Revised Julian calendar
Encyclopedia
The Revised Julian calendar, also known as the Rectified Julian calendar, or, less formally, New calendar, is a calendar
, originated in 1923, which effectively discontinued the 340 years of divergence between the naming of dates sanctioned by those Eastern Orthodox churches adopting it and the Gregorian calendar
that has come to predominate worldwide. This calendar replaced the Ecclesiastical Calendar based on the Julian Calendar hitherto in use by all of the Eastern Orthodox Church. The Revised Julian Calendar temporarily aligned its dates with the Gregorian Calendar proclaimed in 1582 by Pope Gregory XIII
for adoption by the Roman Catholic Church
.
in Constantinople
in May 1923. The synod, chaired by controversial Patriarch Meletius IV of Constantinople
, and called Pan-Orthodox by its defenders, did not have representatives from the remaining Orthodox members of the original Pentarchy
(the Patriarchate of Jerusalem, Antioch, and Alexandria) or from the largest Orthodox Church, the Russian Orthodox Church
, then under persecution from the Bolsheviks, but only effective representation from the Patriarch of Constantinople
and the Patriarch of Serbia
.
This synod synchronized the new calendar with the Gregorian calendar by specifying that the next of the Julian calendar would be in the new calendar, thus dropping thirteen days. It then adopted a leap
rule that differs from that of the Gregorian calendar: years divisible by four are leap years, except that years divisible by 100 are only leap years if dividing the year by 900 leaves a remainder of 200 or 600. This leap rule was proposed by the Serbian scientist Milutin Milanković
, an astronomical delegate to the synod representing the Kingdom of Serbs, Croats and Slovenes. Milanković selected this rule because its mean year was within two seconds of the then current length of the mean tropical year
. The present vernal equinox year, however, is about 12 seconds longer, in terms of mean solar days.
The synod also proposed the adoption of an astronomical
rule for Easter
: Easter was to be the Sunday after the midnight-to-midnight day at the meridian of the Church of the Holy Sepulchre
in Jerusalem (35°13'47.2"E or UT+22055 for the small dome) during which the first full moon
after the vernal equinox occurs. Although the instant of the full moon must occur after the instant of the vernal equinox, it may occur on the same day. If the full moon occurs on a Sunday, Easter is the following Sunday. However, all Eastern Orthodox churches rejected this rule and continue to use the Julian calendar to determine the date of Easter (except for the Finnish Orthodox Church
and the Estonian Orthodox Church which now use the Gregorian Easter).
In 900 Julian years there are = 225 leap days. The Revised Julian leap rule omits seven of nine century leap years, leaving leap days per 900-year cycle. Thus the calendar mean year is 365+ days, but this is actually a double-cycle that reduces to 365+ = 365.24 days, or exactly 365 days 5 hours 48 minutes 48 seconds, which is exactly 24 seconds shorter than the Gregorian mean year of 365.2425 days, so in the long term the average rate at which the Revised Julian pulls ahead of the Gregorian calendar is years per day.
The number of days per Revised Julian cycle = 900 × 365 + 218 = 328,718 days. Taking mod
7 leaves a remainder of 5, so like the Julian calendar the Revised Julian calendar cycle does not contain a whole number of weeks. Therefore, a full repetition of the Revised Julian leap cycle with respect to the seven-day day weekly cycle is seven times longer.
by SOLEX 11 using DE421 mode with extended (80-bit) floating point
precision, high integration order (18th order), and forced solar mass loss ("forced" means taken into account at all times). SOLEX can automatically search for northern hemisphere spring equinox moments by finding when the solar declination
crosses the celestial equator
northward, and then it outputs that data as the Terrestrial Time
day and fraction of day relative to at noon (J2000.0 epoch). The progressive tidal slowing of the Earth rotation rate
was accounted for by subtracting ΔT as calculated by the Espenak
-Meeus
polynomial set recommended at the NASA Eclipses web site to obtain the J2000.0-relative Universal Time
moments, which were then properly converted to Revised Julian dates and Jerusalem local apparent time
, taking local apparent midnight as the beginning of each calendar day. The year range of the chart was limited to dates before the year 4400 AD — by then ΔT is expected to accumulate to about six hours, with an uncertainty of less than 2+1/2 hours.
The chart shows that the long-term equinox drift of the Revised Julian calendar is quite satisfactory, at least until 4400 AD. The medium-term wobble spans about two days because, like the Gregorian calendar
, the leap years of the Revised Julian calendar are not smoothly spread: they occur mostly at intervals of four years but there are occasional eight-year gaps (at 7 out of 9 century years). Evidently each of the authorities responsible for the Gregorian and Revised Julian calendars, respectively, accepted a modest amount of medium-term equinox wobble for the sake of traditionally perceived leap rule mental arithmetic simplicity. Therefore the wobble is essentially a curiosity that is of no practical or ritual concern.
, Alexandria
, Antioch, Greece
, Cyprus
, Romania
, Poland
, and Bulgaria
(the last in 1963), called the New calendarists
. It has not been adopted by the Orthodox churches of Jerusalem, Russia
, Serbia
(including later on the resurrected, though uncanonical Macedonian Orthodox Church
), Georgia
, and the Greek Old Calendarists
. Although Milanković stated that the Russian Orthodox Church adopted the new calendar in 1923, the present church continues to use the Julian calendar for both its fixed festivals and for Easter. A solution to this conundrum is to hypothesize that it was accepted only by the short-lived schism
atic Renovationist Church, which had seized church buildings with the support of the Soviet government while Patriarch Tikhon was under house arrest. After his release, on , he declared that all Renovationist decrees were without grace, presumably including its acceptance of the new calendar.
, when the days begin to lengthen again as the physical sun makes its reappearance, along with the fact that Christ has traditionally been recognized by Christians as the metaphorical and spiritual sun who fulfills Malachi's prophetic words: "the sun of righteousness will shine with healing in its wings" (Malachi 4:2). The identification, based on this prophecy, of Jesus Christ as the "sun of righteousness" is found many times in writings of the early Church fathers and follows from many New Testament references linking Jesus with imagery of sun and light.
The defenders of the new calendar do not regard the Julian calendar as having any particular divine sanction (for more on this, see below); rather, they view the Julian calendar as a device of human technology, and thus subject to improvement or replacement just as many other devices of technology that were in use at the dawn of the Church have been replaced with newer forms of technology.
Supporters of the new calendar can also point to certain pastoral problems that are resolved by its adoption.
(1) Parishes observing the Julian calendar are faced with the problem that parishioners are supposed to continue fasting throughout western Christmas and New Year, seasons when their families and friends are likely to be feasting and celebrating New Year's, often with parties, use of liquor, etc. This situation presents obvious temptations, which are eliminated when the new calendar is adopted.
