Notes on the Orthodox Easter | Notes on Feasts with fixed dates in the Orthodox Calendar

The Orthodox Ecclesiastical Calendar

Last updated 2000 April 7 by M.J. Montes.

Notes on the Orthodox Easter

History

Between AD326 and AD1582, Christianity determined Easter using an algorithm approved by a Church Council in AD325, with the equinox defined as March 21. From AD1054 (when the Orthodox and Catholic Churches split) through AD1582 both the Catholic and Orthodox Churches celebrated Easter on the same date, still using the algorithm from AD325. The Julian Calendar was used by the European (and Christan) communities until the Gregorian reform of 1582.

Since AD1582 October (when the Gregorian Calendar was adopted by much of Catholic Europe), the Orthodox Easter usually falls on dates different than the Western Christian Easter, although apparently the Churches are discussing using the same formula to determine Easter - probably a formula different than that currently used by either Church.

The Orthodox Easter is determined in the Julian Calendar. It has been claimed that Orthodox Easter does not fall on the date of Passover (15 Nisan in the Hebrew Calendar), or before it; this is true recently, but using the modern formulae for determining the date of Passover (rules which go back to the fourth century A.D.), one finds that, in fact, Easter occurred on the first day of Passover several times before the year A.D. 1000. From 1900 until 2099 the Eastern Easter will fall one (45.5%), four (4.5%), or five (21.5%) weeks after the Western Easter - and on the same date in 57 (28.5%) of those years. (I've compiled some Tables showing the offsets between Orthodox and Western Easters from 1583 through 3000 that shows this information.)

Calendar Reform in the Orthodox Church

In the 1923 May there was a well documented meeting that provided for Calendar Reform in of the Orthodox Church. Among other measures, the Orthodox Calendar would have been adjusted to match the Gregorian calendar date; the proposed leap year rule was different than the rule in the Gregorian Calendar, however the calendars would not disagree until AD2800; more often than not, Easter would be celebrated on the same date in both the Eastern and the Western Churches. Except for sporadic use in the 1920's, the calendar reform was not adopted. A wonderful resource examining the calendar reform and its lack of acceptance may be found in the excellent article Counter-reformation in Russian Orthodoxy: Popular Response to Religious Innovation, 1922-1925 by Gregory L. Freeze that appeared in the Summer 1995 issue of Slavic Review. Freeze mentions that soon after the adoption by the second (renovationist) council in 1923 May, the renovationists had a full-scale parish revolt on their hands - the common Orthodox parishioners (in the Soviet Union) did not accept the changes of this council, and indeed, had many other arguements with the renovationists. Other articles concerning Orthodox Calendar Reform that may be found online are: 1) On the Question of the "Revised Julian Calendar" by Father George Lardas; 2) The "Revised" Julian Calendar which offers some explanation of the "New Calendarist views"; and 3) On the Calendar by Father Alexander Lebedeff, which argues for the "Old Calendarist" views.

Algorithms

Alex Kochergin has sent the following information about the Eastern Easter: It has a cycle that (in the Julian Calendar) repeats itself every 532 (19x28) years (since the Julian Solar calendar repeats every 28 years and the Metonic Lunar cycle is 19 years). Eastern Easter tends to occur only after Passover, but only since about A.D 1000. The Gregorian Easter (on the other hand) does not track Passover. For example: in 1997, Passover is 22 April; Western Easter is three weeks EARLIER (30 March) and the Eastern Easter is the Sunday following Passover (27 April). While there are obviously different algorithms used, it is also the case the Julian, Gregorian, and Jewish calendars are slipping relative to each other. The Julian Calendar (and the feasts tied to it) are occuring later in the year (compared to the Gregorian calendar). The Jewish calendar is also moving to later dates in the Gregorian calendar, but at a significantly slower rate than the Julian calendar.

The Date of Orthodox Easter: A variation of Gauss' algorithm

Alex also provided the following algorithm that is based on the algorithm derived by the German mathematician Gauss, the principal simplification is that substitutions have been made for the case of Julian calendars and Orthodox Easters. This algorithm calculates the number of days AFTER March 21 (Julian) that Easter occurs (Note: It is a much simpler calculation than the Western Easter).

RMD(x,y) = remainder when x is divided by y.
R1=RMD(Year,19)
R2=RMD(Year,4)
R3=RMD(Year,7)
RA=19*R1+16
R4=RMD(RA,30)
RB=2*R2+4*R3+6*R4
R5=RMD(RB,7)
RC=R4+R5

The number RC ranges from 1 to 35 which corresponds to March 22 to April 25 in the Julian Calendar (currently April 4 to May 8 on the Gregorian). The Julian Calendar is now 13 days behind the Gregorian, and will be until March 1, 2100 when it will be 14 days behind the Gregorian Calendar.

