Peter's Index Peter's Index   Astronomy Home       Peter's Astronomy Pages

Calendars

by

Peter Eyland

 

Introduction

 

The regularity of a swinging pendulum is based on physical law.  A pendulum can be used in a clock to objectively measure an instant in daily time or to determine the time between events.  However as E.G. Richards wrote, a calendar is a more subjective device that, "enables us to label the days in the past and in the future and to arrange them all in order"[1].  Thus it is a human invention that enables us to mentally link past events and plan for future activities.

 

Calendars are mainly based on three features of nature: the Sun’s apparent daily motion, the Moon’s monthly phases, and the Earth’s yearly seasons.  There is also the movement of the stars in the night sky that relates to daily, seasonal and yearly cycles.  As these do not have a simple mathematical relationship with each other, there are many calendars that are in use today.

 

Calendars seem to have their origin in religious, agricultural and government needs.  Sometimes three separate calendars for each of these areas were used at the same time, as happened, for example, in ancient Egypt.  Be selective in reading the following information and choose the areas of your interest.

 

Astronomical Background

The Solar Day

 

On the Earth, each day the Sun appears to rise somewhere in the Eastern sky and set in the Western sky.  In the Southern hemisphere the Sun tracks in a circular arc through the Northern part of the sky in an anti-clockwise direction[2]. A complete Solar day occurs when the Sun has moved from one position in the sky, e.g. noon, through the night-time and back to that same initial position. The word "day" can describe the complete period or just the bright time.

 

Some cultures start the day when the Sun has set and they tend to have Moon oriented calendars.  Other cultures start the day with sunrise and tend to have calendars related to the position of the Sun at sunrise.  The Romans started their day at mid-night and that is the most accepted position today.  Only one calendar does not have the solar day as its basic unit and that is an Indian one[3].

 

The Sun and the Seasons

 

The yearly seasons are determined by the number of hours the Sun appears in the sky each day.  In the Summer season, the Sun is above the horizon for more than 12 hours each day.  In the Winter season, the Sun is above the horizon for less than 12 hours each day.

 

The number of hours that the Sun is above the horizon is determined by where it rises at dawn and how high it rises in the sky.  To illustrate this consider Sydney, NSW, Australia, which is at Latitude 34o South. 

 

Around September 23rd, the Sun will rise due East at dawn and then by noon will be 34o down from the zenith (as shown below).  This is called the Spring equinox when the length of the daylight is the same as the night-time (12 hours each).  It is the traditional start of the Spring season in the Southern hemisphere[4].

 

 

As Spring days continue from September, each dawn, the Sun will be seen to be rising further towards the South.  It then follows an increasingly longer arc through the sky and will be at higher angles at Noon.

 

 

As shown in the diagram above, around the 21st of December the Sun rises at its most Southerly position and there is the longest period of daylight.  This day is called the Summer solstice because the Sun appears to "stand still" from its dawn Southerly movement. It is the traditional start of the Summer season[5].

 

As Summer days continue from December, the Sun will rise less Southerly each dawn, and by the 21st March, the Sun will again be rising due East (as shown below).  This is called the Autumnal equinox for the Southern hemisphere.

 

 

Autumn days continue from March.  Then around the 21st June, the Sun is rising at its most Northerly position and there is the shortest period of daylight (as shown below). This time is called the Winter solstice because the Sun appears to "stand still" from its dawn Northward movement. It is the traditional start of Winter.

 

As Winter days continue from June, each dawn, the Sun rises less Northerly as shown below.  Around September 23rd, the Sun will again rise due East and Spring arrives.  This completes the yearly cycle of the seasons.

 

A summary diagram of the Sun’s movement at equinoxes and solstices is shown below. The green arc shows the Sun’s path through the sky at the times of the two equinoxes.  The longer red arc shows the Sun’s path for the Summer solstice and the shorter blue arc shows the Sun’s path for the Winter solstice.

 

Ancient megaliths like Stonehenge seem to record the orientations of these sun risings and settings.  The day of the year on which the equinoxes and solstices occur varies slightly because the length of the year is longer than 365 whole days.  When measured a little more accurately, the Solar year is 365.2422 days long[6], i.e. just under 6 hours longer than whole days.  Any greater accuracy than this is not useful because the Earth’s motion is not constant and always changing slightly.

 

Thinking in terms of the Earth’s movement around the Sun, when looking down at the South Pole from space, the Earth revolves in a clockwise manner around the Sun (and also rotates clockwise).  The seasons are caused by a 23.5o tilt of the Earth’s axis (as shown below).  Summer happens in the Southern hemisphere when the geographic South Pole tilts towards the Sun.

 

 

The Earth revolves in an elliptical path around the Sun.  On January 3rd the Earth is closest to the Sun and on July 4th the Earth is furthest from the Sun.

