Dominical letters or Sunday letters are a method used to determine the
day of the week
In many languages, the names given to the seven days of the week are derived from the names of the classical planets in Hellenistic astronomy, which were in turn named after contemporary deities, a system introduced by the Sumerians and late ...
for particular dates. When using this method, each year is assigned a letter (or pair of letters for leap years) depending on which day of the week the year starts.
Dominical letters are derived from the Roman practice of marking the repeating sequence of eight letters A–H (commencing with A on 1 January) on stone calendars to indicate each day's position in the eight-day market week (''
nundinae
The nundinae (), sometimes anglicized to nundines,. were the market days of the ancient Roman calendar, forming a kind of weekend including, for a certain period, rest from work for the ruling class (patricians).
The nundinal cycle, market w ...
''). The word is derived from the number nine due to their practice of
inclusive counting
Counting is the process of determining the number of elements of a finite set of objects, i.e., determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every ele ...
. After the introduction of Christianity a similar sequence of seven letters A–G was added alongside, again commencing with 1 January. The dominical letter marks the Sundays. Nowadays they are used primarily as part of the
computus, which is the method of calculating the date of Easter.
A common year is assigned a single dominical letter, indicating which lettered days are Sundays in that particular year (hence the name, from Latin ''dominica'' for Sunday). Thus, 2017 is A, indicating that all A days are Sunday, and by inference, 1 January 2017 is a Sunday. Leap years are given two letters, the first valid for January 1 – February 28 (or February 24, see below), the second for the remainder of the year.
In
leap year
A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) added to keep the calendar year synchronized with the astronomical year or ...
s, the leap day may or may not have a letter. In the Catholic version it does, but in the
1662
Events
January–March
* January 4 – Dziaddin Mukarram Shah becomes the new Sultan of Kedah, an independent kingdom on the Malay Peninsula, upon the death of his father, Sultan Muhyiddin Mansur.
* January 10 – At the ...
and subsequent Anglican versions it does not. The Catholic version causes February to have 29 days by doubling the sixth day before 1 March, inclusive, thus both halves of the doubled day have a dominical letter of F. The Anglican version adds a day to February that did not exist in common years, 29 February, thus it does not have a dominical letter of its own. After the 1662 reform there was correspondence between the Archbishop of Canterbury and the printer of the Book of Common Prayer, in which it was explained that the feast day of St Matthias now fell on 24 February every year.
In either case, all other dates have the same dominical letter every year, but the days of the dominical letters change within a leap year before and after the intercalary day, 24 February or 29 February.
History and arrangement
According to dominical letters are:
Another one is "Add G, beg C, fad F," and yet another is "At Dover dwell George Brown, Esquire; Good Christopher Finch; and David Fryer."
Dominical letter cycle
*If the letter () of the first day of a month is the dominical letter of the year, the month will have a Friday the 13th. That is to say, if the first day is Sunday, the 13th day will be Friday.
continues:
Of course, "24 February" is not "counted twice". The 23rd is ''ante diem vii kalendas Martias'', the next day in a leap year is ''a.d. bis sextum kal. Mart.'', the next day is the regular ''a.d.vi kal. Mart.'', and so to the end of the month. For example, in 2020 (=ED), all days preceding the leap day will correspond to a common-year E calendar, and all days afterward will correspond to a common-year D calendar. The relevant line of the ''Februarius'' page in the ''Kalendarium'' of a 1913 ''Breviarium Romanum'' reads:
:5 , f, vj, 24, S. MATHIAE APOSTOLI, dupl. 2. class.
The first column is the
epact
The epact ( la, epactae, from grc, ἐπακται ἡμεραι () = added days), used to be described by medieval computists as the age of a phase of the Moon in days on 22 March; in the newer Gregorian calendar, however, the epact is reckone ...
, a replacement for the
golden number, from which the age of the moon was computed and announced in some English cathedrals prior to the Reformation. The second column is the letter, the third the Roman date and the fourth the modern date. A note at the foot of the page reads:
In anno bissextili mensis Februarius est dierum 29. et Festum S. Mathiae celebratur die 25. Februarii et bis dicitur sexto Kalendas, id est die 24. et die 25. et littera Dominicalis, quae assumpta fuit in mense Januario, mutatur in praecedentem; ut si in Januario littera Dominicalis fuerit A, mutatur in praecedentem, quae est g. etc.; et littera f bis servit, 24. et 25.
