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This should not be merged with "metonic cycle." The term Golden Number is still commonly used in Anglicanism, and is printed in tables in the Book of Common Prayer, in reference to the computus of Easter, with no reference or correlation to the Metonic Cycle.
The Golden Number of any year is the same in both the Catholic and Anglican versions of the modern calendar. From a practical point of view, they are one and the same concept. —Preceding unsigned comment added by 75.24.76.3 ( talk) 05:50, 5 April 2009 (UTC)
The years, months, days of the month, and days of the week in the English civil calendar are for all practical purposes identical to the like-named or -numbered years, months, days of the month, and days of the week in the Gregorian calendar. Even the discrepancy regarding whether Feb. 24 or Feb. 29 is regarded as the leap day in a leap year has been tidied up (IIRC, the Catholic Church took care of this several years ago; Feb. 29 is now the leap day). —Preceding unsigned comment added by 75.24.76.3 ( talk) 05:55, 5 April 2009 (UTC)
An encyclopaedia should give the true definition. The UK Act and Prayer Book (q.v.) have words corresponding to
GN := (Y+1) mod 19 ; if GN=0 then GN := 19 ;
Of course, that and
GN := Y mod 19 + 1 ;
are fully equivalent, and the latter should also appear since it is the better way to calculate it. It's not clear to me whether Clavius gave either of those; he has a tabular method good for A.D. 1 to 899999999. 82.163.24.100 ( talk) 20:14, 22 October 2008 (UTC)
On deeper scrutiny, the final paragraph of Clavius' Canon 1 does give, in words, the Act/Book method - Et fi ex divifione nihil remanet, erit Aureus numerus 19.. 82.163.24.100 ( talk) 20:48, 22 October 2008 (UTC)
I recently read that Metonic cycle was known to Brahmins from a very long period back. At least as far back as Kali Yuga i.e. 3102 BCE. The reference can be found in Cassini as quoted by Baily in his classic work "Indian Astronomy" published in 1787. As a matter of fact John Playfair in his book "Works of John Playfair" published in 1822 recalculates Cassini's method and concludes that the golden number of Brahmins was more accurate than given by Metonic cycle. Brahmins still use the number based on 19 solar years equal to 233 lunar years in dating festivals in their calendars. —Preceding unsigned comment added by 173.32.182.222 ( talk) 15:48, 13 October 2009 (UTC)
I have deleted the claim of Hildegard of Bingen's knowledge of the Golden Number. Although the "aureus numerus" is indeed mentioned in her Ordo Virtutum it has nothing to do with calendars but rather refers to the completion of the ten heavenly choirs. AstroLynx ( talk) 12:38, 20 May 2016 (UTC)
They use the number for a 19 year cycle because... What is the point of this number? Ballchef ( talk) 11:53, 19 December 2018 (UTC)
I am pasting this section I deleted for being unsourced as the anglican-orthodox dialogue appears to not have mentioned anything about Easter or golden numbers in their published documents.
Following an initiative by Pope Francis in 2015, it has been proposed that the golden numbers, which are used by both eastern and western churches, form the basis of a common Easter date. Apart from its logistical convenience, it will bring to an end criticisms that in some areas Christ is still preaching while in others he is already crucified.
In 2022 an interdenominational discussion document prepared under the auspices of the International Commission for Anglican-Orthodox Theological Dialogue, (Metropolitan Athenagoras of Belgium, The Rt Revd Graham Usher, Bishop of Norwich, 22 pp), was lodged in the Cathedral Library at Norwich. Comments were invited (the Library is public, the document's title is The prospect of Whitby and its Call Number is 529.3).
Chapter 1 Early differences (page 1) notes:
A letter to the Church of Alexandria after the Council of Nicaea in 325 recorded:
- We further proclaim to you the good news of the agreement concerning the Holy Easter, that this particular also has through your prayers rightly been settled: so 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 and all those who have observed Easter from the beginning.
The penultimate sentence of the chapter (page 2) notes:
Constantine had admonished: 'Think, then, how unseemly it is, that on the same day some should be rejoicing at feasts, while others are still observing a strict fast.'
On the same page, Chapter 2 Summary of developments (which was added on the express instruction of the International Commission) notes:
664: Synod of Whitby. England aligns with Rome. [1]
4 December 1563: The Council of Trent authorises the pope to revise the missal and breviary (but not the calendar)...
1564: Pius V reserves to himself the sole right of interpretation of the enactments...
24 February 1582: Gregory XIII claims the right to unilaterally change the calendar and the date of Easter and does so. Anyone who does not fall into line will be excommunicated.
Page 3 notes:
Queen Elizabeth's astronomical adviser...in 1582 advocated the 'astronomical Easter', an idea rejected by the pope...
At the end of the sixteenth century the Orthodox church issued a series of anathemas against the Gregorian calendar. It is easy to see why:
(1) the Julian calendar is simple to operate. Easter jumps forward in years 3, 6, 8, 11, 14, 17 and 19 of the nineteen-year cycle. This is the same rule which applies in the Jewish calendar, although the Jewish cycle begins three years later. Easter is thus kept in lockstep with Passsover.
(2) the Julian calendar incorporates effective measures to prevent Easter being celebrated on [page 4] or before the Passover. These include:
- If the full moon falls on a Sunday Easter shall be the Sunday after
- The month preceding Easter always has thirty days
- The 'lockstep' safeguard referred to above
The Jewish calendar has a system of delays which prevent certain festivals being observed on certain days of the week. With only the first safeguard, the Gregorian Easter may fall a day or a month before the Passover. Eventually, Easter will fall a month before the Passover every year.
Nineteen Julian years are slightly longer than 235 lunar months, while nineteen Gregorian or Revised Julian years are slightly shorter. Therefore, as time goes on, the eastern and western dates will coincide less and less, and in a few hundred years the western Easter will always precede the eastern one. The common ground is that, since the Synod of Whitby in AD 664, all churches agree that the "full moon" shall be observed on the fourteenth day of the lunar month. From this, the definition of Easter is derived:
EASTER-DAY, on which the rest depend, is always the First Sunday after the Eighteenth Day of Miri, and if the Eighteenth Day of Miri happens upon a Sunday, Easter-Day is the Sunday after. All of which holds until the year 2099 inclusive, after which, on account of adjustments made every three or four hundred years in the calendar used in the calculation (of which Miri is the third month) the reference to the "Eighteenth" day shall be replaced by a reference to the "Nineteenth" day, and so on.
