Pax Calendar

The Pax calendar was invented by James A. Colligan, SJ in 1930 as a perennializing reform of the annualized Gregorian calendar.[1]


Months of the Pax calendar
No. Name Days
01 January 28
02 February 28
03 March 28
04 April 28
05 May 28
06 June 28
07 July 28
08 August 28
09 September 28
10 October 28
11 November 28
12 Columbus 28
13 Pax (leap week) 7
13/14 December 28

The common year is divided into 13 months of 28 days each, whose names are the same as in the Gregorian calendar, except that a month called Columbus occurs between November and December. The first day of every week, month and year would be Sunday.

Unlike other perennial calendar reform proposals, such as the International Fixed Calendar and the World Calendar, it preserves the 7-day week by periodically intercalating an extra seven days to a common year of 52 weeks (364 days). In leap years, a one-week month called Pax would be inserted after Columbus.

To get the same mean year as the Gregorian Calendar this leap week is added to 71 of the 400 years in the cycle. The years with leap week are years whose last two digits are a number that is divisible by six (including 00) or 99: however, if a year number ending in 00 is divisible by 400, then Pax is cancelled.

Duncan Steel mentions the Pax Calendar proposal:[2]

As a matter of fact, this leap-week idea is not a new one. and such calendars have been suggested from time to time. ... In 1930, there was another leap-week calendar proposal put forward, this time by a Jesuit, James A. Colligan, but once more the Easter question scuppered it within the Catholic Church.

New Year's Day

Unlike the International Fixed Calendar, the Pax calendar has a new year day that differs from the Gregorian New Year's Day. This is a necessary consequence of it intercalating a week rather than a day.

The following tables compare the Gregorian dates (left column) of New Year's Day in the Pax Calendar for various years. Dates in December occur in the preceding Gregorian year. Dates in bold are Sundays. The Pax years run sequentially down each column (from second-left to right), and a new column is begun when the year would need to go further up the column. Places marked "leap" means that there was no Pax year in the sequence which corresponded to that Gregorian date.

Jan 04        1931  
Jan 03        1932  1937  1943
Jan 02        leap  1938  1944 1949 1955 
Jan 01  1928  1933  1939  leap 1950 1956 1961 1967
Dec 31  leap  1934  1940  1945 1951 leap 1962 1968 1973 1979
Dec 30  1929  1935  leap  1946 1952 1957 1963 leap 1974 1980 1985
Dec 29  1930  1936  1941  1947 leap 1958 1964 1969 1975 leap 1986
Dec 28        leap  1942  1948 1953 1959 leap 1970 1976 1981 1987
Dec 27                    leap 1954 1960 1965 1971 leap 1982 1988
Dec 26                              leap 1966 1972 1977 1983 leap
Dec 25                                        leap 1978 1984 1989
Dec 24                                                  leap 1990
Jan 02           2000
Jan 01           leap
Dec 31           2001 2007
Dec 30 1991      2002 2008 2013 2019
Dec 29 1992 1997 2003 leap 2014 2020 2025 2031
Dec 28 leap 1998 2004 2009 2015 leap 2026 2032 2037 2043
Dec 27 1993 1999 leap 2010 2016 2021 2027 leap 2038 2044 2049 
Dec 26 1994      2005 2011 leap 2022 2028 2033 2039 leap 2050 
Dec 25 1995      2006 2012 2017 2023 leap 2034 2040 2045 2051 
Dec 24 1996           leap 2018 2024 2029 2035 leap 2046 2052 
Dec 23 leap                     leap 2030 2036 2041 2047 leap 
Dec 22                                    leap 2042 2048 2053 
Dec 21                                              leap 2054 

The next table shows what happens around a typical turn of the century and also the full range (18 Dec to 6 Jan) of 19 days that the Pax Calendar New Year Day varies against the Gregorian calendar.

