Common year starting on Tuesday

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A common year starting on Tuesday is any non-leap year (i.e. a year with 365 days) that begins on Tuesday, 1 January, and ends on Tuesday, 31 December. Its dominical letter hence is F. The current year, 2019 , is a common year starting on Tuesday in the Gregorian calendar. The last such year was 2013 and the next such year will be 2030, or, likewise, 2014 and 2025 in the obsolete Julian calendar, see below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year contains two Friday the 13ths in September and December. Leap years starting on Monday share this characteristic. From July of the year that precedes this year until September in this type of year is the longest period (14 months) that occurs without a Friday the 13th. Leap years starting on Saturday share this characteristic, from August of the common year that precedes it to October in that type of year.

A leap year is a calendar year containing one additional day added to keep the calendar year synchronized with the astronomical or seasonal year. Because seasons and astronomical events do not repeat in a whole number of days, calendars that have the same number of days in each year drift over time with respect to the event that the year is supposed to track. By inserting an additional day or month into the year, the drift can be corrected. A year that is not a leap year is called a common year.

Dominical letters or Sunday letters are a method used to determine the day of the week for particular dates. When using this method, each year is assigned a letter depending on which day of the week the year starts on.

2019 (MMXIX) is the current year, and is a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

Contents

Calendars

Calendar for any common year starting on Tuesday,
presented as common in many English-speaking areas

A common year is a calendar year with 365 days, as distinguished from a leap year, which has 366. More generally, a common year is one without intercalation. The Gregorian calendar,, employs both common years and leap years to keep the calendar aligned with the tropical year, which does not contain an exact number of days.

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ISO 8601-conformant calendar with week numbers for
any common year starting on Tuesday (dominical letter F)

ISO 8601Data elements and interchange formats – Information interchange – Representation of dates and times is an international standard covering the exchange of date- and time-related data. It was issued by the International Organization for Standardization (ISO) and was first published in 1988. The purpose of this standard is to provide an unambiguous and well-defined method of representing dates and times, so as to avoid misinterpretation of numeric representations of dates and times, particularly when data are transferred between countries with different conventions for writing numeric dates and times.

The ISO week date system is effectively a leap week calendar system that is part of the ISO 8601 date and time standard issued by the International Organization for Standardization (ISO) since 1988 and, before that, it was defined in ISO (R) 2015 since 1971. It is used (mainly) in government and business for fiscal years, as well as in timekeeping. This was previously known as "Industrial date coding". The system specifies a week year atop the Gregorian calendar by defining a notation for ordinal weeks of the year.

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Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-four common years per cycle or exactly 11% start on a Tuesday. The 28-year sub-cycle does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Tuesday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
17th century 1602 1613 1619 1630 1641 1647 1658 1669 1675 1686 1697
18th century 1709 1715 1726 1737 1743 1754 1765 1771 1782 1793 1799
19th century 1805 1811 1822 1833 1839 1850 1861 1867 1878 1889 1895
20th century 1901 1907 1918 1929 1935 1946 1957 1963 1974 1985 1991
21st century 2002 2013 2019 2030 2041 2047 2058 2069 2075 2086 2097
22nd century 2109 2115 2126 2137 2143 2154 2165 2171 2182 2193 2199

Julian Calendar

In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks). A leap year has two adjoining dominical letters (one for January and February and the other for March to December in the Church of England as 29 February has no letter). Each of the seven two-letter sequences occurs once within a cycle, and every common letter thrice.

The solar cycle is a 28-year cycle of the Julian calendar with respect to the week. It occurs because leap years occur every 4 years and there are 7 possible days to start a leap year, making a 28-year sequence.

As the Julian calendar repeats after 28 years that means it will also repeat after 700 years, i.e. 25 cycles. The year's position in the cycle is given by the formula ((year + 8) mod 28) + 1). Years 7, 18 and 24 of the cycle are common years beginning on Tuesday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Tuesday.

Julian common years starting on Tuesday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century14091415142614371443145414651471148214931499
16th century1510152115271538154915551566157715831594
17th century16051611162216331639165016611667167816891695
18th century1706171717231734174517511762177317791790
19th century18011807181818291835184618571863187418851891
20th century19021913191919301941194719581969197519861997
21st century20032014202520312042205320592070208120872098

Related Research Articles

Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.

A common year starting on Sunday is any non-leap year that begins on Sunday, 1 January, and ends on Sunday, 31 December. Its dominical letter hence is A. The most recent year of such kind was 2017 and the next one will be 2023 in the Gregorian calendar, or, likewise, 2018 and 2029 in the obsolete Julian calendar, see below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year contains two Friday the 13ths in January and October.

A common year starting on Friday is any non-leap year that begins on Friday, 1 January, and ends on Friday, 31 December. Its dominical letter hence is C. The most recent year of such kind was 2010 and the next one will be 2021 in the Gregorian calendar, or, likewise, 2011 and 2022 in the obsolete Julian calendar. The century year, 2100, will also be a common year starting on Friday in the Gregorian calendar. See below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this common year occurs in August. Leap years starting on Thursday share this characteristic, but also have another one in February.