The date of the full moon is identified in the table below. Both the old (current western) and new (current eastern) methods are given, as they have been in the Breviary since 1582. [2]
Group | Sunday Letter |
Paschal Full Moon (Luna xiv) |
Golden Number |
---|---|---|---|
A | |||
E | 30 March | 16 | |
F | 31 March | 5 | |
G | 1 April | ||
A | 2 April | 13 | |
B | 3 April | 2 | |
C | 4 April | ||
D | 5 April | 10 | |
E | 6 April | ||
F | 7 April | 18 | |
G | 8 April | 7 | |
A | 9 April | ||
B | 10 April | 15 | |
C | 11 April | 4 | |
D | 12 April | ||
E | 13 April | 12 | |
F | 14 April | 1 | |
G | 15 April | ||
A | 16 April | 9 | |
B | 17 April | ||
B | |||
C | 18 April | 17 | |
D | 19 April | 6 | |
C | |||
E | 20 April | ||
F | 21 April | 14 | |
G | 22 April | 3 | |
A | 23 April | ||
B | 24 April | 11 | |
C | 25 April | ||
D | 26 April | 19 | |
E | 27 April | 8 |
To use the table:
The date of Easter is found from numbers which are allotted to certain dates as indicated in the table. For any particular year, the number which is taken is the same as the remainder that is obtained when one is added to the year and the total divided by 19. If there is no remainder 19 is taken. If the number is in Group A, Easter falls on the Sunday following the date against which that number appears. If the number is in Group B, Easter falls on the Sunday of the week commencing with the date against which that number appears.
If the number is in Group C, the date against which it appears is to be treated as a day of March, and Easter falls on the day after the Saturday following that date.
Rules for updating the table
The boundary between Group A and Group B is usually set between 18 and 19 April, but if there are numbers against both 18 and 19 April (as in the 21st century) it's set between 17 and 18 April. The boundary between Group B and Group C is always set between 19 and 20 April. The numbers are moved from time to time, and when they do move it's before Easter in years which are exactly divisible by 100. There are two separate movements:
1. The 'solar correction': the numbers move DOWN a day every time a centennial leap year is dropped (eg 2100)
2. The 'lunar correction': the numbers move UP a day in years giving remainder 200, 500, 800, 1100, 1400, 1800, 2100 and 2400 on division by 2500 (eg 2100).
Sometimes the corrections cancel out - thus in 2100 the numbers stay where they are. For Orthodox Easter the instructions for Groups B and C are ignored. Easter is, from the last lunar correction in 1800 to the year before the next lunar correction in 2100, the Sunday after the Wednesday following the date given by the table current for the relevant century. From 2100 until the year before the following lunar correction (in 2400) replace 'Wednesday' by 'Tuesday', and so on.
Example calculation
On what date does Orthodox Easter fall in 2023?
Page 5 of the document notes:
In the middle east even the Latin rite Catholics and Protestant churches have been observing Orthodox Easter since 1975, and in January 2016 Bishop Mouneer Anis (as he then was) reaffirmed this for Anglicans in Arabia (including the Gulf States), Cyprus, Egypt with North Africa and the Horn of Africa, Iraq, Israel (including occupied territories), Jordan, Lebanon, Persia and Syria.
Page 6 notes:
In 1900 the Macedonian-born academic Maksim Trpkovic published at Belgrade his Reforma Kalendara (Calendar Reform). Based on Barnaba Oriani's proposed reform which became the state calendar of Greece [references cited] it featured epact calculations for the twentieth century and new paschal limits in the 19-year cycle of golden numbers, after which the dates of the new moons repeat.
In 1903 the Holy Synod of the Greek Orthodox Church wrote to the Oecumanical Patriarch stating that the Julian calendar would be preserved.
Page 8 notes:
The Congress deliberated in May and June 1923. Advocating his solution astronomer Milutin Milankovic said that with the proposition of the Serbian delegation (which had previously advocated the newly-introduced state calendar of Greece) the Orthodox Church would have the most precise and most scientific calendar in the Christian world, so it could [page 9] confidently enter any negotiations on the calendar question with Western Churches. An astronomical Easter was adopted, calculated for the meridian of the Church of the Holy Sepulchre in Jerusalem.
There follows Chapter 6 Changes in church law are reversed following rejection by the people. It includes the following on page 9:
Alexandrian patriarch Photius had told the Oecumenical Patriarch on 15 January 1924 (old style) that '...we reject every addition or any change of the calendar before the convocation of an Ecumenical Council, which alone is capable of discussing this question, concerning which Ecumenical Council we propose a speedy convocation .'
Chapter 7 A light at the end of the tunnel (page 11) notes:
A proposal was made in 1997 to impose something very similar to the 1923 agreement on all churches...Under it, Easter would have to break its canonical limits, leaving the way open for Shrove Tuesday to clash with Candlemas [reference cited]. At the end of the explanation the dates of the astronomical, Gregorian and Julian Easters are tabulated for the years 2001-2025 along with the Vernal full moon astron. reckoning and the date of Passover [reference cited]. In eight of those 25 years the full moon at Greenwich fell on the day before the Passover...
On 12 June 2015, at the World Retreat of Priests at the Basilica of St John Lateran in Rome, Pope Francis observed that 'we have to come to an agreement' for a common date on Easter. Lucetta Scaraffia, writing in the Vatican newspaper L'Osservatore Romano, explained that the Pope is offering this initiative to change the date of Easter 'as a gift of unity with the other Christian churches.' [3]
When possible, more sources need to be added for the date of Easter section. I am still not sure what the scope of the interdenominational discussion document is, what churches are involved and what the prospects are for this method being implemented.
I think unless another source comes out specifically talking about the use of golden numbers to calculate Easter or a final agreement, this information would be better added to Reform of the date of Easter. This website claims [4] that they are trying to reach a final agreement by 2025 so presumably more information should come out soon regarding different methods — Preceding unsigned comment added by Safes007 ( talk • contribs) 13:29, 2 January 2023 (UTC)
...blends the political realities of ecclesiastical and state politics, particularly in the Christian East, with the mathematical reasons why varying astronomical calculations cause such confusion on the dates for religious festivals...the celebration of Easter on different days and...the loss of the link with Passover is to be lamented..."
The Commission points out that it is the very opposite of a proposal for "Reform of the date of Easter." The joint proposal by the Oecumenical Patriarch and the pope was floated in 2015. Justin Welby told the British government to get ready to implement it in January 2016 and the Catholic Herald wrote:
When the Archbishop of Canterbury rationalises such a momentous decision by pointing to difficulties over school holidays one has to ask: what is the biggest influence here? Christian unity or relatively frivolous secular concerns? If the latter is a motivation then such a move - to borrow the Holy Father's words - could also prove to be a scandal."