 

The Moon and the Months

 

The Moon changes its appearance every night.  For example, as illustrated below, in about seven days it grows from a slightly illuminated crescent (new Moon) to a half Moon (first quarter), then another seven days or so gives a full Moon.  Around seven days later, the full Moon has diminished to a half Moon on the other side (last quarter), then another seven days or so, to a crescent and finally disappears before the next new Moon starts a new cycle.

 

 

These changes in appearance are known as the phases of the Moon.  The phase of something tells you how far you are through a complete cycle.  A Lunar, or Synodical month is the number of days between seeing the same phase.  When measured accurately enough a lunar month is 29.53 days long.

 

Thinking in terms of the Moon’s movement around the Earth, just before a new Moon appears, the Moon appears dark because it is between the Earth and the Sun (as shown below) and no illuminated part of the Moon is seen from Earth.  If the Moon orbited in the same plane as the Earth around the Sun, the Sun would be eclipsed every month, but the Moon’s orbit is in a slightly inclined plane, making eclipses of the Sun rare.

 

tIME chunklen 7 ignored:
ASCII: ......
HEX: 07D5080D0D1218

 

The basic problem in making a calendar is that there are 365.2422 days in a Solar year and 29.53 days in a Lunar month[7].  These numbers are not simple multiples of each other and give 12.37 lunar months in a year[8].

 

Choosing to make the Solar year the basic unit means abandoning 12 Lunar months in a year, as in the Common or Gregorian calendar.  Choosing to make 12 Lunar months the basic unit means the seasons move through the year, as in the Muslim calendar.  A compromise was a Lunisolar calendar, where extra Lunar months were added from time to time to keep the months roughly in step with the Solar year, as in the ancient Greek and Jewish calendars.

 

The stars and the year

 

The stars can also be used to fix the start of the year.  They are seen to move from East to the West in the night sky.  In the Southern Hemisphere, the stars rotate clockwise through the night around a point in the sky called the South Celestial Pole (SCP).  In the diagrams below[9], this rotation is shown between April 17th 2012 at 8:30 pm and two hours later around 10:30 pm when Sirius would be about to set in the West.

 

 

 

Note that looking up into the diagrams of the sky towards the South Celestial Pole, East is on the left hand side and West on the right.  The long axis of the constellation called the Southern Cross (Crux) points towards the South Celestial Pole.

 

The diagram below gives the perspective of looking down on the South Pole of the Earth (blue circles) as it revolves clockwise in its orbit around the Sun (orange circle).  The distant stars are so far away that they provide a convenient reference direction.

 

 

As the Earth moves from its noon position at the bottom of the diagram, it rotates clockwise in its orbit and position 1 represents one complete rotation with respect to the fixed stars. This time period is called one Sidereal day, from the Latin word sidereus meaning "of the stars".  The stars rotate completely through the sky (i.e. through 360o) in one Sidereal day.

 

It takes a little longer for the Earth to rotate to position 2 where the Sun is back to its noon position and one Solar day has elapsed.  The Solar day is defined as 24 hours long and a Sidereal day works out to be shorter by about 4 minutes[10]. 

 

Thus, because of the time difference a Sidereal day and a Solar day, the stars appear to slip Westwards every night by about 4 minutes.  To get back to their initial position again requires the accumulation of those 4 minutes to add up to one Sidereal day.  This is worked out by dividing the number of minutes in one Sidereal day by the 4 minute time slip.

 

A Sidereal year is the period of time for the stars to slip and then return to an initial position in the sky.  The calculation given above makes the Sidereal year to be 365.25636 days[11], which is about 20 minutes and 23 seconds longer than a Solar year (365.2422 days).

 

 

It actually doesn’t work out as neatly as that, because the Earth has a few wobbles in its orbit and the stars’ positions at the seasonal equinoxes are changing slightly every year[12].  In Babylonian times 2,500 years ago, the zodiac sign Aries matched the dates 21st March – 19th April, i.e. it was positioned with the Sun at the Northern hemisphere Spring equinox.  The stars have moved since then and the zodiac sign Aries would now be 19th April – 4th May and  the equinox occurs in the constellation of Pisces.  These details were known to some of the ancients but not used in any calendars.

.

 

 


Calendars and Religion

 

Emile Durkheim wrote that "religion is an eminently social thing"[13] and the purpose of religious rites within social groups "is to evoke, maintain, or recreate certain mental states"[14].  He argued that this necessarily differentiates time to produce recurring festivals and ceremonies.  Thus he said that a "calendar expresses the rhythm of collective activity while ensuring that regularity"[15].  He noted that "animals have no representation of this kind"[16].

 

Walter Burkert wrote similarly of the ancient Greeks that their religious practices were "concentrated on the festivals, heortai[17], which interrupt and articulate everyday life"[18].  In other words, a festival defined times like a sanctuary defines space[19].  For the ancient Greeks the calendar was built on Lunar months with arbitrary repeats of a month when it was needed to match the seasons, i.e. they were unregulated Lunisolar calendars.  Even though the various Greek tribes had different details, their 12 months were named after festivals to 12 gods.  Drawing attention to this, Burkert wrote that it "is remarkable how little the calendar takes account of the agricultural year"[20].  In particular, there was no month named for sowing, harvest or grape gathering[21].  The festivals had three aspects to them: sacrifices (i.e. shared barbeques), music and drama, and athletic contests or games (called "agones"[22]).

