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EspañolDOMINICAL LETTER
'Dominical letters' are letters A, B, C, D, E, F and G assigned to days in a cycle of 7 with the letter A always set against 1 January as an aid for finding the day of week of a given calendar date and in calculating Easter.
A common year is assigned the dominical letter of its first Sunday. For example 2003 has 5 January as its first Sunday, so it has dominical letter 'E'.
In leap years, the leap day may or may not have a dominical letter. In the original 1582 Catholic version, it did, but in the 1752 Anglican version it did not. The Catholic version caused February to have 29 days by doubling the sixth day before 1 March, inclusive, because 24 February in a common year is marked "duplex", thus both halves of the doubled day had a dominical letter of F.[1][2][3] The Anglican version added a day to February that did not exist in common years, 29 February, thus it did not have a dominical letter of its own.[4][5]
In either case, all other dates have the same dominical letter every year, but the days of the weeks of the dominical letters change within a leap year before and after the intercalary day, 24 February or 29 February. Hence leap years have two dominical letters: the first for January and most or all of February and the second for March to December. The second dominical letter is the dominical letter that the year would have if it wasn't a leap year and the dates in March to December had the same days of the week.
Examples include:
★ 2001 'G'
★ 2002 'F'
★ 2003 'E'
★ 2004 'DC'
★ 2005 'B'
★ 2006 'A'
★ 2007 'G'
★ 2008 'FE'
★ 2009 'D'
★ 2010 'C'
★ 2011 'B'
★ 2012 'AG'
★ 2013 'F'
The dominical letter of a year determines the days of week in its calendar:
★ 'A' common year starting on Sunday
★ 'B' common year starting on Saturday
★ 'C' common year starting on Friday
★ 'D' common year starting on Thursday
★ 'E' common year starting on Wednesday
★ 'F' common year starting on Tuesday
★ 'G' common year starting on Monday
★ 'AG' leap year starting on Sunday
★ 'BA' leap year starting on Saturday
★ 'CB' leap year starting on Friday
★ 'DC' leap year starting on Thursday
★ 'ED' leap year starting on Wednesday
★ 'FE' leap year starting on Tuesday
★ 'GF' leap year starting on Monday
It was a device adopted from the Romans by the old chronologers to aid them in finding the day of the week corresponding to any given date, and indirectly to facilitate the adjustment of the "Proprium de Tempore" to the "Proprium Sanctorum" when constructing the ecclesiastical calendar for any year. The Christian Church, on account of its complicated system of movable and immovable feasts (see Christian calendar), has from an early period been particularly concerned with the regulation and measurement of time. To secure uniformity in the observance of feasts and fasts, it began, even in the patristic age, to supply a ''computus'', or system of reckoning, by which the relation of the solar and lunar years might be accommodated and the celebration of Easter determined. Naturally it adopted the astronomical methods then available, and these methods and the methodology belonging to them, having become traditional, are perpetuated in a measure to this day, even the reform of the calendar, in the prolegomena to the Breviary and Missal.
The Romans were accustomed to divide the year into ''nundinæ'', periods of eight days; and in their ''marble fasti'', or calendars, of which numerous specimens remain, they used the first eight letters of the alphabet to mark the days of which each period was composed. When the Oriental seven-day period, or week, was introduced in the time of Cæsar Augustus, the first seven letters of the alphabet were employed in the same way to indicate the days of this new division of time. In fact, fragmentary calendars on marble still survive in which both a cycle of eight letters — A to H — indicating ''nundinæ'', and a cycle of seven letters — A to G — indicating weeks, are used side by side (see "Corpus Inscriptionum Latinarum", 2nd ed., I, 220; the same peculiarity occurs in the Philocalian Calendar of A.D. 356, ibid., p. 256). This device was imitated by the Christians.