Yet the discussions reported in Zenit are presented as completely new. Although they say astronomers will be consulted there is no explanation of why, after eight years, this has yet to happen. The controversial claim that the date of Easter is not a religious matter but a scientific one is presented as fact. The fact that reform of the date of Easter is not on the agenda of the Orthodox Church, and many Orthodox churches have severed relations with the Oecumenical Patriarch on this account [1] is nowhere mentioned. 79.79.43.32 ( talk) 18:11, 7 January 2023 (UTC)
The claimed source is a document in the Cathedral Library at Norwich. An ISBN, call number, or other unique identifier would be helpful. Elizium23 ( talk) 11:27, 29 December 2022 (UTC)
The textual majority of this article now seems to essentially serve as the personal project of a single unregistered user, beginning late last year. As regards that text, the greater part of is either mere at-length quotations from a single Anglican document, or (For the most part, at least) unsourced claims that must represent either original research or reproduction of the propositions of the aforementioned document. These claims, along with the editor's responses to attempts at revising the article, are often and have often been bewildering.
Given the repeated reverting of proceeding revisions to the article, those reverts being by the aforementioned user, I suppose that some further arbitration is needed. As something encyclopedic, the article as it now stands is unacceptable. Zusty001 ( talk) 18:24, 2 September 2023 (UTC)
14 - March 22; 3 - March 23; 11 - March 25; 19 - March 27; 8 - March 28; 16 - March 30; 5 - March 31; 13 - April 2; 2 - April 3: 10 - April 5; 18 - April 7; 7 - April 8; 15 - April 10: 4 - April 11; 12 - April 13; 1 - April 14; 9 - April 16.
These mark the "paschal full moons" (the fourteenth day of the month), but traditionally they marked the first day, and the traditional format was agreed. Making the change involves subtracting 13 days (14 - 1 = 13), placing them as follows:
14 - March 9; 3 - March 10; 11 - March 12; 19 - March 14; 8 - March 15; 16 - March 17; 5 - March 18; 13 - March 20; 2 - March 21; 10 - March 23; 18 - March 25; 7 - March 26; 15 - March 28; 4 - March 29; 12 - March 31; 1 - April 1; 9 - April 3.
These are the exact dates the numbers appear against in the table. Possibly the attack on the names was made because no technical deficiency in the system was found. There is a reference to them in the source document at page 19:
To assist this, key months have been given the names of Biblical personages and (in one case) the name of a Roman Catholic pope.
The provenance is as follows:
It is of note that although the seventh month of the secular calendar bears the name of a Roman dictator alleged to have bribed his way to power, and the eighth commemorates a dictator who gained lifelong power while claiming to have given full democratic power to the Roman senate, no objection to it is raised on that account. The existing system has fallen into disrepute not least because, although the Book of Common Prayer claims Easter falls on the Sunday following the full moon following the vernal equinox, it frequently doesn't, and the squishing of the golden numbers at the end of the table means the error can be very large. 93.96.9.14 ( talk) 18:07, 12 January 2024 (UTC)
I've accessed the site mentioned, but it's in a language I don't understand. We originally provided an explanation of how to use the golden numbers to calculate both the occidental and the Orthodox Easter, and there is a competent explanation also in the linked article Date of Easter. With the complaint that the section was too long, we concentrated on explaining how the new table is used to give Orthodox Easter. In view of your comment, we can add the information back, and this is the suggested wording:
To calculate the date of occidental Easter, proceed as follows:
1. In the calendar, locate the date of 14 Miri (which is the "paschal full moon").
2. If it falls on or before 17 April, Easter is the Sunday following. If it falls on 18 April and no golden number is marked against 6 April, again Easter is the Sunday following. If it falls on 18 April and a golden number is marked against 6 April, Easter falls on 18 April (if Sunday), and if 18 April is not Sunday Easter falls on the following Sunday.
3. If the paschal full moon falls on 19 April, Easter falls on 19 April (if Sunday), and if 19 April is not Sunday Easter falls on the following Sunday.
4. If the paschal full moon falls on 20 April or later, the date of the paschal full moon is to be treated as a day of March, and Easter falls on the day after the Saturday following that date.
One reason for dispensing with the occidental Easter was that sometimes the instructions direct the festival to be observed on the day of the Jewish Passover, which the ecumenical councils do not permit to happen. 93.96.9.14 ( talk) 17:14, 13 January 2024 (UTC)
Source material must have been published, the definition of which for the purposes of Wikipedia is made available to the public in some form.
Are you aware of this policy? 93.96.38.91 ( talk) 17:58, 21 January 2024 (UTC)
On the Byzantine Forum [4], in a post dated 27 February 2023, "ajk" makes unsubstantiated allegations about the neutrality of the article. It correctly summarises all points of view, and his real objection is that he wants it to mention only his point of view (that the Orthodox Church should adopt the Gregorian calendar and with it the Gregorian Paschalion). The discussion is dominated by him and Mockingbird - perhaps Mockingbird could go there and explain our neutrality policies to him? @ Mockingbird6: 93.96.44.214 ( talk) 12:52, 9 March 2024 (UTC)
References
{{
cite book}}
: CS1 maint: location missing publisher (
link)
A better explanation of the page is needed. Currently, our caption just briefly mentions the leftmost column. It appears that the second column shows the Sunday Letter, but that seems different from the deleted #Method of calculating the date of Easter. The third and fourth column obviously show the day in the Roman fashion. Here is a transcription of these columns:
Extended content
|
---|
3 A Ianuarius b 4 N′ 9 c 3 N′ d 2 N′ 19 e Nonas N′ 8 f 8 Id′ g 7 Id′ 13 A 6 Id′ 2 b 5 Id′ c 4 Id′ 16 d 3 Id′ 5 e 2 Idus f Idus Idꝰ 10 g 19 Kl′ A 18 Kl′ 18 b 17 Kl′ 7 c 16 Kl′ d 15 Kl′ 15 e 14 Kl′ 4 f 13 Kl′ g 12 Kl′ 12 A 11 Kl′ 1 b 10 Kl′ c 9 Kl′ 17 d 8 Kł 6 e 7 Kl′ f 6 Kł 9 g 5 Kl′ A 4 Kl′ 14 b 3 Kl′ 3 c 2 Kl′ |
It would be nice to have transcription and translation of introduction and fifth column, as well. Most pertinent for this article, however, is the leftmost column, which poses a number of questions:
Upon further research on point 2, the discrepancy seems to be no outlier. E.g. the year 1396 has, according to the modulo formula, the golden number 10 (in this table at 19 Kl′) and the year before has the golden number 9, for which there are two entries: at 3 N′ and at 5 Kl′. A synodic year before 19 Kl′ of January 1396 was January 25…26 (depending on rounding error), 3…4 days before the 5 Kl′ of this table. You might say they weren't so exact in the middle ages, but this computation requires no more than simple addition, subtraction and multiplication, and the observation of half a week difference to a full moon, so one should think that they could have done better. Or am I missing something? ◅ Sebastian Helm 🗨 12:59, 27 March 2024 (UTC)
The lunar date for 29 February of a leap year is normally the same as that of the preceding day - thus the lunar date for 28 and 29 February 2028 is 3 Ronan. For use of the letters A - g to find the day of the week see Dominical letter. The months are: (1) Harriet, (2) Ronan, (3) Miri, (4) James, (5) Eloise, (6) Thomas, vii, (8) Nicholas, (9) Catherine, (10) Richard, (11) Emma, (12) Paul. Paul II, a 30-day month, is added between Paul and Harriet 7 times in 19 years. When the golden number is 19, Richard has 29 days instead of 30. See Saltus#Latin (third bullet point).
