Dominical letter

Encyclopedia

**Dominical letters**are letters A, B, C, D, E, F and G assigned to days in a cycle of seven with the letter A always set against 1 January as an aid for finding the day of the week of a given calendar date and in calculating Easter

Computus

Computus is the calculation of the date of Easter in the Christian calendar. The name has been used for this procedure since the early Middle Ages, as it was one of the most important computations of the age....

.

A common year is assigned a single dominical letter, indicating which letter is Sunday (hence the name, from Latin

*dominica*for Sunday). Thus, 2011 is B, indicating that B days are Sunday. Leap years are given two letters, the first indicating the dominical letter for January 1 - February 28 (or February 24, see below), the second indicating the dominical letter for the rest of the year.

In leap year

Leap year

A leap year is a year containing one extra day in order to keep the calendar year synchronized with the astronomical or seasonal year...

s, 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. 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.

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.

## Examples

- 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** - 2014
**E** - 2015
**D** - 2016
**CB**

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

**A**common year starting on SundayCommon year starting on SundayThis is the calendar for any common year starting on Sunday, January 1 or for any year in which “Doomsday” is Tuesday. Examples: Gregorian years 1989, 1995, 2006, 2017 and 2023or Julian year 1917...**B**common year starting on SaturdayCommon year starting on SaturdayThis is the calendar for any common year starting on Saturday, January 1 . Examples: Gregorian years 1994, 2005, 2011 and 2022...**C**common year starting on FridayCommon year starting on FridayThis is the calendar for any common year starting on Friday, January 1 . Examples: Gregorian years 1993, 1999, 2010 and 2021or Julian years 1910 and 1899 ....**D**common year starting on ThursdayCommon year starting on ThursdayThis is the calendar for any common year starting on Thursday, January 1 . Examples: Gregorian years 1987, 1998, 2009, 2015 and 2026...**E**common year starting on WednesdayCommon year starting on WednesdayThis is the calendar for any common year starting on Wednesday, January 1 . Examples: Gregorian years 1986, 1997, 2003, 2014 and 2025or Julian year 1903 ....**F**common year starting on TuesdayCommon year starting on TuesdayThis is the calendar for any common year starting on Tuesday, January 1 . Examples: Gregorian years 1985, 1991, 2002, 2013 and 2019or Julian year 1919 .MillenniumCenturyGregorian Year2nd Millennium:...**G**common year starting on MondayCommon year starting on MondayThis is the calendar for any common year starting on Monday, January 1 . Examples: Gregorian year 1990, 2001, 2007 and 2018or Julian year 1918 ....

**AG**leap year starting on SundayLeap year starting on SundayThis is the calendar for any leap year starting on Sunday, January 1 , such as 1956, 1984, 2012, 2040, or 2068.This is the only leap year with three occurrences of Friday the 13th, each three months apart in January, April, and July....**BA**leap year starting on SaturdayLeap year starting on SaturdayThis is the calendar for any leap year starting on Saturday, January 1 , such as 1972, 2000, 2028 or 2056.Previous year | Next year-Trivia:...**CB**leap year starting on FridayLeap year starting on FridayThis is the calendar for any leap year starting on Friday, January 1 , such as 1932, 1960, 1988, 2016 or 2044.Previous year | Next yearMillenniumCenturyYear2nd Millennium:18th century:17681796...**DC**leap year starting on ThursdayLeap year starting on ThursdayThis is the calendar for any leap year starting on Thursday, January 1 , such as 1948, 1976, 2004, 2032 or 2060.Previous year | Next year...**ED**leap year starting on WednesdayLeap year starting on WednesdayThis is the calendar for any leap year starting on Wednesday, January 1 , such as 1936, 1964, 1992, 2020 or 2048.This kind of year has 53 weeks in the ISO 8601 week - day format.Previous year | Next yearMillenniumCenturyYear...**FE**leap year starting on TuesdayLeap year starting on TuesdayThis is the calendar for any leap year starting on Tuesday, January 1 , such as 1952, 1980, 2008, 2036 or 2064.Previous year | Next yearMillenniumCenturyYear2nd Millennium:18th century: 1760 1788...**GF**leap year starting on MondayLeap year starting on MondayThis is the calendar for any leap year starting on Monday, January 1 , such as 1940, 1968, 1996, 2024 or 2052.MillenniumCenturyYear2nd Millennium:18th century: 1720 1748 1776...