(In a bissextile year the month February is of 29 days and the Feast of St Matthias is celebrated on 25 February, and twice is said on the sixth Kalends, that is on the 24th and 25th, and the Sunday letter, which was assumed in the month of January, is changed to the preceding; so if in January the Sunday letter may have been A, it is changed to the preceding, which is g. etc.; and letter f twice serves, 24th and 25th.)
Dominical letters of the years
The dominical letter of a year provides the link between the date and the day of the week on which it falls. The following are the correspondences between dominical letters and the day of the week on which their corresponding years is day and date:
* A:
common year starting on Sunday
A common year starting on Sunday is any non-leap year (i.e. a year with 365 days) that begins on Sunday, 1 January, and ends on Sunday, 31 December. Its dominical letter hence is A. The most recent year was 2017 and the next one will be 2023 in the ...
has two
Friday the 13ths in the
January and
October
October is the tenth month of the year in the Julian and Gregorian calendars and the sixth of seven months to have a length of 31 days. The eighth month in the old calendar of Romulus , October retained its name (from Latin and Greek ''ôc ...
.
* B:
common year starting on Saturday has one
Friday the 13th in the
May
May is the fifth month of the year in the Julian and Gregorian calendars and is the third of seven months to have a length of 31 days.
May is a month of spring in the Northern Hemisphere, and autumn in the Southern Hemisphere. Therefore, May ...
.
* C:
common year starting on Friday has one
Friday the 13th in the
August
August is the eighth month of the year in the Julian and Gregorian calendars, and the fifth of seven months to have a length of 31 days. Its zodiac sign is Leo and was originally named ''Sextilis'' in Latin because it was the 6th month in ...
.
* D:
common year starting on Thursday has three
Friday the 13ths in the
February,
March
March is the third month of the year in both the Julian and Gregorian calendars. It is the second of seven months to have a length of 31 days. In the Northern Hemisphere, the meteorological beginning of spring occurs on the first day of March ...
and
November.
* E:
common year starting on Wednesday
A common year starting on Wednesday is any non-leap year (a year with 365 days) that begins on Wednesday, 1 January, and ends on Wednesday, 31 December. Its dominical letter hence is E. The most recent year of such kind was 2014, and the next one ...
has one
Friday the 13th in the
June
June is the sixth month of the year in the Julian and Gregorian calendars and is the second of four months to have a length of 30 days, and the third of five months to have a length of less than 31 days. June contains the summer solstice in ...
.
* F:
common year starting on Tuesday has two
Friday the 13ths in the
September
September is the ninth month of the year in both the Julian and Gregorian calendars, the third of four months to have a length of 30 days, and the fourth of five months to have a length of fewer than 31 days. September in the Northern H ...
and
December
December is the twelfth and final month of the year in the Julian and Gregorian calendars and is also the last of seven months to have a length of 31 days.
December got its name from the Latin word ''decem'' (meaning ten) because it was or ...
.
* G:
common year starting on Monday
A common year starting on Monday is any non-leap year (i.e., a year with 365 days) that begins on Monday, 1 January, and ends on Monday, 31 December. Its dominical letter hence is G. The most recent year of such kind was 2018 and the next one wil ...
has two
Friday the 13ths in the
April
April is the fourth month of the year in the Gregorian and Julian calendars. It is the first of four months to have a length of 30 days, and the second of five months to have a length of less than 31 days.
April is commonly associated with ...
and
July
July is the seventh month of the year in the Julian and Gregorian calendars and is the fourth of seven months to have a length of 31 days. It was named by the Roman Senate in honour of Roman general Julius Caesar in 44 B.C., it being the mont ...
.
.
* AG:
leap year starting on Sunday
A leap year starting on Sunday is any year with 366 days (i.e. it includes 29 February) that begins on Sunday, 1 January, and ends on Monday, 31 December. Its dominical letters hence are AG. The most recent year of such kind was 2012 and the next ...
has three
Friday the 13ths in the
January,
April
April is the fourth month of the year in the Gregorian and Julian calendars. It is the first of four months to have a length of 30 days, and the second of five months to have a length of less than 31 days.
