The days of the year are sometimes designated letters A, B, C, D, E, F and G in a cycle of 7 as an aid for finding the day of week of a given calendar date and in calculating Easter. These letters are known as dominical letters. A week 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. ... Easter is the most important religious holiday of the Christian liturgical year, observed in March, April, or May to celebrate the resurrection of Jesus, which Christians believe occurred after his death by crucifixion in AD 30-33 (see Good Friday). ...

A common year has a dominical letter, which is simply the dominical letter of its first Sunday. For example 2003 has 5 January as its first Sunday so has Dominical letter E. January 5 is the 5th day of the year in the Gregorian calendar. ...

In leap years, the leap day has no dominical letter. This ensures that each date has the same dominical letter every year, but causes the days of the weeks of the dominical letters to change within a leap year. Hence leap years have two dominical letters: the first for January and February and the second for March to December. The second dominical letter is the dominical letter of the first Sunday of October (which is the same as for January in a common year). The year 2004 has Dominical letters DC. A leap year (or intercalary year) is a year containing an extra day or month in order to keep the calendar year in sync with an astronomical or seasonal year. ...

Examples include:

• 1996 GF
• 1997 E
• 1998 D
• 1999 C
• 2000 BA
• 2001 G
• 2002 F
• 2003 E
• 2004 DC
• 2005 B
• 2006 A
• 2007 G
• 2008 FE

The dominical letter of a year determines the days of week in its calendar: 1996 (MCMXCVI) is a leap year starting on Monday of the Gregorian calendar, and was designated the International Year for the Eradication of Poverty. ... 1997 (MCMXCVII) is a common year starting on Wednesday of the Gregorian calendar. ... 1998 (MCMXCVIII) is a common year starting on Thursday of the Gregorian calendar, and was designated the International Year of the Ocean. ... 1999 (MCMXCIX) was a common year starting on Friday, and was designated the International Year of Older Persons by the United Nations. ... This article is about the year 2000. ... 2001: A Space Odyssey. ... 2002 (MMII) was a common year starting on Tuesday of the Gregorian calendar. ... 2003 (MMIII) was a common year starting on Wednesday of the Gregorian calendar. ... 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... 2006 (MMVI) is a common year starting on Sunday of the Gregorian calendar. ... 2007 (MMVII) is a common year starting on Monday of the Gregorian calendar. ... 2008 (MMVIII) is a Leap year starting on Tuesday of the Gregorian 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

This is the calendar for any common year starting on Sunday (dominical letter A). ... This is the calendar for any common year starting on Saturday (dominical letter B) e. ... 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 a common year starting on Wednesday (dominical letter E), e. ... This is the calendar for a common year starting on Tuesday (dominical letter F), e. ... This is the calendar for a common year starting on Monday (dominical letter G), e. ... Here is a calendar for any leap year starting on Sunday (dominical letter AG). ... Here is the calendar for any leap year starting on Saturday (dominical letter BA), e. ... This is the calendar for any leap year starting on a Friday (dominical letter CB). ... This is a calendar for any leap year starting on Thursday (dominical letter DC), e. ... This is the calendar for any leap year starting on Wednesday (dominical letter ED), e. ... This is the calendar for a leap year starting on Tuesday (dominical letter FE) January February March Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 5 1 2 1 6 7 8 9... This is a calendar for a leap year starting on Monday (dominical letter GF). ...

History

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 Church, on account of its' complicated system of movable and immovable feasts (see Christian calendar), has from an early period taken upon itself as a special charge to regulate the 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. This article or section should be merged with Liturgical year The Christian Calendar organizes days of the year on which Christian festivals occur. ...

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, and in their calendars the days of the year from 1 January to 31 December were marked with a continuous recurring cycle of seven letters: A, B, C, D, E, F, G. A was always set against 1 January, B against 2 January, C against 3 January, and so on. Thus F fell to 6 January, G to 7 January; A again recurred on 8 January, and also, consequently, on 15 January, 22 January, and 29 January. Continuing in this way, 30 January was marked with a B, 31 January with a C, and 1 February with a D. Supposing this to be carried on through all the days of an ordinary year (i. e. not a leap year), it will be found that a 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: Fasti, a Latin word, refers to the Roman calendar and almanac; and especially, to a long, unfinished poem on the religious festivals of the Roman year and their mythological underpinnings, by the poet Ovid. ... Augustus (plural Augusti) is Latin for majestic or venerable. The greek equivalent is sebastos, or a mere grecization (by changing of the ending) augustos. ... Events February 8 - Roman authorities make an attempt to arrest Athanasius on the accusation of supporting the usurper Magnentius. ... January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... December 31 is the 365th day of the year (366th in leap years) in the Gregorian Calendar. ... January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... January 2 is the second day of the year in the Gregorian calendar. ... January 3 is the 3rd day of the year in the Gregorian calendar. ... January 6 is the 6th day of the year in the Gregorian calendar. ... January 7 is the seventh day of the year in the Gregorian calendar. ... January 8 is the 8th day of the year in the Gregorian Calendar. ... January 15 is the 15th day of the year in the Gregorian calendar. ... January 22 is the 22nd day of the year in the Gregorian calendar. ... January 29 is the 29th day of the year in the Gregorian calendar. ... January 30 is the 30th day of the year in the Gregorian calendar. ... January 31 is the 31st day of the year in the Gregorian Calendar. ... February 1 is the 32nd day of the year in the Gregorian Calendar. ... March 1 is the 60th day of the year in the Gregorian calendar (61st in leap years). ... April 1 is the 91st day of the year (92nd in leap years) in the Gregorian calendar, with 274 days remaining. ... May 1 is the 121st day of the year in the Gregorian calendar (122nd in leap years). ... June 1 is the 152nd day of the year in the Gregorian calendar (153rd in leap years), with 213 days remaining. ... July 1 is the 182nd day of the year (183rd in leap years) in the Gregorian Calendar, with 183 days remaining. ... August 1 is the 213th day of the year in the Gregorian Calendar (214th in leap years), with 152 days remaining. ... September 1 is the 244th day of the year (245th in leap years). ... October 1 is the 274th day of the year (275th in Leap years). ... November 1 is the 305th day of the year (306th in leap years) in the Gregorian Calendar, with 60 days remaining. ... December 1 is the 335th (in leap years the 336th) day of the year in the Gregorian calendar. ...

