Calendar Systems

Calendars are usually based on months and years, where a month is the time between a successive new moon and a year is the time elapsed when a given season returns. Unfortunately, a lunar month is around 29½ days whilst a year is about 12¼ months, which makes things rather difficult.

The Sun

The mean distance of the sun is 92,917,931 miles (149,597,000 km). Despite this amazing distance, the sun is sole source of light and the main provider of warmth on our planet. Although the orbit of the Earth isn’t perfectly circular, this doesn’t significantly contribute to the variations in the lengths of days or temperatures over the seasons. In fact, the tilt of it the planet’s axis is far more important, since this causes a different part of the globe to receive more light at opposite ends of the orbit.

In the summer, for example, the northern hemisphere is pointing more directly at the sun, giving it more hours of daylight and hence more warmth. In the winter, however, the sun faces onto the southern hemisphere, at which time the north receives less light and is colder.

An equinox occurs twice each year, when the sun is exactly over the equator, meaning that there are exactly equal intervals of day and night. A solstice occurs when the sun is at its furthest extreme to the north or south. These extremes run along two lines parallel to the equator; the Tropic of Cancer to the north and the Tropic of Capricorn to the south . The dates of the equinoxes and solstices are given in the following table:-

although the seasons shown here must be reversed for the southern hemisphere.

The Arctic Circle is a line following the northernmost latitude where the sun can reach overhead, whilst the Antarctic Circle is the corresponding southernmost latitude. At the time of the summer solstice, there’s continuous sunshine within the Arctic Circle, whilst those in Antarctic Circle have to live in constant darkness. Similarly, at the time of the winter solstice, the Arctic Circle remains in the dark, whilst the sun shines constantly in the area enclosed by Antarctic Circle.

A solar year, sometimes known as a tropical year, is the period of time it takes for one revolution of the Earth around the sun between successive vernal equinoxes. This comes out at 365.242199 mean solar days. This period of time is influenced by precession, the regular wobble that occurs on the earth’s axis. However, a sidereal year, which is measured using the Earth’s position in relation to other stars, isn’t affected by precession and comes out at the lower figure of 365.25636 days.

The Moon

The moon is only 384,400 km away, its gravitational pull determining the tides on Earth. Its orbit around the Earth takes 27 days, 7 hours and 43 minutes. The movement of the moon has no relation to that of the sun. In fact, it takes 19 years, that’s 235 lunar months, a period known as the Metonic cycle, for the phases of the moon to occur on the same days as in the previous cycle.

The interval from one new moon to the next, known as a synodic month or more commonly as a lunar month, is about 29.53 days.

Lunar and Solar Calendars

A lunar calendar breaks time up into lunar months. Most calendars of this type use months of 29 or 30 days, which goes some way to fit the months into the phases of the moon. Unfortunately, 12 lunar months only cover a period of 354.36 days, which is almost 11 days short of a solar year.

The simplest solution to this problem is that used in true lunar calendars, such as the Islamic calendar, where the months are allowed to ‘slide’ in relation to the solar year, although this is very inconvenient for working out periods of time.

Some cultures get round this difficulty by adding an inter-calendar period at the end of each year, the length of which may need to be adjusted on a periodic basis. One example of such a luni-solar calendar is the Hebrew calendar, in which each month is aligned with a new moon, but a leap month is introduced after the last month to ensure that the whole period fits into the solar year.

The problem can also be neatly avoided by employing a solar calendar, where the phases of the moon are entirely disregarded and the year is fixed to the movement of the sun, invariably requiring occasional leap days to make up for the fact that a year actually lasts 365.242199 days, or to put it another way, 365 days, 5 hours, 48 minutes and 46 seconds.

World Calendars

The following two calendars form the basis of recording dates in the Western world:-

Gregorian

This system, used in the Western world, was introduced by Pope Gregory XIII on October 15, 1582, replacing the older Julian calendar (see below), requiring October 4 of that year to be followed by October 15. The new calendar was in use in the United Kingdom by 1752 and in Russia by 1918.

The calendar is solar, using the following familiar month names:

whose lengths can be memorised using the rhyme:-

30 days hath September,

April, June and November.

All the rest have 31,

Except February with 28 days clear

And 29 each leap year.

This gives a total of 365 days in a normal year and 366 in a leap year. The Gregorian calendar has 97 leap days in every 400 years, normally requiring a leap year every year that’s divisible by four. However, at the end of a century (where the year ends in two zeros) a leap year must be divisible by 400. The leap day itself is inserted at the end of February, the second month of the year.

• Using a leap year every fourth year gives 100 leap years in every 400 years. However, the ‘dropping’ of the three leap years from non-divisible ‘century’ years reduces this to 97.