JAN Paul 30 |
FEB Harr 29 |
MAR Ron 30 |
APR Miri 29 |
MAY Jame 30 |
JUN Eloi 29 |
JUL Thom 30 |
AUG vii 29 |
SEPT Nich 30 |
OCT Cath 29 |
NOV Rich 30 |
DEC Emma 29 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | A 12 | d 1 | d 12 | g 1 | b | e 9 | g | c 17 | f | A | d 3 | f 3 |
2 | b 1 | e | e 1 | A | c 9 | f | A 17 | d 6 | g 14 | b 14 | e | g |
3 | c | f 9 | f | b 9 | d | g 17 | b 6 | e | A 3 | c 3 | f 11 | A 11 |
4 | d 9 | g | g 9 | c | e 17 | A 6 | c | f 14 | b | d | g | b 19 |
5 | e P2 | A 17 | A | d 17 | f 6 | b | d 14 | g 3 | c 11 | e 11 | A 19 | c |
6 | f 17 | b 6 | b 17 | e 6 | g | c 14 | e 3 | A | d | f | b 8 | d 8 |
7 | g 6 | c | c 6 | f | A 14 | d 3 | f | b 11 | e 19 | g 19 | c Em | e 16 |
8 | A | d 14 | d | g 14 | b 3 | e | g 11 | c | f 8 | A 8 | d 16 | f 5 |
9 | b 14 | e 3 | e 14 | A 3 | c | f 11 | A | d 19 | g Ca | b 16 | e 5 | g |
10 | c 3 | f | f 3 | b | d 11 | g | b 19 | e 8 | A 16 | c 5 | f | A 13 |
11 | d | g 11 | g | c 11 | e | A 19 | c 8 | f 16 | b 5 | d | g 13 | b 2 |
12 | e 11 | A | A 11 | d | f 19 | b 8 | d vii | g 5 | c | e 13 | A 2 | c |
13 | f | b 19 | b | e 19 | g 8 | c 16 | e 16 | A | d 13 | f 2 | b | d 10 |
14 | g 19 | c 8 | c 19 | f 8 | A El | d 5 | f 5 | b 13 | e 2 | g | c 10 | e |
15 | A 8 | d 16 | d 8 | g 16 | b 16 | e | g | c 2 | f | A 10 | d | f 18 |
16 | b Ha | e 5 | e Mi | A 5 | c 5 | f 13 | A 13 | d | g 10 | b | e 18 | g 7 |
17 | c 16 | f | f 16 | b | d | g 2 | b 2 | e 10 | A | c 18 | f 7 | A |
18 | d 5 | g 13 | g 5 | c 13 | e 13 | A | c | f | b 18 | d 7 | g | b 15 |
19 | e | A 2 | A | d 2 | f 2 | b 10 | d 10 | g 18 | c 7 | e | A 15 | c 4 |
20 | f 13 | b | b 13 | e | g | c | e | A 7 | d | f 15 | b 4 | d |
21 | g 2 | c 10 | c 2 | f 10 | A 10 | d 18 | f 18 | b | e 15 | g 4 | c | e 12 |
22 | A | d | d | g | b | e 7 | g 7 | c 15 | f 4 | A | d 12 | f 1 |
23 | b 10 | e 18 | e 10 | A 18 | c 18 | f | A | d 4 | g | b 12 | e 1 | g |
24 | c | f 7 | f | b 7 | d 7 | g 15 | b 15 | e | A 12 | c 1 | f | A 9 |
25 | d 18 | g | g 18 | c | e | A 4 | c 4 | f 12 | b 1 | d | g 9 | b |
26 | e 7 | A 15 | A 7 | d 15 | f 15 | b | d | g 1 | c | e 9 | A | c 17 |
27 | f | b 4 | b | e 4 | g 4 | c 12 | e 12 | A | d 9 | f | b 17 | d 6 |
28 | g 15 | c | c 15 | f | A | d 1 | f 1 | b 9 | e | g 17 | c 6 | e |
29 | A 4 | d 4 | g 12 | b 12 | e | g | c | f 17 | A 6 | d | f 14 | |
30 | b | e | A 1 | c 1 | f 9 | A 9 | d 17 | g 6 | b | e 14 | g 3 | |
31 | c 12 | f 12 | d | b | e 6 | c 14 | A | |||||
Harr | Ron | Miri | Jame | Eloi | Thom | vii | Nich | Cath | Rich | Emma | Paul |
The sequence of Sunday letters is manufactured by giving 1 January letter A and repeatedly cycling through the first seven letters of the alphabet to 31 December, which is again A as the year consists of 52 weeks and 1 day, discounting 29 February which has no letter allocated to it. The official table remained unchanged from AD 284, when it was devised, until the modern table replaced it. The dates are Julian, and the table was accurate when it was introduced. The error you cite (one day in 219 years) is against the Gregorian/Revised Julian calendar - against the Julian it is only one day in 308 years. The new moons are now delayed four days from their true places - the error was corrected by moving them up four days and then down 13 days from their new position to locate them in the Gregorian/Revised Julian calendar, which is currently 13 days ahead of the Julian. The net displacement is nine days, so if you move the golden numbers up nine days from where they are in the modern table you will see where they should have been in the old one. The errors immediately become apparent:
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This should not be merged with "metonic cycle." The term Golden Number is still commonly used in Anglicanism, and is printed in tables in the Book of Common Prayer, in reference to the computus of Easter, with no reference or correlation to the Metonic Cycle.