## 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. The Christian Church, due to its complicated system of movable and immovable feasts, has long been 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 system of reckoning (*computus*) by which the relation of the solar and lunar years might be accommodated and the celebration of Easter determined. 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. When the Oriental seven-day period (week) was introduced in the time of Cæsar Augustus

Fasti

In ancient Rome, the fasti were chronological or calendar-based lists, or other diachronic records or plans of official and religiously sanctioned events...

Augustus

Augustus ;23 September 63 BC – 19 August AD 14) is considered the first emperor of the Roman Empire, which he ruled alone from 27 BC until his death in 14 AD.The dates of his rule are contemporary dates; Augustus lived under two calendars, the Roman Republican until 45 BC, and the Julian...

, the first seven letters of the alphabet were employed in the same way to indicate the days of the new division of time. 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.D. 356, ibid., p. 256). This device was imitated by the Christians.

## Dominical letter of a date

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.

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.

Traditionally, the Catholic ecclesiastical calendar treats 24 February as the day added, as this was the Roman leap day, with events normally occurring on 24–28 February moved to 25–29 February. The Anglican and civil calendars treat 29 February 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.The Gregorian calendar

Gregorian calendar

The Gregorian calendar, also known as the Western calendar, or Christian calendar, is the internationally accepted civil calendar. It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582, a papal bull known by its opening words Inter...

repeats every four hundred years. Of the four hundred years in a Gregorian cycle, there are 43 common years with Dominical letter A, 43 common years with B, 43 with C, 43 with E, and 43 with G. Of common years with Dominical letter D and F, there are 44 for each. Of the leap years, there are 13 each with BA, DC, and GF; 14 each with ED and FE, and 15 each with AG and CB.

In the Julian calendar

Julian calendar

The Julian calendar began in 45 BC as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year .The Julian calendar has a regular year of 365 days divided into 12 months...

, the cycle is 28 years, 7 of which are leap years, and the remaining 21 are common years. Each of the seven Dominical letters is split evenly among the 21 common years, and each of the seven double letters for leap years, BA, CB, DC, ED, FE, GF, and AG, occur once in every 28-year cycle.

## Calculation

The dominical letter of a year can be calculated based on any method for calculating the day of the weekCalculating 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.A typical application is to calculate the day of the week on which someone was born or some other special event occurred....

, with letters in reverse order compared to numbers indicating the day of the week.

For example:

- 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

### 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 five of these dates, so there are five possible calendars for each letter. The Pye or directorium

Directorium

Directorium is a Latin word meaning guide; in the later Middle Ages it came to be specially applied to liturgical guides for the recitation of Office and Mass.-Early history:...

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

Epact

The epact was originally defined as the age of the moon in days on January 1, and occurs primarily in connection with tabular methods for determining the date of Easter...

, the Pye identified the correct calendar to use. 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

Bede

Bede , also referred to as Saint Bede or the Venerable Bede , was a monk at the Northumbrian monastery of Saint Peter at Monkwearmouth, today part of Sunderland, England, and of its companion monastery, Saint Paul's, in modern Jarrow , both in the Kingdom of Northumbria...

in his "De temporum ratione

De temporum ratione

The Reckoning of Time is an Anglo-Saxon era treatise written in Latin by the Northumbrian monk Bede in 725. The treatise includes an introduction to the traditional ancient and medieval view of the cosmos, including an explanation of how the spherical earth influenced the changing length of...

", 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; these correspond to Dominical Letters F, E, D, C, B, A, and G, respectively.

## 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 08 9 0 1 2012 3

ED C B A GF E D C BA G F E DC B A G FE D C B AG F

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

Mnemonic

A mnemonic , or mnemonic device, is any learning technique that aids memory. To improve long term memory, mnemonic systems are used to make memorization easier. Commonly encountered mnemonics are often verbal, such as a very short poem or a special word used to help a person remember something,...

phrase "Add G, beg C, fad F".

The following dates, given in day/month form, all have dominical letter C: 4/4, 6/6, 8/8, 10/10, 12/12, 9/5, 5/9, 11/7, 7/11 (see also the Doomsday rule).

We are able to calculate the Dominical letter in this way (function in C

C (programming language)

C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system....

), 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);

}