(2) Another pastoral problem is the tendency of some local American media to focus attention each year on the (N.S.) / (O.S.) celebration of Christmas, even in localities where most Orthodox parishes are following the new calendar. So too, in all likelihood, do certain non-Orthodox churches profit from the Orthodox remaining Old Style, since the observance of Christmas among the Orthodox tends to focus attention on ethnic identifications of the feast, rather than on its Christian, dogmatic significance; which, in turn, tends to foster the impression in the public mind that for the Orthodox, the feast of Christ's Nativity is centered on the observance of the Julian date of that feast, rather than on the commemoration of Christ's birth. Such a focus appears to the defenders of the Revised Julian Calendar and to many non-Orthodox as well, as a practice that is charming and quaint, but also anachronistic, unscientific and hence ultimately unreasonable and even cultish.
(3) Some Orthodox themselves may unwittingly reinforce this impression by ignorance of their own faith and by a consequential exclusive, or excessive, focus on the calendar issue: it has been observed, anecdotally, that some Russians cannot cite any difference in belief or practice between their faith and the faith of western Christians, except for the 13-day calendar difference.
Against the new calendar, the argument is made that inasmuch as the use of the Julian calendar was implicit in the decision of the First Ecumenical Council at Nicaea (325), no authority less than an Ecumenical Council may change this decision. However, the fact is that that Council made no decision or decree at all concerning the Julian Calendar. Its silence constituted an implicit acceptance not of the Julian Calendar, but of the civil calendar, which happened to be, at that time, the Julian calendar (the explicit decision of Nicaea being concerned, rather, with the date of Easter). By virtue of this, defenders of the new calendar argue that no decision by an Ecumenical Council was or is necessary today in order to revise (not abandon) the Julian calendar; and further, that by making the revision, the Church stays with the spirit of Nicaea I by keeping with the civil calendar in all its essentials — while conversely, failure to keep with the civil calendar could be seen as a departure from the spirit of Nicaea I in this respect. Lastly, it is argued that since the adoption of the new calendar evidently involves no change in or departure from the theological or the ethical teachings of Orthodox Christianity, but rather amounts to a merely disciplinary or administrative change — a clock correction of sorts — the authority to enact that change falls within the competency of contemporary, local episcopal authority. Implicit acceptance of this line of reasoning, or something very close to it, underlies the decision to adopt the new calendar by those Orthodox churches which have done so.
It follows that, in general, the defenders of the new calendar hold the view that in localities where the Church's episcopal authority has elected to adopt the new calendar, but where some have broken communion with those implementing this change, it is those who have broken communion who have in fact introduced the disunity, rather than the new calendar itself or those who have adopted it — although most would agree that attempts at various times to mandate the use of the new calendar through compulsion, have magnified the disunity.
To the objection that the new calendar has created problems by adjusting only the fixed calendar, while leaving all of the commemorations on the moveable cycle on the original Julian calendar, the obvious answer, of course, is that the 1923 Synod, which adopted the new calendar, did in fact change the moveable calendar as well, and that calendar problems introduced as a result of the adoption of the (fixed) new calendar alone, would not have existed had the corrections to the moveable calendar also been implemented.
According to the defenders of the new calendar, the argument that the 25 December (N.S.) observance of Christmas is a purely secular observance and is therefore an unsuitable time for Orthodox Christians to celebrate Christ's Nativity, is plainly inaccurate, since the observances of Christ's birth among western Christians (and today, among many Orthodox Christians) obviously occur overwhelmingly in places of worship and involve hymns, prayers, scripture readings, religious dramas, liturgical concerts, and the like. Defenders of the new calendar further note that, to the extent that is a secular observance in the western world, (i.e. O.S.) appears to be becoming one as well, in Orthodox countries that continue to follow the Old Calendar. In Russia, for example, is no longer a spiritual holiday for Orthodox Christians alone, but has now become a national (hence secular) holiday for all Russians, including non-Orthodox Christians, people of other religions, and nonbelievers. Where this will lead in the end remains to be seen.
Among other arguments made by the defenders of the new calendar for their view, are those made on the basis of truth (notwithstanding that the detractors of that calendar make the claim that the Old Style date, , is the true celebration of Christ's Nativity). Arguments from truth can take two forms: (1) If a calendar is a system for reckoning time based on the motions of astronomical bodies — specifically the movements of Sun and Moon, in the case of the church calendar — and if precision or accuracy is understood as one aspect of truth, then a calendar that is more accurate and precise with respect to the motions of those bodies must be regarded as truer than one which is less precise. In this regard, some of those who champion the Old Calendar as truth (rather than for pastoral reasons, as seems to be the case with the national churches that adhere to it) may appear, to those following the new calendar, as the defenders of a fiction. (2) Some defenders of the new calendar argue that the celebration, in any way or form, of two feasts of Christ's Nativity within the same liturgical year is not possible, since according to the faith there is only one celebration of that feast in a given year. On this basis, they argue that those who prefer to observe a "secular" feast of the Nativity on and a "religious" one on , err in respect of the truth that there is but one feast of the Nativity each year.
, and there has been much acrimony between the two parties over the decades since the change, leading sometimes even to violence, especially in Greece
.
Critics see the change in calendar as an unwarranted innovation, influenced by Western society
. They say that no sound theological reason has been given for changing the calendar, that the only reasons advanced are social. The proposal for change was introduced by a Patriarch whose canonical status has been disputed and who was a Freemason.
The argument is also made that since the use of the Julian calendar was implicit in the decision of the First Ecumenical Council at Nicaea (325) which standardized the calculation of the date of Pascha
(Easter
), no authority less than an Ecumenical Council
may change it. The adoption of a new calendar has broken the unity of the church, undoing the whole purpose of the council of Nicaea, so once again, "on the same day some should be fasting whilst others are seated at a banquet."
Liturgical objections to the new calendar stem from the fact that it adjusts only those liturgical celebrations that occur on fixed calendar dates, leaving all of the commemorations on the moveable cycle
on the original Julian calendar. This upsets the harmony and balance of the liturgical year
. (This would not have been a problem if the recommendations of the 1923 synod to use an astronomical rule to reckon the date of Easter, as outlined above, had not been rejected.) This disruption is most noticeable during Great Lent
. Certain feast days are designed to fall during Lent, such as the feast of the Forty Martyrs of Sebaste
. The Feast of the Annunciation
is also intended to fall either before Pascha or during Bright Week
. Sometimes, Annunciation will fall on the day of Pascha itself, a very special concurrence known as Kyrio-Pascha, with special liturgical practices appointed for such an occurrence. However, under the new calendar, Kyrio-Pascha becomes an impossibility. The Apostles' Fast
displays the most difficult aspect of the new calendar. The fast begins on the moveable cycle and ends on the fixed date of 29 June; since the new calendar is 13 days ahead of the traditional Julian calendar, the Apostles' Fast is 13 days shorter for those who follow the new calendar, and some years it is completely abrogated. Furthermore, critics of the new calendar point out the advantage to celebrating Nativity
separately from the secular observances of Christmas
and New Year
, which are associated with partying and alcohol consumption.
