The
Gregorian calendar is the most widely used
calendar in the world. A modification of the
Julian calendar, it was first proposed by the
Calabrian doctor
Aloysius Lilius, and was decreed by
Pope Gregory XIII, for whom it was named, on
24 February 1582 via the
papal bull Inter gravissimas issued from his seat (
Villa Mondragone). Years in the calendar are numbered from the traditional birth year of
Jesus, which has been labeled the "
anno Domini" (AD) era, and is sometimes labeled the "
common era" or the "Christian Era" (CE).
The Gregorian Calendar was devised both because the mean
Julian Calendar year was slightly too long, causing the
vernal equinox to slowly drift backwards in the
calendar year, and because the lunar calendar used to
compute the date of Easter had grown conspicuously in error as well.
The Gregorian calendar system dealt with these problems by dropping a certain number of days to bring the calendar back into synchronization with the seasons, and then slightly shortening the average number of days in a calendar year, by omitting three Julian leap-days every 400 years. The days omitted are in century years which are not divisible by 400 (specifically:
29 February 1700, 1800, 1900; 2100, 2200, 2300; 2500, 2600, 2700; 2900, etc.).
Description
The Gregorian solar calendar is an arithmetical calendar. It counts days as the basic unit of time, grouping them into years of 365 or 366 days. The solar calendar repeats completely every 146,097 days, which fill 400 years, and which also happens to be 20,871 seven-day
weeks. Of these 400 years, 303 (the "common years") have 365 days, and 97 - the
leap years - have 366 days. This gives an average year length of exactly 365.2425 days - or 365 days, 5 hours, 49 minutes and 12 seconds.
A Gregorian year is divided into twelve
months of irregular length (but note that there's a period of 153 days divided over 5 months in an alternating pattern from March to July that repeats from August to December):
A calendar date is fully specified by the year (numbered by some scheme beyond the scope of the calendar itself), the month (identified by name or number), and the day of the month (numbered sequentially starting at 1).
Leap years are all years divisible by 4, with the exception of those divisible by 100, but not by 400. These 366-day years add a 29th day to February, which normally has 28 days. Thus, the essential ongoing differential feature of the Gregorian calendar, as opposed to the Julian calendar, is that the Gregorian omits 3 leap days every 400 years. This difference would have been more noticeable in modern memory were it not for the fact that the year 2000 was a leap year in both the Julian and Gregorian calendar systems.
The
intercalary day in a leap year is known as a
leap day. Since Roman times
24 February (
bissextile) was counted as the leap day, but nowadays
29 February is regarded as the leap day in most countries.
Although the calendar year runs from
1 January to
31 December, sometimes year numbers were based on a different starting point within the calendar. Confusingly, the term "Anno Domini" isn't specific on this point, and actually refers to a family of year numbering systems with different starting points for the years. (See the section below for more on this issue.)
History
Gregorian reform
The motivation of the
Catholic Church in adjusting the calendar was to celebrate
Easter at the time it thought the
First Council of Nicaea had agreed upon in
325. Although a canon of the council implies that all churches used the same Easter, they did not. The Church of Alexandria celebrated Easter on the Sunday after the 14th day of the Moon (computed using the
Metonic cycle) that falls on or after the
vernal equinox, which they placed on
21 March. However, the Church of Rome still regarded
25 March as the equinox and used a different cycle to compute the day of the Moon. By the tenth century all churches (except for some on the eastern border of the
Byzantine Empire) had adopted the Alexandrian Easter, which still placed the vernal equinox on
21 March, although
Bede had already noted its drift in 725—it had drifted even further by the sixteenth century.
Worse, the reckoned Moon that was used to
compute Easter was fixed to the Julian year by a
19 year cycle. However, that approximation built up an error of one day every 310 years, so by the sixteenth century the lunar calendar was out of phase with the real Moon by four days.
The
Council of Trent approved a plan in
1563 for correcting the calendrical errors, requiring that the date of the
vernal equinox be restored to that which it held at the time of the First Council of Nicaea in 325 and that an alteration to the calendar be designed to prevent future drift. This would allow for a more consistent and accurate scheduling of the feast of
Easter.
