from
CalendarsFromTheSky Website
Among their other accomplishments, the ancient Mayas invented a
calendar of remarkable accuracy and complexity. At right is the
ancient Mayan Pyramid in Chichen Itza, Yucatan, Mexico. The Pyramid of
Kukulkan at Chichén Itzá, constructed circa 1050 was built during
the late Mayan period, when Toltecs from Tula became politically
powerful. The pyramid was
used
as a calendar: four stairways, each with 91 steps and a platform at
the top, making a total of 365, equivalent to the number of days in
a calendar year.
The Maya calendar was adopted by the other Mesoamerican nations,
such as the Aztecs and the Toltec, which adopted the mechanics of
the calendar unaltered but changed the names of the days of the week
and the months. An Aztec calendar stone is shown at right (below).
The Maya calendar uses three different dating systems in parallel,
the Long Count, the Tzolkin (divine calendar), and
the Haab (civil
calendar). Of these, only the Haab has a direct relationship to the
length of the year.
A typical Mayan date looks like this:

12.18.16.2.6, 3 Cimi 4
Zotz

12.18.16.2.6 is the Long
Count date

3 Cimi is the Tzolkin
date

4 Zotz is the Haab date
What is the Long
Count?
The Long Count is really a
mixed base20/base18 representation of a number, representing the
number of days since the start of the Mayan era. It is thus akin to
the Julian Day Number.
The basic unit is the kin (day), which is the last component of the
Long Count. Going from right to left the remaining components are:
uinal 
(1 uinal = 20 kin =
20 days) 
tun 
(1 tun = 18 uinal =
360 days = approx. 1 year) 
katun 
(1 katun = 20 tun =
7,200 days = approx. 20 years) 
baktun 
(1 baktun = 20 katun
= 144,000 days = approx. 394 years) 


The kin, tun, and katun
are numbered from 0 to 19.

The uinal are numbered
from 0 to 17.

The baktun are numbered
from 1 to 13.
Although they are not part of the Long
Count, the Mayas had names for larger time spans. The following
names are sometimes quoted, although they are not ancient Maya
terms:

1 pictun = 20 baktun =
2,880,000 days = approx. 7885 years

1 calabtun = 20 pictun =
57,600,000 days = approx. 158,000 years

1 kinchiltun = 20 calabtun =
1,152,000,000 days = approx. 3 million years

1 alautun = 20 kinchiltun =
23,040,000,000 days = approx. 63 million years
The alautun is probably the longest
named period in any calendar.
When did the
Long Count Start?
Logically, the first date in
the Long Count should be 0.0.0.0.0, but as the baktun (the first
component) are numbered from 1 to 13 rather than 0 to 12, this first
date is actually written 13.0.0.0.0.
The authorities disagree on what 13.0.0.0.0 corresponds to in our
calendar. I have come across three possible equivalences:

13.0.0.0.0 = 8 Sep 3114 BC
(Julian) = 13 Aug 3114 BC (Gregorian)

13.0.0.0.0 = 6 Sep 3114 BC
(Julian) = 11 Aug 3114 BC (Gregorian)

13.0.0.0.0 = 11 Nov 3374 BC
(Julian) = 15 Oct 3374 BC (Gregorian)
Assuming one of the first two
equivalences, the Long Count will again reach 13.0.0.0.0 on
21 or 23
December AD 2012  a not too distant future.
The date 13.0.0.0.0 may have been the Mayas' idea of the date of the
creation of the world.
What is the Tzolkin?
The Tzolkin date is a
combination of two "week" lengths.
While our calendar uses a single week of seven days, the Mayan
calendar used two different lengths of week:
 a numbered week of 13 days,
in which the days were numbered from 1 to 13
 a named week of 20 days, in which the names of the days
were:
0. Ahau 
1. Imix 
2. Ik 
3. Akbal 
4. Kan 
5. Chicchan 
6. Cimi 
7. Manik 
8. Lamat 
9. Muluc 
10. Oc 
11. Chuen 
12. Eb 
13. Ben 
14. Ix 
15. Men 
16. Cib 
17. Caban 
18. Etznab 
19. Caunac 

