Lunisolar calendar: Difference between revisions
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A '''lunisolar calendar''' is a [[calendar]] in many [[culture]]s 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. |
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==Examples== |
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The [[Hebrew calendar|Hebrew]], [[Buddhist calendar|Buddhist]], [[Hellenic calendars|Hellenic]], [[Hindu calendar|Hindu lunisolar]], [[Tibetan calendar|Tibetan]], [[Chinese calendar|Chinese]], [[Vietnamese calendar|Vietnamese]], [[Mongolian calendar|Mongolian]], and [[Korean calendar|Korean]] calendars are all lunisolar, as was the [[Japanese calendar]] until 1873, the [[Islamic calendar#Pre-Islamic calendar|pre-Islamic calendar]], the first century Gaulish [[Coligny calendar]], and the [[Babylonian calendar]]. The Chinese, Coligny and |
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Hebrew<ref>The modern Hebrew calendar, since it is based on rules rather than observations, does not exactly track the tropical year, and in fact the average Hebrew year of ~365.2468 days is intermediate between the tropical year (~365.2422 days) and the sidereal year (~365.2564 days) |
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</ref> 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 calendar|Germanic peoples also used a lunisolar calendar]] before their conversion to Christianity. |
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The [[Islamic calendar]] is [[lunar calendar|lunar]], but not a lunisolar calendar because its date is not related to the sun. The [[Julian Calendar|Julian]] and [[Gregorian Calendar]]s are [[solar calendar|solar]], not lunisolar, because their dates do not indicate the moon phase — however, a lunisolar calendar is used in the determination of the Christian celebration of [[Easter]]. |
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== Determining leap months == |
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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 [[Moon phase|phase of the moon]]. The Hawaiians observe the movement of specific stars and insert months accordingly. |
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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: |
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:12.368266...... |
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[[Continued fraction]]s 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: |
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{| border=0 |
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|- |
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| align=right | 12 / || align=right | 1 = || align=left | 12 |
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| align=left | (error = || align=right | −0.368266... synodic months/year) |
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|- |
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| align=right | 25 / || align=right | 2 = || align=left | 12.5 |
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| align=left | (error = || align=right | 0.131734... synodic months/year) |
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|- |
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| align=right | 37 / || align=right | 3 = || align=left | 12.333333... |
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| align=left | (error = || align=right | 0.034933... synodic months/year) |
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|- |
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| align=right | 99 / || align=right | 8 = || align=left | 12.375 |
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| align=left | (error = || align=right | 0.006734... synodic months/year) |
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|- |
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| align=right | 136 / || align=right | 11 = || align=left | 12.363636... |
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| align=left | (error = || align=right | −0.004630... synodic months/year) |
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|- |
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| align=right | 235 / || align=right | 19 = || align=left | 12.368421... |
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| align=left | (error = || align=right | 0.000155... synodic months/year) |
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|- |
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| align=right | 4131 / || align=right | 334 = || align=left | 12.368263... |
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| align=left | (error = || align=right | −0.000003... synodic months/year) |
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|} |
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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. |
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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 [[Computus|Easter calculations]] (or old ''Computus'') in Rome and Alexandria. |
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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). |
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Rome used an 84-year cycle for [[Computus|Easter calculation]]s 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. |
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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. |
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==Calculating a leap month== |
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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: |
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*Year: 365.25, Month: 29.53 |
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*365.25/(12 × 29.53) = 1.0307 |
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*1/0.0307 = 32.57 common months between leap months |
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*32.57/12 − 1 = 1.7 common years between leap years |
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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 (respectively) 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 (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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==Notes== |
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{{reflist}} |
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==References== |
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*[http://aa.usno.navy.mil/faq/docs/calendars.php Introduction to Calendars], US Naval Observatory, Astronomical Applications Department. |
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==See also== |
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*[[Calendar reform]] |
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==External links== |
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*[http://lunarcal.org Perpetual Chinese Lunar Program] |
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*[http://www.pburch.net/lunarcal.html Lunisolar Calendar] |
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* [http://www.hermetic.ch/cal_stud.htm Calendar studies] |
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*[http://planetmath.org/encyclopedia/AcanoALunarCalendarMethod.html Acano: a lunar calendar method] from the Canary Islands |
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<br/><!-- Spacing for aesthetic purposes: so that bottom templates don't stick to text above it --> |
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{{calendars}} |
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{{Chronology}} |
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[[Category:Calendars]] |
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[[Category:Lunisolar calendars]] |
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[[zh-min-nan:Goe̍h-niû-ji̍t-thaû-le̍k]] |
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[[ca:Any embolismal]] |
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[[cs:Lunisolární kalendář]] |
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[[da:Lunisolarkalender]] |
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[[de:Lunisolarkalender]] |
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[[es:Calendario lunisolar]] |
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[[eo:Lunsuna kalendaro]] |
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[[fr:Calendrier luni-solaire]] |
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[[fy:Sinnemoannekalinder]] |
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[[ko:태음태양력]] |
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[[id:Kalender suryacandra]] |
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[[jv:Kalèndher Suryacandra]] |
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[[ka:ლუნისოლარული კალენდარი]] |
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[[hu:Szolunáris naptár]] |
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[[nl:Lunisolaire kalender]] |
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[[ja:太陰太陽暦]] |
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[[no:Lunisolarkalender]] |
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[[pl:Kalendarz księżycowo-słoneczny]] |
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[[pt:Calendário lunissolar]] |
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[[ru:Лунно-солнечный календарь]] |
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[[sq:Lunisolari]] |
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[[si:චන්ද්ර සූර්ය දින දසුන]] |
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[[sk:Lunisolárny kalendár]] |
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[[sr:Лунисоларни календар]] |
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[[sh:Лунисоларни календар]] |
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[[fi:Kuu-aurinkokalenteri]] |
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[[sv:Lunisolarkalender]] |
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[[ta:சூரியசந்திர நாட்காட்டி]] |
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[[th:ปฏิทินสุริยจันทรคติ]] |
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[[vi:Âm dương lịch]] |
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[[zh:阴阳历]] |
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Revision as of 21:41, 4 March 2010
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