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. A page from the Hindu calendar 1871-72. ... In astronomy, a phase of the Moon is any of the aspects or appearances presented by the Moon as seen from Earth, determined by the portion of the Moon that is visibly illuminated by the Sun. ... A year (from Old English gēr) is the time between two recurrences of an event related to the orbit of the Earth around the Sun. ... A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ... This article or section is in need of attention from an expert on the subject. ... The sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. ... This article or section does not adequately cite its references or sources. ... Composite image of the Moon as taken by the Galileo spacecraft on 7 December 1992. ...

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 English also used a lunisolar calendar before their conversion to Christianity^{[citation needed]}. The Buddhist calendar is used on mainland southeast Asia in the countries of Cambodia, Laos, Thailand, and Myanmar (formerly Burma) in several related forms. ... The Hebrew calendar (Hebrew: ‎) or Jewish calendar is the annual calendar used in Judaism. ... A page from the Hindu calendar 1871-72. ... The Tibetan calendar is a lunisolar calendar, that is, the Tibetan year is composed of either 12 or 13 lunar months, each beginning and ending with a new moon. ... The Chinese calendar is a lunisolar calendar, akin to the Hebrew calendar & Hindu Calendar, incorporating elements of a lunar calendar with those of a solar calendar. ... 1912 (MCMXII) was a leap year starting on Monday in the Gregorian calendar (or a leap year starting on Tuesday in the 13-day-slower Julian calendar). ... The Gregorian calendar is the most widely used calendar in the world. ... The traditional Korean calendar is directly derived from the Asian calendar. ... 1894 (MDCCCXCIV) was a common year starting on Monday (see link for calendar). ... The Gregorian calendar is the most widely used calendar in the world. ... Koinobori, flags decorated like koi, are popular decorations around Childrens Day This mural on the wall of a Tokyo subway station celebrates Hazuki, the eighth month. ... 1873 (MDCCCLXXIII) was a common year starting on Wednesday (see link for calendar). ... The Islamic calendar or Muslim calendar (Arabic: التقويم الهجري; at-taqwÄ«m al-hijrÄ«; Persian: گاه‌شماری هجري قمری ‎ Gāhshomāri-ye hejri-ye qamari; also called the Hijri calendar) is the calendar used to date events in many predominantly Muslim countries, and used by Muslims everywhere to determine the proper day on which to... The Roman calendar changed its form several times in the time between the foundation of Rome and the fall of the Roman Empire. ... Centuries: 2nd century BC - 1st century BC - 1st century Decades: 90s BC 80s BC 70s BC 60s BC 50s BC - 40s BC - 30s BC 20s BC 10s BC 0s BC 0s Years: 50 BC 49 BC 48 BC 47 BC 46 BC 45 BC 44 BC 43 BC 42 BC... overview of the re-assembled tablet detail of Mid Samonios The Gaulish Coligny Calendar was found in Coligny, Ain, France (46°23′N 5°21′E) near Lyons in 1897, along with the head of a bronze statue of a youthful male figure. ... (3rd millennium BC – 2nd millennium BC – 1st millennium BC – other millennia) Events Second dynasty of Babylon First Bantu migrations from west Africa The Cushites drive the original inhabitants from Ethiopia, and establish trade relations with Egypt. ... In the Babylonian calendar a year consisted of 12 lunar months, each beginning when a new crescent moon was first sighted low on the western horizon at sunset. ...

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. The Islamic calendar or Muslim calendar (Arabic: التقويم الهجري; at-taqwÄ«m al-hijrÄ«; Persian: گاه‌شماری هجري قمری ‎ Gāhshomāri-ye hejri-ye qamari; also called the Hijri calendar) is the calendar used to date events in many predominantly Muslim countries, and used by Muslims everywhere to determine the proper day on which to... A lunar calendar is a calendar oriented at the moon phase. ... The Julian calendar was introduced in 46 BC by Julius Caesar and came into force in 45 BC (709 ab urbe condita). ... The Gregorian calendar is the most widely used calendar in the world. ... A solar calendar is a calendar whose dates indicate the position of the earth on its revolution around the sun (or equivalently the apparent position of the sun moving on the celestial sphere). ... Easter, the Sunday of the Resurrection, Pascha, or Resurrection Day, is the most important religious feast of the Christian liturgical year, observed at some point between late March and late April each year (early April to early May in Eastern Christianity), following the cycle of the moon. ...