The diagram at right shows the day
symbols, in the same order as the table above.
As
the named week is 20 days and the smallest Long Count digit is 20
days, there is synchrony between the two; if, for example, the last
digit of today's Long Count is 0, today must be Ahau; if it is 6, it
must be Cimi.
Since the numbered and the named week
were both "weeks," each of their name/number change daily;
therefore, the day after 3 Cimi is not 4 Cimi, but 4 Manik, and the
day after that, 5 Lamat.
The next time Cimi rolls around, 20 days
later, it will be 10 Cimi instead of 3 Cimi. The next 3 Cimi will
not occur until 260 (or 13 x 20) days have passed. This 260day
cycle also had goodluck or badluck associations connected with
each day, and for this reason, it became known as the "divinatory
year."
The "years" of the Tzolkin calendar are not counted.
When did the
Tzolkin Start?
Long Count 13.0.0.0.0 corresponds to 4 Ahau. The authorities agree
on this.
What is the
Haab?
The Haab was the civil calendar of the Mayas. It consisted of 18
"months" of 20 days each, followed by 5 extra days, known as Uayeb.
This gives a year length of 365 days.
The names of the month were:
1. 
Pop 
7. 
Yaxkin 
13. 
Mac 
2. 
Uo 
8. 
Mol 
14. 
Kankin 
3. 
Zip 
9. 
Chen 
15. 
Muan 
4. 
Zotz 
10. 
Yax 
16. 
Pax 
5. 
Tzec 
11. 
Zac 
17. 
Kayab 
6. 
Xul 
12. 
Ceh 
18. 
Cumku 

In contrast to the Tzolkin dates, the Haab month names changed every
20 days instead of daily; so the day after 4 Zotz would be 5 Zotz,
followed by 6 Zotz ... up to 19 Zotz, which is followed by 0 Tzec.
The days of the month were numbered from 0 to 19. This use of a 0th
day of the month in a civil calendar is unique to the Maya system;
it is believed that the Mayas discovered the number zero, and the
uses to which it could be put, centuries before it was discovered in
Europe or Asia.
The Uayeb days acquired a very derogatory reputation for bad luck;
known as "days without names" or "days without souls," and were
observed as days of prayer and mourning. Fires were extinguished and
the population refrained from eating hot food. Anyone born on those
days was "doomed to a miserable life."
The years of the Haab calendar are not counted.
The length of the Tzolkin year was 260 days and the length of the
Haab year was 365 days. The smallest number that can be divided
evenly by 260 and 365 is 18,980, or 365×52; this was known as the
Calendar Round. If a day is, for example, "4 Ahau 8 Cumku," the next
day falling on "4 Ahau 8 Cumku" would be 18,980 days or about 52
years later.
Among the Aztec, the end of a Calendar
Round was a time of public panic as it was thought the world might
be coming to an end. When the Pleaides crossed the horizon on 4 Ahau
8 Cumku, they knew the world had been granted another 52year
extension.
When did the
Haab Start?
Long Count 13.0.0.0.0 corresponds to 8 Cumku. The authorities agree
on this.
Did the Mayas
Think a Year Was 365 Days?
Although there were only 365 days in the Haab year, the Mayas were
aware that a year is slightly longer than 365 days, and in fact,
many of the monthnames are associated with the seasons; Yaxkin, for
example, means "new or strong sun" and, at the beginning of the Long
Count, 1 Yaxkin was the day after the winter solstice, when the sun
starts to shine for a longer period of time and higher in the sky.
When the Long Count was put into motion,
it was started at 7.13.0.0.0, and 0 Yaxkin corresponded with
Midwinter Day, as it did at 13.0.0.0.0 back in 3114 B.C.E. The
available evidence indicates that the Mayas estimated that a 365day
year precessed through all the seasons twice in 7.13.0.0.0 or
1,101,600 days.
We can therefore derive a value for the Mayan estimate of the year
by dividing 1,101,600 by 365, subtracting 2, and taking that number
and dividing 1,101,600 by the result, which gives us an answer of
365.242036 days, which is slightly more accurate than the 365.2425
days of the Gregorian calendar.
(This apparent accuracy could, however, be a simple coincidence. The
Mayas estimated that a 365day year precessed through all the
seasons twice in 7.13.0.0.0 days. These numbers are only accurate to
23 digits. Suppose the 7.13.0.0.0 days had corresponded to 2.001
cycles rather than 2 cycles of the 365day year, would the Mayas
have noticed?)
In ancient times, the Mayans had a tradition of a 360day year. But
by the 4th century B.C.E. they took a different approach than either
Europeans or Asians. They maintained three different calendars at
the same time. In one of them, they divided a 365day year into
eighteen 20day months followed by a fiveday period that was part
of no month. The fiveday period was considered to be unlucky.
