Paschalion

The Paschalion of the Orthodox Church combines the metonic and solar calendrical cycles to determine the date of Pascha for a given year. A common formula to determine the date of Pascha was created in connection with the First Ecumenical Council, held at Nicea in A.D. 325.
 
== Early History ==
The origin of annual festivals in Christianity is obscure. St. Paul (1 Cor. 16.8) and St. Luke (Acts 2.1, 12.3, 20.6, 27.9) refer to Jewish annual festivals expecting their Gentile readers to know what is meant. Chapters 5-10 of John's Gospel is structured around the cycle of Jewish annual festivals, and all the Gospels' passion narratives are set at the time of Passover and the Feast of Unleavened Bread. But nowhere are Christian annual observances are explicitly mentioned. Then, beginning in the mid-2nd century, evidence appears of Pascha and commemorations of martyrs. The commemorations of martyrs were held on fixed dates in the solar calendar. Pascha was computed according to a lunar calendar. This suggests the possibility that the annual Pascha entered Christianity earlier than martyrs' festivals, and that it may have been part of Christianity's initial Jewish inheritance.
Initially the date of Pascha was fixed by consulting Jewish informants to learn when the Jewish month of Nisan would fall, and setting Pascha to the third Sunday in Jewish Nisan, the Sunday of Unleavened Bread. But beginning in the third century there are indications that some Christians were becoming dissatisfied with this reliance on the Jewish calendar. The chief complaint was that the third week in Jewish Nisan was sometimes placed before the spring equinox. Peter, bishop of Alexandria (early 4th century A.D.), in a statement preserved in the preface to the Chronicon Paschale, expresses this view:On the fourteenth day of [the month], being accurately observed after the equinox, the ancients celebrated the Passover, according to the divine command. Whereas the men of the present day now celebrate it before the equinox, and that altogether through negligence and error.Those who held this view began to experiment with independent computations that would always place Pascha in the spring season. Traditionalists, however, felt that the old custom of consulting the Jewish community should continue, even if it sometimes placed Pascha before the equinox. Epiphanius of Salamis (Panarion 3.1.10) quotes a version of the Apostolic Constitutions used by the sect of the Audiani which represents this school of thought: Do not do your own computations, but instead observe Passover when your brethren from the circumcision do. If they err [in the computation], it is no matter to you.The controversy was formally resolved by the Council of Nicea, which determined that a single system should be adopted by all the churches, and that this system should be independent of the Jewish calendar. The old custom of consulting the Jewish community was thus formally abandoned, though in practice independent computations had long been used at the influential city of Alexandria, so that the council may simply have been ratifying what was already the emerging, if still somewhat controversial, consensus. On the other hand, the comments of canonists, preachers, and chroniclers indicates that the old custom of placing Easter in the month of Nisan as computed by the Jewish community continued to have adherents for generations.
== The Nicene Formula ==
The computational system that was eventually worked out derives from the calendrical experiments made at Alexandria beginning in the mid-3rd century. According to this system, Pascha is the first Sunday following the date of the Paschal Full Moon ("PFM") for a given year. The PFM is not, however, as commonly thought, the first full moon following the vernal equinox. Rather, the PFM is the first Ecclesiastical Full Moon ("EFM") date that falls on or after March 21 (or, what is the same thing, the first Ecclesiastical Full Moon that follows March 20). Ecclesiastical Full Moons are calendar dates that approximate astronomical full moons using a cycle that repeats every 19 years. March 21 is the date used for determining the PFM because it was near the date of the vernal equinox in the late 3rd and early 4th century A.D., when the Paschal cycle was first being developed. This formula is called Nicene because some commentators in later generations attributed it to the Nicene council.