The days of the year from 1 January to 31 December are marked with a continuous recurring cycle of seven letters: A, B, C, D, E, F, G. A is always set against 1 January, B against 2 January, C against 3 January, and so on. Thus F falls to 6 January, G to 7 January; A again recurs on 8 January, and also, consequently, on 15 January, 22 January, and 29 January. Continuing in this way, 30 January is marked with a B, 31 January with a C, and 1 February with a D. This is carried on through all the days of an ordinary year (i. e. not a leap year). Thus D corresponds to 1 March, G to 1 April, B to 1 May, E to 1 June, G to 1 July, C to 1 August, F to 1 September, A to 1 October, D to 1 November, and F to 1 December — a result which Durandus recalled by the following distich:
:Alta Domat Dominus, Gratis Beat Equa Gerentes
:Contemnit Fictos, Augebit Dona Fideli.
Another one is:
:Add G, beg C, fad F.
Clearly, if 1 January is a Sunday, all the days marked by A will also be Sundays; If 1 January is a Saturday, Sunday will fall on 2 January which is a B, and all the other days marked B will be Sundays; if 1 January is a Monday, then Sunday will not come until 7 January, a G, and all the days marked G will be Sundays.
This being explained, the Dominical Letter of any year is defined to be that letter of the cycle A, B, C, D, E, F, G, which corresponds to the day upon which the first Sunday (and every subsequent Sunday) falls.
It is plain, however, that when a leap year occurs, a complication is introduced. February has then 29 days. Traditionally, the Anglican and civil calendars added this extra day to the end of the month, while the Catholic ecclesiastical calendar counted 24 February twice. But in either case, 1 March is then one day later in the week than 1 February, or, in other words, in the rest of the year the Sundays come, within the month, a day earlier than they would in a common year. This is expressed by saying that a leap year has two Dominical Letters, the second being the letter which precedes that with which the year started. For example, 1 January 1907, was a Tuesday; the first Sunday fell on 6 January, or an F. F was, therefore, the Dominical Letter for 1907. The first of January, 1908, was a Wednesday, the first Sunday fell on 5 January, and E was the Dominical Letter for January and February, but as 1908 was a leap year, its Sundays after February came a day sooner than in a normal year and were Ds. The year 1908, therefore, had a double Dominical Letter, ED. In 1909, 1 January was a Friday and the Dominical Letter was C. In 1910 and 1911, 1 January fell respectively on Saturday and Sunday and the Dominical Letters were B and A.
To find the Dominical Letter for any year is done by partly applying any method for calculating the day of the week, where letters are in reversed order compared to numbers indicating the day of the week.
Thus:
★ ignore periods of 400 years
★ considering the second letter in the case of a leap year:
★
★ for one century within two multiples of 400, go forward two letters from BA for 2000, hence C, E, G.
★
★ for remaining years, go back one letter every year, two for leap years (this corresponds to writing two letters, no letter is skipped).
★
★ to avoid up to 99 steps within a century, there is a choice of several shortcuts, e.g.:
★
★
★ go back one letter for every 12 years
★
★
★ ignore multiples of 28 years (note that when jumping from e.g. 1900 to 1928 the ''last'' letter of 1928 is the same as the letter of 1900)
★
★
★ apply steps between multiples of 10, writing from right to left:
2000 1990 1980 1970 1960 1950 1940 1930 1920 1910 1900
BA G FE D CB A GF E DC B .G
★ Note the dummy step (we skip A between 1900 and 1910) because 1900 is not a leap year.
For example, to find the Dominical Letter of the year 1913:
★ 1900 is G
★ 1910 is B
★ count B A GF E, 1913 is E
Similarly, for 2007:
★ 2000 is BA
★ count BA G F E DC B A G, 2007 is G
For 2065:
★ 2000 is BA
★ 2012 is AG, 2024 is GF, 2036 is FE, 2048 is ED, 2060 is DC, then B A G FE D, 2065 is D
★ or from 2000 to 2060 in steps of 10, written backward: DC B AG F ED C BA, starting from 2000 is BA we get 2060 is DC, then again B A G FE D, 2065 is D (or, writing the last part backward too: D FE G A B B AG F ED C BA)
★ or ignore 56 years, 2056 is BA, count G F E DC B A G FE D, 2065 is D
For years outside the range of this table, use the fact that the dominical letters repeat exactly every 400 years.
