Paschalion

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Great and Holy Pascha

The Paschalion of the Orthodox Church is a set of rules for determining the date of Pascha that traditionally has been implemented by calendrical tables combining Metonic lunar cycles with the Julian solar year. The rules are attributed to the First Ecumenical Council (held at Nicea in 325); the cyclical Paschal tables that emerged in connection with the Council were based on 3rd and 4th century Alexandrian prototypes, and then transposed into Julian dates by Dionysius Exiguus in the 6th century.[1]

Contents

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 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 celebration 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 resolved at the Council of Nicea. Although the decision was not recorded as a canon, its synodal letter to the Church in Alexandria conveys “...the good news of the agreement concerning the holy Easter, ...that all our brethren in the East who formerly followed the custom of the Jews are henceforth to celebrate the said most sacred feast of Easter at the same time with the Romans and yourselves.”[2] The Emperor Constantine confirmed this agreement in a letter to bishops that had not attended the Council, announcing two things: (1) "...the most holy festival of Easter should be everywhere celebrated on one and the same day. ...(So) cheerfully accept what is observed with such general unanimity of sentiment in the city of Rome, throughout Italy, Africa, all Egypt, Spain, France, Britain, Libya, the whole of Greece, and the dioceses of Asia, Pontus, and Cilicia;" and (2) "We have cast aside (the Jewish) way of calculating the date of the festival (because) ...we should never allow Easter to be kept twice in one and the same (solar) year!"[3]

Thus, the old custom of consulting the Jewish calculation of Nisan 14 and celebrating Pascha according to that date was formally rejected, and the independent computations long in use at the influential city of Alexandria became the emerging, if still somewhat controversial, consensus. On the other hand, the comments of canonists, preachers, and chroniclers indicate 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 Alexandrian and Roman methods of determining the date of Pascha were based on three principles: (1) Pascha was always after the vernal equinox, (2) it was to follow, but not coincide with, the first full moon of spring, and (3) it was always to be on a Sunday. A fourth principle – and one enunciated following Nicea I – is implicit in the first three: namely, (4) the date of Pascha was not to depend on the Jewish dates for Passover in any way. This last criterion was met by formulating the Paschalion entirely in terms of astronomical events and the weekly cycle of days.[4]

The computational system that eventually prevailed was based on calendrical experiments made at Alexandria beginning in the mid-3rd century.[5] According to this system, Pascha is the first Sunday following the date of the Paschal Full Moon (PFM, also called the νομικον φασκα, "nomikon faska" in Greek) for a given year. The computational PFM is not, however, the first full moon following the vernal equinox as determined by direct observation or by high-accuracy astronomical computations. Rather, the PFM is the first Ecclesiastical Full Moon (EFM) date that falls on or after March 21.[6] Ecclesiastical Full Moons are calendar dates that approximate astronomical full moons using a cycle that repeats every 19 years. March 21 was the date used by the Alexandrians 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 Paschal tables were first being compiled.

The Zonaras Proviso

The decision of the Nicene council concerning Pascha was that it should be computed independently of any Jewish computations: hence, a Paschalion that is consistent with Nicene principles cannot have any built-in dependence on the Jewish calendar. Nevertheless, possibly as early as the 12th century and certainly in recent times it has been widely believed[7] that Christian Pascha is required always to follow, and never coincide with, the first day of Passover, which is Nisan 15 in the Jewish calendar. By the 12th century the errors in the Julian calendar's equinoctial date and age of the moon had accumulated to the degree that Pascha did, in fact, always follow Jewish Nisan 15. This state of affairs continues to the present day, even though the Jewish calendar suffers from a slight solar drift of its own, because the Julian calendar's errors accumulate more rapidly than the Jewish calendar's.

