A calendar reform is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar.
Most calendars have several rules which could be altered by reform:
- Whether and how days are grouped into subdivisions such as months and weeks, and days outside those subdivisions, if any.
- Which years are leap years and common years and how they differ.
- Numbering of years, selection of the epoch, and the issue of year zero.
- Start of the year (such as Southern solstice, January 1, March 1, Northward equinox, Easter).
- If a week is retained, the start, length, and names of its days.
- Start of the day (midnight, sunrise, noon, or sunset).
- If months are retained, number, lengths, and names of months,
- Special days and periods (such as leap day or intercalary day).
- Alignment with social cycles.
- Alignment with astronomic cycles.
- Alignment with biological cycles.
- Literal notation of dates.
Historical reforms 
Historically, most calendar reforms have been made in order to synchronize the calendar in use with the astronomical year (either solar or sidereal) and/or the synodic month in lunar or lunisolar calendars. Most reforms for calendars have been to make them more accurate. This has happened to various lunar and lunisolar calendars, and also the Julian calendar when it was modified into the Gregorian calendar.
The fundamental problem of the calendar is the imperfect divisibility of whole numbers into an irrational number (fitting whole days into a month; fitting whole days or whole months into a year). The physics of orbital mechanics does not phase-lock the rotation of the Earth (the day) to its revolution (the year), nor the rotation of the Earth (the day) to the revolution of the Moon (the month). Therefore any attempt to divide a month into days or a year into days will leave a fractional remainder of a partial day. Likewise, any attempt to divide a year into months will leave a fractional remainder of a partial month. Such remainders accumulate from one period to the next thereby driving the cycles out of synch.
A typical solution for forcing synchronization is called 'intercalation'. This is an artificial harmonization that, after the fractional remainders have sufficiently accumulated, adds a whole day (or month) into the cycle. An alternative solution is to ignore the mismatch and simply let the cycles continue to drift apart. The general strategies include:
- The lunar calendar solution, which fits days into the lunar cycle month, adding an extra day when needed, while ignoring the annual solar cycle of the seasons.
- The solar calendar solution, which fits artificial months into the year, adding an extra day into one month when needed, while ignoring the lunar cycle of new/full moons.
- The lunisolar calendar solution, which keeps both the lunar and solar cycles, adding an extra month into the year when needed.
An obvious disadvantage of the lunisolar method of inserting a whole extra month is the large irregularity of the length of the year from one to the next. The simplicity of a lunar calendar may tend to be seen as less advantageous at larger latitudes where seasonal effects are experienced more strongly. Identifying the lunar cycle month requires straightforward observation of the Moon on a clear night. However, identifying seasonal cycles requires much more methodical observation of stars or a device to track solar day-to-day progression, such as that established at places like Stonehenge. After centuries of empirical observations, the theoretical aspects of calendar construction could become more refined, enabling predictions that identified the need for reform.
Reform of lunar and lunisolar calendars 
There have been 50 to 100 reforms of the traditional Chinese calendar over 2500 years, most of which were intended to better fit the calendar months to astronomical lunations and to more accurately add the extra month so that the regular months maintain their proper seasonal positions, even though each seasonal marker can occur anywhere within its month. There have been at least four similar reforms of the lunisolar version of the Hindu calendar, all intended to make the month a better match to the lunation and to make the year a better fit to the sidereal year. There have been reforms of the 'solar' version of the Hindu calendar which changed the distribution of the days in each month to better match the length of time that the Sun spends in each sidereal zodiacal sign. The same applies to the Buddhist calendar. The first millennium reform of the Hebrew calendar changed it from an observational calendar into a calculated calendar. The Islamic calendar was a reform of the preceding lunisolar calendar which utterly divorced it from the solar year.
Julian/Gregorian reforms 
At the time when Julius Caesar took power in Rome, the Roman calendar had ceased to reflect the year accurately. The provision of adding an intercalary month to the year when needed had not been applied consistently, because it affected the length of terms of office.