,----,----,----,----,
|1600|1700|1800|1900|
|2000|2100|2200|2300|
,-----------+----+----+----+----|
| 00| BA | C | E | G |
|-----------+----+----+----+----|
|85 57 29 01| G | B | D | F |
|86 58 30 02| F | A | C | E |
|87 59 31 03| E | G | B | D |
|88 60 32 04| DC | FE | AG | CB |
|-----------+----+----+----+----|
|89 61 33 05| B | D | F | A |
|90 62 34 06| A | C | E | G |
|91 63 35 07| G | B | D | F |
|92 64 36 08| FE | AG | CB | ED |
|-----------+----+----+----+----|
|93 65 37 09| D | F | A | C |
|94 66 38 10| C | E | G | B |
|95 67 39 11| B | D | F | A |
|96 68 40 12| AG | CB | ED | GF |
|-----------+----+----+----+----|
|97 69 41 13| F | A | C | E |
|98 70 42 14| E | G | B | D |
|99 71 43 15| D | F | A | C |
| 72 44 16| CB | ED | GF | BA |
|-----------+----+----+----+----|
| 73 45 17| A | C | E | G |
| 74 46 18| G | B | D | F |
| 75 47 19| F | A | C | E |
| 76 48 20| ED | GF | BA | DC |
|-----------+----+----+----+----|
| 77 49 21| C | E | G | B |
| 78 50 22| B | D | F | A |
| 79 51 23| A | C | E | G |
| 80 52 24| GF | BA | DC | FE |
|-----------+----+----+----+----|
| 81 53 25| E | G | B | D |
| 82 54 26| D | F | A | C |
| 83 55 27| C | E | G | B |
| 84 56 28| BA | DC | FE | AG |
'-----------+----+----+----+----|
|1600|1700|1800|1900|
|2000|2100|2200|2300|
'----'----'----'----'
,---,---,---,---,---,---,---,---,---,---,---,---,
|Jan|Feb|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec|
,---------------+---+---+---+---+---+---+---+---+---+---+---+---|
|(29) 22 15 8 1| A | D | D | G | B | E | G | C | F | A | D | F |
|---------------+---+---+---+---+---+---+---+---+---+---+---+---|
|(30) 23 16 9 2| B | E | E | A | C | F | A | D | G | B | E | G |
|(31) 24 17 10 3| C | F | F | B | D | G | B | E | A | C | F | A |
| 25 18 11 4| D | G | G | C | E | A | C | F | B | D | G | B |
| 26 19 12 5| E | A | A | D | F | B | D | G | C | E | A | C |
| 27 20 13 6| F | B | B | E | G | C | E | A | D | F | B | D |
|---------------+---+---+---+---+---+---+---+---+---+---+---+---|
| 28 21 14 7| G | C | C | F | A | D | F | B | E | G | C | E |
'---------------'---'---'---'---'---'---'---'---'---'---'---'---'
But the Dominical Letter had another very practical use in the days before the ''Ordo divini officii recitandi'' was printed annually, and when, consequently, a priest had often to determine the ''Ordo'' for himself. As can be seen in the article Epact, Easter Sunday may be as early as 22 March or as late as 25 April, and there are consequently 35 possible days on which it may fall. It is also evident that each Dominical Letter allows five possible dates for Easter Sunday. Thus, in a year whose Dominical Letter is A (i. e. when 1 January is a Sunday), Easter must be either on 26 March, 2 April, 9 April, 16 April, or 23 April, for these are all the Sundays within the defined limits. But according as Easter falls on one or another of these Sundays we shall get a different calendar, and hence there are five, and only five, possible calendars for years whose Dominical Letter is A. Similarly, there are five possible calendars for years whose Dominical Letter is B, five for C, and so on, thirty-five possible combinations in all. Now, advantage was taken of this principle in the arrangement of the old Pye or directorium which preceded the present "Ordo". The 35 possible calendars were all included therein and numbered, respectively, primum A, secundum A, tertium A, etc.; primum B, secundum B, etc. Hence for anyone wishing to use the Pye the first thing to determine was the Dominical Letter of the year, and then by means of the Golden Number or the Epact, and by the aid of a simple table, to find which of the five possible calendars assigned to that Dominical Letter belonged to the year in question. Such a table as that just referred to, but adapted to the reformed calendar and in more convenient shape, will be found at the beginning of every Breviary and Missal under the heading, "Tabula Paschalis nova reformata".