The Golden Number of any year is the same in both the Catholic and Anglican versions of the modern calendar. From a practical point of view, they are one and the same concept. —Preceding unsigned comment added by 75.24.76.3 ( talk) 05:50, 5 April 2009 (UTC)
The years, months, days of the month, and days of the week in the English civil calendar are for all practical purposes identical to the like-named or -numbered years, months, days of the month, and days of the week in the Gregorian calendar. Even the discrepancy regarding whether Feb. 24 or Feb. 29 is regarded as the leap day in a leap year has been tidied up (IIRC, the Catholic Church took care of this several years ago; Feb. 29 is now the leap day). —Preceding unsigned comment added by 75.24.76.3 ( talk) 05:55, 5 April 2009 (UTC)
An encyclopaedia should give the true definition. The UK Act and Prayer Book (q.v.) have words corresponding to
GN := (Y+1) mod 19 ; if GN=0 then GN := 19 ;
Of course, that and
GN := Y mod 19 + 1 ;
are fully equivalent, and the latter should also appear since it is the better way to calculate it. It's not clear to me whether Clavius gave either of those; he has a tabular method good for A.D. 1 to 899999999. 82.163.24.100 ( talk) 20:14, 22 October 2008 (UTC)
On deeper scrutiny, the final paragraph of Clavius' Canon 1 does give, in words, the Act/Book method - Et fi ex divifione nihil remanet, erit Aureus numerus 19.. 82.163.24.100 ( talk) 20:48, 22 October 2008 (UTC)
I recently read that Metonic cycle was known to Brahmins from a very long period back. At least as far back as Kali Yuga i.e. 3102 BCE. The reference can be found in Cassini as quoted by Baily in his classic work "Indian Astronomy" published in 1787. As a matter of fact John Playfair in his book "Works of John Playfair" published in 1822 recalculates Cassini's method and concludes that the golden number of Brahmins was more accurate than given by Metonic cycle. Brahmins still use the number based on 19 solar years equal to 233 lunar years in dating festivals in their calendars. —Preceding unsigned comment added by 173.32.182.222 ( talk) 15:48, 13 October 2009 (UTC)
I have deleted the claim of Hildegard of Bingen's knowledge of the Golden Number. Although the "aureus numerus" is indeed mentioned in her Ordo Virtutum it has nothing to do with calendars but rather refers to the completion of the ten heavenly choirs. AstroLynx ( talk) 12:38, 20 May 2016 (UTC)
They use the number for a 19 year cycle because... What is the point of this number? Ballchef ( talk) 11:53, 19 December 2018 (UTC)
I am pasting this section I deleted for being unsourced as the anglican-orthodox dialogue appears to not have mentioned anything about Easter or golden numbers in their published documents.
Following an initiative by Pope Francis in 2015, it has been proposed that the golden numbers, which are used by both eastern and western churches, form the basis of a common Easter date. Apart from its logistical convenience, it will bring to an end criticisms that in some areas Christ is still preaching while in others he is already crucified.
In 2022 an interdenominational discussion document prepared under the auspices of the International Commission for Anglican-Orthodox Theological Dialogue, (Metropolitan Athenagoras of Belgium, The Rt Revd Graham Usher, Bishop of Norwich, 22 pp), was lodged in the Cathedral Library at Norwich. Comments were invited (the Library is public, the document's title is The prospect of Whitby and its Call Number is 529.3).
Chapter 1 Early differences (page 1) notes:
A letter to the Church of Alexandria after the Council of Nicaea in 325 recorded:
- We further proclaim to you the good news of the agreement concerning the Holy Easter, that this particular also has through your prayers rightly been settled: so 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 and all those who have observed Easter from the beginning.
The penultimate sentence of the chapter (page 2) notes:
Constantine had admonished: 'Think, then, how unseemly it is, that on the same day some should be rejoicing at feasts, while others are still observing a strict fast.'
On the same page, Chapter 2 Summary of developments (which was added on the express instruction of the International Commission) notes:
664: Synod of Whitby. England aligns with Rome. [1]
4 December 1563: The Council of Trent authorises the pope to revise the missal and breviary (but not the calendar)...
1564: Pius V reserves to himself the sole right of interpretation of the enactments...
24 February 1582: Gregory XIII claims the right to unilaterally change the calendar and the date of Easter and does so. Anyone who does not fall into line will be excommunicated.
Page 3 notes:
Queen Elizabeth's astronomical adviser...in 1582 advocated the 'astronomical Easter', an idea rejected by the pope...
At the end of the sixteenth century the Orthodox church issued a series of anathemas against the Gregorian calendar. It is easy to see why:
(1) the Julian calendar is simple to operate. Easter jumps forward in years 3, 6, 8, 11, 14, 17 and 19 of the nineteen-year cycle. This is the same rule which applies in the Jewish calendar, although the Jewish cycle begins three years later. Easter is thus kept in lockstep with Passsover.
(2) the Julian calendar incorporates effective measures to prevent Easter being celebrated on [page 4] or before the Passover. These include:
- If the full moon falls on a Sunday Easter shall be the Sunday after
- The month preceding Easter always has thirty days
- The 'lockstep' safeguard referred to above
The Jewish calendar has a system of delays which prevent certain festivals being observed on certain days of the week. With only the first safeguard, the Gregorian Easter may fall a day or a month before the Passover. Eventually, Easter will fall a month before the Passover every year.
Nineteen Julian years are slightly longer than 235 lunar months, while nineteen Gregorian or Revised Julian years are slightly shorter. Therefore, as time goes on, the eastern and western dates will coincide less and less, and in a few hundred years the western Easter will always precede the eastern one. The common ground is that, since the Synod of Whitby in AD 664, all churches agree that the "full moon" shall be observed on the fourteenth day of the lunar month. From this, the definition of Easter is derived:
EASTER-DAY, on which the rest depend, is always the First Sunday after the Eighteenth Day of Miri, and if the Eighteenth Day of Miri happens upon a Sunday, Easter-Day is the Sunday after. All of which holds until the year 2099 inclusive, after which, on account of adjustments made every three or four hundred years in the calendar used in the calculation (of which Miri is the third month) the reference to the "Eighteenth" day shall be replaced by a reference to the "Nineteenth" day, and so on.