The Julian reform lengthened seven months and replaced the intercalary month with an intercalary day to be added every four years to February. This produced a noticeably more accurate calendar, but it was based on a length for the year of 365 days and 6 hours (365.25 d). In fact, the tropical year is about 11 minutes and 14 seconds less than that. This had the effect of adding about three quarters of an hour every four years. The effect accumulated from 325 until by the 16th century, when the Northward equinox fell on March 10 or 11.
Under Pope Gregory XIII the leap rule was altered: century years which are not divisible by 400 would not be leap years. So 1700, 1800, and 1900 were not leap years, and 2100, 2200 and 2300 will not be either. This rule makes the mean year 365.2425 days (365 d, 5 h, 49 min, 12 s) long. While this does not synchronize the years entirely, it would require a few thousand years to accumulate a day.
So that the Northward equinox would have the same date in the new Gregorian Calendar as it had in the Julian calendar (March 21), ten days were dropped so that October 5 became October 15 in 1582. This reform took several centuries to spread through the nations that used the Julian calendar, although the Russian church year still uses the Julian calendar. Those nations that adopted this calendar on or after 1700 had to drop more than ten days: Great Britain, for instance, dropped eleven.
When noting dates occurring within the period, "Old Style" and "New Style" are used to distinguish which calendar was used by the person who recorded the date.
In 1923, Milutin Milanković proposed to a synod of some Eastern Orthodox Churches at Constantinople that only those centennial years (those ending in '00) that leave a remainder of 200 or 600 upon division by 900 would be leap years, decreasing the average year length to 365.242222 days. These remainders were chosen to delay the first year (after 1923) that this calendar would disagree with the Gregorian calendar as much as possible, until 2800. It was adopted by some Eastern Orthodox Churches under the names Revised Julian calendar or New calendar, but was rejected by others.
The Gregorian calendar is currently used by most of the world. There is also an international standard describing the calendar, ISO 8601, with some differences to traditional conceptions in many cultures.
Since the last papal reform, several proposals have been offered to make the Western calendar more useful or regular. Very few reforms have gained official acceptance. The rather different decimal French Republican Calendar was one such official reform, but was abolished twelve years later by Napoleon. After World War II the newly-formed United Nations continued efforts of its predecessor, the League of Nations, to establish the proposed World Calendar but postponed the issue after a veto from the US government, which was mainly based upon concerns of religious groups about the proposed days that would be outside the seven-day week cycle ("blank days") and thus disrupt having a sabbath every seven days. Independently the World Council of Churches still tries to find a common rule for the date of Easter, which might be eased by a new common calendar.
|360 ÷ 7 = 51 3⁄7||360 ÷ 12 = 30|
|364 ÷ 7 = 52 = 4 × 13||364 ÷ 12 = 30 1⁄3|
|365 ÷ 7 = 52 1⁄7||365 ÷ 12 = 30 5⁄12|
|366 ÷ 7 = 52 2⁄7||366 ÷ 12 = 30 1⁄2|
Reformers cite several problems with the Gregorian calendar:
- It is not perennial. Each year starts on a different day of the week and calendars expire every year.
- It is difficult to determine the weekday of any given day of the year or month.
- Months are not equal in length, nor regularly distributed across the year, and so some people rely on mnemonics (e.g. "Thirty days hath September" or knuckle counting) to remember the lengths of months.
- The year's four quarters (of three full months each) are not equal (being of 90/91, 91, 92 and 92 days respectively). Business quarters that are equal would make accounting easier.
- Its epoch (origin) is religious. The same applies to month and weekday names in many languages.
- Each month has no connection with the lunar phases.
- Solstices and equinoxes do not coincide with either the beginning of the Gregorian months, or the midpoint of the months.
It is hard to solve all these issues in just one calendar.