The fix was to come in two stages. First, it was necessary to approximate the correct length of a solar year. The value chosen was 365.2425 days in decimal notation. This is 365;14,33 days in
sexagesimal notation—the length of the
tropical year, rounded to two sexagesimal positions; this was the value used in the major astronomical tables of the day. Although close to the
mean tropical year of 365.24219 days, it's even closer to the
vernal equinox year of 365.2424 days; this fact made the choice of approximation particularly appropriate as the purpose of creating the calendar was to ensure that the vernal equinox would be near a specific date (
21 March). (See
Accuracy).
The second stage was to devise a model based on the approximation which would provide an accurate yet simple, rule-based calendar. The formula designed by
Aloysius Lilius was ultimately successful. It proposed a 10-day correction to revert the drift since Nicaea, and the imposition of a leap day in only 97 years in 400 rather than in 1 year in 4. To implement the model, it was provided that
years divisible by 100 would be leap years only if they were divisible by 400 as well. So, in the last millennium, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. In this millennium, 2100, 2200, 2300 and 2500 won't be leap years, but 2400 will be. This theory was expanded upon by
Christopher Clavius in a closely argued, 800 page volume. He would later defend his and Lilius's work against detractors.
The 19-year cycle used for the lunar calendar was also to be corrected by one day every 300 or 400 years (8 times in 2500 years) along with corrections for the years (1700, 1800, 1900, 2100 et cetera) that are no longer leap years. In fact, a new method for
computing the date of Easter was introduced.
Lilius originally proposed that the 10-day correction should be implemented by deleting the Julian leap day on each of its ten occurrences during a period of 40 years, thereby providing for a gradual return of the equinox to
21 March. However, Clavius's opinion was that the correction should take place in one move and it was this advice which prevailed with Gregory. Accordingly, when the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of ten days. The last day of the Julian calendar was Thursday
October 4 1582 and this was followed by the first day of the Gregorian calendar, Friday
October 15 1582 (the cycle of weekdays wasn't affected).
However, only four (Catholic) countries adopted the new calendar on the date specified by the bull. Other Catholic countries experienced some delay before adopting the reform; and non-Catholic countries, not being subject to the decrees of the Pope, initially rejected or simply ignored the reform altogether, although they all eventually adopted it. Hence, the dates "
October 5 1582" to "
14 October 1582" (inclusive) are still valid dates in many countries.
Adoption
Spain,
Portugal, the
Polish-Lithuanian Commonwealth, and most of
Italy implemented the new calendar on Friday,
15 October 1582, following Julian Thursday,
October 4 1582. The Spanish and Portuguese colonies adopted the calendar later due to the slowness of communication in those days.
France adopted the new calendar on Monday,
20 December 1582, following Sunday,
December 9 1582. The Protestant
Dutch provinces of Holland and Zeeland also adopted it in December of that year.
Most non-Catholic countries initially objected to adopting a Catholic invention, especially during the
Counter-Reformation (of which Gregory was a leading proponent); some
Protestants feared the new calendar was part of a plot to return them to the Catholic fold., Protestants resisted the calendar imposed by the
Hapsburg Monarchy. In parts of
Ireland, Catholic rebels till their defeat in the
Nine Years' War kept the "new" Easter in defiance of
the English-loyal authorities; later Catholics practising in secret petitioned the
Propaganda Fide for
dispensation from observing the new calendar, as it signalled their disloyalty.
The
Kingdom of Great Britain and thereby the rest of the
British Empire (including the eastern part of what is now the
United States) adopted the Gregorian calendar in 1752 under the provisions of the
Calendar Act 1750; by which time it was necessary to correct by
eleven days (Wednesday,
September 2 1752 being followed by Thursday,
September 14 1752) to account for
February 29 1700 (Julian). A few years later, when the son of
the Earl of Macclesfield (who had been influential in passing the calendar law) ran for a seat in
Parliament in Oxfordshire as a
Whig in 1754, dissatisfaction with the calendar reforms was one of a number of issues raised by his
Tory opponents. In 1755, William Hogarth made a painting (and an engraved print from the painting) loosely based on these elections, in which the campaign slogan "Give us our Eleven Days" appears (on floor at lower right); this was later misunderstood, giving rise to apocryphal stories of widespread riots at the change-over.
