Weekly calendar

Weekly calendars are annual calendars , the main subdivision of which is not months but weeks . Such calendars can also be used in parallel with monthly calendars within a calendar system. In particular, the international standard ISO 8601 indirectly defines a weekly calendar through the numbering of the calendar weeks.

Leap years

The ISO weekly calendar depends on the Gregorian calendar in that the Gregorian year is normally divided into 52 full weeks (364 days), including up to 3 days each from December of the previous year on the one hand and January of the following year on the other, and if necessary - every 5 to 6 years - a 53rd week is added (thus 371 days).

Weekly calendars that are supposed to be compatible with ISO 8601 follow a 400-year cycle in which there are 71 years with leap weeks, while there are 97 Gregorian leap years (with February 29th ) in the same period .

(400 - 97) a 365 d / a + 97 a 366 d / a = (400 - 71) a 364 d / a + 71 a 371 d = 146097 d
146097 d ÷ 400 a = 365.2425 d / a = 365 d + 5 h + 49 min + 12 s

In every cycle that  begins in any year with the number 400 · n  + 1 (e.g. n = 5 for 2001), these are the years with 53 weeks, i.e. H. they start on a Thursday and end on a Thursday in common years or a Friday in leap years:

004 , 009, 015, 020 , 026, 032 , 037, 043, 048 , 054, 060 , 065, 071, 076 , 082, 088 , 093, 099, 105, 111, 116 , 122, 128 , 133, 139, 144 , 150, 156 , 161, 167, 172 , 178, 184 , 189, 195, 201, 207, 212 , 218, 224 , 229, 235, 240 , 246, 252 , 257, 263, 268 , 274, 280 , 285, 291, 296 , 303, 308 , 314, 320 , 325, 331, 336 , 342, 348 , 353, 359, 364 , 370, 376 , 381, 387, 392 , 398.

Changeover

The years in which January 1st is a Monday in the Gregorian calendar and which would therefore make it a little easier to switch to a compatible weekly calendar are as follows:

001, 007, 018, 024, 029, 035, 046, 052, 057, 063, 074, 080, 085, 091, 103, 114, 120, 125, 131, 142, 148, 153, 159, 170, 176, 181, 187, 198, 210, 216, 221, 227, 238, 244, 249, 255, 266, 272, 277, 283, 294, 300, 306, 312, 317, 323, 334, 340, 345, 351, 362, 368, 373, 379, 390, 396.

Implementations and suggestions

Although weekly calendars can, in principle, be used in parallel with the usual monthly calendar, and also are used by business, there are various proposals to rearrange the months (and quarters ) so that they usually contain a round and even number of complete weeks.

13 month calendar

With a uniform month length of 4 weeks, 13 months fit into a normal weekly year of 364 days. There are different calendar designs that make use of this fact and differ in several details: You can provide a 365th day annually and a 366th day in leap years that do not belong to any week or month and are inserted at different points in the year, or Like ISO 8601, they introduce a 53rd intermittent week, which in turn belongs to different months or can form its own 14th month, which is usually at the end of the year, but can in principle be inserted between any 2 months. Some reform proposals provide for new names for all months (some also for the days of the week), while others are limited to the additional month (e.g. Jaktober), which in turn occurs at different points in the year - usually in the middle or at the end - can be inserted.

The former includes the positivist calendar , which was developed in 1849 by Auguste Comte (hence the Comte calendar). While he kept the traditional weekday names, he renamed the months and individual days of the year after famous people. Not least because of this, he was unable to assert himself in this form. In 1923 it was converted into the International Perpetual Calendar by Moses Cotsworth . Cotsworth kept the traditional month names, only the 13th month in the middle of the year he called either Sol or Midi . Both calendars have one additional day in normal years and two in leap years. In the Comte calendar they are white days at the end of the year, in the international perpetual calendar the extra day is at the end of the year, while the leap day is at the end of June.

A variant of both calendars is the New Earth calendar . It has the same month lengths and, like the International Perpetual Calendar, uses the traditional month names. Only the 13th month in the middle of the year is called Luna . Unlike the International Eternal and Positivist Calendars, the New Earth Calendar does not use additional days , but instead inserts a leap week at the end of the year.

This system with a uniform month length enables a statistical comparison with previous and following months, but it is difficult to break down into quarters, so that it is more interesting for branches of the economy without large seasonal fluctuations than for others.

Quarterly calendar

In the economy, it is customary to divide the year into 4 quarters for accounting purposes, which contain 13 full working weeks instead of 3 full months . In some branches of the economy in some countries these are again artificially divided into 2 months of 4 weeks and one month of 5 weeks. This division can take the form of a 5-4-4, 4-5-4, or 4-4-5, with the latter being the most common scheme. The business or accounting year can in principle begin at any point in the calendar year, but mostly at the beginning of a month or the beginning of a week (Monday or Sunday) close to it, although sometimes the definition is based on the end (at the end of the month or on a Sunday or Saturday ) is preferred.

Marco Mastrofini's world calendar is a practical draft for a quarterly calendar . Each quarter has three months in it, of which the first month has 31 and the remaining months have 30 days. In addition, similar to the International Perpetual Calendar, there is an additional world day at the end of the year and, in leap years, a leap day at the end of June. A variant of the world calendar is the common civil calendar . In contrast to the world calendar, the last month of a quarter always has 31 days. It also inserts a leap week instead of the additional days. This is in the middle of the year and bears the name "Newton" because it is outside the monthly rhythm.

In this system, the statistical comparison of previous and subsequent quarters as well as between the previous and subsequent quarters and months of the year is meaningfully possible, but not between the previous and subsequent month.