April is commonly associated with ...
and
July
July is the seventh month of the year in the Julian and Gregorian calendars and is the fourth of seven months to have a length of 31 days. It was named by the Roman Senate in honour of Roman general Julius Caesar in 44 B.C., it being the mont ...
.
* BA:
leap year starting on Saturday A leap year starting on Saturday is any year with 366 days (i.e. it includes 29 February) that begins on Saturday, 1 January, and ends on Sunday, 31 December. Its dominical letters hence are BA. The most recent year of such kind was 2000 and the n ...
has one
Friday the 13th in the
October
October is the tenth month of the year in the Julian and Gregorian calendars and the sixth of seven months to have a length of 31 days. The eighth month in the old calendar of Romulus , October retained its name (from Latin and Greek ''ôc ...
.
* CB:
leap year starting on Friday A leap year starting on Friday is any year with 366 days (i.e. it includes 29 February) that begins on Friday 1 January and ends on Saturday 31 December. Its dominical letters hence are CB. The most recent year of such kind was 2016 and the next one ...
has one
Friday the 13th in the
May
May is the fifth month of the year in the Julian and Gregorian calendars and is the third of seven months to have a length of 31 days.
May is a month of spring in the Northern Hemisphere, and autumn in the Southern Hemisphere. Therefore, May ...
.
* DC:
leap year starting on Thursday A leap year starting on Thursday is any year with 366 days (i.e. it includes 29 February) that begins on Thursday 1 January, and ends on Friday 31 December. Its dominical letters hence are DC. The most recent year of such kind was 2004 and the next ...
has two
Friday the 13ths in the
February and
August
August is the eighth month of the year in the Julian and Gregorian calendars, and the fifth of seven months to have a length of 31 days. Its zodiac sign is Leo and was originally named ''Sextilis'' in Latin because it was the 6th month in ...
.
* ED:
leap year starting on Wednesday A leap year starting on Wednesday is any year with 366 days (i.e. it includes 29 February) that begins on Wednesday 1 January and ends on Thursday 31 December. Its dominical letters hence are ED. The most recent year of such kind was 2020 and t ...
has two
Friday the 13ths in the
March
March is the third month of the year in both the Julian and Gregorian calendars. It is the second of seven months to have a length of 31 days. In the Northern Hemisphere, the meteorological beginning of spring occurs on the first day of March ...
and
November.
* FE:
leap year starting on Tuesday
A leap year starting on Tuesday is any year with 366 days (i.e. it includes 29 February) that begins on Tuesday, 1 January, and ends on Wednesday, 31 December. Its dominical letters hence are FE. The most recent year of such kind was 2008 and the n ...
has one
Friday the 13th in the
June
June is the sixth month of the year in the Julian and Gregorian calendars and is the second of four months to have a length of 30 days, and the third of five months to have a length of less than 31 days. June contains the summer solstice in ...
.
* GF:
leap year starting on Monday
A leap year starting on Monday is any year with 366 days (i.e. it includes 29 February) that begins on Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letters hence are GF. The most recent year of such kind was 1996 and the n ...
has two
Friday the 13ths in the
September
September is the ninth month of the year in both the Julian and Gregorian calendars, the third of four months to have a length of 30 days, and the fourth of five months to have a length of fewer than 31 days. September in the Northern H ...
and
December
December is the twelfth and final month of the year in the Julian and Gregorian calendars and is also the last of seven months to have a length of 31 days.
December got its name from the Latin word ''decem'' (meaning ten) because it was or ...
.
The
Gregorian calendar
The Gregorian calendar is the calendar used in most parts of the world. It was introduced in October 1582 by Pope Gregory XIII as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years dif ...
repeats every 400 years (i. e., every four centuries). Of the 400 years in one Gregorian cycle, there are:
* 44
common years for each single Dominical letter D and F;
* 43 common years for each single Dominical letter A, B, C, E, and G;
* 15
leap year
A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) added to keep the calendar year synchronized with the astronomical year or ...
s for each double Dominical letter AG and CB;
* 14 leap years for each double Dominical letter ED and FE;
* 13 leap years for each double Dominical letter BA, DC, and GF.