=== The Zonaras Proviso ===
The decision of the Nicene council concerning Easter was that it should be computed independently of any Jewish computations: Christians were to compute their own, Christian, Nisan, and set Easter to its third Sunday, rather than setting it to the third Sunday in Jewish Nisan. Hence a paschalion that is consistent with Nicene principles cannot have any built-in dependence on the Hebrew calendar. Nevertheless, at least since the 12th century it has been widely believed that Christian Easter is required always to follow, never coincide with, the first day of Unleavened Bread (Nisan 15) in the Hebrew calendar. By the 12th century the errors in the Julian calendar's equinox date and age of the moon had accumulated to where Easter did, in fact, always follow Jewish Nisan 15. This state of affairs continues to the present day, even though the Hebrew calendar suffers from a slight solar drift of its own, since the Julian calendar's errors accumulate more rapidly than the Hebrew calendar's. The 11th-12th century canonist Joannes Zonaras seems to have been the first to state the principle that Easter must always follow Hebrew Nisan 15. The principle is called the Zonaras proviso after him.
== Implementation ==
The following table shows the Julian and Gregorian calendar date of the Julian Paschal Full Moon (PFM) for each year of the 19-year cycle. To determine the position of a given year in the 19-year cycle, add 1 to the A.D. number of the year and divide by 19. The remainder is the year's position in the cycle. If there is no remainder, the year is the 19th of the cycle. Hence 1994 was year 19 of its cycle, and 1995 was year 1 of its cycle.
The Gregorian calendar equivalences are valid from 1900 to 2099.
Year of cycle	Julian calendar date of Julian PFM	Gregorian calendar date of Julian PFM
1 	April 5 	April 18
2 	March 25 	April 7
3 	April 13 	April 26
4 	April 2 	April 15
5 	March 22 	April 4
6 	April 10 	April 23
7 	March 30 	April 12
8 	April 18 	May 1
9 	April 7 	April 20
10 	March 27 	April 9
11 	April 15 	April 28
12 	April 4 	April 17
13 	March 24 	April 6
14 	April 12 	April 25
15 	April 1 	April 14
16 	March 21 	April 3
17 	April 9 	April 22
18 	March 29 	April 11
19 	April 17 	April 30
Pascha is always the Sunday following the Paschal Full Moon. Since the PFM is simply the 14th day of the Paschal lunar month, this means that Pascha is the third Sunday in the Paschal lunar month, and can fall on any date in the lunar month from the 15th (the day after the PFM) to the 21st (seven days after the PFM). That the structure of the Paschal lunar month is modelled on that of the scriptural month of 'Aviv (now called Nisan) should be clear. The Paschal lunar month is analogous to the month of 'Aviv. It is in effect a Christian 'Aviv or Nisan'. The 14th day, the Paschal Full Moon, is analogous to the day of the Passover sacrifice, and the third week, the 15th to the 21st, the week whose Lord's Day is Pascha, is analogous to the Week of Unleavened Bread.
==Shortcomings of the Julian Paschalion==
===Solar-side flaws===
Because of the inaccuracy of the Julian Calendar's solar year, Pascha is drifting later into the year for those who use the Julian Paschalion. Even though for those using the Julian Calendar Pascha will always be sometime in March or April, it will eventually be celebrated in the northern hemisphere in the summer, the autumn, and then the winter. (For those using the Revised Julian Calendar, the calendar date of Pascha is drifting along with its astronomical position.) 
===Lunar-side flaws===
Additionally the Julian Ecclesiastical Full Moons are deviating further with time from the astronomical full moons: The EFM now falls 3 to 5 days after the corresponding astronomical full moon (see table). 
The Gregorian Calendar, which includes its own revised Paschalion, has neither of these problems.
Gregorian EFM 2008	Astronomical full moon 2008
(day starting at midnight UT)	Gregorian calendar date 
of Julian EFM 2008
Jan 22 	Jan 22	Jan 26
Feb 20 	Feb 21	Feb 25
Mar 22 	Mar 21	Mar 26
Apr 20 	Apr 20	Apr 25
May 20 	May 20	May 24
Jun 18 	Jun 18	Jun 23
Jul 18 	Jul 18	Jul 22
Aug 16 	Aug 16	Aug 21
Sep 15 	Sep 15	Sep 19
Oct 14 	Oct 14	Oct 19
Nov 13 	Nov 13	Nov 17
Dec 12 	Dec 12	Dec 17
== The Gregorian Reform ==
In October 1582, the Roman Catholic Church adopted a major calendar reform designed to correct the Julian calendar's defects. The Julian calendar then in common use was based on an average year of 365.25 days, slightly longer than the mean tropical year of 365.2422 days and the mean vernal equinox year of 365.2424 days. Since 19 Julian years were taken to be equal to 235 lunar months, the average lunar month in the Julian calendar was 29.530851 days, somewhat longer than the astronomical mean synodic month of 29.530589 days. The new calendar eliminated the 10-day drift in the vernal equinox, and the 3-to-4 day deviation in the age of the moon, that had accumulated since the Julian Paschalion had come into use, and laid down rules that would slow the rate of accumulation of errors in the future.