Critics also point out that proponents of the new calendar tend to use worldly rather than spiritual justification for changing the calendar: wanting to "party with everyone else" at Christmas; concern that the gradual shift in the Julian calendar will somehow negatively affect the celebration of feasts that are linked to the seasons of the year. However, opponents counter that the seasons are reversed in the southern hemisphere
, where the liturgical celebrations are no less valid. The validity of this argument is questionable, since the feasts of the Orthodox Church were not changed no matter where they were celebrated, and Orthodox services were held in the southern hemisphere with little issue centuries before the introduction of the new calendar.
Proponents also argue that the new calendar is somehow more "scientific", but opponents argue that science is not the primary concern of the Church; rather, the Church is concerned with other-worldliness, with being "in the world, but not of it", fixing the attention of the faithful on eternity. Scientifically speaking, neither the Gregorian calendar nor the new calendar is absolutely precise. This is because the solar year cannot be evenly divided into 24 hour segments. So any public calendar is imprecise; it is simply an agreed-upon designation of days.
From a spiritual perspective, Old Calendarists also point to a number of miraculous occurrences which occur on the Old Calendar exclusively, such as the "descent of the cloud on the mount" on the feast of the Transfiguration. After the calendar change was instituted, the followers of the Old Calendar in Greece apparently witnessed the appearance of a cross in the sky, visible to thousands on the feast of the Exaltation of the Holy Cross, 1925, of which eyewitness accounts were recorded.
For such special events, if the original Julian date and year is known then the option always exists to calculate what was the proleptic Revised Julian date of that event and then observe its anniversary on that day, if that could be socially and ritually accepted.
, although those authors explicitly ignored the Revised Julian calendar. Their book, which will be referred to hereinafter as "CC3", should be consulted for methods to handle BC
dates and the traditional omission of a year zero, both of which will be ignored here. They define the MOD
operator as x MOD y = x − y × floor(x / y), because that expression is valid for negative and floating point operands, returning the remainder
from dividing x by y while discarding the quotient
. Expressions like floor(x / y) return the quotient from dividing x by y while discarding the remainder.
IF isLeapYear THEN
END IF
The arithmetic given here will not "crash" if an invalid date is given. To verify that a given date is a valid Revised Julian date, convert it to an ordinal day count and then back to a Revised Julian date — if the final date differs from the given date then the given date is invalid. This method should also be used to validate any implementation of calendrical arithmetic, by iteratively checking thousands of random and sequential dates for such errors.
To convert a Revised Julian date to any other calendar, first convert it to an ordinal day count, and then all that is needed is a function to convert the ordinal days count to that calendar.
To convert a date from any other calendar to a Revised Julian date, first convert that calendar date to an ordinal day count, then convert ordinal days to the Revised Julian date.
The following constant defined midnight at the start of Revised Julian date Monday, as the beginning of the first ordinal day. This moment was Julian Day
number 1721425.5.
CC3 outlines functions for Gregorian and Julian calendar conversions, as well as many other calendars, always calculating in terms of the ordinal day number, which they call the "fixed date" or rata die
(RD), assigning the number 1 to the Gregorian calendar epoch. The arithmetic herein, by using the same ordinal day numbering epoch, is fully compatible with all CC3 functions for calendrical calculations and date inter-conversions.
You can assign a different integer to the Revised Julian epoch, for the purpose of numbering ordinal days relative to some other epoch, but if you do so then take the epoch difference into account when using any CC3 calendar functions and when converting an ordinal day number to a weekday number.
Optionally the ordinal day number can include a fractional component to represent the time as the elapsed fraction of a day. The ordinal day number of the J2000 moment ( noon) was 730120.5.
If month is after February then subtract 1 day for a leap year or subtract 2 days for a common year:
Finally subtract a day for each prior century year (most of which are non-leap) and then add back in the number of prior century leap years:
Finally, calculate the day number within the month by subtracting the Fixed days count for the start of the month from the originally given Fixed days count, and then add one day:
Don't be tempted to omit subtracting the RJepoch just because it is offset by adding +1. As written, this expression is robust even if you assign a value other than one to the epoch.
Calendar
A calendar is a system of organizing days for social, religious, commercial, or administrative purposes. This is done by giving names to periods of time, typically days, weeks, months, and years. The name given to each day is known as a date. Periods in a calendar are usually, though not...
, originated in 1923, which effectively discontinued the 340 years of divergence between the naming of dates sanctioned by those Eastern Orthodox churches adopting it and the Gregorian calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
that has come to predominate worldwide. This calendar replaced the Ecclesiastical Calendar based on the Julian Calendar hitherto in use by all of the Eastern Orthodox Church. The Revised Julian Calendar temporarily aligned its dates with the Gregorian Calendar proclaimed in 1582 by Pope Gregory XIII
Pope Gregory XIII
Pope Gregory XIII , born Ugo Boncompagni, was Pope from 1572 to 1585. He is best known for commissioning and being the namesake for the Gregorian calendar, which remains the internationally-accepted civil calendar to this date.-Youth:He was born the son of Cristoforo Boncompagni and wife Angela...
for adoption by the Roman Catholic Church
Roman Catholic Church
The Catholic Church, also known as the Roman Catholic Church, is the world's largest Christian church, with over a billion members. Led by the Pope, it defines its mission as spreading the gospel of Jesus Christ, administering the sacraments and exercising charity...
.
Description
The new calendar was proposed for adoption by the Orthodox churches at a synodSynod
A synod historically is a council of a church, usually convened to decide an issue of doctrine, administration or application. In modern usage, the word often refers to the governing body of a particular church, whether its members are meeting or not...
in Constantinople
Constantinople
Constantinople was the capital of the Roman, Eastern Roman, Byzantine, Latin, and Ottoman Empires. Throughout most of the Middle Ages, Constantinople was Europe's largest and wealthiest city.-Names:...
in May 1923. The synod, chaired by controversial Patriarch Meletius IV of Constantinople
Patriarch Meletius IV of Constantinople
Meletius IV was the Ecumenical Patriarch of Constantinople from 1921 to 1923. He also served as Greek Patriarch of Alexandria under the episcopal name Meletius II from 1926 to 1935...
, and called Pan-Orthodox by its defenders, did not have representatives from the remaining Orthodox members of the original Pentarchy
Pentarchy
Pentarchy is a term in the history of Christianity for the idea of universal rule over all Christendom by the heads of five major episcopal sees, or patriarchates, of the Roman Empire: Rome, Constantinople, Alexandria, Antioch, and Jerusalem...
(the Patriarchate of Jerusalem, Antioch, and Alexandria) or from the largest Orthodox Church, the Russian Orthodox Church
Russian Orthodox Church
The Russian Orthodox Church or, alternatively, the Moscow Patriarchate The ROC is often said to be the largest of the Eastern Orthodox churches in the world; including all the autocephalous churches under its umbrella, its adherents number over 150 million worldwide—about half of the 300 million...
, then under persecution from the Bolsheviks, but only effective representation from the Patriarch of Constantinople
Patriarch of Constantinople
The Ecumenical Patriarch is the Archbishop of Constantinople – New Rome – ranking as primus inter pares in the Eastern Orthodox communion, which is seen by followers as the One, Holy, Catholic, and Apostolic Church....
and the Patriarch of Serbia
Patriarch of Serbia
This is a list of the Archbishops and Patriarchs of Peć and the Serbs from the creation of the church as an archdiocese in 1219 to today's Patriarchate. The list includes all the Archbishops and Patriarchs that led the Serbian Orthodox community under Patriarchate of Peć...