 

Mesopotamia

 

By contrast, in Mesopotamia, the names of the months "were derived from agricultural activities and seasonal phenomena"[23].  There were two seasons in Mesopotamia, "Planting" (Autumn and Winter) and "Harvesting" (Spring and Summer).  In Babylonia the names of the month seem to have been called activities like "sheep shearing" or "ploughing"[24].  The Babylonians had 12 Lunar months in a year, as records from about 2400 BCE show, and inserted an extra month from time to time.  This was to keep the barley harvest (which occurred at the end of our May) within the first month of the year. To ensure there was enough food in the kingdom, it was the Babylonian king’s responsibility, at the beginning of the year, to offer the first fruits of the harvest to the gods.[25]

 

Eventually the unregulated addition of months (called "intercalation") gave way to a formal structure over 19 years, as described and adopted by the Greek named Meton[26].

 

Table of the Metonic Cycle

 

The "Metonic cycle" is based on 235 Lunar months in 19 Solar years[27].  With generally 12 Lunar months in a year there were also 7 years with 13 months, as shown in the table above.  An initial allocation of 30 days per month made them too long, so one day was dropped every 64 days[28].  The table shows the result with the months generally alternating between 29 and 30 days, except for the consecutive 30-day months highlighted in yellow.  The average month length defined this way was 29.5319 days, compared with the modern value of 29.5306 days.

 

Egypt

 

The Egyptian calendar had three seasons.  The Egyptian year began at the end of August when the Nile started flooding, so the first season was called "akhet" (Inundation).  Then starting in late December, as the waters receded, came "peret" (Emergence) and then in late April came "shemu" (Dryness)[29].  What differed with this Egyptian calendar was that it ignored the Lunar months and instead had 12 months of 30 days each, with an extra 5 or 6 day "epagomenal" holiday period to keep the year in step with the seasons[30].  Each month had three periods of 10 days each that were called "decans".

 

The Egyptians later introduced a 24-hour day and adopted a Mesopotamian 7 day week[31].  In the order of their cycles, from longest period to shortest, the 7 "planets" of the ancient world were Saturn, Jupiter, Mars, The Sun, Venus, Mercury, and the Moon[32].  As shown below, each of these seven gods was deemed to govern particular hours through each 24-hour day.  The first hour of the first day was given to Saturn, and the second hour of the first day was given to Jupiter, and so on until the first day ended with Mars in hour 24.  The Sun, as the next in order, governed the first hour of the second day and gave its name to that day.  Continuing this allocation through the week gave the name order: Saturn, Sun, Moon, Mars, Mercury, Jupiter and Venus.  The names Saturday, Sunday and Monday should be clear in their origin from Saturn, The Sun and the Moon.  Tuesday comes from the Norse god Tiw, who was identified with Mars, Wednesday from Wodin (Mercury), Thursday from Thor (Jupiter) and Friday from Frigg (Venus).

 

Table 21.1 from E.G. Richards:  Assignment of planets to the hours of the day

Hour

Day 1
Saturday

Day 2
Sunday

Day 3
Monday

Day 4
Tuesday

Day 5
Wednesday

Day 6
Thursday

Day 7
Friday

1

Saturn

Sun

Moon

Mars

Mercury

Jupiter

Venus

2

Jupiter

Venus

Saturn

Sun

Moon

Mars

Mercury

3

Mars

Mercury

Jupiter

Venus

Saturn

Sun

Moon

4

Sun

Moon

Mars

Mercury

Jupiter

Venus

Saturn

5

Venus

Saturn

Sun

Moon

Mars

Mercury

Jupiter

6

Mercury

Jupiter

Venus

Saturn

Sun

Moon

Mars

7

Moon

Mars

Mercury

Jupiter

Venus

Saturn

Sun

8

Saturn

Sun

Moon

Mars

Mercury

Jupiter

Venus

9

Jupiter

Venus

Saturn

Sun

Moon

Mars

Mercury

10

Mars

Mercury

Jupiter

Venus

Saturn

Sun

Moon

11

Sun

Moon

Mars

Mercury

Jupiter

Venus

Saturn

12

Venus

Saturn

Sun

Moon

Mars

Mercury

Jupiter

13

Mercury

Jupiter

Venus

Saturn

Sun

Moon

Mars

14

Moon

Mars

Mercury

Jupiter

Venus

Saturn

Sun

15

Saturn

Sun

Moon

Mars

Mercury

Jupiter

Venus

16

Jupiter

Venus

Saturn

Sun

Moon

Mars

Mercury

17

Mars

Mercury

Jupiter

Venus

Saturn

Sun

Moon

18

Sun

Moon

Mars

Mercury

Jupiter

Venus

Saturn

19

Venus

Saturn

Sun

Moon

Mars

Mercury

Jupiter

20

Mercury

Jupiter

Venus

Saturn

Sun

Moon

Mars

21

Moon

Mars

Mercury

Jupiter

Venus

Saturn

Sun

22

Saturn

Sun

Moon

Mars

Mercury

Jupiter

Venus

23

Jupiter

Venus

Saturn

Sun

Moon

Mars

Mercury

24

Mars

Mercury

Jupiter

Venus

Saturn

Sun

Moon

The regent of the day is the planet assigned to the first hour (6 a.m.). The day takes its name from the regent.