The Dominical Letter does not seem to have been familiar to Bede in his "De temporum ratione", but in its place he adopts a similar device of seven numbers which he calls ''concurrentes'' (De Temp. Rat., cap. liii), of Greek origin. The Concurrents are numbers denoting the days of the week on which 24 March falls in the successive years of the solar cycle, 1 standing for Sunday, 2 (feria secunda) for Monday, 3 for Tuesday, and so on. It is sufficient here to state that the relation between the Concurrents and the Dominical Letter is the following:
:Concurrents 1 2 3 4 5 6 7
:Concurrent 1 = F (Dominical Letter)
:Concurrent 2 = E
:Concurrent 3 = D
:Concurrent 4 = C
:Concurrent 5 = B
:Concurrent 6 = A
:Concurrent 7 = G
There exist patterns in the dominical letters, which are very useful for mental calculation.
'Patterns for years:'
To use these patterns, choose and remember a year to use as a starting point, such as 2000=BA.
Note that because of the complicated Gregorian leap-year rules, these patterns break near some century changes. Note the reverse alphabetical order.
1992 3 4 5 96 7 8 9 2000 1 2 3 04 5 6 7 2008
ED C B A GF E D C BA G F E DC B A G FE
and
(note the reversed order of the years
as well as of the letters)
2040 2030 2020 2010 2000 1990 1980 1970 1960 1950
AG F ED C BA G FE D CB A
| | | | | | | | | |
G FE D CB A GF E DC B AG
2046 2036 2026 2016 2006 1996 1986 1976 1966 1956
'Patterns for days of the month:'
The dominical letters for the first day of each month form the nonsense mnemonic phrase "Add G, beg C, fad F".
The following dates, given in month/day form, all have dominical letter C: 4/4, 6/6, 8/8, 10/10, 12/12, 5/9, 9/5, 7/11, 11/7 (see also the Doomsday rule).
We are able to calculate the Dominical letter in this way (function in C), where:
★ m = month
★ y = year
★ s = "style"; 0 for Julian, otherwise Gregorian.
char dominical(int m,int y,int s){
int leap;
int a,b;
leap=(s
a=(y%100)%28;
b=(s==0)
★ (4+(y%700)/100+2
★ (a/4)+6
★ ((!leap)
★ (1+(a%4))+(leap)
★ ((9+m)/12)))%7+
(s!=0)
★ (2
★ (1+(y%400)/100+(a/4))+6
★ ((!leap)
★ (1+(a%4))+(leap)
★ ((9+m)/12)))%7;
b=(b==0)
★ (b+7)+(b!=0)
★ b;
return (char)(64+b);
}
1. Peter Archer, ''The Christian Calendar and the Gregorian Reform'' (New York: Fordham University Press, 1941) p.5
2. Bonnie Blackburn, Leofranc Holford-Strevens, ''The Oxford Companion to the Year'' (Oxford: Oxford University Press, 1999), p.829
3. Calendarium (Calendar attached to the papal bull "Inter gravissimas")
4. ”Anno vicesimo quarto Georgii II. c.23” (1751), ''The Statutes at Large, from Magna Charta to the end of the Eleventh Parliament of Great Britain, Anno 1761'', ed. Danby Pickering, p.194.
5. J. K. Fotheringham, "Explanation: The Calendar", ''The Nautical Almanac and Astronomical Ephemeris for the year 1931'', pp.735-747, p.745, ''... 1938'', pp.790-806, p.803.
★
★
★ Catholic Encyclopedia article on Dominical letter
A common year is assigned the dominical letter of its first Sunday. For example 2003 has 5 January as its first Sunday, so it has dominical letter 'E'.