Alta Domat Dominus, Gratis Beat Equa Gerentes

Contemnit Fictos, Augebit Dona Fideli.

Now, as a moment's reflection shows, 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. January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... January 2 is the second day of the year in the Gregorian calendar. ... January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... January 7 is the seventh day of the year in the Gregorian calendar. ...

It is plain, however, that when a leap year occurs, a complication is introduced. February has then twenty-nine 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, for the rest of the year the Sundays come 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, 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 are B and A. February 24 is the 55th day of the year in the Gregorian Calendar. ... March 1 is the 60th day of the year in the Gregorian calendar (61st in leap years). ... February 1 is the 32nd day of the year in the Gregorian Calendar. ... January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... 1907 (MCMVII) was a common year starting on Tuesday (see link for calendar). ... January 6 is the 6th day of the year in the Gregorian calendar. ... January 5 is the 5th day of the year in the Gregorian calendar. ... January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ...

Calculation

This, of course, is all very simple, but the advantage of tile device lies, like that of an algebraical expression, in its being a mere symbol adaptable to any year. By constructing a table of letters and days of the year, A always being set against 1 January, we can at once see the relation between the days of the week and the day of any month, if only we know the Dominical Letter. This may always be found by the following rule of De Morgan's, which gives the Dominical Letter for any year, or the second Dominical Letter if it be leap year: January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ...

1. Add 1 to the given year.
2. Take the quotient found by dividing the given year by 4 (neglecting the remainder).
3. Take 16 from the centurial figures of the given year if that can be done.
4. Take the quotient of III divided by 4 (neglecting the remainder).
5. From the sum of I, II and IV, subtract III.
6. Find the remainder of V divided by 7: this is the number of the Dominical Letter, supposing A, B, C, D, E, F, G to be equivalent respectively to 6, 5, 4, 3, 2, 1, 0.

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

(Steps 1, 2, & 4) 1914 + 478 + 0 = 2392

(3) 19 - 16 = 3

(5) 2392 - 3 = 2389

(6) 2389 / 7 = 341, remainder 2.

Therefore, the Dominical Letter is 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 thirty-five 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 thirty-five 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 epact (from Greek: epaktai hèmerai = added days) is, as the second Canon of the Gregorian Calendar reform puts it, nothing else than the number of days which the common solar year of 365 days surpasses the common lunar year of 354 days (Latin: Epacta nihil aliud est quam... March 22 is the 81st day of the year in the Gregorian Calendar (82nd in Leap years). ... April 25 is the 115th day of the year in the Gregorian Calendar (116th in leap years). ... January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. ... March 26 is the 85th day of the year in the Gregorian Calendar (86th in leap years). ... 2 April is the 92nd day of the year (93rd in leap years) in the Gregorian calendar, with 273 days remaining. ... April 9 is the 99th day of the year in the Gregorian calendar (100th in leap years). ... April 16 is the 106th day of the year in the Gregorian calendar (107th in leap years). ... April 23 is the 113th day of the year in the Gregorian Calendar (114th in leap years). ...

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: Bede depicted in an early medieval manuscript Depiction of Bede from the Nuremberg Chronicle, 1493 Bede (Latin Beda), also known as Saint Bede or, more commonly, the Venerable Bede (ca. ... March 24 is the 83rd day of the year in the Gregorian Calendar (84th in Leap years). ...

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". A mnemonic (pronounced in American English, in British English) is a memory aid. ...

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. This was stolen from the Doomsday algorithm. The Doomsday algorithm is a way of calculating the day of the week of a given date. ...

References

• This article incorporates text from the public domain Catholic Encyclopedia.
• This article incorporates text from the 1911 Encyclopædia Britannica, which is in the public domain.

The public domain comprises the body of all creative works and other knowledge—writing, artwork, music, science, inventions, and others—in which no person or organization has any proprietary interest. ... The Catholic Encyclopedia (also referred to as the Old Catholic Encyclopedia today) is an English-language encyclopedia published in 1913 by the The Encyclopedia Press, designed to give authoritative information on the entire cycle of Catholic interests, action and doctrine. // History The writing of the encyclopedia began on January 11... Supporters contend that the Eleventh Edition of the Encyclopædia Britannica (1910-1911) represents the sum of human knowledge at the beginning of the 20th century; indeed, it was advertised as such. ... The public domain comprises the body of all creative works and other knowledge—writing, artwork, music, science, inventions, and others—in which no person or organization has any proprietary interest. ...

External links

• Catholic Encyclopedia article on Dominical letter