 

The Week

 

The word week comes from "wice" in Old English, indicating "a turning" or "succession" of days.  As previously indicated, the Egyptians initially had a 10-day week.  The French Revolution of 1792 and the Russian Revolution of 1917 also saw the introduction of a 10-day week, but the authorities were forced to change back to a 7-day week because people were afraid of what would happen to them if they did not turn up in church on Sundays, or they opened their shops on Sunday.  The seven-day week has now been so entrenched in the Jewish, Christian and Muslim calendars that any attempt to change the 7-day cycle will meet with considerable religious opposition.

 

The Romans had an 8-day week of market days, called "nundinae", which they inherited from the Etruscans[33].  They were labeled from A to G.  This was in addition to their complicated designation of Lunar month days (kalends, nones and ides), which counted up from a New Moon and then counted down towards the next one[34].

 

In Central America there was a 9-day cycle because there were 9 lords of the night and a 13-day cycle for the 13 lords of the heavens. The Baha'i religion has a 19-day cycle. There was also a 20-day cycle among Yucatec Maya and Nahuatl from their base-20 number system[35].

 

There have been many different week lengths throughout history, ranging from 4 days to 20 days.  The common 7-day week seems to have its origin in being roughly one quarter of a Lunar month.  There is also deep religious meaning from ancient texts describing creation.

 

The Chinese Calendar

 

For the Chinese Emperor, e.g. Yao Tien, the intentions of Heaven were vital for his rule and the prosperity of the state.  Chinese Astrologers used a "Lunar Zodiac", with the sky divided into 28 Equatorial Hsiu or Lunar Mansions, which represented each day of a Lunar month[36].

 

Calendars were also important and the Chinese have (among others) a Lunisolar calendar and a Solar one[37]. The Solar calendar is fixed to the equinoxes and solstices, with the year divided into 24 periods of 15 or 16 days that are called Qi or Ch’i (fortnights, seasons, vapours, aura).  These are the closest equivalent to the Western zodiac, but also represent the 12 musical notes of the chromatic scale – 12 ascending then 12 descending[38].

 

Table from D.Walters: the Twenty-Four Ch’i, or Solar Periods

Ch’i

Seasonal effect

Stellar alignment

Li Ch’un

Spring starts

Midpoint of Aquarius

Yu Shui

Rain water

Sun enters Pisces

Ching Chih

Insects waken

Midpoint of Pisces

Ch’un Fen

Spring equinox

Sun enters Aries

Ch’ing Ming

Clear and bright

Midpoint of Aries

Ku Yu

Corn rain

Sun enters Taurus

Li Hsia

Summer starts

Midpoint of Taurus

Hsiao Man

Corn sprouting

Sun enters Gemini

Mang Chung

Corn in ear

Midpoint of Gemini

Hsia Chih

Summer solstice

Sun enters Cancer

Hsiao Shu

Little heat

Midpoint of Cancer

Ta Shu

Great heat

Sun enters Leo

Li Ch’iu

Autumn starts

Midpoint of Leo

Ch’u Shu

Heat ends

Sun enters Virgo

Pai Lu

White dew

Midpoint of Virgo

Ch’iu Fen

Autumn equinox

Sun enters Libra

Han Lu

Cold dew

Midpoint of Libra

Shuang Chiang

Frost descends

Sun enters Scorpio

Li Tung

Winter starts

Midpoint of Scorpio

Hsiao Hsueh

Little snow

Sun enters Sagittarius

Ta Hsueh

Great snow

Midpoint of Sagittarius

Tung Chih

Winter solstice

Sun enters Capricorn

Hsiao Han

Little cold

Midpoint of Capricorn

Ta Han

Great cold

Sun enters Aquarius

 

The Lunisolar calendar always has the New Moon on the first day of a month, and the Full Moon on the 15th day and uses a form of the Metonic cycle.  To keep the year in step with the seasons, New Year’s Day is chosen to "occur on the first day of the first or second New Moon after the [Northern Hemisphere] Winter solstice"[39]. The Winter solstice is always in the 11th month.  Similarly, the Spring equinox is in the 2nd month, the Summer solstice is in the 5th month, and the Autumn equinox is in the 8th month.