Under provision 6 (
Times of Payment of Rents, Annuities) of the
Calendar Act 1750, Great Britain made special provisions to make sure that monthly or yearly payments wouldn't become due until the dates that they originally would have in the Julian calendar. From 1753 until 1799, the tax year in Great Britain began on
5 April, which was the "old style" new tax year of
March 25. A 12th skipped Julian leap day in 1800 changed its start to
6 April. It wasn't changed when a 13th Julian leap day was skipped in 1900, so the tax year in the
United Kingdom still begins
6 April.
"Old Style" (OS) and
"New Style" (NS) are sometimes added to dates to identify which system is used in the
British Empire and other countries that didn't immediately change. In Britain it's usual to map most dates from the
Julian year onto the Gregorian year without converting the day and month. But because the start of the year didn't change until the same year that the Gregorian calendar was introduced, OS/NS is particularly relevant for dates which fall between
1 January and
25 March. For example the execution of King
Charles I is usually recorded as having taken place on
30 January 1649 (NS), but in contemporary documents it's recorded as having taken place on
30 January 1648.
Denmark,
Norway and the Protestant states of
Germany adopted the solar portion of the new calendar on Monday,
1 March 1700, following Sunday,
18 February 1700, due to the influence of
Ole Rømer, but didn't adopt the lunar portion. Instead, they decided to calculate the date of Easter astronomically using the instant of the vernal equinox and the full moon according to
Kepler's
Rudolphine Tables of 1627. They finally adopted the lunar portion of the Gregorian calendar in 1776. The remaining provinces of the
Dutch Republic also adopted the Gregorian calendar in 1700.
Sweden's relationship with the Gregorian Calendar had a difficult birth. Sweden started to make the change from the OS calendar and towards the NS calendar in 1700, but it was decided to make the (then 11 day) adjustment gradually, by excluding the leap days (
29 February) from each of 11 successive leap years, 1700 to 1740. In the meantime, not only would the Swedish calendar be out of step with both the Julian calendar and the Gregorian calendar for 40 years, but also the difference wouldn't be static but would change every 4 years. This strange system clearly had great potential for endless confusion when working out the dates of Swedish events in this 40 year period. To make matters worse, the system was poorly administered and the leap days that should have been excluded from 1704 and 1708 were not excluded. The Swedish calendar should by now have been 8 days behind the Gregorian, but it was still in fact 10 days behind. King
Charles XII wisely recognised that the gradual change to the new system wasn't working and he abandoned it. However, rather than now proceeding directly to the Gregorian calendar (as in hindsight seems to have been the sensible and obvious thing to do), it was decided to revert to the Julian calendar. This was achieved by introducing the unique date
30 February in the year 1712, adjusting the discrepancy in the calendars from 10 back to 11 days. Sweden finally adopted the Gregorian calendar in 1753, when Wednesday,
17 February was followed by Thursday,
1 March, Since Finland was under Swedish rule at that time, it did the same.
In
Alaska, the change took place when Friday,
October 6,
1867 was followed again by Friday,
October 18 after the US purchase of Alaska from Russia, which was still on the Julian calendar. Instead of 12 days, only 11 were skipped, and the day of the week was repeated on successive days, because the
International Date Line was shifted from Alaska's eastern to western boundary along with the change to the Gregorian calendar.