The date of the full moon is identified in the table below. Both the old (current western) and new (current eastern) methods are given, as they have been in the Breviary since 1582. [2]
Group | Sunday Letter |
Paschal Full Moon (Luna xiv) |
Golden Number |
---|---|---|---|
A | |||
E | 30 March | 16 | |
F | 31 March | 5 | |
G | 1 April | ||
A | 2 April | 13 | |
B | 3 April | 2 | |
C | 4 April | ||
D | 5 April | 10 | |
E | 6 April | ||
F | 7 April | 18 | |
G | 8 April | 7 | |
A | 9 April | ||
B | 10 April | 15 | |
C | 11 April | 4 | |
D | 12 April | ||
E | 13 April | 12 | |
F | 14 April | 1 | |
G | 15 April | ||
A | 16 April | 9 | |
B | 17 April | ||
B | |||
C | 18 April | 17 | |
D | 19 April | 6 | |
C | |||
E | 20 April | ||
F | 21 April | 14 | |
G | 22 April | 3 | |
A | 23 April | ||
B | 24 April | 11 | |
C | 25 April | ||
D | 26 April | 19 | |
E | 27 April | 8 |
To use the table:
The date of Easter is found from numbers which are allotted to certain dates as indicated in the table. For any particular year, the number which is taken is the same as the remainder that is obtained when one is added to the year and the total divided by 19. If there is no remainder 19 is taken. If the number is in Group A, Easter falls on the Sunday following the date against which that number appears. If the number is in Group B, Easter falls on the Sunday of the week commencing with the date against which that number appears.
If the number is in Group C, the date against which it appears is to be treated as a day of March, and Easter falls on the day after the Saturday following that date.
Rules for updating the table
The boundary between Group A and Group B is usually set between 18 and 19 April, but if there are numbers against both 18 and 19 April (as in the 21st century) it's set between 17 and 18 April. The boundary between Group B and Group C is always set between 19 and 20 April. The numbers are moved from time to time, and when they do move it's before Easter in years which are exactly divisible by 100. There are two separate movements:
1. The 'solar correction': the numbers move DOWN a day every time a centennial leap year is dropped (eg 2100)
2. The 'lunar correction': the numbers move UP a day in years giving remainder 200, 500, 800, 1100, 1400, 1800, 2100 and 2400 on division by 2500 (eg 2100).
Sometimes the corrections cancel out - thus in 2100 the numbers stay where they are. For Orthodox Easter the instructions for Groups B and C are ignored. Easter is, from the last lunar correction in 1800 to the year before the next lunar correction in 2100, the Sunday after the Wednesday following the date given by the table current for the relevant century. From 2100 until the year before the following lunar correction (in 2400) replace 'Wednesday' by 'Tuesday', and so on.
Example calculation
On what date does Orthodox Easter fall in 2023?
Page 5 of the document notes:
In the middle east even the Latin rite Catholics and Protestant churches have been observing Orthodox Easter since 1975, and in January 2016 Bishop Mouneer Anis (as he then was) reaffirmed this for Anglicans in Arabia (including the Gulf States), Cyprus, Egypt with North Africa and the Horn of Africa, Iraq, Israel (including occupied territories), Jordan, Lebanon, Persia and Syria.
Page 6 notes:
In 1900 the Macedonian-born academic Maksim Trpkovic published at Belgrade his Reforma Kalendara (Calendar Reform). Based on Barnaba Oriani's proposed reform which became the state calendar of Greece [references cited] it featured epact calculations for the twentieth century and new paschal limits in the 19-year cycle of golden numbers, after which the dates of the new moons repeat.
In 1903 the Holy Synod of the Greek Orthodox Church wrote to the Oecumanical Patriarch stating that the Julian calendar would be preserved.
Page 8 notes:
The Congress deliberated in May and June 1923. Advocating his solution astronomer Milutin Milankovic said that with the proposition of the Serbian delegation (which had previously advocated the newly-introduced state calendar of Greece) the Orthodox Church would have the most precise and most scientific calendar in the Christian world, so it could [page 9] confidently enter any negotiations on the calendar question with Western Churches. An astronomical Easter was adopted, calculated for the meridian of the Church of the Holy Sepulchre in Jerusalem.
There follows Chapter 6 Changes in church law are reversed following rejection by the people. It includes the following on page 9:
Alexandrian patriarch Photius had told the Oecumenical Patriarch on 15 January 1924 (old style) that '...we reject every addition or any change of the calendar before the convocation of an Ecumenical Council, which alone is capable of discussing this question, concerning which Ecumenical Council we propose a speedy convocation .'
Chapter 7 A light at the end of the tunnel (page 11) notes:
A proposal was made in 1997 to impose something very similar to the 1923 agreement on all churches...Under it, Easter would have to break its canonical limits, leaving the way open for Shrove Tuesday to clash with Candlemas [reference cited]. At the end of the explanation the dates of the astronomical, Gregorian and Julian Easters are tabulated for the years 2001-2025 along with the Vernal full moon astron. reckoning and the date of Passover [reference cited]. In eight of those 25 years the full moon at Greenwich fell on the day before the Passover...
On 12 June 2015, at the World Retreat of Priests at the Basilica of St John Lateran in Rome, Pope Francis observed that 'we have to come to an agreement' for a common date on Easter. Lucetta Scaraffia, writing in the Vatican newspaper L'Osservatore Romano, explained that the Pope is offering this initiative to change the date of Easter 'as a gift of unity with the other Christian churches.' [3]
When possible, more sources need to be added for the date of Easter section. I am still not sure what the scope of the interdenominational discussion document is, what churches are involved and what the prospects are for this method being implemented.
I think unless another source comes out specifically talking about the use of golden numbers to calculate Easter or a final agreement, this information would be better added to Reform of the date of Easter. This website claims [4] that they are trying to reach a final agreement by 2025 so presumably more information should come out soon regarding different methods — Preceding unsigned comment added by Safes007 ( talk • contribs) 13:29, 2 January 2023 (UTC)
...blends the political realities of ecclesiastical and state politics, particularly in the Christian East, with the mathematical reasons why varying astronomical calculations cause such confusion on the dates for religious festivals...the celebration of Easter on different days and...the loss of the link with Passover is to be lamented..."
The Commission points out that it is the very opposite of a proposal for "Reform of the date of Easter." The joint proposal by the Oecumenical Patriarch and the pope was floated in 2015. Justin Welby told the British government to get ready to implement it in January 2016 and the Catholic Herald wrote:
When the Archbishop of Canterbury rationalises such a momentous decision by pointing to difficulties over school holidays one has to ask: what is the biggest influence here? Christian unity or relatively frivolous secular concerns? If the latter is a motivation then such a move - to borrow the Holy Father's words - could also prove to be a scandal."