The 12th century canonist Joannes Zonaras seems to have been the first to state the principle that Pascha must always follow Jewish Nisan 15, so the principle is called the “Zonaras Proviso” after him. Zonaras derived his new rule from his reading of Apostolic Canon 7, which states:
"If any Bishop, or Presbyter, or Deacon celebrate the holy day of Easter before the vernal equinox with the Jews, let him be deposed."[7]
Zonaras, commenting on this Canon, wrote
Ἐαρινὴν ἰσημερίαν τινὲς τὴν κε᾽ φασὶ τοῦ Μαρτίου· τινὲς δἐ τὴν κε᾽ τοῦ Ἀπριλλίου. Οῖμαι δὲ μήτ᾽ ἐκείνην μήτε ταυτην τὸν κανόνα λέγειν· ὡς ὲπι τὸ πολὺ γὰρ τὸ Πάσχα πρὸ τῆς κε᾽ τοῦ Ἀπριλλίου ἑορτάζεσθαι είωθεν· ἔστι δὲ ὅτε καὶ πρὸ τῆσ κε᾽ τοῦ Μαρτίου, ὡς συμβαίνειν (εἰ οὔτως νοοϊτο ἡ ἐαρινὴ ἰσημερία) παρὰ τὸν κανόνα τοῦτον τὸ Πάσχα ἑορτάζεσθαι. Ἔοικεν οὐν ἄλλο τι ἐαρινὴν ἰσεμερίαν τοὺς συνετοὺς ἀποστόλους ὀνομάζειν. Ἡ δὲ πᾶσα τοῦ κανόνα, διαταγὴ τοῦτό ὲστι, τὸ μὴ μετὰ Ἰουδαίων (ἤγουν κατ᾽ αὐτὴν τὴν ἡμέραν) ἑορτάζειν τὀ Πάσχα Χριστιανούς. Χρὴ γὰρ προηγεϊσθαι τὴν ανέορτον ἐκείνων ἑορτὴν, καὶ οὕτω τὸ καθ᾽ ἡμᾶς τελεϊσθαι Πάσχα. Ὁ δὲ μὴ τοῦτο ποιῶν ἱερομένο, καθαιρεθήσεται. Τοὺτο δὲ καὶ ἡ ἐν Ἀντιοχείᾳ σύνοδος ἐν πρώτῳ κανόνι διετάξατο, λέγουσα τῆς ἐν Νικαίᾳ πρώτης συνόδου ὄρον εὶναι περὶ τῆς ἑορτῆς τοῦ Πάσχα· εἰ καὶ μὴ εὑρισκεται ὲν τοῖς κανόσι τῆσ ἐν Νικαίᾳ συνόδου τοιοῦτος κανών.[8]
which can be read as
Some say the Spring equinox is the 25th day of March; others, the 25th day of April. I deem that the canon refers to neither the one nor the other. For Pascha is often celebrated before the 25th of April; and there are times when it is celebrated before the 25th of March; so that, (if "Spring equinox" were so understood) Pascha is being celebrated in violation of this canon. Whence it appears that the wise apostles call something else the "Spring equinox." So the whole thrust of the canon is this, that Christians should not celebrate Pascha with the Jews, that is, on the same day. For it is fitting that their feast (which is no feast) is done first; and thus we do our Pascha. If one consecrated to God does this even once, he is removed from orders. The synod in Antioch also ordered this, in their first canon, where they stated that this was decreed concerning the feast of Pascha by the synod of Nicea, although no such canon is found in the canons of the Nicene synod.

So Zonaras read the word "equinox" out of the canon entirely, deciding that the canon must refer to something else: "Their feast (which is no feast) must be done first; and thus we do our Pascha." If Zonaras was restating the rule that Pascha must always fall after the Paschal Full Moon and never coincide with it, then this reading has no foundation in the 4th century historical context, or in the plain meaning of the sentence: The canon clearly refers to the rule of the equinox, not to the rule of the full moon. If Zonaras meant that the Jewish festival of 15 Nisan, as computed on the Jewish calendar, must precede the Christian Pascha, then he was interpreting the canon to mean almost the opposite of what it means in fact, and replacing the rule of independence with a rule of dependence.

The 14th-century canon lawyer Matthew Blastares also enumerated the paschalion's principles in a way that can be taken to require dependence on the Jewish calendar.
First, that it is necessary to celebrate the Pascha after the spring equinox; second, that it is not the same day as the Jewish festival; third, that it is not merely after the equinox, but after the first full moon following the equinox; and fourth, that (it is) the Sunday immediately after the full moon."[9]

If by "the Jewish festival" Blastares simply meant the Paschal Full Moon or nomikon faska, then his second principle is redundant, merely restating the third principle in other words. If he meant the 15th of Nisan on the Rabbinic Jewish calendar, then, as Zonaras may have done before him, he replaced the Nicene rule of independence from the Jewish calendar with a rule that the paschalion must instead depend on it.

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. In both cases, however, the drift is very slow compared to human lifetimes - it amounts to approximately one week every 1000 years. So, for example, it would take an amount of time longer than all recorded history just for Pascha to end up being celebrated after the summer solstice in the northern hemisphere.

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 Byzantine Proposal of 1324

In the 14th century Nicephoras Gregoras calculated the current error in dating the vernal equinox to be three days, and proposed a reform of the Julian calendar to Andronicus II. The reform was not adopted, apparently from lack of popular or political support; and in fact would have corrected less than half of the seven-day error that actually existed at that time.[10]

The Gregorian Proposal of 1582

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, and Eastern churches refused to adopt it on the grounds that the new Roman tables sometimes placed Pascha on the day of the vernal full moon, instead of after it as the Nicene principles required. In 1583 the Council of Constantinople forbade use of the new calendar and Paschalion, making adherence to the Julian calendar a test of Orthodoxy in territories where Roman Catholic Uniate churches were being established.

The Orthodox 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, using a midnight to midnight day to date the full moon.[11] This agreement was never permanently implemented in any Orthodox diocese. But the Revised Julian calendar, a more accurate version of the Gregorian calendar, which was introduced by the same congress has been adopted by some jurisdictions for celebrating the fixed feasts of the liturgical year.