Thus years which begin as A, C, or F occur 58 times in 400 years, years that begin as D or E 57 times, and those that begin as B or G just 56 times. The end of a year preceding a given year has the next letter (so A years are preceded by years ending as B), so years ending as B, D, or G occur 58 times in 400 years, those ending as E or F 57 times, and those ending as C or A 56 times. This means, for example, that Christmas falls on a Saturday or Monday (C and A years, resp.) 56 times in 400 years, whereas it falls on Friday, Sunday, or Tuesday (D, B, and G years, resp.) 58 times.
The
Julian calendar
The Julian calendar, proposed by Roman consul Julius Caesar in 46 BC, was a reform of the Roman calendar. It took effect on , by edict. It was designed with the aid of Greek mathematicians and astronomers such as Sosigenes of Alexandr ...
repeats every 28 years. Of the 28 years in one Julian cycle, there are:
* 3 common years for each single Dominical letter A, B, C, D, E, F, and G;
* 1 leap year for each double Dominical letter BA, CB, DC, ED, FE, GF, and AG.
Calculation
The dominical letter of a year can be calculated based on any method for
calculating the day of the week
The determination of the day of the week for any date may be performed with a variety of algorithms. In addition, perpetual calendars require no calculation by the user, and are essentially lookup tables.
A typical application is to calculate the ...
, with letters in reverse order compared to numbers indicating the day of the week.
![Lier Zimmertoren Clock detail 09](https://upload.wikimedia.org/wikipedia/commons/d/d2/Lier_Zimmertoren_Clock_detail_09.JPG)
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, the table below can be used.
Red for the first two months of leap years.
For example, to find the Dominical Letter of the year 1913:
*1900 is G and 13 corresponds to 5
*G + 5 = G − 2 = E, 1913 is E
Similarly, for 2007:
*2000 is BA and 7 corresponds to 6
*A + 6 = A − 1 = G, 2007 is G
For 2065:
*2000 is BA and 65 mod 28 = 9 corresponds to 3
*A + 3 = A − 4 = D, 2065 is D
The odd plus 11 method
A simpler method suitable for finding the year's dominical letter was discovered in 2010. It is called the "odd plus 11" method.
The procedure accumulates a running total ''T'' as follows:
# Let ''T'' be the year's last two digits.
#If ''T'' is odd, add 11.
#Let ''T'' = .
#If ''T'' is odd, add 11.
#Let ''T'' = ''T'' mod 7.
#Count forward ''T'' letters from the century's dominical letter (A, C, E or G see above) to get the year's dominical letter.
The formula is
:
De Morgan's rule
This rule was stated by
Augustus de Morgan:
#Add 1 to the given year.
#Take the quotient found by dividing the given year by 4 (neglecting the remainder).
#Take 16 from the centurial figures of the given year if that can be done.
#Take the quotient of III divided by 4 (neglecting the remainder).
#From the sum of I, II and IV, subtract III.
#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.
So the formulae (using the
floor function
In mathematics and computer science, the floor function is the function that takes as input a real number , and gives as output the greatest integer less than or equal to , denoted or . Similarly, the ceiling function maps to the least int ...
) for the Gregorian calendar is
:
It is equivalent to
:
and
:
(where
= last two digits of the year,
= century part of the year).
For example, to find the Dominical Letter of the year 1913:
:1. (1 + 1913 + 478 + 0 − 3) mod 7 = 2
:2. (1913 + 478 + 4 − 19 − 1) mod 7 = 2
:3. (13 + 3 + 15 -1) mod 7 = 2
:Hence, the Dominical Letter is E in the Gregorian calendar.
De Morgan's rules no. 1 and 2 for the Julian calendar:
:
and
To find the Dominical Letter of the year 1913 in the Julian calendar:
:*(1913 + 478 − 3) mod 7 = 1
:Hence, the Dominical Letter is F in the Julian calendar.
In leap years the formulae above give the Dominical Letter for the last ten months of the year. To find the Dominical Letter for the first two months of the year to the leap day (inclusive) subtract 1 from the calculated number representing the original Dominical Letter; if the new number is less than 0, it must be changed to 6.