Symmetry 4-5-4

This calendar design uses Monday as the first day of the week in accordance with ISO 8601. In common years it has four quarters of exactly the same length (13 weeks or 91 days), and each month begins on a Monday. The months - with the traditional names - are either four or five weeks (28 or 35 days) long; the middle month of each quarter is the longer one. In addition, a leap week of normal length is added to December every five to six years - once every 400 years in the seventh year. The calendar is therefore not very lunar.

Instead of depending on the Gregorian monthly calendar, Bromberg prefers an astronomically more precise method for calculating leap years, in which 52 leap weeks are evenly distributed over a 293-year cycle.

(293-52) * 364 + 52 * 371 = 87724 + 19292 = 107016
107016 ÷ 293 = 365.242320819 = 365 d + 5 h + 48 min + approx. 56.52 s
Annual calendar according to Sym454
1 January February March
2 April May June
3 July August September
4th October November December
 MW 1 2 3 4th 5
Mon Tuesday Wed do Fr. Sat So
1 2 3 4th 5 6th 7th
8th 9 10 11 12 13 14th
15th 16 17th 18th 19th 20th 21st
22nd 23 24 25th 26th 27 28

Mon Tuesday Wed do Fr. Sat So
1 2 3 4th 5 6th 7th
8th 9 10 11 12 13 14th
15th 16 17th 18th 19th 20th 21st
22nd 23 24 25th 26th 27 28
29 30th 31 32 33 34 35
Mon Tuesday Wed do Fr. Sat So
1 2 3 4th 5 6th 7th
8th 9 10 11 12 13 14th
15th 16 17th 18th 19th 20th 21st
22nd 23 24 25th 26th 27 28
29 30th 31 32 33 34 35
Annual calendar according to Sym454
month Mon Tuesday Wed do Fr. Sat So MW week
Jan Apr Jul Oct 1 2 3 4th 5 6th 7th 1 1 14th 27 40
8th 9 10 11 12 13 14th 2 2 15th 28 41
15th 16 17th 18th 19th 20th 21st 3 3 16 29 42
22nd 23 24 25th 26th 27 28 4th 4th 17th 30th 43
Feb May Aug Nov 1 2 3 4th 5 6th 7th 1 5 18th 31 44
8th 9 10 11 12 13 14th 2 6th 19th 32 45
15th 16 17th 18th 19th 20th 21st 3 7th 20th 33 46
22nd 23 24 25th 26th 27 28 4th 8th 21st 34 47
29 30th 31 32 33 34 35 5 9 22nd 35 48
March Jun Sep Dec 1 2 3 4th 5 6th 7th 1 10 23 36 49
8th 9 10 11 12 13 14th 2 11 24 37 50
15th 16 17th 18th 19th 20th 21st 3 12 25th 38 51
22nd 23 24 25th 26th 27 28 4th 13 26th 39 52
29 30th 31 32 33 34 35 5 53

The name Symmetry 454 comes from the fact that each quarter consists of three months with 4 + 5 + 4 weeks (91 days). Evenly divided quarters are advantageous for the economy (financial planning) and also for statistical studies (quarterly statistics are more comparable). The only exception to these 91-day quarters is the last quarter in leap years, where a fifth week is added to December. Also, according to this calendar, all months would have a full number of weeks, not partial weeks.

All holidays, birthdays and anniversaries would be fixed and would take place annually on the same weekday in the same week of the year. To do this, either the previous month-day date is retained or the date is selected in the new calendar applied backwards. If November 9 were a day of celebration and remembrance in Germany because of its diverse historical significance, this would not be found in the Symmetry calendar: In 1918 it was a Saturday, in 1938 a Wednesday and in 1989 a Thursday, in Sym454 it was a Tuesday and in Sym303130 a Thursday.

Easter could be set on April 7th, which would also fix all other previously movable Christian holidays. Although the Easter rule creates the connection between the Gregorian solar calendar and the Gregorian lunar calendar, the Catholic Church in 1975 proposed that from 1977 Easter / Passover always be celebrated on the Sunday after the second Saturday in April, whereas in 1997 the World Council of Churches (WCC) proposed a calendar-free, purely astronomical regulation based on the Council of Nicaea .

Symmetry 0-1-0

Alternatively or in parallel, Bromberg suggests a more conservative calendar with 30- and 31-day months (and 37 in leap year December) without an even number of weeks ( symmetry 0-1-0 or 30-31-30 ).

Annual calendar according to Sym010
month Mon Tuesday Wed do Fr. Sat So MW week
Jan Apr Jul Oct 1 2 3 4th 5 6th 7th 1 1 14th 27 40
8th 9 10 11 12 13 14th 2 2 15th 28 41
15th 16 17th 18th 19th 20th 21st 3 3 16 29 42
22nd 23 24 25th 26th 27 28 4th 4th 17th 30th 43
Feb May Aug Nov 29 30th 1 2 3 4th 5 1 5 18th 31 44
6th 7th 8th 9 10 11 12 2 6th 19th 32 45
13 14th 15th 16 17th 18th 19th 3 7th 20th 33 46
20th 21st 22nd 23 24 25th 26th 4th 8th 21st 34 47
27 28 29 30th 31 1 2 5 9 22nd 35 48
March Jun Sep Dec 3 4th 5 6th 7th 8th 9 1 10 23 36 49
10 11 12 13 14th 15th 16 2 11 24 37 50
17th 18th 19th 20th 21st 22nd 23 3 12 25th 38 51
24 25th 26th 27 28 29 30th 4th 13 26th 39 52
31 32 33 34 35 36 37 5 53