The World Council of Churches Proposal of 1997

A consultation of Catholic, Orthodox and Protestant delegates met in Aleppo, Syria and issued an agreed statement recommending that all member churches work toward a common method of dating Pascha based on the three original Nicene principles, but employing astronomical observations from the meridian of Jerusalem instead of any cyclical tabular computation.[12] This was essentially the same proposal as that of 1923, and was not implemented in the proposed year of 2001 when Eastern and Western dates for Pascha coincided. Resistance to such a reform by Orthodox jurisdictions is apparently rooted in respect for a widespread belief that March 21st Julian was designated by the Nicene Fathers to be the only true vernal equinox, and nourished by persistent fears that changing the received tradition for dating Pascha would endanger the integrity Orthodoxy’s witness to the Patristic Tradition by creating a purely “cosmetic” unity with other Churches.[13]

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. See http://www.tertullian.org/fathers/dionysius_exiguus_easter_01.htm for the Paschal cycle of Dionysius; and http://en.wikipedia.org/wiki/Dionysius_Exiguus for an account of the transposition.

2. See http://www.ccel.org/ccel/schaff/npnf214.vii.ix.html.

3. Eusebius, Vita Constantine III:18-20, Nicene and Post-Nicene Fathers, Vol. 14, pp. 54-55. Also available at http://www.fourthcentury.com/index.php/urkunde-26.

4. James Campbell, “The Paschalion: An Icon of Time,” St. Vladimir’s Theological Quarterly, Vol. 28 No. 4 (1984) pp. 245-262. Also available at https://www.academia.edu/8246608/The_Paschalion_An_Icon_of_Time.

5. The basic system can be found in the “Paschal Canon” of the Alexandrian scholar Anatolius, Bishop of Laodicea, which was composed c. 277 A.D. See http://www.ccel.org/ccel/schaff/anf06.vi.iii.ii.i.html and following pages.

6. Until the 6th century the Paschal tables used in Rome were based on the conventional date of March 25th for the vernal equinox. Jones, “The Development of the Latin Ecclesiastical Calendar” in Bedae, Opera de Temporibus (Cambridge: Medieval Academy of America, 1943), pp. 1-104.

7. The Rudder, Apostolic Canon 7, available at http://www.holytrinitymission.org/books/english/cannons_apostles_rudder.htm . Also The Rudder, Cummings ed. (Chicago: The Orthodox Christian Education Society, 1957). The Rudder's words "after the Passover of the Jews" may simply refer to the paschalion's Paschal Full Moon, not to any date in the Jewish calendar. In practice, it is often understood to mean the 15th of Nisan in the Rabbinic Jewish calendar. See for example http://orthodoxwitness.org/over-the-rooftops/how-the-date-of-pascha-is-determined/2/ (Last visited April 15, 2015) where the author states that Pascha in 2015 is set to April 12 2015 to avoid coinciding with "the Jewish Passover" which he dates (incorrectly) to April 5, and that Pascha 2016 is set to May 1 to avoid coinciding with the Jewish Passover which he dates to April 22. This last date corresponds to 14 (not 15) Nisan 5776 and so is the Jewish Passover in a strict sense, but April 22, 2015 is a Friday, not a Sunday. In any case, the author clearly uses "Jewish Passover" to refer to a date on the Jewish calendar, and not to the paschalion's Paschal Full Moon, which falls on Tuesday, April 7 in 2015 and on Tuesday, April 26 in 2016. James Campbell, cited in Reference 4 above, also indicates that he believes that the "after Passover" rule requires an external reference to the Rabbinic Jewish calendar when he accuses the Gregorian paschalion of violating the rule. (Reference 4 above, text at footnote 14.)

8. Joannes Zonaras, Commentary on Apostolic Canon 7, Migne, PG 137, 49-50.

9. Matthew Blastaris, Syntagma Alphabeticum, Migne, PG 145, 96D-97A.

10. See Guiland, Essai sur Nicephore Gregoras (Paris: P. Geuthner, 1926), pp. 282-284. Also, Dictionnaire de Théogogie Catholique (Paris, 1911) Tome 11, col. 455; and Welborn, "Calendar Reform in the 13th Century" (Chicago: University of Chicago Dissertation, 1935), p. 31.

11. M. Milankovitch, "Das Ende des julianischen Kalenders und der neue Kalender der orientalischen Kirchen", Astronomische Nachrichten 220, 379-384(1924).

12. See World Council of Churches / Middle East Council of Churches Consultation, “Towards a Common Date for Easter” (1997); available at http://www.oikoumene.org/en/resources/documents/wcc-commissions/faith-and-order-commission/i-unity-the-church-and-its-mission/towards-a-common-date-for-easter/index?set_language=en.

13. For an example of this, see Fr. Luke Luhl, “The Proposal for a Common Date to Celebrate Pascha and Easter,” Orthodox Christian Information Center (1997); available at http://orthodoxinfo.com/ecumenism/common_luhl.aspx.

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