Jan 06                                           2301 2307
Jan 05                                           2302 2308
Jan 04                                           2303 leap
Jan 03                                           2304 2309
Jan 02                 2101 2107                 leap 2310
Jan 01                 2102 2108                 2305 2311
Dec 31                 2103 leap            2300 2306 2312
Dec 30                 2104 2109                      leap
Dec 29                 leap 2110
Dec 28                 2105 2111   2291
Dec 27           2100  2106 2112   2292 2297
Dec 26                      leap   leap 2298
Dec 25                             2293 2299
Dec 24 2091 leap                   2294
Dec 23 2092 2097                   2295
Dec 22 leap 2098                   2296
Dec 21 2093 2099                   leap
Dec 20 2094                        
Dec 19 2095
Dec 18 2096 

Alternative proposals by Colligan

Colligan published multiple alternative methods of organising the months, including three 12-month plans in addition to the 13-month plan, and in a follow-up work focuses on two possible 12-month calendars, in which Pax would be between September and October. He also provided two alternatives to the leap week plan, either extending one or two Mondays per year to 48 hours or making Pax a month of 28 or 21 days to be added 18 times in 400 years.[3]

Sources and references

  • Lance Latham (1998). Standard C Date/Time Library: programming the world's calendars and clocks. CMP Books. p. 471. ISBN 0-87930-496-0.
  1. ^ James A. Colligan (1930). "Original proposal for the Pax Calendar". Rick McCarty.
  2. ^ Duncan Steel (2000). Marking Time: The Epic Quest to Invent the Perfect Calendar. John Wiley & Sons, Inc. p. 288, 422. ISBN 0-471-29827-1.
  3. ^ Colligan, James (1933). An unchangeable calendar without blank days and with only two days of the present calendar changed. University of San Francisco.
Calendar reform

Calendar reform or calendrical reform, is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar design.

Gregorian calendar

The Gregorian calendar is the calendar used in most of the world. It is named after Pope Gregory XIII, who introduced it in October 1582. The calendar spaces leap years to make the average year 365.2425 days long, approximating the 365.2422-day tropical year that is determined by the Earth's revolution around the Sun. The rule for leap years is:

Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the year 2000 is.

The calendar was developed as a correction to the Julian calendar, shortening the average year by 0.0075 days to stop the drift of the calendar with respect to the equinoxes. To deal with the 10 days' difference (between calendar and reality) that this drift had already reached, the date was advanced so that 4 October 1582 was followed by 15 October 1582. There was no discontinuity in the cycle of weekdays or of the Anno Domini calendar era. The reform also altered the lunar cycle used by the Church to calculate the date for Easter (computus), restoring it to the time of the year as originally celebrated by the early Church.

The reform was adopted initially by the Catholic countries of Europe and their overseas possessions. Over the next three centuries, the Protestant and Eastern Orthodox countries also moved to what they called the Improved calendar, with Greece being the last European country to adopt the calendar in 1923. To unambiguously specify a date during the transition period, (or in history texts), dual dating is sometimes used to specify both Old Style and New Style dates (abbreviated as O.S and N.S. respectively). Due to globalization in the 20th century, the calendar has also been adopted by most non-Western countries for civil purposes. The calendar era carries the alternative secular name of "Common Era".

Hanke–Henry Permanent Calendar

The Hanke–Henry Permanent Calendar (HHPC) is a proposal for calendar reform. It is one of many examples of leap week calendars, calendars which maintain synchronization with the solar year by intercalating entire weeks rather than single days. It is a modification of a previous proposal, Common-Civil-Calendar-and-Time (CCC&T). With the Hanke–Henry Permanent Calendar, every calendar date always falls on the same day of the week.

Leap week calendar

A leap week calendar is a calendar system with a whole number of weeks every year, and with every year starting on the same weekday. Most leap week calendars are proposed reforms to the civil calendar, in order to achieve a perennial calendar. Some, however, such as the ISO week date calendar, are simply conveniences for specific purposes.

The ISO calendar in question is a variation of the Gregorian calendar that is used (mainly) in government and business for fiscal years, as well as in timekeeping. In this system a year (ISO year) has 52 or 53 full weeks (364 or 371 days).