The new calendar was called the Gregorian after its sponsor, Pope Gregory XIII.
== The Rejected Proposal of 1923 ==
A congress of Orthodox bishops meeting in 1923 under the presidency of Patriarch Meletios IV agreed to set Pascha by means of precise astronomical computations referred to the meridian of Jerusalem.[1] This agreement was, however, never permanently implemented in any Orthodox diocese.
== East and West Today ==
The Roman Catholic and Protestant West eventually adopted the Gregorian Calendar for civil and ecclesiastical purposes, including the determination of Pascha. The Orthodox East, however, was not so quick to change. Even when the traditionally Orthodox countries began to adopt the Gregorian Calendar for civil purposes, the Orthodox Church retained the Julian Calendar and original Paschalion. For the sake of convenience, the date of Pascha is often transposed to the coincident date on the Gregorian Calendar for reference. 
Because of the difference in calendars and formulas, Western Easter and Orthodox Pascha do not often coincide. Under current rules, they can differ from each other by 0, 1, 4, or 5 weeks. They are in separate lunations (meaning that they are 4 or 5 weeks apart because their respective cycles identify different lunar months as the Paschal lunar month) in years 3, 8, 11, 14, and 19 of the 19-year cycle, and in the same lunation (0 or 1 week apart) in the other years.
== Algorithms ==
Many notable mathematicians have developed algorithms for determining the date of Orthodox Pascha over the centuries. This simple and elegant one was devised by the brilliant mathematician Jacques Oudin in the 1940s:
N.B. -- In this formula MOD is the modulus function, in which the first number is divided by the second and only the remainder is returned. Further, all division is integer division, in which remainders are discarded. Thus 22 MOD 7 = 1 but 22 / 7 = 3.
 G = year MOD 19
 I = ((19 * G) + 15) MOD 30
 J = (year + (year/4) + I) MOD 7
 L = I - J
 Easter Month = 3 + ((L + 40)/44)
 Easter Day = L + 28 - 31 * (Easter Month/4)
Easter Month will be a number corresponding to a calendar month (e.g., 4 = April) and Easter Day will be the day of that month. Note that this returns the date of Pascha on the Julian calendar. To get the corresponding date on the Gregorian calendar, add 13 days (14 days after March 1, 2100).
== Online Paschalion Utility ==
The date of Pascha and many Pascha-dependent dates can be found (e.g., the start of Great Lent, Pentecost, etc.) through this online JavaScript Paschalion utility (works best with IE3 or Netscape 3 or above).
This site allows the user to enter a year and uses Oudin's algorithm to compute the relevant dates. Although the Orthodox (Julian-based) formulas are used, the utility returns the corresponding Gregorian calendar dates. For example, in 2006 Pascha falls on Sunday, April 10, on the Julian calendar. That date corresponds to April 23 on the Gregorian calendar.
A perpetual Paschalion utility is available here. The utility was created by Aleksandr Andreev of Duke University and calculates Pascha and associated feasts for any series of years. It also calculates the numbers used in Paschal calculations which can be found in an Orthodox Typicon.
==References==
1. M. Milankovitch, "Das Ende des julianischen Kalenders und der neue Kalender der orientalischen Kirchen", Astronomische Nachrichten 220, 379-384(1924). 
==See also==
*Church Calendar
*Gaussian Formulae
*Kyriopascha
== External links ==
*Concerning the Date of Pascha and the 1st Ecumenical Council, by Archbishop Peter (L'Huillier) of New York
*The Calendar Issue in the Orthodox Church, by John Parsells (PDF)
*Frequently Asked Questions about Calendars by Claus Tondering (everything you ever wanted to know)
*Calendar and Easter Topics
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