The average length of a year in the Gregorian system is 365.2425 days, which is very close to the solar year of 365.242199 days, being accurate to one day in every 2,800 years. In practice, minor adjustments are made every few years.

Finding the date of Easter sunday is complicated. The Council of Nicaea of 325 AD defined it as the first Sunday after the first full moon following the vernal equinox. This occurs after March 21, although should this fall on the actual sunday the date moves on to the next Sunday. To add to the complexity, April 19 is always used instead of April 26 and April 18 is sometimes used in place of April 25. It’s also worth noting that the date of this new moon is set by the moon’s hypothetical position, as defined by the ecclesiastical calendar, which places it one or two days later than the real new moon.

The dates of other Christian events are calculated by subtracting or adding days in relation to Easter sunday, as shown in the following table:-

Julian

This calendar, first introduced by Gaius Julius Caesar in 46 BC, was established in the Christian world following the Council of Nicaea in 325 AD. Today, very few people use it, apart from some Greek Orthodox groups who employ it to determine the dates of religious events.

Although almost identical to the Gregorian calendar, this system uses a leap day every four years, so that every year lasts 365¼ days, which is around 11 minutes too long. As a result, the solstices drift in relation to the calendar over time, culminating in an error of one day in every 128 years.

By 1582, when much of Europe adopted the Gregorian calendar, the vernal equinox, originally set to March 25, had shifted itself back to March 11. To fix this, the new calendar dropped ten days and set the equinox at March 21. By 1752, when Britain adapted the Gregorian calendar, things were no better: the country was 11 days behind the Continent, who had already adopted the new system.

• The suffix OS is sometimes used on dates using the Julian calendar, OS meaning Old Style. Similarly, Gregorian dates are known as New Style and have the suffix NS.

The numbering of years, as used the Gregorian system, has caused confusion, especially during the millennium. The year AD (Anno Domini) 1, sometimes known as 1 CE (Common Era), is immediately preceded by 1 BC (Before Christ), also known as 1 BCE (Before Common Era), there being no year zero. On this basis, the year of the millennium should have been 2001.

• The Julian calendar shouldn’t be confused with Julian date, also known as Julian day, a count of days since January 1st, 4713 BC, which is believed to be the start of the Egyptian calendar (Scalinger-Era). The Julian day for 1 January, 2000 comes out as 2,451,545.

The most common of the other world calendars are listed in alphabetical order as follows:-

Bahá’í

Unlike other calendars that use 12 months in each year, the Bahá’í system, which is a solar calendar, employs 19 months, each of 19 days. In addition, the years follow the 19-year cycle of the Báb, an important element of the Bahá’í faith. The months and days have the following names:-

An extra inter-calendar period called Ayyam-i-Ha is inserted after Mulk and is often treated as an extra short month. The years are named as follows:-

Chinese Lunar

This ancient and obsolete calendar is based on a 60-year cycle, with 12 months of 29 or 30 days, with an extra month interposed after each half cycle. Years are counted from 2637 BC.

Chinese Luni-Solar

This calendar is still used in China, although the Gregorian calendar was adopted in 1912, the first year of the Chinese Republic, with years numbered from this date. The months and years of the older luni-solar calendar are fixed to the sun and moon, with each month starting on the day of a new moon in Beijing. The months are numbered from 1 to 12, or 13 where a leap month is required. A leap month is defined as not containing a solar term, meaning that the longitude of the sun isn’t a multiple of 30° during the month. The winter solstice is located in the 11^th month (including leap months) of the previous year, making it tricky to calculate the day of the Chinese New Year.

Coptic

This solar calendar, based on the ancient Egyptian solar calendar, is used by Christian Copts, who are descendants of the people of the Pharaohs. It has 12 months, each of 30 days, named as follows:-

The calendar is aligned to the solar year by introducing an inter-calendar period, often treated as an extra short month and known as al-Nasi. This follows the month of Misra and has a length of five or six days. These days, also known as epagomenal days, were also used in the ancient Egyptian calendar.

Ethiopic

Employed in Ethiopia, this calendar is basically the same as the Coptic calendar (see above) but begins on a different year and employs the following month names:-

plus an inter-calendar period or extra short month called Paguemen, relating the the epagomenal days of the old Egyptian calendar.

Hebrew

This luni-solar calendar is used by Israel and the Jewish faith. The year is aligned to the solar year, although the months normally match the phases of the moon. The 12 months of a common year are:-

each having alternately 29 or 30 days, giving a total of 354 days, which is 11 days short of a year. To keep alignment with the solar year, a thirteenth month of 29 days, known as Adar II or ve Adar, is added every second or third year during the calendar’s 19-year cycle. This occurs seven times in the cycle, when Adar is renamed as Adar I.