Leap week calendars vary on whether the concept of month is preserved and whether the month (if preserved) has a whole number of weeks. The Pax Calendar and Hanke-Henry Permanent Calendar preserve or modify the Gregorian month structure. The ISO week date and the Weekdate Dating System are examples of leap week calendars that eliminate the month.Most leap week calendars take advantage of the 400-year cycle of the Gregorian calendar, which has exactly 20,871 weeks. With 329 common years of 52 weeks plus 71 leap years of 53 weeks, leap week calendars would synchronize with the Gregorian every 400 years (329 × 52 + 71 × 53 = 20,871).

List of calendars

This is a list of calendars. Included are historical calendars as well as proposed ones. Historical calendars are often grouped into larger categories by cultural sphere or historical period; thus O'Neil (1976) distinguishes the groupings Egyptian calendars (Ancient Egypt), Babylonian calendars (Ancient Mesopotamia), Indian calendars (Hindu and Buddhist traditions of the Indian subcontinent), Chinese calendars and Mesoamerican calendars.

These are not specific calendars but series of historical calendars undergoing reforms or regional diversification.

In Classical Antiquity, the Hellenic calendars inspired the Roman calendar, including the solar Julian calendar introduced in 45 BC. Many modern calendar proposals, including the Gregorian calendar itself, are in turn modifications of the Julian calendar.

Perennial calendar

A perennial calendar is a calendar that applies to any year, keeping the same dates, weekdays and other features.

Perennial calendar systems differ from most widely used calendars which are annual calendars. Annual calendars include features particular to the year represented, and expire at the year's end. A perennial calendar differs also from a perpetual calendar, which is a tool or reference to compute the weekdays of dates for any given year, or for representing a wide range of annual calendars.

For example, most representations of the Gregorian calendar year include weekdays and are therefore annual calendars, because the weekdays of its dates vary from year to year. For this reason, proposals to perennialize the Gregorian calendar typically introduce one or another scheme for fixing its dates on the same weekdays every year.

Perpetual calendar

A perpetual calendar is a calendar valid for many years, usually designed to allow the calculation of the day of the week for a given date in the future.

For the Gregorian and Julian calendars, a perpetual calendar typically consists of one of two general variations:

14 one-year calendars, plus a table to show which one-year calendar is to be used for any given year. These one-year calendars divide evenly into two sets of seven calendars: seven for each common year (year that does not have a February 29) with each of the seven starting on a different day of the week, and seven for each leap year, again with each one starting on a different day of the week, totaling fourteen. (See Dominical letter for one common naming scheme for the 14 calendars.)

Seven (31-day) one-month calendars (or seven each of 28–31 day month lengths, for a total of 28) and one or more tables to show which calendar is used for any given month. Some perpetual calendars' tables slide against each other, so that aligning two scales with one another reveals the specific month calendar via a pointer or window mechanism.The seven calendars may be combined into one, either with 13 columns of which only seven are revealed, or with movable day-of-week names (as shown in the pocket perpetual calendar picture).

Note that such a perpetual calendar fails to indicate the dates of moveable feasts such as Easter, which are calculated based on a combination of events in the Tropical year and lunar cycles. These issues are dealt with in great detail in Computus.

An early example of a perpetual calendar for practical use is found in the manuscript GNM 3227a.

The calendar covers the period of 1390–1495 (on which grounds the manuscript is dated to c. 1389).

For each year of this period, it lists the number of weeks between Christmas day and Quinquagesima. This is the first known instance of a tabular form of perpetual calendar allowing the calculation of the moveable feasts that became popular during the 15th century.

Solar calendar

A solar calendar is a calendar whose dates indicate the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as standard in the world, is an example of a solar calendar.

The main other type of calendar is a lunar calendar, whose months correspond to cycles of Moon phases. The months of the Gregorian calendar do not correspond to cycles of Moon phase.

Nearly universal
In wide use
In more
limited use
By specialty
Displays and
Year naming

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