Most plans evolve around the solar year of little more than 365 days. This number does not divide well by seven or twelve, which are the traditional numbers of days per week and months per year respectively. The nearby numbers 360, 364 and 366 are divisible in better ways. There are also lunar centric proposals.
|Comparison of proposed solar calendar reforms (Gregorian/ISO Date equivalents)|
|Author||New Year's Day||Jan
|13||Extra calendrical days||Intercalary days||Starts at|
Jan 1 (01.01)
|28||28||28||28||28||28||28||28||28||28||28||28||28||Festival of the Dead (13.29), Festival of Holy Women (13.30)||Festival of Holy Women (13.30)|
Jan 1 (01.01)
|28||28||28||28||28||28||28||28||28||28||28||28||28||Leap D. (07.00), Year Day (13.29)||Leap D. (07.00) (W27.0)|
|28||28||28||28||28||28||28||28||28||28||28||28||28||Leap week 13.1-7 moving Dec from 13 to 14|
|31||30||30||31||30||30||31||30||30||31||30||30||World Leap D. (Jun 31/ 07.00), World D. (Dec 31/ 12.31)||World Leap D. (Jun 31/ 07.00) (W27.0)|
N. Winter Solstice, 01.01
|91||91||91||91||D-92 (04.92), B-92 (02.92)||B-92 (02.92) (W27.0)|
|30||30||31||30||30||31||30||30||31||30||30||31||*||*Newton 07.1–7, moves following months forward 1|
|Cesare Emiliani||Jan 1||31||28||31||30||31||30||31||31||30||31||30||31||Same as Gregorian||January 1, 10000 BC|
|Double Week Calendar||Jan 1||31||29||31||30||31||30||30||31||30||31||29||31||Every 292nd week is doubled|
Perennial calendars 
Many calendar reforms have offered solutions to make the Gregorian calendar perennial. These reforms would make it easy to work out the day of week of a particular date, and would make changing calendars each year unnecessary. There are, roughly speaking, two options to achieve this goal: leap week calendars and intercalary days. Both make it easier to work out the day of week by having exactly 52 weeks in each year. The former add a whole 53rd week every five or six years, the latter have an extra day not belonging to any week and two such in leap years. Proposals mainly differ in their selection of a leap rule, placing of the leap item (usually middle or end of the year), in the start day of the week and year, in the number (12 or 13) and size of months and in connected naming; some are compatible to the week date of ISO 8601.
The World Calendar, favored by the UN in the 1950s, and the International Fixed Calendar, quite popular among economists between the World Wars, are proposals that start each year on a Sunday. The remaining 364 days then form 52 weeks of 7 days. The World Calendar has every quarter beginning on the same day of week. In the World Calendar, the 365th and 366th day are considered holidays and named Worlds Day and Leap Year Day. These "off-calendar" days stand outside the seven-day week and caused some religious groups to strongly oppose adoption of The World Calendar. Such concerns helped prevent the World Calendar from being adopted. Supporters of the World Calendar, however, argue that the religious groups' opposition overlooked every individual's right to celebrate these holidays as extra days of worship, or Sabbaths. This option, they reason, maintained the seven-day worship cycle for those who share that concern, while allowing benefits of a perennial calendar to be shared by all.
Leap week calendars add a leap week of seven days to the calendar every five or six years to keep the calendar roughly in step with the tropical year. They have years of either 364 days (52 weeks) or 371 days (53 weeks), thus preserving the 7-day week.
Some calendars have quarters of regularly patterned uneven months e.g. a 35 day (five week) month and a pair of 28 day (four week) months, with a leap week appended to the final month when needed. The Common Civil Calendar and Time calendar, known now as the Hanke-Henry Permanent Calendar has months of 30 and 31 days, but inserts a leap week in the middle of the year, when needed.
The 53-week calendar, used in government and in business for fiscal years, is a variant of this concept. Each year of this calendar can be up to 371 days long.
Still other proposals abandon attempts to make the calendar perennial, instead opting for eleven 30-day months and one long month at the end of 35 (or 36) days.
13-month calendars 
Some calendar reformers seek to equalize the length of each month in the year. This is often accomplished by creating a calendar that has 13 months of 4 weeks (28 days) each, making 364 days. The earliest known proposal of this type was the Georgian Calendar (1745) by Rev. Hugh Jones.