The order of months shown here is that employed for the ecclesiastical calendar, with Nisan (occurring in March or April) as the first month, corresponding to the seventh month in the civil calendar. This means that the Jewish New Year, known as Rosh Hashanah, is at the beginning of Tishri, whilst the festival of Yom Kippur is on the tenth day of the same month.

Leap days are used to adjust the length of Heshvan or Kislev, so as to ensure that Yom Kippur is on a Saturday and Hoshana Rabba is on another day, and to correct the overall length of the calendar. For example, of the common years, as described above, a regular year has 354 days, an abundant year, also known as a perfect year, has 355, whilst a deflective year has only 353. In leap years, however (see above), the number of days can be 383, 384 or 385 respectively.

The Hebrew calendar begins in 3760 BC, corresponding to the Biblical date of creation.

The Jews have also given has the non-lunar concept of the week, which originated in the Babylon empire and consists of seven days. The Jewish version incorporates a special seventh day, the ‘day of rest’ now known as Saturday. Although this concept was transferred by Christian communities to the sunday of each week, many Christians also consider this day to be the first day of the week.

Hindu Lunar

This luni-solar calendar finds the start of each month and number of day from the motion of the moon, the names of the months matching to the longitudinal position of the moon at the middle of the month. The month names are:-

As with the Hindu Solar calendar there are two versions of this calendar, the first based on the calculated length of the solar year, the second on the Surya-Siddhanta algorithms for lunar motion (see below). Occasional leap months are inserted should a new moon occur while the sun is in the same astrological sign of the heavens. Very rarely, when the sun travels through a sign between new months, a month is skipped

Unlike other calendars, which normally count day numbers from 1, each day is numbered according to the phase of the moon at sunrise, each lunar day being ¹⁄30 of a lunar month. As a consequence, with a lunar month being slightly less than 30 days, some days are skipped.

With the later version of the calendar, some days can also be ‘duplicated’ as a result of variations in the lunar month caused by the Earth’s rotation around the sun. Such days are identified using a double-quote mark or called a second day, as in ‘second 10 in Sravana’.

Hindu Solar

This calendar uses the following month names, also known as houses of the zodiac:-

each of 30 or 31 days.The oldest version of this calendar, as used in astrology, is based on the mean motion of the sun. Amazingly, the ancient Hindus calculated a solar year to be ^1577917500⁄4320000 days, which is accurate to about three minutes. The later version of the calendar is based on the 1,000-year old Surya-Siddhanta algorithms, which are used to accurately locate the position of the sun.

Indian Civil

In order to unify the different calendar systems used through India, the National Calendar of India was created in 1957. The dates of this calendar roughly correspond to the Gregorian calendar, using 30 or 31 days in each month, although the years are counted from AD 78.

Islamic

Unlike many systems, this a strictly lunar calendar, which is used by Muslims and Islamic countries. The start of each month is found by observing the phase of the moon, which means the actual date can vary by up to two days. The 12 months, alternately of 30 and 29 days, are named as follows:-

giving a calendar year of only 354 days, although a leap day is added to the last month of each second and third year. Since the calendar isn’t linked to the solar year, the months drift backwards through the seasons, making a complete cycle in 32½ Gregorian years, corresponding to approximately 33½ Muslim years.

The Islamic calendar begins on July 16, 622 AD, corresponding to the flight of Mohammed from Mecca to Medina. For this reason, Islamic dates may carry the suffix AH, meaning ‘after the Hegira’.

Mayan

This is only of historical interest, since the following three calendars are no longer used:-

Long Count

A simple count of days, beginning on 6 September 3114 BC (Julian), which was used for recording events. Each day is known as a Kin, multiples of which were expressed using the following units

Haab

This civil calendar consists of 365 days, roughly aligning itself with the solar year. It consists of the following 18 months, each consisting of 20 days:-

with an inter-calendar period of 5 days after the last month and known as Uayeb, often treated as a short month. The Haab years aren’t numbered.

Tzolken

This religious calendar has interlocked cycles of 13 days in 20 names. The names are:-

In this very strange system both cycles rotate at the same time, meaning for example, that the date of 4 Ik is followed by 5 Akbal. Combining this with the Haab calendar gives a cycle of around 52 years.

Persian

This solar calendar is used in Iran, and also in a different form in Afghanistan. It employs the following names for its 12 months:-

A leap day is instead into the month of Esfand to keep alignment with the solar year.

References

1997 Grolier Multimedia Encyclopedia, © 1997, Grolier Inc.

IBM World Book 1999 Encyclopedia Standard Edition, IBM

World Calendar documentation, 1998, In Phase Consulting

©Ray White 2004.