.
This synod synchronized the new calendar with the Gregorian calendar by specifying that the next of the Julian calendar would be in the new calendar, thus dropping thirteen days. It then adopted a leap
Leap year
A leap year is a year containing one extra day in order to keep the calendar year synchronized with the astronomical or seasonal year...
rule that differs from that of the Gregorian calendar: years divisible by four are leap years, except that years divisible by 100 are only leap years if dividing the year by 900 leaves a remainder of 200 or 600. This leap rule was proposed by the Serbian scientist Milutin Milanković
Milutin Milankovic
Milutin Milanković was a Serbian geophysicist and civil engineer, best known for his theory of ice ages, suggesting a relationship between Earth's long-term climate changes and periodic changes in its orbit, now known as Milankovitch cycles. Milanković gave two fundamental contributions to global...
, an astronomical delegate to the synod representing the Kingdom of Serbs, Croats and Slovenes. Milanković selected this rule because its mean year was within two seconds of the then current length of the mean tropical year
Tropical year
A tropical year , for general purposes, is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice...
. The present vernal equinox year, however, is about 12 seconds longer, in terms of mean solar days.
The synod also proposed the adoption of an astronomical
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
rule for Easter
Easter
Easter is the central feast in the Christian liturgical year. According to the Canonical gospels, Jesus rose from the dead on the third day after his crucifixion. His resurrection is celebrated on Easter Day or Easter Sunday...
: Easter was to be the Sunday after the midnight-to-midnight day at the meridian of the Church of the Holy Sepulchre
Church of the Holy Sepulchre
The Church of the Holy Sepulchre, also called the Church of the Resurrection by Eastern Christians, is a church within the walled Old City of Jerusalem. It is a few steps away from the Muristan....
in Jerusalem (35°13'47.2"E or UT+22055 for the small dome) during which the first full moon
Full moon
Full moon lunar phase that occurs when the Moon is on the opposite side of the Earth from the Sun. More precisely, a full moon occurs when the geocentric apparent longitudes of the Sun and Moon differ by 180 degrees; the Moon is then in opposition with the Sun.Lunar eclipses can only occur at...
after the vernal equinox occurs. Although the instant of the full moon must occur after the instant of the vernal equinox, it may occur on the same day. If the full moon occurs on a Sunday, Easter is the following Sunday. However, all Eastern Orthodox churches rejected this rule and continue to use the Julian calendar to determine the date of Easter (except for the Finnish Orthodox Church
Finnish Orthodox Church
The Finnish Orthodox Church is an autonomous Orthodox archdiocese of the Patriarchate of Constantinople. The Church has a legal position as a national church in the country, along with the Evangelical Lutheran Church of Finland....
and the Estonian Orthodox Church which now use the Gregorian Easter).
Arithmetic
The following are Gregorian minus Revised Julian date differences, calculated for the beginning of March in each century year, which is where differences arise or disappear, until 8000 AD. These are exact arithmetic calculations, not depending on any astronomy. A negative difference means that the proleptic Revised Julian calendar was behind the proleptic Gregorian calendar. A positive difference means that the Revised Julian calendar will be ahead of the Gregorian calendar, which will first occur on :| Century Difference |
100 0 |
200 −1 |
300 −1 |
400 0 |
500 0 |
600 −1 |
700 −1 |
800 0 |
900 0 |
1000 0 |
|---|---|---|---|---|---|---|---|---|---|---|
| Century Difference |
1100 −1 |
1200 0 |
1300 0 |
1400 0 |
1500 −1 |
1600 0 |
1700 0 |
1800 0 |
1900 0 |
2000 0 |
| Century Difference |
2100 0 |
2200 0 |
2300 0 |
2400 0 |
2500 0 |
2600 0 |
2700 0 |
2800 +1 |
2900 0 |
3000 0 |
| Century Difference |
3100 0 |
3200 +1 |
3300 0 |
3400 0 |
3500 0 |
3600 +1 |
3700 +1 |
3800 0 |
3900 0 |
4000 +1 |
| Century Difference |
4100 +1 |
4200 0 |
4300 0 |
4400 +1 |
4500 +1 |
4600 +1 |
4700 0 |
4800 +1 |
4900 +1 |
5000 +1 |
| Century Difference |
5100 0 |
5200 +1 |
5300 +1 |
5400 +1 |
5500 +1 |
5600 +1 |
5700 +1 |
5800 +1 |
5900 +1 |
6000 +1 |
| Century Difference |
6100 +1 |
6200 +1 |
6300 +1 |
6400 +2 |
6500 +1 |
6600 +1 |
6700 +1 |
6800 +2 |
6900 +1 |
7000 +1 |
| Century Difference |
7100 +1 |
7200 +2 |
7300 +2 |
7400 +1 |
7500 +1 |
7600 +2 |
7700 +2 |
7800 +1 |
7900 +1 |
8000 +2 |
In 900 Julian years there are = 225 leap days. The Revised Julian leap rule omits seven of nine century leap years, leaving leap days per 900-year cycle. Thus the calendar mean year is 365+ days, but this is actually a double-cycle that reduces to 365+ = 365.24 days, or exactly 365 days 5 hours 48 minutes 48 seconds, which is exactly 24 seconds shorter than the Gregorian mean year of 365.2425 days, so in the long term the average rate at which the Revised Julian pulls ahead of the Gregorian calendar is years per day.
The number of days per Revised Julian cycle = 900 × 365 + 218 = 328,718 days. Taking mod
Modulo operation
In computing, the modulo operation finds the remainder of division of one number by another.Given two positive numbers, and , a modulo n can be thought of as the remainder, on division of a by n...
7 leaves a remainder of 5, so like the Julian calendar the Revised Julian calendar cycle does not contain a whole number of weeks. Therefore, a full repetition of the Revised Julian leap cycle with respect to the seven-day day weekly cycle is seven times longer.
Epoch
The epoch of the Julian calendar was on the Saturday before the Monday that was the epoch of the Gregorian calendar. In other words, Gregorian = Julian . The Revised Julian reform not only changed the leap rule but also made the epoch the same as that of the Gregorian calendar. This seems to have been carried out implicitly, and even scientific articles make no mention of it. Nevertheless, it is impossible to implement calendrical calculations and calendar date conversion software without appreciating this detail and taking the 2-day shift into account. If the original Julian calendar epoch is mistakenly used in such calculations then there is no way to reproduce the currently accepted dating of the Revised Julian calendar, which yields no difference between Gregorian and Revised Julian dates in the 21st century.March equinox
The following is a scatter plot of actual astronomical northward equinox moments as numerically integratedNumerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of...
by SOLEX 11 using DE421 mode with extended (80-bit) floating point
Floating point
In computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...
precision, high integration order (18th order), and forced solar mass loss ("forced" means taken into account at all times). SOLEX can automatically search for northern hemisphere spring equinox moments by finding when the solar declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...
crosses the celestial equator
Celestial equator
The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earth's equator. In other words, it is a projection of the terrestrial equator out into space...
northward, and then it outputs that data as the Terrestrial Time
Terrestrial Time
Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of the Earth....
day and fraction of day relative to at noon (J2000.0 epoch). The progressive tidal slowing of the Earth rotation rate
Tidal acceleration
Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite , and the primary planet that it orbits . The "acceleration" is usually negative, as it causes a gradual slowing and recession of a satellite in a prograde orbit away from the primary, and a corresponding...
was accounted for by subtracting ΔT as calculated by the Espenak
Fred Espenak
Fred Espenak is an American astrophysicist. He works at the Goddard Space Flight Center. He is best known for his work on eclipse predictions....