Yet the discussions reported in Zenit are presented as completely new. Although they say astronomers will be consulted there is no explanation of why, after eight years, this has yet to happen. The controversial claim that the date of Easter is not a religious matter but a scientific one is presented as fact. The fact that reform of the date of Easter is not on the agenda of the Orthodox Church, and many Orthodox churches have severed relations with the Oecumenical Patriarch on this account [1] is nowhere mentioned. 79.79.43.32 ( talk) 18:11, 7 January 2023 (UTC)
The claimed source is a document in the Cathedral Library at Norwich. An ISBN, call number, or other unique identifier would be helpful. Elizium23 ( talk) 11:27, 29 December 2022 (UTC)
The textual majority of this article now seems to essentially serve as the personal project of a single unregistered user, beginning late last year. As regards that text, the greater part of is either mere at-length quotations from a single Anglican document, or (For the most part, at least) unsourced claims that must represent either original research or reproduction of the propositions of the aforementioned document. These claims, along with the editor's responses to attempts at revising the article, are often and have often been bewildering.
Given the repeated reverting of proceeding revisions to the article, those reverts being by the aforementioned user, I suppose that some further arbitration is needed. As something encyclopedic, the article as it now stands is unacceptable. Zusty001 ( talk) 18:24, 2 September 2023 (UTC)
14 - March 22; 3 - March 23; 11 - March 25; 19 - March 27; 8 - March 28; 16 - March 30; 5 - March 31; 13 - April 2; 2 - April 3: 10 - April 5; 18 - April 7; 7 - April 8; 15 - April 10: 4 - April 11; 12 - April 13; 1 - April 14; 9 - April 16.
These mark the "paschal full moons" (the fourteenth day of the month), but traditionally they marked the first day, and the traditional format was agreed. Making the change involves subtracting 13 days (14 - 1 = 13), placing them as follows:
14 - March 9; 3 - March 10; 11 - March 12; 19 - March 14; 8 - March 15; 16 - March 17; 5 - March 18; 13 - March 20; 2 - March 21; 10 - March 23; 18 - March 25; 7 - March 26; 15 - March 28; 4 - March 29; 12 - March 31; 1 - April 1; 9 - April 3.
These are the exact dates the numbers appear against in the table. Possibly the attack on the names was made because no technical deficiency in the system was found. There is a reference to them in the source document at page 19:
To assist this, key months have been given the names of Biblical personages and (in one case) the name of a Roman Catholic pope.
The provenance is as follows:
It is of note that although the seventh month of the secular calendar bears the name of a Roman dictator alleged to have bribed his way to power, and the eighth commemorates a dictator who gained lifelong power while claiming to have given full democratic power to the Roman senate, no objection to it is raised on that account. The existing system has fallen into disrepute not least because, although the Book of Common Prayer claims Easter falls on the Sunday following the full moon following the vernal equinox, it frequently doesn't, and the squishing of the golden numbers at the end of the table means the error can be very large. 93.96.9.14 ( talk) 18:07, 12 January 2024 (UTC)
I've accessed the site mentioned, but it's in a language I don't understand. We originally provided an explanation of how to use the golden numbers to calculate both the occidental and the Orthodox Easter, and there is a competent explanation also in the linked article Date of Easter. With the complaint that the section was too long, we concentrated on explaining how the new table is used to give Orthodox Easter. In view of your comment, we can add the information back, and this is the suggested wording:
To calculate the date of occidental Easter, proceed as follows:
1. In the calendar, locate the date of 14 Miri (which is the "paschal full moon").
2. If it falls on or before 17 April, Easter is the Sunday following. If it falls on 18 April and no golden number is marked against 6 April, again Easter is the Sunday following. If it falls on 18 April and a golden number is marked against 6 April, Easter falls on 18 April (if Sunday), and if 18 April is not Sunday Easter falls on the following Sunday.
3. If the paschal full moon falls on 19 April, Easter falls on 19 April (if Sunday), and if 19 April is not Sunday Easter falls on the following Sunday.
4. If the paschal full moon falls on 20 April or later, the date of the paschal full moon is to be treated as a day of March, and Easter falls on the day after the Saturday following that date.
One reason for dispensing with the occidental Easter was that sometimes the instructions direct the festival to be observed on the day of the Jewish Passover, which the ecumenical councils do not permit to happen. 93.96.9.14 ( talk) 17:14, 13 January 2024 (UTC)
Source material must have been published, the definition of which for the purposes of Wikipedia is made available to the public in some form.
Are you aware of this policy? 93.96.38.91 ( talk) 17:58, 21 January 2024 (UTC)
On the Byzantine Forum [4], in a post dated 27 February 2023, "ajk" makes unsubstantiated allegations about the neutrality of the article. It correctly summarises all points of view, and his real objection is that he wants it to mention only his point of view (that the Orthodox Church should adopt the Gregorian calendar and with it the Gregorian Paschalion). The discussion is dominated by him and Mockingbird - perhaps Mockingbird could go there and explain our neutrality policies to him? @ Mockingbird6: 93.96.44.214 ( talk) 12:52, 9 March 2024 (UTC)
References
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cite book}}
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link)
A better explanation of the page is needed. Currently, our caption just briefly mentions the leftmost column. It appears that the second column shows the Sunday Letter, but that seems different from the deleted #Method of calculating the date of Easter. The third and fourth column obviously show the day in the Roman fashion. Here is a transcription of these columns:
Extended content
|
---|
3 A Ianuarius b 4 N′ 9 c 3 N′ d 2 N′ 19 e Nonas N′ 8 f 8 Id′ g 7 Id′ 13 A 6 Id′ 2 b 5 Id′ c 4 Id′ 16 d 3 Id′ 5 e 2 Idus f Idus Idꝰ 10 g 19 Kl′ A 18 Kl′ 18 b 17 Kl′ 7 c 16 Kl′ d 15 Kl′ 15 e 14 Kl′ 4 f 13 Kl′ g 12 Kl′ 12 A 11 Kl′ 1 b 10 Kl′ c 9 Kl′ 17 d 8 Kł 6 e 7 Kl′ f 6 Kł 9 g 5 Kl′ A 4 Kl′ 14 b 3 Kl′ 3 c 2 Kl′ |
It would be nice to have transcription and translation of introduction and fifth column, as well. Most pertinent for this article, however, is the leftmost column, which poses a number of questions:
Upon further research on point 2, the discrepancy seems to be no outlier. E.g. the year 1396 has, according to the modulo formula, the golden number 10 (in this table at 19 Kl′) and the year before has the golden number 9, for which there are two entries: at 3 N′ and at 5 Kl′. A synodic year before 19 Kl′ of January 1396 was January 25…26 (depending on rounding error), 3…4 days before the 5 Kl′ of this table. You might say they weren't so exact in the middle ages, but this computation requires no more than simple addition, subtraction and multiplication, and the observation of half a week difference to a full moon, so one should think that they could have done better. Or am I missing something? ◅ Sebastian Helm 🗨 12:59, 27 March 2024 (UTC)
The lunar date for 29 February of a leap year is normally the same as that of the preceding day - thus the lunar date for 28 and 29 February 2028 is 3 Ronan. For use of the letters A - g to find the day of the week see Dominical letter. The months are: (1) Harriet, (2) Ronan, (3) Miri, (4) James, (5) Eloise, (6) Thomas, vii, (8) Nicholas, (9) Catherine, (10) Richard, (11) Emma, (12) Paul. Paul II, a 30-day month, is added between Paul and Harriet 7 times in 19 years. When the golden number is 19, Richard has 29 days instead of 30. See Saltus#Latin (third bullet point).
