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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 week (also called sennight or sevennight) is a unit of Time longer than a Day and shorter than a Month. Computus ( Latin for Computation) is the Calculation of the date of Easter in the Christian calendar.

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. Events 1477 - Battle of Nancy: Charles the Bold is killed and Burgundy becomes part of France.

In leap years, the leap day may or may not have a dominical letter. A leap year (or intercalary year) is a year containing one or more extra days (or in the case of Lunisolar calendars an extra month in order to keep the 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. Events 86 BC - Lucius Cornelius Sulla, at the head of a Roman Republic army enters in Athens, removing the Tyrant Events 303 - Galerius, Roman Emperor, publishes his edict that begins the persecution of Christians in his portion of the [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. Leap years Although the modern calendar counts a year as 365 days a complete revolution around the sun takes approximately 365 days and 6 hours [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. Events 303 - Galerius, Roman Emperor, publishes his edict that begins the persecution of Christians in his portion of the Leap years Although the modern calendar counts a year as 365 days a complete revolution around the sun takes approximately 365 days and 6 hours 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:

The dominical letter of a year determines the days of week in its calendar:

Contents

History

Dominical letters were a device adopted from the Romans by 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. Year 2001 ( MMI) was a Common year starting on Monday according to the Gregorian calendar. See also 2002 (disambiguation Year 2002 ( MMII) was a Common year starting on Tuesday of the Gregorian calendar. Year 2003 ( MMIII) was a Common year starting on Wednesday of the Gregorian calendar. "MMIV" redirects here For the Modest Mouse album see " Baron von Bullshit Rides Again " Year 2005 ( MMV) was a Common year starting on Saturday (link displays full calendar of the Gregorian calendar. Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common This article is about the year For the film see 2009 Lost Memories. For the film see 2010 The Year We Make Contact. For the book see 2010 Odyssey Two. 2011 ( MMXI) will be a Common year starting on Saturday of the Gregorian calendar. 2012 ( MMXII) will be a Leap year starting on Sunday of the Gregorian calendar. 2013 ( MMXIII) will be a Common year starting on Tuesday of the Gregorian calendar. This is the calendar for any Common year starting on Sunday ( Dominical letter A) or for any year in which “ Doomsday ” is Tuesday This is the Calendar for any Common year starting on Saturday ( Dominical letter B) This is the Calendar for any Common year starting on Friday ( Dominical letter C) This is the Calendar for any Common year starting on Thursday ( Dominical letter D) This is the calendar for any Common year starting on Wednesday ( Dominical letter E) This is the Calendar for any Common year starting on Tuesday ( Dominical letter F) This is the Calendar for any common year starting on Monday ( Dominical letter G) This is the Calendar for any Leap year starting on Sunday ( Dominical letter AG) such as 2012. This is the Calendar for any Leap year starting on Saturday ( Dominical letter BA) such as 2000. This is the Calendar for any Leap year starting on Friday ( Dominical letter CB) such as 1988. This is the Calendar for any Leap year starting on Thursday ( Dominical letter DC) such as 2004. This is the Calendar for any Leap year starting on Wednesday ( Dominical letter ED) such as 1992. This is the Calendar for any Leap year starting on Tuesday ( Dominical letter FE) such as 2008. This is the Calendar for any Leap year starting on Monday ( Dominical letter GF) such as 1996. [6] The Christian Church, due to its complicated system of movable and immovable feasts, has long been concerned with the regulation and measurement of time. The Gregorian calendar is the most widely used Calendar in the world today To secure uniformity in the observance of feasts and fasts, it began, even in the patristic age, to supply a system of reckoning (computus) by which the relation of the solar and lunar years might be accommodated and the celebration of Easter determined. [6] It adopted the astronomical methods that were available at the time, and these methods and their methodology have become traditional and 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 dividing the year into nundinæ, periods of eight days; and in their marble calendars (fasti), of which numerous specimens remain, they used the first eight letters of the alphabet (A to H) to mark the days of which each period was composed. The Roman calendar changed its form several times in the time between the foundation of Rome and the fall of the Roman Empire. Fasti, a Latin word refers to the Roman calendar and Almanac; and especially to a long possibly unfinished poem on the religious festivals When the Oriental seven-day period (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 the new division of time. Augustus ( Latin: IMPERATOR·CAESAR·DIVI·FILIVS·AVGVSTVS September 23 63 BC – August 19 AD 14) born Gaius Octavius Thurinus, was Some surviving (albeit fragmentary) marble calendars show both cycles side by side (see "Corpus Inscriptionum Latinarum", 2nd ed. , I, 220; the same peculiarity occurs in the Philocalian Calendar of A. The Chronography of 354, also known as the Calendar of 354, was a 4th century Illuminated manuscript, which was produced in 354 AD for a wealthy Roman Christian D. 356, ibid. Events By Place Roman Empire February 8 — Roman authorities make an attempt to arrest Athanasius on the accusation of supporting , 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. New Year See also New Year The Ancient Romans began their consular year on January 1st since 153 BC Events 406 – Vandals, Alans and Suebians cross the Rhine, beginning an invasion of Gallia. A is always set against 1 January, B against 2 January, C against 3 January, and so on. New Year See also New Year The Ancient Romans began their consular year on January 1st since 153 BC Events 366 - The Alamanni cross the frozen Rhine River in large numbers invading the Roman Empire. Events 1431 - Joan of Arc is handed over to the Bishop Pierre Cauchon. 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. Events 1066 - Harold Godwinson is crowned King of England. 1205 - Philip of Swabia becomes King Events 1325 - Alfonso IV becomes King of Portugal. 1558 - France takes Calais, the last continental Events 871 - Battle of Ashdown - Ethelred of Wessex defeats a Danish invasion army Events 588 BC - Nebuchadrezzar II of Babylon lays siege to Jerusalem under Zedekiah 's reign Events 565 - Eutychius is deposed as Patriarch of Constantinople by John Scholasticus. Events 904 - Sergius III comes out of retirement to take over the papacy from the deposed Antipope Christopher. Continuing in this way, 30 January is marked with a B, 31 January with a C, and 1 February with a D. Events 1648 - Eighty Years' War: The Treaty of Münster is signed ending the conflict between the Netherlands and Spain Events 1504 - France cedes Naples to Aragon. 1606 - Gunpowder Plot: Guy Fawkes Events 1327 - Teenaged Edward III is crowned King of England, but the country is ruled by his mother Queen 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. Events 86 BC - Lucius Cornelius Sulla, at the head of a Roman Republic army enters in Athens, removing the Tyrant Events 527 - Byzantine Emperor Justin I names his nephew Justinian I as co-ruler and successor to the throne Events 305 - Diocletian and Maximian retire from the office of Roman Emperor. Events 193 - Roman Emperor Didius Julianus is Assassinated 987 - Hugh Capet is elected "July 1st" redirects here For the Ayumi Hamasaki song see H (song. Events 30 BC - Octavian (later known as Augustus enters Alexandria, Egypt, bringing it under the control of the Roman Events 462 - Possible start of first Byzantine indiction cycle. Events 331 BC - Alexander the Great defeats Darius III of Persia in the Battle of Gaugamela. Events 996 - Emperor Otto III issues a deed to Gottschalk Bishop of Freising which is the oldest known document using the name Ostarrîchi Events 800 - Charlemagne judges the accusations against Pope Leo III in the Vatican This article is about Durandus of Mende you may be looking for the philosopher Durandus of Saint-Pourçain. A couplet is a pair of lines of verse. It usually consists of two lines that rhyme and have the same meter