 

In addition to the Lunisolar and Solar calendars, the Chinese have a concurrent 10-day and 12-day cycle, which gives a 60-day cycle of binomes[40].  The 10-day Heavenly Stems cycle has these names[41]: Chia, I, Ping, Ting, Wu, Chi, Keng, Hsin, Jen, and Kuei. The 12-day Earthly Branches cycle has these month names (given with their auspices): Tzu (Start), Ch’ou (Close), Yin (Establishing), Mao (Dividing), Ch’en (Filling), Ssu (Equating), Wu (Fixing), Wei (Regulating), Shen (Breaking), Yu (Danger), Hsu (Perfecting), and Hai (Receiving).  Thus Jen Wu is the 19th day of the 60-day cycle, as shown in the table below.  Six cycles of 60 days approximate the Chinese year.

 

Stems and Branches

1

Chia

Tzu

16

Chi

Mao

31

Chia

Wu

46

Chi

Yu

2

I

Ch’ou

17

Keng

Ch’en

32

I

Wei

47

Keng

Hsu

3

Ping

Yin

18

Hsin

Ssu

33

Ping

Shen

48

Hsin

Hai

4

Ting

Mao

19

Jen

Wu

34

Ting

Yu

49

Jen

Tzu

5

Wu

Ch’en

20

Kuei

Wei

35

Wu

Hsu

50

Kuei

Ch’ou

6

Chi

Ssu

21

Chia

Shen

36

Chi

Hai

51

Chia

Yin

7

Keng

Wu

22

I

Yu

37

Keng

Tzu

52

I

Mao

8

Hsin

Wei

23

Ping

Hsu

38

Hsin

Ch’ou

53

Ping

Ch’en

9

Jen

Shen

24

Ting

Hai

39

Jen

Yin

54

Ting

Ssu

10

Kuei

Yu

25

Wu

Tzu

40

Kuei

Mao

55

Wu

Wu

11

Chia

Hsu

26

Chi

Ch’ou

41

Chia

Ch’en

56

Chi

Wei

12

I

Hai

27

Keng

Yin

42

I

Ssu

57

Keng

Shen

13

Ping

Tzu

28

Hsin

Mao

43

Ping

Wu

58

Hsin

Yu

14

Ting

Ch’ou

29

Jen

Ch’en

44

Ting

Wei

59

Jen

Hsu

15

Wu

Yin

30

Kuei

Ssu

45

Wu

Shen

60

Kuei

Hai

 

A Chinese "epoch" is 3600 years, i.e. 60 cycles of 60 years.  The 60-year cycle is labeled by Stems and Branches and also sub-divided into 5 "Great Years" of 12 years each[42].  The 12-year names, even though called Branches, have (relatively) recently been given the popularly known animal names[43].

 

The Julian and Gregorian Calendars

 

The second king of Rome, Numa (715 BCE – 672 BCE), seems to have inherited a calendar with only 10 months (March to December) and 304 days long.  How it worked is unknown.  Numa re-organised the number of days in the months and added two months that were originally given 28 days each.  The extra months were February and January in that order, and this gave a 354-day lunar year.  At a later time, January was given an extra day (because even numbers were unlucky) then put before February and moved to the start of the year.  An extra month, named Mercedonius, was then intercalated from time to time to put the year in step with the seasons[44].

 

Table of Old Roman Months

Month name

Number of days

Martius

31

Aprilis

29

Maius

31

Iunius

29

Quintilis (Iulius)

31

Sextilis (Augustus)

29

September

29

October

31

November

29

December

29

Ianuarius

29

Februarius

28

Mercedonius

22/23

 

Julius Caesar (107 BCE - 44 BCE) inherited a calendar in confusion, because by the year 46 BCE the Roman calendar was three months ahead of the seasons.  The new Julian Calendar abandoned any connection with the Moon, changed the month lengths to the current ones and dropped Mercedonius. Every four years became a "leap" year with 29 days in February giving an average year length of 365.25 days.  After Julius Caesar was assassinated Quintilis was re-named July in his honour[45].

 

Inclusive Roman numbering inclined the religious authorities (called "pontifices" or bridge makers) to misunderstand "one in four" and so they inserted February 29 every 3 years.  By 9 BCE the year was 3 days ahead so Augustus ordered no more February 29ths until 8 CE.  Sextilis was also re-named August in honour of Augustus[46].

 

The difference between 365.25 and 365.2422 is about one day in 128 years.  By the time of Constantine, more than 300 years after Augustus, the year was about 3 days ahead of the seasons.  From the 4th century CE, Christmas day was celebrated on the Northern Hemisphere Winter solstice, which by then had moved three days from the 22nd of December to the 25th.  This has never been corrected because of arguments like those of Pope Benedict XVI who said that December 25th was nine months from the day of Jesus’ conception, which he declared to be March 25.

 

As the centuries passed, the date of the Christian Easter became problematic as the full Moon after the Spring equinox got more and more out of step with the tabulated year.  Responding to this, after some 350 years of argument, Pope Gregory XIII (1502 CE – 1585 CE) signed a decree on 24 February 1582 that the calendar be corrected.  The solution was to make centenary years, e.g. 1600 CE, only to be leap years if divisible by 400.  Thus 1700 CE was not a leap year, despite being divisible by 4 as the Julian calendar prescribed.  To implement this reform, the day after Thursday 4th October 1583 became Friday 15th October[47]. 