The Positivist calendar (1849), created by Auguste Comte, was based on a 364-day year which included one or two “blank” days. Each of the 13 months had 28 days and exactly four weeks, and each started on a Monday. The International Fixed Calendar is a more modern descendant of this calendar.
Some proposals add one or two days to the calendar each year to account for the annual solar cycle, while others keep these days off the calendar entirely, to make the calendar perennial.
In 1993, Jose Arguelles founded The World Thirteen Moon Calendar Change Peace Movement with his wife Lloydine.
Dividing the years into 52 weeks creates 13 months of 28 days (4 weeks), and 4 quarters of 91 days (13 weeks). This creates months and quarters of fixed, even duration, but not quarters containing a whole number of months.
Lunisolar calendars 
Lunisolar calendars usually have 12 or 13 months of 29 or 30 days.
Some propose to improve leap rules of existing calendars, such as the Hebrew calendar. The Rectified Hebrew calendar uses a more accurate leap cycle of 4366 months per 353-year cycle, with 130 leap years per cycle, and a progressively shorter molad interval, intended to replace the 19-year leap cycle and the constant molad interval of the traditional fixed arithmetic Hebrew calendar, respectively.
Calendar proposals that introduce a thirteenth month or change the Julian-Gregorian system of months often also propose new names for these months. New names have also been proposed for days out of the week cycle (e.g. 365th and leap) and weeks out of the month cycle.
Proposals to change the traditional month and weekday names are less frequent. The Gregorian calendar obtains its names mostly from gods of historical religions (e.g. Thursday from Nordic Thor or March from Roman Mars) or leaders of vanished empires (July and August from the first Cæsars), or ordinals that got out of synchronization (September through December, originally seventh through tenth, now ninth through twelfth).
Calendar reformers, therefore, seek to correct what they see as deficiencies by focusing on more homogeneous sets of individuals, who usually share common traits.
Comte’s Positivist calendar, for example, proposed naming the 13 months in his calendar after figures from religion, literature, philosophy and science. Similarly, the Hermetic Lunar Week Calendar uses 12 or 13 lunar months named after 13 contributors to research on psychoactive plants and chemicals. The Simple Lunisolar Calendar names its months after the letters of the Greek alphabet.
Some, such as Karl Palmen, have suggested to reuse an existing 13 × 4 naming system. The one found is playing cards. Thus either months are numbered Ace, Two through Ten, Jack, Queen and King with four weeks each, named after the four suits (♠♣♥♦); or the roles are reversed if the calendar has four quarters with thirteen weeks each. Leap days or weeks are assigned the Joker. This system has internationalisation problems, though, because even where the 52-card deck is known, the order of suits may vary. Also the contemporary ISO basic Latin alphabet has 26 letters, which could be used, together with a further binary indicator, as keys for 52 weeks.
See also 
Specific proposals 
There have been many specific calendar proposals to replace the Gregorian Calendar:
The following count one or more days outside the standard seven-day week:
- Positivist calendar
- The World Calendar
- International Fixed Calendar
- Invariable Calendar
- World Season Calendar
- Tranquility Calendar
The following are leap week calendars:
The following track the moon as well as the sun:
There have also been proposals to revise the way years are numbered:
Reform of the Islamic calendar:
Since the beginning of the 21st century, there is a trend within the Muslim communities of North America and Europe to substitute a lunar calendar based on calculations to the traditional Islamic method of monthly observation of the new moon to declare the beginning of the new month in each country separately. The details are in the following study:
- Khalid Chraibi, The reform of the Islamic calendar: the terms of the debate, Tabsir.net, September 2012
Further reading 
- Steel, Duncan (2000). Marking Time: The Epic Quest to Invent the Perfect Calendar. New York: Wiley. ISBN 0-471-29827-1.
- 13-month proposals
- Other specific proposals
- Catholic Encyclopedia "Reform of the Calendar" Historical information