A common year starting on Monday is any non-leap year 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 will be 2029 in the Gregorian calendar, or likewise, 2013 and 2019 in the obsolete Julian calendar. The century year, 1900, was also a common year starting on Monday in the Gregorian calendar. See below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year of this type contains two Friday the 13ths in April and July. Leap years starting on Sunday share this characteristic, but also have another in January.

A leap year starting on Sunday is any year with 366 days that begins on Sunday, 1 January, and ends on Monday, 31 December. Its dominical letters hence are AG, such as the years 1888, 1928, 1956, 1984, 2012, 2040, 2068, 2096, 2108, 2136, 2164, and 2192 in the Gregorian calendar or, likewise, 1996 and 2024 in the obsolete Julian calendar.

A leap year starting on Monday is any year with 366 days that begins on Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letters hence are GF, such as the years 1912, 1940, 1968, 1996, 2024, 2052, 2080, and 2120 in the Gregorian calendar or, likewise, 2008, 2036, and 2064 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in September and December. Common years starting on Tuesday share this characteristic.

A common year starting on Wednesday is any non-leap year 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 will be 2025 in the in the Gregorian calendar or, likewise, 2009, 2015, and 2026 in the obsolete Julian calendar. The century year, 1800, was also a common year starting on Wednesday in the Gregorian calendar, see below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this common year occurs in June. Leap years starting on Tuesday share this characteristic.

A leap year starting on Tuesday is any year with 366 days that begins on Tuesday, 1 January, and ends on Wednesday, 31 December. Its dominical letters hence are FE, such as the years 1884, 1924, 1952, 1980, 2008, 2036, 2064, 2092, and 2104 in the Gregorian calendar or, likewise, 1964, 1992, and 2020 in the obsolete Julian calendar. Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this leap year occurs in June. Common years starting on Wednesday share this characteristic.

A common year starting on Saturday is any non-leap year that begins on Saturday, 1 January, and ends on Saturday, 31 December. Its dominical letter hence is B. The most recent year of such kind was 2011 and the next one will be 2022 in the Gregorian calendar or, likewise, 2017 and 2023 in the obsolete Julian calendar, see below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this common year occurs in May. Leap years starting on Friday share this characteristic.

A common year starting on Thursday is any non-leap year that begins on Thursday, 1 January, and ends on Thursday, 31 December. Its dominical letter hence is D. The most recent year of such kind was 2015 and the next one will be 2026 in the Gregorian calendar or, likewise, 2010 and 2021 in the obsolete Julian calendar, see below for more. This common year contains the most Friday the 13ths; specifically, the months of February, March, and November. Leap years starting on Sunday share this characteristic. From February until March in this type of year is also the shortest period that occurs within a Friday the 13th.

A leap year starting on Saturday is any year with 366 days that begins on Saturday, 1 January, and ends on Sunday, 31 December. Its dominical letters hence are BA, such as the years 1916, 1944, 1972, 2000, and 2028 in the Gregorian calendar or, likewise, 2012 and 2040 in the obsolete Julian calendar. In the Gregorian calendar all centennial leap years start on Saturday; the next such year will be 2400, see below for more.

A leap year starting on Friday is any year with 366 days that begins on Friday 1 January and ends on Saturday 31 December. Its dominical letters hence are CB, such as the years 1808, 1836, 1864, 1892, 1904, 1932, 1960, 1988, 2016, 2044, 2072, and 2112 in the Gregorian calendar or, likewise, 2000 and 2028 in the obsolete Julian calendar. Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this leap year occurs in May. Common years starting on Saturday share this characteristic.

A leap year starting on Thursday is any year with 366 days that begins on Thursday 1 January, and ends on Friday 31 December. Its dominical letters hence are DC, such as the years 1880, 1920, 1948, 1976, 2004, 2032, 2060, and 2088, in the Gregorian calendar or, likewise, 1988, 2016, and 2044 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in February and August.

A leap year starting on Wednesday is any year with 366 days that begins on Wednesday, 1 January, and ends on Thursday, 31 December. Its dominical letters hence are ED, such as the years 1908, 1936, 1964, 1992, 2020, 2048, 2076, and 2116 in the Gregorian calendar or, likewise, 2004 and 2032 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in March and November. Common years starting on Thursday share this characteristic, but also have another in February.

Doomsday rule way of calculating the day of the week of a given date

The Doomsday rule is an algorithm of determination of the day of the week for a given date. It provides a perpetual calendar because the Gregorian calendar moves in cycles of 400 years.

In the Gregorian calendar, a year ending in "00" that is divisible by 400 is a century leap year, with the intercalation of February 29 yielding 366 days instead of 365. Century years that are not divisible by 400 are not leap years but common years of 365 days. For example, the years 1600, 2000, and 2400 are century leap years since those numbers are divisible by 400, while 1700, 1800, 1900, 2100, 2200, and 2300 are common years despite being divisible by 4. Leap years divisible by 400 always start on a Saturday; thus the leap day February 29 in those years always falls on a Tuesday.

References

  1. Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
  2. Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.