 

The Gregorian calendar is the Julian calendar with the extra rule about centenary years.  The new calendar was implemented at different times in different countries. The Orthodox Christian Church adopted a revised Julian calendar in 1923 by dropping 13 days and implementing a slightly different rule about centenary years. The anniversary of the Russian Revolution in October 1917 now occurs in November.

 

The Jewish Calendar

 

Evidence from the 10th century BCE is that the calendar was Lunisolar, and likely had months starting with a sighting of the New Moon.  The known month names from that period are the 1st month "Abib" (new fruits?), 2nd month "Ziv" (flowers?), 7th month "Ethanum" (fruits?) and 8th month "Bul" (rain?). These suggest a year starting in the Autumn.  The year had to be adjusted so that a sheaf of barley could to be offered to God on the day after the Passover festival.

 

The Jews adopted the Lunisolar Babylonian calendar after 597 BCE when many Jews were deported to Babylon.  The year now started near the Spring equinox.  The sighting of the New Moon near Jerusalem was needed to verify that the month had started.  After 70 CE when Jews were again deported, this became very difficult.

 

A "definitive theory-based calendar"[48] is often attributed to Rabbi Hillel II in the 4th century, who using a Metonic cycle and a "theoretical Moon" of constant Lunations, came up with a year length of 365.24682 days.  This means that the Jewish year will slip ahead of the seasons by about one day every 216 years.  Various rules give 6 types of year as shown in the table below.

 

TABLE 17.3 The distribution of the days of the year among the months

Month

Common year

Embolismic year

 

d

r

a

D

R

A

Tishri

30

30

30

30

30

30

Heshvan

29

29

30

29

29

30

Kislev

29

30

30

29

30

30

Tevet

29

29

29

29

29

29

Shevet

30

30

30

30

30

30

Adar

29

29

29

30

30

30

Adar II*

--

--

--

29

29

29

Nisan

30

30

30

30

30

30

Iyyar

29

29

29

29

29

29

Sivan

30

30

30

30

30

30

Tammuz

29

29

29

29

29

29

Av

30

30

30

30

30

30

Elul

29

29

29

29

29

29

 

353

354

355

383

384

385

*Adar II is often called Veadar.

Key : the length of the year is indicated by the letter used in the character of the year, which are deficient (d, D), regular (r, R) and abundant (a, A).

 

The starting point of the Jewish calendar is 4 hours 204 chalakim[49] into Monday, 7 October 3761 BCE (Julian calendar).

 

The Islamic Calendar

 

Before the prophet Muhammad (570 CE – 632 CE), the Arabs used a Lunisolar calendar with unregulated intercalations of a month.  There were two "closed" seasons, between the 1st - 7th month and the 11th - 12th month, in which warfare was forbidden.  By using different intercalations, some tribes could attack others without them being prepared. The prophet Muhammad strongly disapproved of this ruse and decreed in 632 CE, that there should be no further intercalations and a strictly Lunar calendar should be used.  At the same time, he allowed that warfare against "infidels" was permissible in any month[50]. As the Islamic year has about 354 days the festivals move through the Solar year.

 

Table 18.1 from E.G. Richards:  The months of the Islamic calendar

 

Name*

Days

Likely derivation ‡

1

Muharram

30

Sacred month; no war

2

Safar

29

Yellow (saffron), autumnal

3

Rabî' I

30

Grazing season

4

Rabî' II

29

 

5

Jumada I

30

Hard, frozen, winter

6

Jumada II

29

 

7

Rajab

30

Sacred month

8

Sha'bân

29

Dispersed, tribes seek water

9

Ramadân

30

Burnt, hot

10

Shawwâl

29

Camels become pregnant

11

Dhu'l-qu'da

30

Sacred month, time of truce

12

Dhu'l-hejji

29

Sacred month, time of pilgrimage

*The spelling of the transliteration of these names varies quite widely.

‡ The original meanings of the months lost their seasonal connotation when intercalations were abolished.

 

The last month in "kabisah" or "embolismic" years has 30 days.  This one-day intercalation occurs in years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 and 29 of a 30-year cycle[51]. 

 

Al-Biruni (973 CE – 1048 CE) "seems to have believed in the tangible and scientifically detectable powers of astral influence"[52].

 

 

Eras

 

In the earliest times, the years were simply named by notable events that happened in them.  Later a Regnal dating system emerged by numbering years from the first month that started the year after a new king’s accession[53].  Assyrian king lists mark time from the end of the 3rd millennium BCE to the middle of the 1st millennium, and "synchronous lists set the reigns of Assyrian and Babylonian kings in parallel"[54].  China also used Regnal years, but now Western writers date years continuously from the reign of the Yellow Emperor, (Huang Di) given as either 2637 BCE or 2697 BCE[55].