JAN Paul 30 |
FEB Harr 29 |
MAR Ron 30 |
APR Miri 29 |
MAY Jame 30 |
JUN Eloi 29 |
JUL Thom 30 |
AUG vii 29 |
SEPT Nich 30 |
OCT Cath 29 |
NOV Rich 30 |
DEC Emma 29 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | A 12 | d 1 | d 12 | g 1 | b | e 9 | g | c 17 | f | A | d 3 | f 3 |
2 | b 1 | e | e 1 | A | c 9 | f | A 17 | d 6 | g 14 | b 14 | e | g |
3 | c | f 9 | f | b 9 | d | g 17 | b 6 | e | A 3 | c 3 | f 11 | A 11 |
4 | d 9 | g | g 9 | c | e 17 | A 6 | c | f 14 | b | d | g | b 19 |
5 | e P2 | A 17 | A | d 17 | f 6 | b | d 14 | g 3 | c 11 | e 11 | A 19 | c |
6 | f 17 | b 6 | b 17 | e 6 | g | c 14 | e 3 | A | d | f | b 8 | d 8 |
7 | g 6 | c | c 6 | f | A 14 | d 3 | f | b 11 | e 19 | g 19 | c Em | e 16 |
8 | A | d 14 | d | g 14 | b 3 | e | g 11 | c | f 8 | A 8 | d 16 | f 5 |
9 | b 14 | e 3 | e 14 | A 3 | c | f 11 | A | d 19 | g Ca | b 16 | e 5 | g |
10 | c 3 | f | f 3 | b | d 11 | g | b 19 | e 8 | A 16 | c 5 | f | A 13 |
11 | d | g 11 | g | c 11 | e | A 19 | c 8 | f 16 | b 5 | d | g 13 | b 2 |
12 | e 11 | A | A 11 | d | f 19 | b 8 | d vii | g 5 | c | e 13 | A 2 | c |
13 | f | b 19 | b | e 19 | g 8 | c 16 | e 16 | A | d 13 | f 2 | b | d 10 |
14 | g 19 | c 8 | c 19 | f 8 | A El | d 5 | f 5 | b 13 | e 2 | g | c 10 | e |
15 | A 8 | d 16 | d 8 | g 16 | b 16 | e | g | c 2 | f | A 10 | d | f 18 |
16 | b Ha | e 5 | e Mi | A 5 | c 5 | f 13 | A 13 | d | g 10 | b | e 18 | g 7 |
17 | c 16 | f | f 16 | b | d | g 2 | b 2 | e 10 | A | c 18 | f 7 | A |
18 | d 5 | g 13 | g 5 | c 13 | e 13 | A | c | f | b 18 | d 7 | g | b 15 |
19 | e | A 2 | A | d 2 | f 2 | b 10 | d 10 | g 18 | c 7 | e | A 15 | c 4 |
20 | f 13 | b | b 13 | e | g | c | e | A 7 | d | f 15 | b 4 | d |
21 | g 2 | c 10 | c 2 | f 10 | A 10 | d 18 | f 18 | b | e 15 | g 4 | c | e 12 |
22 | A | d | d | g | b | e 7 | g 7 | c 15 | f 4 | A | d 12 | f 1 |
23 | b 10 | e 18 | e 10 | A 18 | c 18 | f | A | d 4 | g | b 12 | e 1 | g |
24 | c | f 7 | f | b 7 | d 7 | g 15 | b 15 | e | A 12 | c 1 | f | A 9 |
25 | d 18 | g | g 18 | c | e | A 4 | c 4 | f 12 | b 1 | d | g 9 | b |
26 | e 7 | A 15 | A 7 | d 15 | f 15 | b | d | g 1 | c | e 9 | A | c 17 |
27 | f | b 4 | b | e 4 | g 4 | c 12 | e 12 | A | d 9 | f | b 17 | d 6 |
28 | g 15 | c | c 15 | f | A | d 1 | f 1 | b 9 | e | g 17 | c 6 | e |
29 | A 4 | d 4 | g 12 | b 12 | e | g | c | f 17 | A 6 | d | f 14 | |
30 | b | e | A 1 | c 1 | f 9 | A 9 | d 17 | g 6 | b | e 14 | g 3 | |
31 | c 12 | f 12 | d | b | e 6 | c 14 | A | |||||
Harr | Ron | Miri | Jame | Eloi | Thom | vii | Nich | Cath | Rich | Emma | Paul |
The sequence of Sunday letters is manufactured by giving 1 January letter A and repeatedly cycling through the first seven letters of the alphabet to 31 December, which is again A as the year consists of 52 weeks and 1 day, discounting 29 February which has no letter allocated to it. The official table remained unchanged from AD 284, when it was devised, until the modern table replaced it. The dates are Julian, and the table was accurate when it was introduced. The error you cite (one day in 219 years) is against the Gregorian/Revised Julian calendar - against the Julian it is only one day in 308 years. The new moons are now delayed four days from their true places - the error was corrected by moving them up four days and then down 13 days from their new position to locate them in the Gregorian/Revised Julian calendar, which is currently 13 days ahead of the Julian. The net displacement is nine days, so if you move the golden numbers up nine days from where they are in the modern table you will see where they should have been in the old one. The errors immediately become apparent: