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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.
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 |
Day 2 |
Day 3 |
Day 4 |
Day 5 |
Day 6 |
Day 7 |
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
|
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
|
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
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