 

The Ancient Greeks measured their years in Olympiads, which were 4-year cycles that allegedly started from 776 BCE.  This was in use from the 4th century BCE until the 4th century CE.  The 3rd year of the 6th Olympiad (Ol. 6,3) marks 23 years from the first Olympic games and equates to the year that the City of Rome was founded[56].

 

The Romans used Consular dating at first.  This means the year was identified by the names of the two Roman Consuls that were appointed each year.  Justinian ended this practice in 541 CE by not appointing Consuls and instituted Regnal dating.  Marcus Terentius Varro introduced a new method of dating in the first century BCE by dating years from the founding of the city of Rome.  The founding of Rome was taken to be 753 BCE.  These dates were abbreviated as AUC from "anno urbis conditae" which translates as "in the year of the founded city".  Thus 607 CE is AUC 1360.  The start of an AUC year was initially on April 21st, but modern historians simply use January 1st.

 

 

Diocletian started a reign of terror for Christians and a later consequence was that Christians inaugurated the "Era of Diocletian", also called the "Era of Martyrs", by dating events from 29th August 284 CE[57].  The 29th August was New Year’s Day by the Julian calendar in Egypt.  It was in use up to year 887 of the Era of Diocletian, or AD 1170.

 

Dionysius Exiguus ("Short Dennis") set out to introduce a new set of tables for Easter using a 95-year cycle of months (i.e. 5 Metonic cycles)[58].  In 525 CE he inaugurated a new "Christian Era".  History was divided, by a calculation of the birth of Jesus, into "Anno Domini" i.e. AD (in the year of our Lord) and "Before Christ" i.e. BC. There was no year zero and he seems to have made some mistakes in his calculations.  The widely used "Common Era" takes over Christian dating, but uses the designations "Before the Common Era" (BCE) and "Common Era" (CE).

 

Caliph Umar I set up the Islamic calendar to start from 16th July 622 CE (Julian calendar). Dates after this year are designated AH from "Anno Hegirae" i.e. in the year of the Hijra.  The actual date of prophet Muhammad’s Flight from Mecca to Medina or his arrival in Medina is not known and probably happened a couple of months later than July.  Umar wanted a seamless change between the old-type year with its intercalations and the new-type year without intercalations.  He selected 9th April 631 CE as the end of the old type and the start of the new one.  Calculating 9 years back from this date using no intercalations, he arrived at 16th July[59].

 

The Hindu calendar calculates dates from the 18th February 3102 BCE in the proleptic Julian calendar.  It represents the start of the Kali Yuga.  The Indian National calendar has a zero year in 78 CE.

 

The Jewish calendar sets the beginning of the world in 3761 BCE, so dating is designated "Anno Mundi" or AM meaning "in the year of the world".  This was first used by Maimonides in 1178 CE, though Jews have had calendars from much earlier.

 

Final Word

 

There are 365.2422 days in a Solar year and 29.53 days in a Lunar month giving 12.37 lunar months in a year.  Solar calendars abandon 12 Lunar months in a year and align the seasons with the year.  Lunar calendars define the year as 12 Lunar months making the seasons move through the year.  Lunisolar calendars add extra Lunar months either in an unregulated way or follow something like the Metonic 19 year cycle.  The complexities of the numbers meant that many complicated calendars were used throughout history.

 

Calendars seem to have their origin in religious, agricultural and government needs. To demonstrate some sort of control over the food supply kings needed to maintain regular festivals to the gods.  Farmers needed to know when to plant and harvest.  For protection and maintenance, taxes needed to be paid to the ruler.  These factors meant that people needed a calendar to regulate and organise their activities. 

 

Bibliography

 

A. Aveni, "People and the Sky", Thames and Hudson, London, 2008

W. Burkert, "Greek Religion", trans John Raffan, Harvard, Cambridge Massachusetts, 1985

E. Durkheim, "The Elementary Forms of Religious Life", trans K.E.Fields, The Free Press, New York, 1995

J-J. Glassner, "Mesopotamian Chronicles" ed. Benjamin R. Foster, Brill, Boston, 2005

E.G. Richards, "Mapping Time: The Calendar and Its History", Oxford University Press, 1999

MacAstronomica, by Jaques and Alexandre Trottier

D.Walters, The Complete Guide to Chinese Astrology, Watkins, London, 2005



[1] E.G. Richards "Mapping Time: The Calendar and Its History", Oxford University Press, 1999, p3

[2] In the Northern hemisphere the Sun tracks clockwise through the Southern part of the sky. The idea of "clockwise" arises from this motion.

[3] One Indian Luna calendar uses a period of time called a tithi.  It is the mean time between full moons divided by 30, or about 0.984353 days. See E.G. Richards, p.181.

[4] In NSW the starting days of the seasons are set by Parliament.

[5] Though in some cultures it is called mid-Summer’s day.

[6] E.G. Richards, ibid, p.93 gives 365.242190 +- 0.003 days

[7] E.G. Richards, ibid, p.93 gives 29.530589 with a variation of 0.3 days.  Variation in the first decimal place (0.3) makes the numbers following it dubious and shows considerable deviations occur.