-Meeus
Jean Meeus
Jean Meeus is a Belgian astronomer specializing in celestial mechanics. The asteroid 2213 Meeus is named after him.Jean Meeus studied mathematics at the University of Leuven in Belgium, where he received the Degree of Licentiate in 1953...
polynomial set recommended at the NASA Eclipses web site to obtain the J2000.0-relative Universal Time
Universal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...
moments, which were then properly converted to Revised Julian dates and Jerusalem local apparent time
Solar time
Solar time is a reckoning of the passage of time based on the Sun's position in the sky. The fundamental unit of solar time is the day. Two types of solar time are apparent solar time and mean solar time .-Introduction:...
, taking local apparent midnight as the beginning of each calendar day. The year range of the chart was limited to dates before the year 4400 AD — by then ΔT is expected to accumulate to about six hours, with an uncertainty of less than 2+1/2 hours.
The chart shows that the long-term equinox drift of the Revised Julian calendar is quite satisfactory, at least until 4400 AD. The medium-term wobble spans about two days because, like the Gregorian calendar
Gregorian calendar
The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...
, the leap years of the Revised Julian calendar are not smoothly spread: they occur mostly at intervals of four years but there are occasional eight-year gaps (at 7 out of 9 century years). Evidently each of the authorities responsible for the Gregorian and Revised Julian calendars, respectively, accepted a modest amount of medium-term equinox wobble for the sake of traditionally perceived leap rule mental arithmetic simplicity. Therefore the wobble is essentially a curiosity that is of no practical or ritual concern.
Adoption
The new calendar has been adopted by the Orthodox churches of ConstantinopleEcumenical Patriarchate of Constantinople
The Ecumenical Patriarchate of Constantinople , part of the wider Orthodox Church, is one of the fourteen autocephalous churches within the communion of Orthodox Christianity...
, Alexandria
Greek Orthodox Church of Alexandria
The Greek Orthodox Church of Alexandria, also known as the Patriarchate of Alexandria and All Africa is an autocephalous Greek Orthodox Church within the wider communion of Orthodox Christianity.Officially, it is called the Greek Orthodox Patriarchate of Alexandria to distinguish it from the...
, Antioch, Greece
Church of Greece
The Church of Greece , part of the wider Greek Orthodox Church, is one of the autocephalous churches which make up the communion of Orthodox Christianity...
, Cyprus
Cypriot Orthodox Church
The Church of Cyprus is an autocephalous Greek church within the communion of Orthodox Christianity. It is one of the oldest Eastern Orthodox autocephalous churches, achieving independence from the Patriarchate of Antioch and All the East in 431...
, Romania
Romanian Orthodox Church
The Romanian Orthodox Church is an autocephalous Eastern Orthodox church. It is in full communion with other Eastern Orthodox churches, and is ranked seventh in order of precedence. The Primate of the church has the title of Patriarch...
, Poland
Polish Orthodox Church
The Polish Autocephalous Orthodox Church, commonly known as the Polish Orthodox Church, , is one of the autocephalous Eastern Orthodox Churches in full communion...
, and Bulgaria
Bulgarian Orthodox Church
The Bulgarian Orthodox Church - Bulgarian Patriarchate is an autocephalous Eastern Orthodox Church with some 6.5 million members in the Republic of Bulgaria and between 1.5 and 2.0 million members in a number of European countries, the Americas and Australia...
(the last in 1963), called the New calendarists
New calendarists
The New calendarists are those Eastern Orthodox Churches that adopted the Revised Julian calendar, namely the Orthodox churches of Constantinople, Alexandria, Antioch, Greece, Cyprus, Romania, Poland, Bulgaria, and most of the Orthodox Church in America...
. It has not been adopted by the Orthodox churches of Jerusalem, Russia
Russian Orthodox Church
The Russian Orthodox Church or, alternatively, the Moscow Patriarchate The ROC is often said to be the largest of the Eastern Orthodox churches in the world; including all the autocephalous churches under its umbrella, its adherents number over 150 million worldwide—about half of the 300 million...
, Serbia
Serbian Orthodox Church
The Serbian Orthodox Church is one of the autocephalous Orthodox Christian churches, ranking sixth in order of seniority after Constantinople, Alexandria, Antioch, Jerusalem, and Russia...
(including later on the resurrected, though uncanonical Macedonian Orthodox Church
Macedonian Orthodox Church
The Macedonian Orthodox Church – Ohrid Archbishopric or just Macedonian Orthodox Church is the body of Christians who are united under the Archbishop of Ohrid and Macedonia, exercising jurisdiction over Macedonian Orthodox Christians in the Republic of Macedonia and in exarchates in the Macedonian...
), Georgia
Georgian Orthodox and Apostolic Church
The Georgian Apostolic Autocephalous Orthodox Church is an autocephalous part of the Eastern Orthodox Church. Since the 4th century AD, Georgian Orthodoxy has been the state religion of Georgia, and it remains the country's largest religious institution....
, and the Greek Old Calendarists
Greek Old Calendarists
Greek Old Calendarists are groups that separated from the Orthodox Church of Greece or from the Patriarchate of Constantinople, precipitated by disagreement over the abandonment of the traditional Julian Calendar.- History :Up until the early 20th century, the Eastern Orthodox Church used the...
. Although Milanković stated that the Russian Orthodox Church adopted the new calendar in 1923, the present church continues to use the Julian calendar for both its fixed festivals and for Easter. A solution to this conundrum is to hypothesize that it was accepted only by the short-lived schism
Schism (religion)
A schism , from Greek σχίσμα, skhísma , is a division between people, usually belonging to an organization or movement religious denomination. The word is most frequently applied to a break of communion between two sections of Christianity that were previously a single body, or to a division within...
atic Renovationist Church, which had seized church buildings with the support of the Soviet government while Patriarch Tikhon was under house arrest. After his release, on , he declared that all Renovationist decrees were without grace, presumably including its acceptance of the new calendar.