Dominical letter in relation to the Doomsday Rule
The "doomsday" concept in the
doomsday algorithm is mathematically related to the Dominical letter. Because the letter of a date equals the dominical letter of a year (DL) plus the day of the week (DW), and the letter for the
doomsday
Doomsday may refer to:
* Eschatology, a time period described in the eschatological writings in Abrahamic religions and in doomsday scenarios of non-Abrahamic religions.
* Global catastrophic risk, a hypothetical event explored in science and fict ...
is C except for the portion of leap years before
February 29
February 29, also known as leap day or leap year day, is a date added to leap years. A leap day is added in various solar calendars (calendars based on the Earth's revolution around the Sun), including the Gregorian calendar standard in mos ...
in which it is D, we have:
:
Note: G = 0 = Sunday, A = 1 = Monday, B = 2 = Tuesday, C = 3 = Wednesday, D = 4 = Thursday, E = 5 = Friday, and F = 6 = Saturday, i.e. in our context, C is mathematically identical to 3.
Hence, for instance, the doomsday of the year 2013 is Thursday, so DL = (3 − 4) mod 7 = 6 = F. The dominical letter of the year 1913 is E, so DW = (3 − 5) mod 7 = 5 = Friday.
All in one table
If the year of interest is not within the table, use a tabular year which gives the same remainder when divided by 400 (
Gregorian calendar
The Gregorian calendar is the calendar used in most parts of the world. It was introduced in October 1582 by Pope Gregory XIII as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years dif ...
) or 700 (
Julian calendar
The Julian calendar, proposed by Roman consul Julius Caesar in 46 BC, was a reform of the Roman calendar. It took effect on , by edict. It was designed with the aid of Greek mathematicians and astronomers such as Sosigenes of Alexandr ...
). In the case of the
Revised Julian calendar
The Revised Julian calendar, or less formally the new calendar, is a calendar proposed in 1923 by the Serbian scientist Milutin Milanković as a more accurate alternative to both Julian and Gregorian calendars. At the time, the Julian calendar ...
, find the date of
Easter
Easter,Traditional names for the feast in English are "Easter Day", as in the '' Book of Common Prayer''; "Easter Sunday", used by James Ussher''The Whole Works of the Most Rev. James Ussher, Volume 4'') and Samuel Pepys''The Diary of Samuel ...
Sunday (see the section "Calculating Easter Sunday", subsection "Revised Julian calendar" below) and enter it into the "Table of letters for the days of the year" below. If the year is a leap year, the dominical letter for January and February is found by inputting the date of
Easter Monday. Note the different rules for leap years:
*Gregorian calendar: every year which divides exactly by 4, but of century years only those which divide exactly by 400; therefore ignore the left-hand letter given for a century year which is not a leap year.
*Julian calendar: every year which divides exactly by 4.
*Revised Julian calendar: every year which divides exactly by 4, but of century years only those which give the remainder 200 or 600 when divided by 900.
Years with special dominical letters
When a country switched to the Gregorian calendar, there could be some unusual combinations of dominical letters.
Some examples
* 1582: Many Catholic countries switched to the Gregorian calendar Friday 15 October. The table above indicates that year 1582 had the dominical letter G in the Julian calendar and C in the Gregorian one. So the dominical letters for 1582 in these Catholic countries became GC for mixing the two calendars used in this legal year, a special combination not seen before and after with a single calendar used in the same legal year.
* 1752: The British Empire and its colonies switched to the Gregorian calendar Thursday 14 September. 1752, a leap year, had in the Julian calendar dominical letters ED and in the Gregorian one dominical letters BA, so the dominical letters for 1752 in Britain were EDA, a very special combination which also only applies to this legal year.
Calculating Easter Sunday
Enter the "all in one table" to find the date of the paschal full moon, then use the "week table" below to find the day of the week on which it falls. Easter is the following Sunday.