In
Russia the Gregorian calendar was accepted after the
October Revolution (so named because it took place in October 1917 in the Julian calendar). On
24 January 1918 the
Council of People's Commissars issued a
Decree that Wednesday,
31 January 1918 was to be followed by Thursday,
14 February 1918.
The last country of Eastern Orthodox Europe to adopt the Gregorian calendar was
Greece on Thursday,
1 March 1923, following Wednesday,
15 February 1923. However, these were all civil adoptions—none of the national churches accepted it. Instead, a
Revised Julian calendar was proposed in May 1923 which dropped 13 days in 1923 and adopted a different leap year rule that resulted in no difference between the two calendars until 2800. The Orthodox churches of
Constantinople,
Alexandria,
Antioch,
Greece,
Cyprus,
Romania,
Poland, and
Bulgaria adopted the Revised Julian calendar, so these
New calendarists would celebrate the
Nativity along with the Western churches on
25 December in the Gregorian calendar until 2800. The Orthodox churches of
Jerusalem,
Russia,
Serbia,
Georgia and the
Greek Old Calendarists didn't accept the Revised Julian calendar. These
Old Calendarists continue to celebrate the Nativity on
25 December in the Julian calendar, which is
7 January in the Gregorian calendar until 2100. All of the other Eastern churches, the
Oriental Orthodox churches (
Coptic,
Ethiopian,
Eritrean,
Syrian,
Armenian) and the
Assyrian Church, continue to use their own calendars, which usually result in fixed dates being celebrated in accordance with the Julian calendar. All Eastern churches continue to use the Julian Easter with the sole exception of the
Finnish Orthodox Church, which has adopted the Gregorian Easter.
Adoption in Eastern Asia
The
Republic of China (ROC) formally adopted the Gregorian calendar at its founding on
1 January 1912, but China soon descended into a period of warlordism with different warlords using different calendars. With the
unification of China under the
Kuomintang in October 1928, the
Nationalist Government decreed that effective
1 January 1929 the Gregorian calendar would be used thenceforth. However, China retained the Chinese traditions of numbering the months and a modified
Era System, backdating the first year of the ROC to 1912; this system is still in use in
Taiwan where this ROC government retains control. Upon its foundation in 1949, the
People's Republic of China continued to use the Gregorian calendar with numbered months, but abolished the ROC Era System and adopted the Western fashion of naming years.
Japan replaced the traditional lunisolar calendar with the Gregorian calendar on
1 January 1873, but, like China, continued to number the months, and used reign names instead of the
Common Era:
Meiji 1=1868,
Taisho 1=1912,
Showa 1=1926,
Heisei 1=1989, and so on. The "Western calendar" (西暦,
seireki) using western year numbers, is also widely accepted by civilians and to a lesser extent by government agencies.
Korea started using the Gregorian calendar on
1 January 1896 due to Japanese influence. The lunisolar
Korean calendar used immediately before that day was based on the lunisolar
Chinese calendar.
Timeline
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from:1583 till:1583 text:"1583~Austria; Catholic Switzerland and Germany"
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Proleptic Gregorian calendar
The Gregorian calendar can, for certain purposes, be extended backwards to dates preceding its official introduction, producing the
proleptic Gregorian calendar. However, this proleptic calendar should be used with great caution.
For ordinary purposes, the dates of events occurring prior to
15 October 1582 are generally shown as they appeared in the Julian calendar, and
not converted into their Gregorian equivalents.
However, events occurring in countries where the Gregorian calendar was introduced later than
4 October 1582 are a little more contentious. For example, in Great Britain and its overseas possessions (then including the American colonies), the new calendar wasn't introduced until
14 September 1752. How, then, would people date events occurring in Britain and her possessions in the 170 years between 1582 and 1752? The answer depends very much on the context, but writers who want to avoid confusion make it absolutely clear which calendar is being used. People have generally avoided changing historical records in Britain deriving from this period; however, it's often highly desirable to translate particular
Old Style dates into their
New Style equivalents, such as where the context includes reference to other countries that had already converted to New Style before Britain did. A notable exception is the
Twelfth of July, celebrated by
Orangemen as the anniversary of the
Battle of the Boyne on
12 July 1690 (New Style).
If comparisons of dates are done using different calendars, we can encounter apparent logical absurdities such as
William and Mary of Orange seeming to arrive in London to accept the English crown, a week or so before they left the
Netherlands.