Defense
The basic justification for the new calendar is the known errors of the Julian calendar, which will in the course of time lead to a situation in which those following the Julian calendar will be reckoning the month of December (and the feast of Christ's Nativity) during the heat of summer, August and its feasts during the deep cold of winter, Pascha during the autumn season, and the November feasts in the springtime. This would conflict with the Church's historic practice of celebrating Christ's birth on , a date chosen for a number of reasons. One of the reasons mentioned by Bennet is the time of the winter solsticeWinter solstice
Winter solstice may refer to:* Winter solstice, astronomical event* Winter Solstice , former band* Winter Solstice: North , seasonal songs* Winter Solstice , 2005 American film...
, when the days begin to lengthen again as the physical sun makes its reappearance, along with the fact that Christ has traditionally been recognized by Christians as the metaphorical and spiritual sun who fulfills Malachi's prophetic words: "the sun of righteousness will shine with healing in its wings" (Malachi 4:2). The identification, based on this prophecy, of Jesus Christ as the "sun of righteousness" is found many times in writings of the early Church fathers and follows from many New Testament references linking Jesus with imagery of sun and light.
The defenders of the new calendar do not regard the Julian calendar as having any particular divine sanction (for more on this, see below); rather, they view the Julian calendar as a device of human technology, and thus subject to improvement or replacement just as many other devices of technology that were in use at the dawn of the Church have been replaced with newer forms of technology.
Supporters of the new calendar can also point to certain pastoral problems that are resolved by its adoption.
(1) Parishes observing the Julian calendar are faced with the problem that parishioners are supposed to continue fasting throughout western Christmas and New Year, seasons when their families and friends are likely to be feasting and celebrating New Year's, often with parties, use of liquor, etc. This situation presents obvious temptations, which are eliminated when the new calendar is adopted.
(2) Another pastoral problem is the tendency of some local American media to focus attention each year on the (N.S.) / (O.S.) celebration of Christmas, even in localities where most Orthodox parishes are following the new calendar. So too, in all likelihood, do certain non-Orthodox churches profit from the Orthodox remaining Old Style, since the observance of Christmas among the Orthodox tends to focus attention on ethnic identifications of the feast, rather than on its Christian, dogmatic significance; which, in turn, tends to foster the impression in the public mind that for the Orthodox, the feast of Christ's Nativity is centered on the observance of the Julian date of that feast, rather than on the commemoration of Christ's birth. Such a focus appears to the defenders of the Revised Julian Calendar and to many non-Orthodox as well, as a practice that is charming and quaint, but also anachronistic, unscientific and hence ultimately unreasonable and even cultish.
(3) Some Orthodox themselves may unwittingly reinforce this impression by ignorance of their own faith and by a consequential exclusive, or excessive, focus on the calendar issue: it has been observed, anecdotally, that some Russians cannot cite any difference in belief or practice between their faith and the faith of western Christians, except for the 13-day calendar difference.
Against the new calendar, the argument is made that inasmuch as the use of the Julian calendar was implicit in the decision of the First Ecumenical Council at Nicaea (325), no authority less than an Ecumenical Council may change this decision. However, the fact is that that Council made no decision or decree at all concerning the Julian Calendar. Its silence constituted an implicit acceptance not of the Julian Calendar, but of the civil calendar, which happened to be, at that time, the Julian calendar (the explicit decision of Nicaea being concerned, rather, with the date of Easter). By virtue of this, defenders of the new calendar argue that no decision by an Ecumenical Council was or is necessary today in order to revise (not abandon) the Julian calendar; and further, that by making the revision, the Church stays with the spirit of Nicaea I by keeping with the civil calendar in all its essentials — while conversely, failure to keep with the civil calendar could be seen as a departure from the spirit of Nicaea I in this respect. Lastly, it is argued that since the adoption of the new calendar evidently involves no change in or departure from the theological or the ethical teachings of Orthodox Christianity, but rather amounts to a merely disciplinary or administrative change — a clock correction of sorts — the authority to enact that change falls within the competency of contemporary, local episcopal authority. Implicit acceptance of this line of reasoning, or something very close to it, underlies the decision to adopt the new calendar by those Orthodox churches which have done so.
It follows that, in general, the defenders of the new calendar hold the view that in localities where the Church's episcopal authority has elected to adopt the new calendar, but where some have broken communion with those implementing this change, it is those who have broken communion who have in fact introduced the disunity, rather than the new calendar itself or those who have adopted it — although most would agree that attempts at various times to mandate the use of the new calendar through compulsion, have magnified the disunity.
To the objection that the new calendar has created problems by adjusting only the fixed calendar, while leaving all of the commemorations on the moveable cycle on the original Julian calendar, the obvious answer, of course, is that the 1923 Synod, which adopted the new calendar, did in fact change the moveable calendar as well, and that calendar problems introduced as a result of the adoption of the (fixed) new calendar alone, would not have existed had the corrections to the moveable calendar also been implemented.
According to the defenders of the new calendar, the argument that the 25 December (N.S.) observance of Christmas is a purely secular observance and is therefore an unsuitable time for Orthodox Christians to celebrate Christ's Nativity, is plainly inaccurate, since the observances of Christ's birth among western Christians (and today, among many Orthodox Christians) obviously occur overwhelmingly in places of worship and involve hymns, prayers, scripture readings, religious dramas, liturgical concerts, and the like. Defenders of the new calendar further note that, to the extent that is a secular observance in the western world, (i.e. O.S.) appears to be becoming one as well, in Orthodox countries that continue to follow the Old Calendar. In Russia, for example, is no longer a spiritual holiday for Orthodox Christians alone, but has now become a national (hence secular) holiday for all Russians, including non-Orthodox Christians, people of other religions, and nonbelievers. Where this will lead in the end remains to be seen.
Among other arguments made by the defenders of the new calendar for their view, are those made on the basis of truth (notwithstanding that the detractors of that calendar make the claim that the Old Style date, , is the true celebration of Christ's Nativity). Arguments from truth can take two forms: (1) If a calendar is a system for reckoning time based on the motions of astronomical bodies — specifically the movements of Sun and Moon, in the case of the church calendar — and if precision or accuracy is understood as one aspect of truth, then a calendar that is more accurate and precise with respect to the motions of those bodies must be regarded as truer than one which is less precise. In this regard, some of those who champion the Old Calendar as truth (rather than for pastoral reasons, as seems to be the case with the national churches that adhere to it) may appear, to those following the new calendar, as the defenders of a fiction. (2) Some defenders of the new calendar argue that the celebration, in any way or form, of two feasts of Christ's Nativity within the same liturgical year is not possible, since according to the faith there is only one celebration of that feast in a given year. On this basis, they argue that those who prefer to observe a "secular" feast of the Nativity on and a "religious" one on , err in respect of the truth that there is but one feast of the Nativity each year.
Criticism
While the new calendar has been adopted by many of the smaller national churches, a majority of Orthodox Christians continue to adhere to the traditional Julian calendarJulian calendar
The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...
, and there has been much acrimony between the two parties over the decades since the change, leading sometimes even to violence, especially in Greece
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....
.
Critics see the change in calendar as an unwarranted innovation, influenced by Western society
Westernization
Westernization or Westernisation , also occidentalization or occidentalisation , is a process whereby societies come under or adopt Western culture in such matters as industry, technology, law, politics, economics, lifestyle, diet, language, alphabet,...