Week table: Julian and Gregorian calendars for AD years since 1 March AD 4
Note that this table does not work for AD years at the early stage of the real Julian calendar before 1 March AD 4
or for any BC year, except when using the Julian calendar rules for proleptic dates (which are different from effective historic dates, whose effective calendar in use depended on the location of dated events or the location of the person using the calendar, sometimes differently between political/civil or religious purposes in places where both calendars still coexisted). The duration of months, and the number and placement of intercalated days also changed inconsistently before AD 42 in the early local Julian calendars which used native names for the months, depending on places and years, causing finally a lot of confusion in the population (so dating events precisely in that period is often difficult, unless they are correlated with observed lunar cycles, or with days of the week, or with another calendar).
In these early AD years and in all BC years, with the effective Julian calendars used locally to align the counting of years (but still with the tradition inherited from the earlier
Roman calendar
The Roman calendar was the calendar used by the Roman Kingdom and Roman Republic. The term often includes the Julian calendar established by the reforms of the dictator Julius Caesar and emperor Augustus in the late 1stcenturyBC and sometim ...
for noting days in each year), a variable number of days at end of the months (after the last day of its ''ides'' but before the last day of ''calends'' which started the next month) were also still counted relatively from the start of the next named month (on the last day of its ''calends''), and years were theoretically starting on 1 March (but with the last days of the year in February also counted from the New Year's Day in March). As well, all these early years were effectively counted inclusively and positively from a different, much earlier epoch in other eras, such as the supposed foundation of Rome, or the accession to power of a local ruler (and still not relatively to the ''supposed'' date of birth of Christ, which was fixed later arbitrarily by a Christian reform for the modern Julian calendar so that this epoch for the Christian era starts now on 1 January in ''proleptic'' year AD 1 of the modern Julian calendar, but the real date of birth of Christ is still not known precisely but certainly falls before, somewhere in the last few BC years).
Instructions
For Julian dates before 1300 and after 1999 the year in the table which differs by an exact multiple of 700 years should be used. For Gregorian dates after 2299, the year in the table which differs by an exact multiple of 400 years should be used. The values "
r0" through "
r6" indicate the remainder when the Hundreds value is divided by 7 and 4 respectively, indicating how the series extend in either direction. Both Julian and Gregorian values are shown 1500–1999 for convenience.
The corresponding numbers in the far left hand column on the same line as each component of the date (the hundreds, remaining digits and month) and the day of the month are added together. This total is then divided by 7 and the remainder from this division located in the far left hand column. The day of the week is beside it. Bold figures (e.g., 04) denote leap year. If a year ends in 00 and its hundreds are in bold it is a leap year. Thus 19 indicates that 1900 is not a Gregorian leap year, (but bold 19 in the Julian column indicates that it ''is'' a Julian leap year, as are all Julian ''x''00 years). 20 indicates that 2000 is a leap year. Use bold Jan and Feb only in leap years.
For determination of the day of the week (1 January 2000, Saturday)
*
the day of the month: 1
*
the month: 6
*
the year: 0
*
the century mod 4 for the Gregorian calendar and mod 7 for the Julian calendar 0
*
adding . Dividing by 7 leaves a remainder of 0, so the day of the week is Saturday.
Revised Julian calendar
* Use the Julian portion of the table of paschal full moons. Use the "week table" (remembering to use the "Julian" side) to find the day of the week on which the paschal full moon falls. Easter is the following Sunday and it is a Julian date. Call this date ''JD''.
* Subtract 100 from the year.
* Divide the result by 100. Call the number obtained (omitting fractions) ''N''.
* Evaluate . Call the result (omitting fractions) ''S''.
* The Revised Julian calendar date of Easter is .
Example. What is the date of Easter in 2017?
. . Golden number is 4. Date of paschal full moon is 2 April (Julian). From "week table" 2 April 2017 (Julian) is Saturday. . . . . . . . Easter Sunday in the Revised Julian calendar is .
Calculate the day of the week in the Revised Julian calendar
Note that the date (and hence the day of the week) in the
Revised Julian and Gregorian calendars is the same up until 28 February 2800, and that for large years it may be possible to subtract 6300 or a multiple thereof before starting so as to reach a year within or closer to the table.
To look up the weekday of any date for any year using the table, subtract 100 from the year, divide the number obtained by 100, multiply the resulting quotient (omitting fractions) by seven and divide the product by nine. Note the quotient (omitting fractions). Enter the table with the Julian year, and just before the final division add 50 and subtract the quotient noted above.