In leap years, the leap day may or may not have a dominical letter. In the original 1582 Catholic version, it did, but in the 1752 Anglican version it did not. The Catholic version caused February to have 29 days by doubling the sixth day before 1 March, inclusive, because 24 February in a common year is marked "duplex", thus both halves of the doubled day had a dominical letter of F.[1][2][3] The Anglican version added a day to February that did not exist in common years, 29 February, thus it did not have a dominical letter of its own.[4][5]
In either case, all other dates have the same dominical letter every year, but the days of the weeks of the dominical letters change within a leap year before and after the intercalary day, 24 February or 29 February. Hence leap years have two dominical letters: the first for January and most or all of February and the second for March to December. The second dominical letter is the dominical letter that the year would have if it wasn't a leap year and the dates in March to December had the same days of the week.
Examples include:
★ 2001 'G'
★ 2002 'F'
★ 2003 'E'
★ 2004 'DC'
★ 2005 'B'
★ 2006 'A'
★ 2007 'G'
★ 2008 'FE'
★ 2009 'D'
★ 2010 'C'
★ 2011 'B'
★ 2012 'AG'
★ 2013 'F'
The dominical letter of a year determines the days of week in its calendar:
★ 'A' common year starting on Sunday
★ 'B' common year starting on Saturday
★ 'C' common year starting on Friday
★ 'D' common year starting on Thursday
★ 'E' common year starting on Wednesday
★ 'F' common year starting on Tuesday
★ 'G' common year starting on Monday
★ 'AG' leap year starting on Sunday
★ 'BA' leap year starting on Saturday
★ 'CB' leap year starting on Friday
★ 'DC' leap year starting on Thursday
★ 'ED' leap year starting on Wednesday
★ 'FE' leap year starting on Tuesday
★ 'GF' leap year starting on Monday
History
It was a device adopted from the Romans by the old chronologers to aid them in finding the day of the week corresponding to any given date, and indirectly to facilitate the adjustment of the "Proprium de Tempore" to the "Proprium Sanctorum" when constructing the ecclesiastical calendar for any year. The Christian Church, on account of its complicated system of movable and immovable feasts (see Christian calendar), has from an early period been particularly concerned with the regulation and measurement of time. To secure uniformity in the observance of feasts and fasts, it began, even in the patristic age, to supply a ''computus'', or system of reckoning, by which the relation of the solar and lunar years might be accommodated and the celebration of Easter determined. Naturally it adopted the astronomical methods then available, and these methods and the methodology belonging to them, having become traditional, are perpetuated in a measure to this day, even the reform of the calendar, in the prolegomena to the Breviary and Missal.
The Romans were accustomed to divide the year into ''nundinæ'', periods of eight days; and in their ''marble fasti'', or calendars, of which numerous specimens remain, they used the first eight letters of the alphabet to mark the days of which each period was composed. When the Oriental seven-day period, or week, was introduced in the time of Cæsar Augustus, the first seven letters of the alphabet were employed in the same way to indicate the days of this new division of time. In fact, fragmentary calendars on marble still survive in which both a cycle of eight letters — A to H — indicating ''nundinæ'', and a cycle of seven letters — A to G — indicating weeks, are used side by side (see "Corpus Inscriptionum Latinarum", 2nd ed., I, 220; the same peculiarity occurs in the Philocalian Calendar of A.D. 356, ibid., p. 256). This device was imitated by the Christians.
Dominical letter of a date (month and day)
The days of the year from 1 January to 31 December are marked with a continuous recurring cycle of seven letters: A, B, C, D, E, F, G. A is always set against 1 January, B against 2 January, C against 3 January, and so on. Thus F falls to 6 January, G to 7 January; A again recurs on 8 January, and also, consequently, on 15 January, 22 January, and 29 January. Continuing in this way, 30 January is marked with a B, 31 January with a C, and 1 February with a D. This is carried on through all the days of an ordinary year (i. e. not a leap year). Thus D corresponds to 1 March, G to 1 April, B to 1 May, E to 1 June, G to 1 July, C to 1 August, F to 1 September, A to 1 October, D to 1 November, and F to 1 December — a result which Durandus recalled by the following distich:
:Alta Domat Dominus, Gratis Beat Equa Gerentes
:Contemnit Fictos, Augebit Dona Fideli.