Another one is:

Add G, beg C, fad F.

Yet another:

At Dover dwell George Brown, Esquire; Good Christopher Finch; and David Fryer.

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. New Year See also New Year The Ancient Romans began their consular year on January 1st since 153 BC New Year See also New Year The Ancient Romans began their consular year on January 1st since 153 BC Events 366 - The Alamanni cross the frozen Rhine River in large numbers invading the Roman Empire. New Year See also New Year The Ancient Romans began their consular year on January 1st since 153 BC Events 1325 - Alfonso IV becomes King of Portugal. 1558 - France takes Calais, the last continental

Traditionally, the Catholic ecclesiastical calendar treats February 24 (the day on which the Gregorian calendar was decreed) as the day added; events normally occurring on February 24-28 are moved to February 25-29. The Gregorian calendar is the most widely used Calendar in the world today The Anglican and civil calendars treat February 29 as the day added to leap years, and do not shift events in this way.

Dominical letter of a year

The Dominical Letter of a year is defined as the letter of the cycle corresponding to the day upon which the first Sunday (and thus every subsequent Sunday) falls. Leap years have two Dominical Letters, the second of which is the letter of the cycle preceding the first; the second letter describes the portion of the year after the leap day.

Calculation

The Dominical Letter of a year can be calculated based on any method for calculating the day of the week, with letters in reverse order compared to numbers indicating the day of the week. This article details various mathematical Algorithms to calculate the Day of the Week for any particular date in the past or future

For example:

2000 1990 1980 1970 1960 1950 1940 1930 1920 1910 1900
 BA   G    FE   D    CB   A    GF   E    DC   B    . G

For example, to find the Dominical Letter of the year 1913:

Similarly, for 2007:

For 2065:

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

The Dominical Letter had another practical use in the days before the Ordo divini officii recitandi was printed annually (thus often requiring priests to determine the Ordo on their own). 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; each Dominical Letter allows 5 of these dates, so there are 5 possible calendars for each letter. Events 238 - Gordian I and his son Gordian II are proclaimed Roman emperor. Events 1607 - Eighty Years' War: The Dutch fleet destroys the anchored Spanish fleet at Gibraltar. The Pye or directorium which preceded the present Ordo took advantage of this principle, including all 35 calendars and labeling them primum A, secundum A, tertium A, and so on. Hence, based on the Dominical Letter of the year and the epact, the Pye identified the correct calendar to use. The epact (from Greek epaktai hèmerai = added days is a quantification of the difference between the solar and lunar calendars A similar table, but adapted to the reformed calendar and in more convenient shape, is 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. Bede (ˈbiːd (also Saint Bede, the Venerable Bede, or (from Latin Beda (beda (c De temporum ratione ( English: On The Reckoning Of Time) is a treatise written in Latin by the Northumbrian Anglo-Saxon 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; these correspond to Dominical Letters F, E, D, C, B, A, and G, respectively. Events 1401 - Mongol emperor Timur sacks Damascus. 1603 - James VI of Scotland

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". A mnemonic device (nəˈmɒnɪk is a Memory aid Commonly met mnemonics are often verbal something such as a very short poem or a special word used to help a person remember

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). The Doomsday rule or Doomsday algorithm is a way of Calculating the day of the week of a given date

We are able to calculate the Dominical letter in this way (function in C), where:

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. Inter gravissimas was a Papal bull issued by Pope Gregory XIII on February 24, 1582. 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.
  6. ^ a b Dominical letter Catholic Encyclopedia]

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