. They say that no sound theological reason has been given for changing the calendar, that the only reasons advanced are social. The proposal for change was introduced by a Patriarch whose canonical status has been disputed and who was a Freemason.
The argument is also made that since the use of the Julian calendar was implicit in the decision of the First Ecumenical Council at Nicaea (325) which standardized the calculation of the date of Pascha
Computus
Computus is the calculation of the date of Easter in the Christian calendar. The name has been used for this procedure since the early Middle Ages, as it was one of the most important computations of the age....
(Easter
Easter
Easter is the central feast in the Christian liturgical year. According to the Canonical gospels, Jesus rose from the dead on the third day after his crucifixion. His resurrection is celebrated on Easter Day or Easter Sunday...
), no authority less than an Ecumenical Council
Ecumenical council
An ecumenical council is a conference of ecclesiastical dignitaries and theological experts convened to discuss and settle matters of Church doctrine and practice....
may change it. The adoption of a new calendar has broken the unity of the church, undoing the whole purpose of the council of Nicaea, so once again, "on the same day some should be fasting whilst others are seated at a banquet."
Liturgical objections to the new calendar stem from the fact that it adjusts only those liturgical celebrations that occur on fixed calendar dates, leaving all of the commemorations on the moveable cycle
Paschal cycle
The Paschal cycle in the Eastern and Oriental Orthodox Churches, is the cycle of the moveable feasts built around Pascha . The cycle consists of approximately ten weeks before and seven weeks after Pascha. The ten weeks before Pascha are known as the period of the Triodion...
on the original Julian calendar. This upsets the harmony and balance of the liturgical year
Liturgical year
The liturgical year, also known as the church year, consists of the cycle of liturgical seasons in Christian churches which determines when feast days, including celebrations of saints, are to be observed, and which portions of Scripture are to be read. Distinct liturgical colours may appear in...
. (This would not have been a problem if the recommendations of the 1923 synod to use an astronomical rule to reckon the date of Easter, as outlined above, had not been rejected.) This disruption is most noticeable during Great Lent
Great Lent
Great Lent, or the Great Fast, is the most important fasting season in the church year in Eastern Christianity, which prepares Christians for the greatest feast of the church year, Pascha . In many ways Great Lent is similar to Lent in Western Christianity...
. Certain feast days are designed to fall during Lent, such as the feast of the Forty Martyrs of Sebaste
Forty Martyrs of Sebaste
The Forty Martyrs of Sebaste or the Holy Forty were a group of Roman soldiers in the Legio XII Fulminata whose martyrdom in 320 for the Christian faith is recounted in traditional martyrologies.They were killed near Sebaste, in Lesser Armenia, victims of the persecutions of Licinius,...
. The Feast of the Annunciation
Annunciation
The Annunciation, also referred to as the Annunciation to the Blessed Virgin Mary or Annunciation of the Lord, is the Christian celebration of the announcement by the angel Gabriel to Virgin Mary, that she would conceive and become the mother of Jesus the Son of God. Gabriel told Mary to name her...
is also intended to fall either before Pascha or during Bright Week
Bright Week
Bright Week or Renewal Week is the name used by the Eastern Orthodox Church and Eastern Catholic Churches of the Byzantine Rite for the period of seven days beginning on Pascha and continuing up to the following Sunday, which is known as Thomas Sunday...
. Sometimes, Annunciation will fall on the day of Pascha itself, a very special concurrence known as Kyrio-Pascha, with special liturgical practices appointed for such an occurrence. However, under the new calendar, Kyrio-Pascha becomes an impossibility. The Apostles' Fast
Apostles' Fast
The Apostles' Fast, also called the Fast of the Holy Apostles, the Fast of Peter and Paul, or sometimes St. Peter's Fast, is a fast observed by Eastern Orthodox, Oriental Orthodox and Eastern Catholic Christians...
displays the most difficult aspect of the new calendar. The fast begins on the moveable cycle and ends on the fixed date of 29 June; since the new calendar is 13 days ahead of the traditional Julian calendar, the Apostles' Fast is 13 days shorter for those who follow the new calendar, and some years it is completely abrogated. Furthermore, critics of the new calendar point out the advantage to celebrating Nativity
Nativity of Jesus
The Nativity of Jesus, or simply The Nativity, refers to the accounts of the birth of Jesus in two of the Canonical gospels and in various apocryphal texts....
separately from the secular observances of Christmas
Christmas
Christmas or Christmas Day is an annual holiday generally celebrated on December 25 by billions of people around the world. It is a Christian feast that commemorates the birth of Jesus Christ, liturgically closing the Advent season and initiating the season of Christmastide, which lasts twelve days...
and New Year
New Year
The New Year is the day that marks the time of the beginning of a new calendar year, and is the day on which the year count of the specific calendar used is incremented. For many cultures, the event is celebrated in some manner....
, which are associated with partying and alcohol consumption.
Critics also point out that proponents of the new calendar tend to use worldly rather than spiritual justification for changing the calendar: wanting to "party with everyone else" at Christmas; concern that the gradual shift in the Julian calendar will somehow negatively affect the celebration of feasts that are linked to the seasons of the year. However, opponents counter that the seasons are reversed in the southern hemisphere
Southern Hemisphere
The Southern Hemisphere is the part of Earth that lies south of the equator. The word hemisphere literally means 'half ball' or "half sphere"...
, where the liturgical celebrations are no less valid. The validity of this argument is questionable, since the feasts of the Orthodox Church were not changed no matter where they were celebrated, and Orthodox services were held in the southern hemisphere with little issue centuries before the introduction of the new calendar.
Proponents also argue that the new calendar is somehow more "scientific", but opponents argue that science is not the primary concern of the Church; rather, the Church is concerned with other-worldliness, with being "in the world, but not of it", fixing the attention of the faithful on eternity. Scientifically speaking, neither the Gregorian calendar nor the new calendar is absolutely precise. This is because the solar year cannot be evenly divided into 24 hour segments. So any public calendar is imprecise; it is simply an agreed-upon designation of days.
From a spiritual perspective, Old Calendarists also point to a number of miraculous occurrences which occur on the Old Calendar exclusively, such as the "descent of the cloud on the mount" on the feast of the Transfiguration. After the calendar change was instituted, the followers of the Old Calendar in Greece apparently witnessed the appearance of a cross in the sky, visible to thousands on the feast of the Exaltation of the Holy Cross, 1925, of which eyewitness accounts were recorded.
For such special events, if the original Julian date and year is known then the option always exists to calculate what was the proleptic Revised Julian date of that event and then observe its anniversary on that day, if that could be socially and ritually accepted.
Revised Julian calendrical calculations
The calendrical arithmetic discussed here is adapted from Gregorian and Julian calendar arithmetic published by Dershowitz and ReingoldEdward Reingold
Edward M. Reingold is a computer scientist active in the fields of algorithms, data structures, graph drawing, and calendrical calculations.He has co-authored the standard text on calendrical calculations, Calendrical Calculations, with Nachum Dershowitz...
