average of 12.369047... synodic months per year (with error=0.011123... synodic months/year, a less good approximation than the regular 8-year Athenian cycle or the Metonic 19-year cycle).
The last listed approximation with the 334-years cycle (4131 synodic months, including 15 embolismic months) 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 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.
[edit] Further examples
[edit] Simple lunisolar calendar
The Simple Lunisolar Calendar is a proposal for calendar reform by Robert Pontisso. It is a non-radical lunisolar calendar which uses the 7-day week. Each year starts from the Gregorian December 3 - January 1. Each month starts on or close to the day of the new moon. All the months except the sixth have fixed lengths. The months are named after the letters of the Greek alphabet and their names and the number of days they have are:
| No. | Name | Days |
|---|---|---|
| 1 | Alpha | 30 |
| 2 | Beta | 29 |
| 3 | Gamma | 30 |
| 4 | Delta | 29 |
| 5 | Epsilon | 30 |
| 6 | Zeta | 29 but 30 in years divisible by 5, except divisible by 200, 500 or 1000, these years are known as abundant years |
| 7 | Eta | 30 |
| 8 | Theta | 29 |
| 9 | Iota | 30 |
| 10 | Kappa | 29 |
| 11 | Lambda | 30 |
| 12 | Mu | 29 |
| 13 | Nu | 30 but only comes in leap years every 3 or 2 years |
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If 30 days or more are left after Mu 29 till the Gregorian new year's day then an extra month Nu is added. The Gregorian new year's day must fall in the month of Alpha. Given that December 25, 2000 is Alpha 1, 2001 the calendar continues from this date. This calendar is simple and easy to use.
This calendar cannot replace the Gregorian calendar, because it is necessary to know the Gregorian date when determining whether the year has a month Nu. It would run alongside the Gregorian Calendar much like the ISO week date calendar would. The chart on the website [1] shows the Gregorian date for the first day of each month in this calendar for the years 2001 - 2500.
The months jitter a lot because the month lengths are fixed, the abundant years non-uniformly spread and also the non-uniformity of leap years, which are caused by the fact that the Gregorian leap years are non-uniformly spread and also it's Alpha 1 that has to be on December 3 - January 1, not the actual new moon, as the months jitter.
Karl Palmen suggested the there be 20 abundant years every 103 years spread as evenly as possible, so the each abundant year occurs five years after the previous, except for three every 103 years that occur six years after the previous. These three exceptions would occur in intervals of 36, 36 and 31 years.
[edit] The Hermetic lunar week calendar
The Hermetic Lunar Week Calendar (HLWC) is by Peter Meyer. It is a lunisolar calendar which uses the lunar week (a quarter of a lunation). Each week has normally 7 days, sometimes 8, occasionally 6 and rarely 9 (average 7.382647 days). HLWC time is 6 hours behind conventional time. Each week begins on the HLWC day after the dark moon (new moon), half moon (waxing), full moon or half moon (waning). Each month starts on the HLWC day after the dark moon (new moon) and each year starts on the HLWC day after the closest dark moon (new moon) to the vernal equinox. Each month has 29 or 30 days. Each year has 12 or 13 months. The names of the months are:
- Artaud
- Benjamin
- Clark
- De Quincy
- Ellis
- Furst
- Grof
- Hofmann
- Izumi
- Janiger
- Kesey
- Lilly
- McKenna (leap month, occurs every 3 or 2 years in no cycle)
The names of the weeks of the months are Weekone, Weektwo, Weekthree and Weekfour. The names of the days of the week in four possible weeks are:
| 6 days | 7 days | 8 days | 9 days | |
|---|---|---|---|---|
| 1 | Dayone | Dayone | Dayone | Dayone |
| 2 | Daytwo | Daytwo | Daytwo | Daytwo |
| 3 | Daythree | Daythree | Daythree | Daythree |
| 4 | Dayfour | Dayfour | Dayfour | Dayfour |
| 5 | Dayfive | Dayfive | Dayfive | Dayfive |
| 6 | Moonday | Freeday | Herday | Nineday |
| 7 | - | Moonday | Freeday | Herday |
| 8 | - | - | Moonday | Freeday |
| 9 | - | - | - | Moonday |
In the Hermetic Lunar Week Calendar, months are observably related to the phases of the Moon. The Julian/Gregorian calendar lacks any correlation with the lunar cycle. The HLWC date is written as year-month-week-day. For example, 2006 October 21 Saturday corresponds to 5006 Grof Weekfour Moonday. This calendar doesn't use the 7-day week. This calendar is timezone independent and calculation is based on the HLWC GMT timezone. In the GMT timezone, the dark moon (new moon), half moon (waxing or waning) and full moon always occur on Moonday.
[edit] References
Introduction to Calendars, US Naval Observatory, Astronomical Applications Department.
[edit] See also
[edit] 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.
- The Meyer-Palmen Solilunar Calendar "Page includes more information about the correspondence between solar months and lunar months, and highlights the properties of a lunisolar calendar.
- A simple lunisolar calendar As the name suggests, this is a simple example of a lunisolar calendar that utilises the Gregorian calendar. A discussion of issues that affect accuracy is included.
- Hermetic Lunar Week Calendar The section Regularity of the Calendar contains an excellent comparison to this lunisolar calendar and the Gregorian calendar.