[8] 365.2422/29.53 = 12.37 to the two decimal places of the lunation

[9] From the computer program MacAstronomica, by Jaques and Alexandre Trottier

[10] About 3 minutes 56 seconds or 3.9316723 seconds, making the Sidereal day to be 1436.0683 minutes or 23.9345 hours long. See R. Hannah, "Greek & Roman Calendars Constructions of Time in the Classical World", Duckworth, 2005, p.12

[11] 1436.0683/3.9316723 = 365.25636

[12] For more information look up precession, nutation and libration.

[13] E.Durkheim, "The Elementary Forms of Religious Life", trans K.E.Fields, The Free Press, New York, 1995, p.9.

[14] E.Durkheim, ibid, p.9

[15] E.Durkheim, ibid, p.10

[16] E.Durkheim, ibid, p.10.n6

[17] pronounced with three syllables as hay-or-tai

[18] W.Burkert "Greek Religion", trans John Raffan, Harvard, Cambridge Massachusetts, 1985, p 225

[19] W.Burkert, ibid, p.99

[20] W.Burkert, ibid, p.226

[21] W.Burkert, ibid, p.226

[22] pronounced with three syllables as ag-on-es

[23] R.Hannah, ibid, p.27

[24] E.G.Richards, ibid, p.227, but the names seem to be uncertain as different sources give different meanings.

[25] E.G. Richards, ibid, p.147

[26] R.Hannah, ibid, p.52-58

[27] 19 years * 12.37 Lunar months per year = 235.03 Lunar months

[28] 30 * 235 = 7050 days which is 110 days too long for 19 Solar years (6940 days), and 7050/110 = 64. E.G. Richards, ibid, p.95

[29] R.Hannah, ibid, p.86, 89-91, 113, and E.G.Richards, ibid, p.154.  For a web link see for example, http://www.philae.nu/akhet/Seasons.html

[30] There is doubt that the 6th day in "leap" years was ever implemented properly, despite the "decree of Canopus" in 238 BCE that instituted it.

[31] Seven days is a quarter of a Lunar month in practical terms.

[32] Saturn 29 years, Jupiter 12 years, Mars 687 days, Sun, 365 days, Venus 224 days, Mercury 88 days, Moon 29 days

[33] The "nundinae" indicate "between the nines" as the Romans used inclusive numbering. E.G. Richards, ibid, p.275

[34] R.Hannah, ibid, pp.100,101

[35] E.G. Richards, ibid, p.275

[36] D.Walters, ibid, pp,81ff

[37] D.Walters, The Complete Guide to Chinese Astrology, Watkins, London, 2005, pp.51, 52

[38] D.Walters, ibid, pp.52, 54

[39] D.Walters, ibid, p.55

[40] That is, putting two names together. See D.Walters, ibid, pp.60, 74

[41] They are likely to be the names of gods in an ancient ten-day week. See D.Walters, ibid, p.72

[42] Also called the Jupiter cycle, from the 12 years of Jupiter’s circuit. See D.Walters, ibid, p.15

[43] Rat, Ox, Tiger, Rabbit, Dragon, Snake, Horse, Sheep, Monkey, Cock, Dog, Pig.  2012 has the year of the Dragon.

[44] "Mercedonius derives from 'merces' or 'wages' because people were paid for their labour in this season".  E.G.Richards, ibid, p.207

[45] E.G.Richards, ibid, p.214

[46] E.G.Richards, ibid, p.215

[47] These days were selected because there were no important festivals on them. E.G.Richards, ibid, p.251

[48] E.G.Richards, ibid, p.223

[49] Jewish hours are subdivided into 1080 chalaks, making 10 chalakim about three seconds. E.G.Richards, ibid, p.223

[50] E.G.Richards, ibid, p.231

[51] A 30-year cycle has 360 months which is 10,631 days. This gives 10,631/360 = 29.53056 days per Lunar month. Islamic months gain on the mean astronomical Moon by about one day in 2500 Islamic years. E.G.Richards, ibid, p.232

[52] A. Aveni, "People and the Sky", Thames and Hudson, London, 2008, p.183

[53] E.G.Richards, ibid, p.148

[54] Jean-Jacques Glassner,  "Mesopotamian Chronicles" ed. Benjamin R. Foster, Brill, Boston, 2005. p.17.   http://www.livius.org/k/kinglist/assyrian.html

[55] See http://www.chinaknowledge.de/History/Myth/wudi-rulers.html also http://www.math.nus.edu.sg/aslaksen/calendar/chinese.shtml

[56] R.Hannah, ibid, p.150

[57] Diocletian’s accession was actually 20th November 284 CE.  See R.Hannah, ibid, p.154

[58] R.Hannah, ibid, pp.153-7

[59] E.G.Richards, ibid, p.233


Peter's Index Peter's Index    Astronomy Home  top of page  top of page

email Write me a note if you found this useful