, although those authors explicitly ignored the Revised Julian calendar. Their book, which will be referred to hereinafter as "CC3", should be consulted for methods to handle BC
Anno Domini
and Before Christ are designations used to label or number years used with the Julian and Gregorian calendars....
dates and the traditional omission of a year zero, both of which will be ignored here. They define the MOD
Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....
operator as x MOD y = x − y × floor(x / y), because that expression is valid for negative and floating point operands, returning the remainder
Remainder
In arithmetic, the remainder is the amount "left over" after the division of two integers which cannot be expressed with an integer quotient....
from dividing x by y while discarding the quotient
Quotient
In mathematics, a quotient is the result of division. For example, when dividing 6 by 3, the quotient is 2, while 6 is called the dividend, and 3 the divisor. The quotient further is expressed as the number of times the divisor divides into the dividend e.g. The quotient of 6 and 2 is also 3.A...
. Expressions like floor(x / y) return the quotient from dividing x by y while discarding the remainder.
Leap rule
isLeapYear = (year MOD 4 = 0)IF isLeapYear THEN
- IF year MOD 100 = 0 THEN
- Century = (year / 100) MOD 9
- isLeapYear = (Century=2) OR (Century=6)
- END IF
END IF
Fixed Days
Calendrical calculations are made consistent and straightforward for arithmetic operations if dates are first converted to an ordinal number of days relative to an agreed-upon epoch, in this case the Revised Julian epoch, which was the same as the Gregorian epoch. To find the difference between any two Revised Julian dates, convert both to ordinal day counts and simply subtract. To find a past or future date, convert a given date to an ordinal day count, subtract or add the desired number of days, then convert the result to a Revised Julian date.The arithmetic given here will not "crash" if an invalid date is given. To verify that a given date is a valid Revised Julian date, convert it to an ordinal day count and then back to a Revised Julian date — if the final date differs from the given date then the given date is invalid. This method should also be used to validate any implementation of calendrical arithmetic, by iteratively checking thousands of random and sequential dates for such errors.
To convert a Revised Julian date to any other calendar, first convert it to an ordinal day count, and then all that is needed is a function to convert the ordinal days count to that calendar.
To convert a date from any other calendar to a Revised Julian date, first convert that calendar date to an ordinal day count, then convert ordinal days to the Revised Julian date.
The following constant defined midnight at the start of Revised Julian date Monday, as the beginning of the first ordinal day. This moment was Julian Day
Julian day
Julian day is used in the Julian date system of time measurement for scientific use by the astronomy community, presenting the interval of time in days and fractions of a day since January 1, 4713 BC Greenwich noon...
number 1721425.5.
- RJepoch = 1
CC3 outlines functions for Gregorian and Julian calendar conversions, as well as many other calendars, always calculating in terms of the ordinal day number, which they call the "fixed date" or rata die
Rata Die
Rata Die is a system for assigning numbers to calendar days , independent of any calendar, for the purposes of calendrical calculations....
(RD), assigning the number 1 to the Gregorian calendar epoch. The arithmetic herein, by using the same ordinal day numbering epoch, is fully compatible with all CC3 functions for calendrical calculations and date inter-conversions.
You can assign a different integer to the Revised Julian epoch, for the purpose of numbering ordinal days relative to some other epoch, but if you do so then take the epoch difference into account when using any CC3 calendar functions and when converting an ordinal day number to a weekday number.
Optionally the ordinal day number can include a fractional component to represent the time as the elapsed fraction of a day. The ordinal day number of the J2000 moment ( noon) was 730120.5.
Revised Julian to Fixed Days
Convert a year, month, and day to the corresponding fixed day number:- PriorYear = year − 1
- FixedDays = RJepoch + 365 × PriorYear + floor(PriorYear / 4) + floor((367 × month − 362) / 12) + day − 1
If month is after February then subtract 1 day for a leap year or subtract 2 days for a common year:
- IF month > 2 THEN
- IF isLeapYear(year) THEN
- FixedDays = FixedDays − 1
- ELSE
- FixedDays = FixedDays − 2
- END IF
- IF isLeapYear(year) THEN
- END IF
Finally subtract a day for each prior century year (most of which are non-leap) and then add back in the number of prior century leap years:
- PriorCenturies = floor(PriorYear / 100)
- FixedDays = FixedDays − PriorCenturies + floor((2 × PriorCenturies + 6) / 9)
Fixed days to Revised Julian
Convert an ordinal day number to the corresponding Revised Julian year, month, and day, starting by removing any fractional time-of-day portion:- Days = floor(FixedDays) − RJepoch + 1
- PriorCenturies = floor(Days / 36524)
- RemainingDays = Days − 36524 × PriorCenturies - floor((2 × PriorCenturies + 6) / 9)
- PriorSubcycles = floor(RemainingDays / 1461)
- RemainingDays = RemainingDays MOD 1461
- PriorSubcycleYears = floor(RemainingDays / 365)
- year = 100 × PriorCenturies + 4 × PriorSubcycles + PriorSubcycleYears
- RemainingDays = RemainingDays MOD 365
- IF RemainingDays = 0 THEN
- This is either the 365th day of a common year, or the 365th or 366th day of a leap year. Either way, we have to decrement the year because we went one year too far:
- year = year − 1
- IF isLeapYear(year) AND PriorSubcycles=0 THEN RemainingDays=366 ELSE RemainingDays=365
- END IF
- PriorDays = RemainingDays − 1
- IF isLeapYear(year) THEN correction = 1 ELSE correction = 0
- IF PriorDays < (31+28+correction) THEN correction = 0 ELSE correction = 2 − correction
- Month = floor((12 × (PriorDays + correction) + 373) / 367)
Finally, calculate the day number within the month by subtracting the Fixed days count for the start of the month from the originally given Fixed days count, and then add one day:
- Day = FixedDays - RevisedJulianToFixed(year, month, 1) + 1
Fixed days to weekday number
Convert the ordinal number of days since the Revised Julian epoch to a weekday number (Sunday=1 through Saturday = 7):- WeekdayNumber = (floor(FixedDays) − RJepoch + 1) MOD 7 + 1
Don't be tempted to omit subtracting the RJepoch just because it is offset by adding +1. As written, this expression is robust even if you assign a value other than one to the epoch.
External links
- The Calendar of the Orthodox Church by Dr. Lewis J. Patsavos, Ph.D.
- The "Revised" Julian Calendar: Memorandum of Explanation by the Holy Synod (Orthodox Church in America)
- Liturgical Havoc Wreaked by the "New Julian" Calendar by Hieromonk Cassian
- The Essence of the Church Calendar
- On the Question of the "Revised Julian Calendar" by Father George Lardas
- The 70th Anniversary of the Pan-Orthodox Congress, Part I of II by Bishop Photius of Triaditsa
- The 70th Anniversary of the Pan-Orthodox Congress, Part II of II by Bishop Photius of Triaditsa
- Freeware calendar date conversion and astronomy events calculator for Windows. Interconverts dates of Revised Julian, Julian, Gregorian and several other calendars.