Another one is:
:Add G, beg C, fad F.
Clearly, if 1 January is a Sunday, all the days marked by A will also be Sundays; If 1 January is a Saturday, Sunday will fall on 2 January which is a B, and all the other days marked B will be Sundays; if 1 January is a Monday, then Sunday will not come until 7 January, a G, and all the days marked G will be Sundays.
Dominical letter of a year
This being explained, the Dominical Letter of any year is defined to be that letter of the cycle A, B, C, D, E, F, G, which corresponds to the day upon which the first Sunday (and every subsequent Sunday) falls.
It is plain, however, that when a leap year occurs, a complication is introduced. February has then 29 days. Traditionally, the Anglican and civil calendars added this extra day to the end of the month, while the Catholic ecclesiastical calendar counted 24 February twice. But in either case, 1 March is then one day later in the week than 1 February, or, in other words, in the rest of the year the Sundays come, within the month, a day earlier than they would in a common year. This is expressed by saying that a leap year has two Dominical Letters, the second being the letter which precedes that with which the year started. For example, 1 January 1907, was a Tuesday; the first Sunday fell on 6 January, or an F. F was, therefore, the Dominical Letter for 1907. The first of January, 1908, was a Wednesday, the first Sunday fell on 5 January, and E was the Dominical Letter for January and February, but as 1908 was a leap year, its Sundays after February came a day sooner than in a normal year and were Ds. The year 1908, therefore, had a double Dominical Letter, ED. In 1909, 1 January was a Friday and the Dominical Letter was C. In 1910 and 1911, 1 January fell respectively on Saturday and Sunday and the Dominical Letters were B and A.
Calculation
To find the Dominical Letter for any year is done by partly applying any method for calculating the day of the week, where letters are in reversed order compared to numbers indicating the day of the week.
Thus:
★ ignore periods of 400 years
★ considering the second letter in the case of a leap year:
★
★ for one century within two multiples of 400, go forward two letters from BA for 2000, hence C, E, G.
★
★ for remaining years, go back one letter every year, two for leap years (this corresponds to writing two letters, no letter is skipped).
★
★ to avoid up to 99 steps within a century, there is a choice of several shortcuts, e.g.:
★
★
★ go back one letter for every 12 years
★
★
★ ignore multiples of 28 years (note that when jumping from e.g. 1900 to 1928 the ''last'' letter of 1928 is the same as the letter of 1900)
★
★
★ apply steps between multiples of 10, writing from right to left:
2000 1990 1980 1970 1960 1950 1940 1930 1920 1910 1900
BA G FE D CB A GF E DC B .G
★ Note the dummy step (we skip A between 1900 and 1910) because 1900 is not a leap year.
For example, to find the Dominical Letter of the year 1913:
★ 1900 is G
★ 1910 is B
★ count B A GF E, 1913 is E
Similarly, for 2007:
★ 2000 is BA
★ count BA G F E DC B A G, 2007 is G
For 2065:
★ 2000 is BA
★ 2012 is AG, 2024 is GF, 2036 is FE, 2048 is ED, 2060 is DC, then B A G FE D, 2065 is D
★ or from 2000 to 2060 in steps of 10, written backward: DC B AG F ED C BA, starting from 2000 is BA we get 2060 is DC, then again B A G FE D, 2065 is D (or, writing the last part backward too: D FE G A B
★ or ignore 56 years, 2056 is BA, count G F E DC B A G FE D, 2065 is D
Complete tables
Table of dominical letters for years
For years outside the range of this table, use the fact that the dominical letters repeat exactly every 400 years.