Shakespeare and
Cervantes apparently died on exactly the same date (
23 April 1616), but in fact Cervantes predeceased Shakespeare by ten days in real time (for dating these events, Spain used the new calendar, but Britain used the old calendar). This coincidence however has allowed
UNESCO to make
23 April the
World Book and Copyright Day.
Astronomers avoid this ambiguity by the use of the
Julian day number.
For dates before the year 1, unlike the proleptic Gregorian calendar used in the
international standard ISO 8601, the traditional proleptic Gregorian calendar (like the Julian calendar) doesn't have a
year 0 and instead uses the ordinal numbers 1, 2, … both for years AD and BC. Thus the traditional timeline is 2 BC, 1 BC, AD 1, and AD 2. ISO 8601 uses
astronomical year numbering which includes a year 0 and negative numbers before it. Thus the ISO 8601 timeline is -0001, 0000, 0001, and 0002.
Confusion with British versus American usage
Dates in America prior to 1752 are usually now shown in the New Style form, while In Britain it's usual to map most dates from the
Julian year onto the Gregorian year without converting the day and month, but because the start of the year in England didn't change until the same year that the Gregorian calendar was introduced, year adjustments are made for dates which fall between
1 January and
25 March.
For example
George Washington was born on
11 February (OS), his birthday is now celebrated on
22 February (NS), even though he himself continued to celebrate his birthday on
February 11, while the execution of King
Charles I is usually recorded as having taken place on
30 January 1649, even though in contemporary documents it's recorded as having taken place on
30 January 1648.
However, neither of these practices is universal in either country, so it's sometimes very unclear which calendar is being used, and this can lead to false assumptions, which can lead to dates being inaccurately converted from one calendar to the other. Since the resurgence of interest in the history of the calendar, more information about the real dates (according to various calendars) of events has been forthcoming and many previous errors have been corrected. While these changes are welcome, there's still much scope for confusion; specifically noting the calendar being used can help the reader understand the dates involved.
Difference between Gregorian and Julian calendar dates
Since the introduction of the Gregorian calendar, the difference between faster Gregorian (New Style) and slower Julian (Old Style) calendar dates has increased by three days every four centuries:
Beginning of the year
The
Ancient Romans had begun their years on
1 January. During the
Middle Ages under the influence of the Christian Church, many countries moved the start of the year to one of several important Christian festivals —
25 December (the
Nativity of Jesus),
1 March,
25 March (the
Annunciation), or even
Easter. but from the 12
th century to 1752 the year in England began on
25 March (
Lady Day). So for example the Parliamentary record records the execution of
Charles I occurring in 164
8, (as the year didn't end until 24 March,) although modern histories adjust the start of the year to January 1 and record the execution as occurring in 164
9.
Most Western European countries changed the start of the year to
1 January before they adopted the Gregorian calendar. For example Scotland changed the start of the Scottish New Year to
1 January in 1600 (this means that 1599 was a short year). England, Ireland and the British colonies changed the start of the year to
1 January in 1752, (so 1751 was a short year with only 282 days). Later that year in September the Gregorian calendar was introduced throughout Britain and the British colonies (See the section
Adoption). These two reforms were implemented by the
Calendar (New Style) Act 1750. || Adoption of
Gregorian Calendar
|-
|
Venice || 1522 || 1582
|-
|
Holy Roman Empire || 1544 || from 1583
|-
|
Spain,
Portugal, and
Southern Netherlands || 1556 || 1582
|-
|
Prussia || 1559 || 1700
|-
|
Denmark || 1559 || 1700
|-
|
Sweden || 1559 || 1753
|-
|
France || 1564 || 1582
|-
|
Lorraine || 1579 || 1682
|-
|
Dutch Republic || 1583 || from 1582
|-
|
Scotland || 1600 || 1752
|-
|
Russia || 1700 || 1918
|-
|
Tuscany || 1721 || 1750
|-
|
British Empire except Scotland || 1752 || 1752
|}
Neither the papal bull nor its attached canons explicitly fix such a date, though it's implied by two tables of