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. Calendar reform is any proposed reform of a calendar. ... The Hermetic Lunar Week Calendar (HLWC) is a proposal for calendar reform by Peter Meyers. ... Illumination of Earth by Sun on the day of equinox The vernal equinox (or spring equinox) marks the beginning of astronomical spring. ... The Simple Lunisolar Calendar is a proposal for calendar reform by Robert Pontisso. ... December 3 is the 337th (in leap years the 338th) day of the year in the Gregorian calendar. ... January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... The Meyer-Palmen Solilunar Calendar is a proposal for calendar reform by Peter Meyer and Karl Palmen. ...

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. Intercalation is the insertion of an extra day or month into some calendar years to make the calendar follow the seasons. ... Ecliptic longitude (celestial longitude) is one of the co-ordinates which can be used to define the location of an astronomical object on the celestial sphere in ecliptic coordinates. ... In astronomy, a phase of the Moon is any of the aspects or appearances presented by the Moon as seen from Earth, determined by the portion of the Moon that is visibly illuminated by the Sun. ...

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: In Egyptian mythology, Month is an alternate spelling for Menthu. ... A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ...

 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: In mathematics, a continued fraction is an expression such as where a0 is some integer and all the other numbers an are positive integers. ...

 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. Computus (Latin for computation) is the calculation of the date of Easter in the Christian calendar. ...

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). The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the year (specifically, the seasonal tropical year) and the synodic month. ... Meton of Athens was a mathematician, astronomer and engineer who lived in Athens in the 5th century BCE. He is best known for the 19-year Metonic Cycle which he introduced into the Athenian luni-solar calendar as a method of calculating dates. ... Eclipses may occur repeatedly, separated by some specific interval of time: this interval is called an eclipse cycle. ...

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). Events February 7 - Leo I becomes East Roman emperor. ... This article or section does not cite its references or sources. ... The Synod of Whitby was an important synod which eventually led to the unification of the church in Britain. ... Events September, Synod of Whitby Births Deaths Xuanzang, famous Chinese Buddhist monk. ...

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. A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ... The sidereal year is the time for the Sun to return to the same position in respect to the stars of the celestial sphere. ...

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. The Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the year (specifically, the seasonal tropical year) and the synodic month. ... The Sun is the star at the center of the Solar System. ... This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... The plane of the ecliptic is well seen in this picture from the 1994 lunar prospecting Clementine spacecraft. ...

Further examples

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: Calendar reform is any proposed reform of a calendar. ... How does space sound? Barren and desolate? An empty vacuum of astral winds spinning the darkened horizons. ... For the TV station in the Peoria-Bloomington, Illinois market, see WEEK-TV. A week is a unit of time longer than a day and shorter than a month. ... For information on the calendar, see: Gregorian Calendar For the music style, see: Gregorian chant For medieval usage see: Gregorian reform For the music group see: Gregorian (music group) For the University in Rome: Gregorian University This is a disambiguation page — a navigational aid which lists pages that might otherwise... December 3 is the 337th (in leap years the 338th) day of the year in the Gregorian calendar. ... January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... The Greek alphabet is an alphabet that has been used to write the Greek language since about the 9th century BCE. It was the first alphabet in the narrow sense, that is, a writing system using a separate symbol for each vowel and consonant alike. ...