,----,----,----,----,
|1600|1700|1800|1900|
|2000|2100|2200|2300|
,-----------+----+----+----+----|
| 00| BA | C | E | G |
|-----------+----+----+----+----|
|85 57 29 01| G | B | D | F |
|86 58 30 02| F | A | C | E |
|87 59 31 03| E | G | B | D |
|88 60 32 04| DC | FE | AG | CB |
|-----------+----+----+----+----|
|89 61 33 05| B | D | F | A |
|90 62 34 06| A | C | E | G |
|91 63 35 07| G | B | D | F |
|92 64 36 08| FE | AG | CB | ED |
|-----------+----+----+----+----|
|93 65 37 09| D | F | A | C |
|94 66 38 10| C | E | G | B |
|95 67 39 11| B | D | F | A |
|96 68 40 12| AG | CB | ED | GF |
|-----------+----+----+----+----|
|97 69 41 13| F | A | C | E |
|98 70 42 14| E | G | B | D |
|99 71 43 15| D | F | A | C |
| 72 44 16| CB | ED | GF | BA |
|-----------+----+----+----+----|
| 73 45 17| A | C | E | G |
| 74 46 18| G | B | D | F |
| 75 47 19| F | A | C | E |
| 76 48 20| ED | GF | BA | DC |
|-----------+----+----+----+----|
| 77 49 21| C | E | G | B |
| 78 50 22| B | D | F | A |
| 79 51 23| A | C | E | G |
| 80 52 24| GF | BA | DC | FE |
|-----------+----+----+----+----|
| 81 53 25| E | G | B | D |
| 82 54 26| D | F | A | C |
| 83 55 27| C | E | G | B |
| 84 56 28| BA | DC | FE | AG |
'-----------+----+----+----+----|
|1600|1700|1800|1900|
|2000|2100|2200|2300|
'----'----'----'----'
Table for days of the year
,---,---,---,---,---,---,---,---,---,---,---,---,
|Jan|Feb|Mar|Apr|May|Jun|Jul|Aug|Sep|Oct|Nov|Dec|
,---------------+---+---+---+---+---+---+---+---+---+---+---+---|
|(29) 22 15 8 1| A | D | D | G | B | E | G | C | F | A | D | F |
|---------------+---+---+---+---+---+---+---+---+---+---+---+---|
|(30) 23 16 9 2| B | E | E | A | C | F | A | D | G | B | E | G |
|(31) 24 17 10 3| C | F | F | B | D | G | B | E | A | C | F | A |
| 25 18 11 4| D | G | G | C | E | A | C | F | B | D | G | B |
| 26 19 12 5| E | A | A | D | F | B | D | G | C | E | A | C |
| 27 20 13 6| F | B | B | E | G | C | E | A | D | F | B | D |
|---------------+---+---+---+---+---+---+---+---+---+---+---+---|
| 28 21 14 7| G | C | C | F | A | D | F | B | E | G | C | E |
'---------------'---'---'---'---'---'---'---'---'---'---'---'---'
Practical use for the clergy
But the Dominical Letter had another very practical use in the days before the ''Ordo divini officii recitandi'' was printed annually, and when, consequently, a priest had often to determine the ''Ordo'' for himself. As can be seen in the article Epact, Easter Sunday may be as early as 22 March or as late as 25 April, and there are consequently 35 possible days on which it may fall. It is also evident that each Dominical Letter allows five possible dates for Easter Sunday. Thus, in a year whose Dominical Letter is A (i. e. when 1 January is a Sunday), Easter must be either on 26 March, 2 April, 9 April, 16 April, or 23 April, for these are all the Sundays within the defined limits. But according as Easter falls on one or another of these Sundays we shall get a different calendar, and hence there are five, and only five, possible calendars for years whose Dominical Letter is A. Similarly, there are five possible calendars for years whose Dominical Letter is B, five for C, and so on, thirty-five possible combinations in all. Now, advantage was taken of this principle in the arrangement of the old Pye or directorium which preceded the present "Ordo". The 35 possible calendars were all included therein and numbered, respectively, primum A, secundum A, tertium A, etc.; primum B, secundum B, etc. Hence for anyone wishing to use the Pye the first thing to determine was the Dominical Letter of the year, and then by means of the Golden Number or the Epact, and by the aid of a simple table, to find which of the five possible calendars assigned to that Dominical Letter belonged to the year in question. Such a table as that just referred to, but adapted to the reformed calendar and in more convenient shape, will be found at the beginning of every Breviary and Missal under the heading, "Tabula Paschalis nova reformata".