saint's days, one labeled 1582 which ends on
31 December, and another for any full year that begins on
1 January. It also specifies its
epact relative to
1 January, in contrast with the Julian calendar, which specified it relative to
22 March. These would have been the inevitable result of the above shift in the beginning of the Julian year.
During the period between 1582, when the first countries adopted the Gregorian calendar, and 1923, when the last European country adopted it, it was often necessary to indicate the date of some event in both the Julian calendar and in the Gregorian calendar, for example, "10/21 February 1751/52", where the dual year accounts for some countries already beginning their numbered year on
1 January while others were still using some other date. Even before 1582, the year sometimes had to be double dated because of the different beginnings of the year in various countries. Woolley, writing in his biography of
John Dee (1527-1608/9), notes that immediately after 1582 English letter writers "customarily" used "two dates" on their letters, one OS and one NS.
Months of the year
English speakers sometimes remember the number of days in each month by the use of the traditional
mnemonic verse:
» Thirty days hath September,
April, June, and November. » All the rest have thirty-one,
excepting February alone, » which hath twenty-eight.
Leap year cometh one year in four, » in which February hath one day more.
(The
hath in the first line of the poem is also given as
has or
have.)
Alternate endings include:
» except for February alone,
which has twenty-eight days each year, » and twenty-nine days each leap year.
» excepting February alone,
which has twenty-eight days or, » in a leap year, adds one more.
» which has but twenty-eight, in fine,
till leap year gives it twenty-nine.
» which has eight and a score,
until leap year gives it one day more.
» which hath twenty-eight days clear,
and twenty-nine in each leap year.
» in each leap we assign,
February twenty-nine.
» When short February's done,
all the rest have thirty-one.
» (except February,)
February alone don't hold the line, » for three years it has twenty-eight,
and the fourth year twenty-nine.
» but February, it's done
at twenty-eight, but add one more » whenever the year divides by four.
A shorter, satirical modern alternate ending is:
» but silly old February spoils the fun.
A language-independent alternative used in many countries is to hold up your two fists with the index knuckle of your left hand against the index knuckle of your right hand. Then, starting with January from the little knuckle of your left hand, count knuckle, space, knuckle, space through the months. A knuckle represents a month of 31 days, and a space represents a short month (a 28- or 29-day February or any 30-day month). The junction between the hands isn't counted, so the two index knuckles represent July and August. This method also works by starting the sequence on the right hand's little knuckle, and continue toward to the left. You can also use just one hand; after counting the fourth knuckle as July, start again counting the first knuckle as August. A similar mnemonic can be found on a
piano keyboard: starting on the key F for January, moving up the keyboard in
semitones, the black notes give the short months, the white notes the long ones.
The Origins of English naming used by the Gregorian calendar:
- January: Janus (Roman god of gates, doorways, beginnings and endings)
- February: Februus (Etruscan god of death) Februarius (mensis) (Latin for "month of purification (rituals)" it's said to be a Sabine word, the last month of ancient pre-450 BC Roman calendar). It is related to fever.
- March: Mars (Roman god of war)
- April: Aprilis (mensis) (Latin for "month of Venus," second month of ancient Roman calendar)
- May: Maia Maiestas (Roman goddess)
- June: Juno (Roman goddess, wife of Jupiter)
- July: Julius Caesar (Roman dictator) (month was formerly named Quintilis, the fifth month of the calendar of Romulus)
- August: Augustus (first Roman emperor) (month was formerly named Sextilis, the sixth month of Romulus)
- September: septem (Latin for seven, the seventh month of Romulus)
- October: octo (Latin for eight, the eighth month of Romulus)
- November: novem (Latin for nine, the ninth month of Romulus)
- December: decem (Latin for ten, the tenth month of Romulus)
Week
In conjunction with the system of months there's a system of
weeks. A physical or electronic calendar provides conversion from a given date to the
weekday, and shows multiple dates for a given weekday and month.