The Date of Orthodox Easter: An algorithm based on Oudin's Algorithm

Another simple algorithm is listed in the Calendar FAQ by Claus Tondering . It is based on Oudin's algorithm, and is also simple and elegant.
Copyright and disclaimer
------------------------
        This document is Copyright (C) 1996 by Claus Tondering.
        E-mail: c-t@pip.dknet.dk.
        The document may be freely distributed, provided this
        copyright notice is included and no money is charged for
        the document.

        This document is provided "as is". No warranties are made as
        to its correctness.

2.9.6. Isn't there a simpler way to calculate [Orthodox] Easter?
-----------------------------------------------------
This is an attempt to boil down the information given in the previous
sections (the divisions are integer divisions, in which remainders are
discarded): 

[Note: 22%7=1 ; 22/7=3, so % returns the remainder, and / neglects the
remainder.] 

G = year % 19
I = (19*G + 15) % 30
J = (year + year/4 + I) % 7
L = I - J
EasterMonth = 3 + (L + 40)/44
EasterDay = L + 28 - 31*(EasterMonth/4)

[Note: Orthodox Easter is then EasterDay of EasterMonth in the Julian
       Calendar. You will need to add the correct offset to obtain the 
       date in the Gregorian Calendar. From Julian Mar 1, 1900, to Julian
       Feb 29, 2100, the correction is to add 13 days to the Julian date to
       obtain the Gregorian date.]

This algorithm is based in part on the algorithm of Oudin (1940) and
quoted in "Explanatory Supplement to the Astronomical Almanac",
P. Kenneth Seidelmann, editor.

People who want to dig into the workings of this algorithm, may be
interested to know that
    G is the Golden Number-1
    I is the number of days from 21 March to the Paschal full moon
    J is the weekday for the Paschal full moon (0=Sunday, 1=Monday,
      etc.)
    L is the number of days from 21 March to the Sunday on or before
      the Pascal full moon (a number between -6 and 28)

Using these algorithms, I have made tables for the date of Orthodox Easter, tabulated in both the Julian and Gregorian calendars for AD 1875-2124.

Carter's algorithm, Butcher's algorithm, and Oudin's algorithm are algorithms for the Western Churches.

Movable Feasts Associated with Easter

The Ecclesiastical Calendar uses the algorithm above to determine the date of Easter. In addition, the following feasts related to Easter are provided by the Ecclesiastical Calendar.
	Days before Easter 		Days after Easter
Triodon			70	Ascension	39
Sat. of Souls		57	Sat. of Souls	48
Meat Fare		56	Pentecost	49
2nd Sat. of Souls	50	All Saints	56
Lent Begins		48
St. Theodore		43
Sun. of Orthodoxy	42
Sat. of Lazarus		 8
Palm Sunday		 7
Good Friday		 2

Calculate an Ecclesiastical Calendar.


Notes on Feasts with Fixed Dates
in the Orthodox Calendar

The date of Fixed celebrations in the Orthodox calendar is made more difficult by the fact that there are currently differing schools of thought on whether to use the Gregorian or the Julian calendar to determine the date of the Feasts that occur on fixed dates. The two schools of thought are the "Old Calendarists" and the "New Calendarists".

The Old Calendarists use the Julian Calendar to determine the date of ALL religious feasts. This means that Christmas and Epiphany (for example) are 25 Dec. and 6 Jan. JULIAN, repectively. This (currently!) translates to 7 Jan. and 19 Jan. Gregorian, respectively.

The New Calendarists use the Julian Calendar to determine the date of Easter (and celebrations related to Easter) while using the Gregorian calendar to determine the date of fixed celebrations. Thus New Calendarists celebrate Christmas and Epiphany on the same date as the Western Christians, Dec. 25 and 6 Jan. GREGORIAN (respectively). Currently, the New Calendarists are celebrating the fixed feasts 13 days prior to the celebrations of the Old Calendarists.

Acknowledgements

Special thanks to Alex Kochergin, John Cross, and Damien Wyart for useful discussions concerning the content of this page, and to Claus Tondering for maintaining and providing the Calendar FAQ. Please also consult the Resources and Acknowledgements section of the Ecclesiastical Calendar page.

Back to the Ecclesiastical calendar.


Disclaimer: The views and writings presented here are my own, and are NOT the responsibility of Smart Net.
Last updated 2000 April 7.
Copyright © 1996-2000 by Marcos J. Montes.
Marcos Montes
mmontes@no.spam.smart.net