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. Look up alfa, alpha in Wiktionary, the free dictionary. ... Beta (upper case Β, lower case β) is the second letter of the Greek alphabet. ... Gamma (uppercase Γ, lowercase γ) is the third letter of the Greek alphabet. ... Look up Δ, δ in Wiktionary, the free dictionary. ... Look up Ε, ε in Wiktionary, the free dictionary. ... Zeta or ZETA can refer to: // Zeta (letter), of the Greek alphabet Zeta functions, in mathematics Riemann zeta function Tropical Storm Zeta (2005), formed in December 2005 and lasted through January 2006 Z-pinch, in fusion power Zeta (Mexico), a magazine from Tijuana, Mexico Zeta River, in Montenegro Zeta plain... ETA symbol or ETA (Basque for Basque Homeland and Freedom; IPA pronunciation: [) is a paramilitary Basque nationalist organization. ... Look up Θ, θ in Wiktionary, the free dictionary. ... For programming language, see Iota and Jot. ... For other uses, see Kappa (disambiguation). ... Look up Λ, λ in Wiktionary, the free dictionary. ... Look up MU, Mu, mu in Wiktionary, the free dictionary. ... Look up Nu in Wiktionary, the free dictionary. ... Here are the leap years of The Simple Lunisolar Calendar for the years 2001 - 2210. ... This article or section cites very few or no references or sources. ... December 30 is the 364th day of the year (365th in leap years) in the Gregorian Calendar, with 1 day remaining. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... For information on the calendar, see: Gregorian Calendar For the music style, see: Gregorian chant For medieval usage see: Gregorian reform For the music group see: Gregorian (music group) For the University in Rome: Gregorian University This is a disambiguation page — a navigational aid which lists pages that might otherwise... Look up Nu in Wiktionary, the free dictionary. ... For information on the calendar, see: Gregorian Calendar For the music style, see: Gregorian chant For medieval usage see: Gregorian reform For the music group see: Gregorian (music group) For the University in Rome: Gregorian University This is a disambiguation page — a navigational aid which lists pages that might otherwise... Look up alfa, alpha in Wiktionary, the free dictionary. ... December 25 is the 359th day of the year (360th in leap years) in the Gregorian calendar, with 6 days remaining in the year. ... 2000 (MM) was a leap year starting on Saturday of the Gregorian calendar. ... 2001 (MMI) was a common year starting on Monday of the Gregorian calendar. ...

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 ISO week date system is a leap week calendar system that is part of the ISO 8601 date and time standard. ...

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.

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: Lunation is the mean time for one lunar phase cycle (i. ... Illumination of Earth by Sun on the day of equinox The vernal equinox (or spring equinox) marks the beginning of astronomical spring. ...

1. Artaud
2. Benjamin
3. Clark
4. De Quincy
5. Ellis
6. Furst
7. Grof
8. Hofmann
9. Izumi
10. Janiger
11. Kesey
12. Lilly
13. 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: Antonin Artaud Antoine Marie Joseph Artaud, better known as Antonin Artaud (born September 4, 1896, in Marseille; died March 4, 1948 in Paris) was a French playwright, poet, actor and director. ... Walter Benjamin (July 15, 1892 – September 27, 1940) was a German Marxist literary critic, essayist, translator, and philosopher. ... Thomas de Quincey from the frontispiece of Revolt of the Tartars, Thomas de Quincey (August 15, 1785 – December 8, 1859) was an English author and intellectual. ... Henry Havelock Ellis (February 2, 1859 - July 8, 1939), known as Havelock Ellis, was a British doctor, sexual psychologist and social reformer. ... Stanislav Grof (born 1931 in Prague, Czechoslovakia) is one of the founders of the field of transpersonal psychology and a pioneering researcher into the use of altered states of consciousness for purposes of healing, growth, and insight. ... Dr. Dr. Albert Hofmann (born January 11, 1906) is a prominent Swiss scientist best known as the father of LSD. He was born in Baden, Switzerland, and studied chemistry at the University of Zürich. ... Dr. Oscar Janiger was a University of California Irvine Psychiatrist who was best known for his LSD research, which lasted from 1954 to 1962. ... Kenneth Elton Kesey (September 17, 1935 – November 10, 2001) was an American author, best known for his novel, One Flew Over the Cuckoos Nest, and as a (counter) cultural figure who, some consider, was a link between the beat generation of the 1950s and the hippies of the 1960s. ... John Lilly John Cunningham Lilly (January 6, 1915 – September 30, 2001) was an American physician, psychoanalyst and writer. ... Terence Kemp McKenna (November 16, 1946 – April 3, 2000) was a writer and philosopher. ...

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. For the Manfred Mann album, see 2006 (album). ... October 21 is the 294th day of the year (295th in leap years) in the Gregorian calendar, with 71 days remaining. ... This article or section does not cite its references or sources. ... For the TV station in the Peoria-Bloomington, Illinois market, see WEEK-TV. A week is a unit of time longer than a day and shorter than a month. ...

References

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

See also

• Month
• Solar calendar
• Lunar calendar

Look up Month in Wiktionary, the free dictionary. ... A solar calendar is a calendar whose dates indicate the position of the earth on its revolution around the sun (or equivalently the apparent position of the sun moving on the celestial sphere). ... A lunar calendar is a calendar oriented at the moon phase. ...

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.