Calculating the day of the week isn't very simple, because of the irregularities in the Gregorian system. When the Gregorian calendar was introduced, the week cycle was continued unbroken. So Thursday,
4 October 1582 was followed by Friday
15 October.
The
ISO week date connects Gregorian years and weeks, defining a
leap week calendar with so-called "ISO years" deviating at the beginning and end up to 3 days from Gregorian years, and with week numbers by year.
Origins of English week day names used by the Gregorian Calendar:
Monday - moon day (celestial), a modernization of "Monnendaeg"
Tuesday - Tyr's day (Old Norse god - Tiw in Old English, Teiw in Proto-Germanic)
Wednesday - Woden's day (Old English god - Norse Odin, German Wotan)
Thursday - Thor's day (Old Norse god)
Friday - Frigg's day (Old Norse goddess) (Friday is often erroneously associated with Freyja)
Saturday - Saturn's day (Roman god)
Sunday - sun day (celestial), a modernization of "Sunnendaeg"
Distribution of dates by day of the week
Since the 400-year cycle of the Gregorian calendar consists of a whole number of weeks, each cycle has a fixed distribution of weekdays among calendar dates. It then becomes possible that this distribution isn't even.
Indeed, because there are 97 leap years in every 400 years in the Gregorian Calendar, there are on average 13 for each starting weekday in each cycle. This already shows that the frequency isn't the same for each weekday, which is due to the effects of the "common" centennial years (1700, 1800, 1900, 2100, 2200 etc.).
The absence of an extra day in such years causes the following leap year (1704, 1804, 1904, 2104 etc.) to start on the same day of the week as the leap year twelve years before (1692, 1792, 1892, 2092 etc.). Similarly, the leap year eight years after a "common" centennial year (1708, 1808, 1908, 2108 etc.) starts on the same day of the week as the leap year immediately prior to the "common" centennial year (1696, 1796, 1896, 2096 etc.). Thus, those days of the week on which such leap years begin gain an extra year or two in each cycle. In each cycle there are:
13 leap years starting on Monday
14 leap years starting on Tuesday
14 leap years starting on Wednesday
13 leap years starting on Thursday
15 leap years starting on Friday
13 leap years starting on Saturday
15 leap years starting on Sunday
Note that as a cycle, this pattern is symmetric with respect to the low Saturday value.
A leap year starting on Sunday means the next year doesn't start on Monday, so more leap years starting on Sunday means fewer years starting on Monday, etc. Thus the pattern of number of years starting on each day is inverted and shifted by one weekday: 56, 58, 57, 57, 58, 56, 58 (symmetric with respect to the high Sunday value).
The number of common years starting on each day is found by subtraction: 43, 44, 43, 44, 43, 43, 43.
The frequency of a particular date being on a particular weekday can easily be derived from the above (for dates in March and later, relate them to the next New Year).
See also the cycle of Doomsdays.
Accuracy
The Gregorian calendar improves the approximation made by the Julian calendar by skipping three Julian leap days in every 400 years, giving an average year of 365.2425 mean solar days long, which has an error of about one day per 3300 years with respect to the mean tropical year of 365.24219 days but less than half this error with respect to the vernal equinox year of 365.24237 days. Both are substantially more accurate than the one day in 128 years error of the Julian calendar (average year 365.25 days).
In the 19th century, Sir John Herschel proposed a modification to the Gregorian calendar with 969 leap days per 4000 years, instead of 970 leap days that the Gregorian calendar would insert over the same period. This would reduce the average year to 365.24225 days. Herschel's proposal would make the year 4000 common instead of leap. While this modification has often been proposed since, it has never been officially adopted.
On timescales of thousands of years, the Gregorian calendar falls behind the seasons drastically because the slowing down of the Earth's rotation makes each day slightly longer over time (see tidal acceleration and leap second) while the year maintains a more uniform duration. The equinox will occur earlier than now by a number of days approximately equal to 
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