The Dominical Letter does not seem to have been familiar to Bede in his "De temporum ratione", but in its place he adopts a similar device of seven numbers which he calls ''concurrentes'' (De Temp. Rat., cap. liii), of Greek origin. The Concurrents are numbers denoting the days of the week on which 24 March falls in the successive years of the solar cycle, 1 standing for Sunday, 2 (feria secunda) for Monday, 3 for Tuesday, and so on. It is sufficient here to state that the relation between the Concurrents and the Dominical Letter is the following:
:Concurrents 1 2 3 4 5 6 7
:Concurrent 1 = F (Dominical Letter)
:Concurrent 2 = E
:Concurrent 3 = D
:Concurrent 4 = C
:Concurrent 5 = B
:Concurrent 6 = A
:Concurrent 7 = G
Use for mental calculation
There exist patterns in the dominical letters, which are very useful for mental calculation.
'Patterns for years:'
To use these patterns, choose and remember a year to use as a starting point, such as 2000=BA.
Note that because of the complicated Gregorian leap-year rules, these patterns break near some century changes. Note the reverse alphabetical order.
1992 3 4 5 96 7 8 9 2000 1 2 3 04 5 6 7 2008
ED C B A GF E D C BA G F E DC B A G FE
and
(note the reversed order of the years
as well as of the letters)
2040 2030 2020 2010 2000 1990 1980 1970 1960 1950
AG F ED C BA G FE D CB A
| | | | | | | | | |
G FE D CB A GF E DC B AG
2046 2036 2026 2016 2006 1996 1986 1976 1966 1956
'Patterns for days of the month:'
The dominical letters for the first day of each month form the nonsense mnemonic phrase "Add G, beg C, fad F".
The following dates, given in month/day form, all have dominical letter C: 4/4, 6/6, 8/8, 10/10, 12/12, 5/9, 9/5, 7/11, 11/7 (see also the Doomsday rule).
We are able to calculate the Dominical letter in this way (function in C), where:
★ m = month
★ y = year
★ s = "style"; 0 for Julian, otherwise Gregorian.
char dominical(int m,int y,int s){
int leap;
int a,b;
leap=(s
0&&y%4
0)||(s!=0&&(y%4==0&&y%100!=0||y%400==0));a=(y%100)%28;
b=(s==0)
★ (4+(y%700)/100+2
★ (a/4)+6
★ ((!leap)
★ (1+(a%4))+(leap)
★ ((9+m)/12)))%7+
(s!=0)
★ (2
★ (1+(y%400)/100+(a/4))+6
★ ((!leap)
★ (1+(a%4))+(leap)
★ ((9+m)/12)))%7;
b=(b==0)
★ (b+7)+(b!=0)
★ b;
return (char)(64+b);
}
References
1. Peter Archer, ''The Christian Calendar and the Gregorian Reform'' (New York: Fordham University Press, 1941) p.5
2. Bonnie Blackburn, Leofranc Holford-Strevens, ''The Oxford Companion to the Year'' (Oxford: Oxford University Press, 1999), p.829
3. Calendarium (Calendar attached to the papal bull "Inter gravissimas")
4. ”Anno vicesimo quarto Georgii II. c.23” (1751), ''The Statutes at Large, from Magna Charta to the end of the Eleventh Parliament of Great Britain, Anno 1761'', ed. Danby Pickering, p.194.
5. J. K. Fotheringham, "Explanation: The Calendar", ''The Nautical Almanac and Astronomical Ephemeris for the year 1931'', pp.735-747, p.745, ''... 1938'', pp.790-806, p.803.
★
★
External links
★ Catholic Encyclopedia article on Dominical letter
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