Example: What is the day of the week of 27 January 8315?
, , , , . 2015 is 700 years ahead of 1315, so 1315 is used. From the table: for hundreds (13): 6. For remaining digits (15): 4. For month (January): 0. For date (27): 27. . . Day of week = Tuesday.
Dominical letter
To find the dominical letter, calculate the day of the week for either 1 January or 1 October. If it is Sunday, the Sunday Letter is A, if Saturday B, and similarly backwards through the week and forwards through the alphabet to Monday, which is G.
Leap years have two letters, so for January and February calculate the day of the week for 1 January and for March to December calculate the day of the week for 1 October.
Leap years are all years that divide exactly by four, with the following exceptions:
Gregorian calendar – all years divisible by 100, except those that divide exactly by 400.
Revised Julian calendar – all years divisible by 100, except those with a remainder of 200 or 600 when divided by 900.
Clerical utility
The dominical letter had another practical utility in the period prior to the annual printing of the ''Ordo divini officii recitandi'', in which period, therefore, Christian
clergy
Clergy are formal leaders within established religions. Their roles and functions vary in different religious traditions, but usually involve presiding over specific rituals and teaching their religion's doctrines and practices. Some of the ter ...
were often required to determine the ''Ordo'' independently. Easter Sunday may be as early as 22 March or as late as 25 April, and consequently there are 35 possible days on which it may occur; each dominical letter includes 5 potential dates of these 35, and thus there are 5 possible ecclesiastical calendars for each letter. The Pye or
Directorium "''Directorium''" is a Latin word denoting a guide. In the later Middle Ages it was specially applied to Catholic liturgical guides for praying the Divine Office and Holy Mass.
Early history
For example, in the early fifteenth century Clement May ...
which preceded the present ''Ordo'' took advantage of this principle by delineating all 35 possible calendars and denoting them by the formula "primum A", "secundum A", "tertium A", et cetera. Hence, based on the dominical letter of the year and the
epact
The epact ( la, epactae, from grc, ἐπακται ἡμεραι () = added days), used to be described by medieval computists as the age of a phase of the Moon in days on 22 March; in the newer Gregorian calendar, however, the epact is reckone ...
, the Pye identified the correct calendar to use. A similar table, adapted to the reformed calendar and in more convenient form, is included in the beginning of every
breviary and
missal under the heading "Tabula Paschalis nova reformata".
Saint Bede does not seem to have been familiar with dominical letters, given his "
De temporum ratione"; in its place he adopted a similar device of Greek origin consisting of seven numbers, which he denominated "''concurrentes''" (''De Temp. Rat.'', Chapter LIII). The "concurrents" are numbers that denote the days of the week on which 24 March occurs in the successive years of the solar cycle, 1 denoting Sunday, 2 (''feria secunda'') for Monday, 3 for Tuesday, et cetera; these correspond to dominical letters F, E, D, C, B, A, and G, respectively.
Use for computer calculation
Computers are able to calculate the Dominical letter for the first day of a given month in this way (function in
C), where:
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m = month
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y = year
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s = "style"; 0 for Julian, otherwise Gregorian.
char dominical(int m, int y, int s)
Years are also given a dominical letter or pair of dominical letters according to the first day in January and last day in December: when they are equal, only the first letter is given. The dominical letter of the last day of December just precedes in the ordered cycle (G,F,E,D,C,B,A), the dominical letter of the first day in January for the next year.
See also
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Determination of the day of the week
The determination of the day of the week for any date may be performed with a variety of algorithms. In addition, perpetual calendars require no calculation by the user, and are essentially lookup tables.
A typical application is to calculate the ...
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Lectionary#Three-year cycle
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Runic calendar
A Runic calendar (also Rune staff or Runic Almanac) is a perpetual calendar, variants of which were used in Northern Europe until the 19th century. A typical runic calendar consisted of several horizontal lines of symbols, one above the o ...
References
Citations
Sources
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Further reading
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{{Time measurement and standards
Easter date
Gregorian calendar
Julian calendar
Latin script
Sunday
Articles with example C code