MAYAN CALENDAR DESCRIPTION
Stephen P. Morse
, San Francisco
The Mayan calendar is not a single calendar, but rather a series of
calendars. The two described here are the Mayan Long Count and
the Mayan Calendar Round. The Mayan calendar round is itself a
combination of two calendars, namely the Tzolkin calendar and the Haab
MAYAN LONG-COUNT CALENDAR
A Mayan Long-Count date is specified by a sequence of five
fields. The names of the fields are kin, winal, tun, katun, and
baktun. They are related as follows:
1 kin is 1 day
1 winal is 20 kin, which is 20 days (a long-count month)
1 tun is 18 winal, which is 360 days (a long-count year)
1 katun is 20 tun, which is 20 long-count years
1 baktun = 20 katun, which is 400 long-count years
The first day in the Long-Count calendar is 0 baktun, 0 katun, 0 tun, 0
winal, 0 kin. It is written as 0.0.0.0.0 and it corresponds to 11
August -3113 in the Gregorian calendar.
Note that minus sign in the year -3113. See the discussion at the
end of this page about negative year numbers.
END OF THE MAYAN LONG-COUNT CALENDAR
The maximum date that can be designated in the Long-Count notation is
184.108.40.206.19. It corresponds to the Gregorian date of 12
October 4772. That is the last date of the Mayan calendar.
The popularized date of December 20, 2012 has a Long-Count value of
220.127.116.11.19. It is not the end of the calendar but is the last
day having a baktun value of 12. The next day, December 21, 2012
is 18.104.22.168.0. Such end of baktuns occur approximately every 400
years, and no cataclysmic event has occurred at the end of the 12
MAYAN HAAB CALENDAR
A date in the Haab calendar is specified by a day and a month.
There are 18 months of 20 days and 1 month of 5 days, making a 365 day
year. The months are
Pop, Wo', Sip, Sotz', Sek,
Xul, Yaxk'in, Mol, Ch'en, Yax,
Sak', Keh, Mak, k'ank'in, Muwan,
Pax, K'ayab, Kumk'u, and Weyeb'.
Wayeb' is the 5-day month.
The days of each month are numbered starting from 0 instead of
1. So the first day of the year is 0 Pop and the last day is 4
Wayeb'. There is no year
indication in the Haab calendar so there is no way to distinguish
between an event on a date in one year from an event on that same date
in another year.
MAYAN TZOLKIN CALENDAR
A date in the Tzolkin calendar is specified by a day number and a day
name. The day number starts at 1 and goes up to 13. There
are 20 day names, namely
Imix, Ik, Akbai, Kan, Chiccan,
Cimi, Manik, Lamut, Mulic, Oc,
Chuen, Eb, Ben, Ix, Men,
Cib, Caban, Etznab, Cauac, and Ahau
This is different from the usual notation of a month and day in that
both the day name and day number are incremented on each new day.
For example, the day after 4 Ix is 5 Men.
Since there are 20 day names and 13 day numbers, the year contains 260
days. Like the Haab calender, there is no year indication
in the Tzolkin calendar.
MAYAN CALENDAR ROUND
Since there is no year indication in either the Haab calendar or the
Tzolkin calendar, they cannot be used to distinguish between events
that occur on the same date but in different years. But by
combining the dates in the two calendars, such a distinction can be
made. That is, each day can be specified by the combination of
its Haab date and Tzokin date. That combination starts to repeat
after 52 Haab years (of 365 days) because that is the same number of
days as 73 Tzolkin years (of 260 days). Both have 18,980 days.
This period exceeded the expected lifetime of a person in olden days,
so it was fine for recording dates unambiguously in a person's lifetime.
The calendar can be extended to additional years by including a cycle
number -- that is, keeping track of the number of times that the
cycle occurs. As noted above, the origin of the Longcount
calendar is 11 August -3113. That corresponds to 4 Ahau
(Tzolkin), 8 Kumk'u (Haab), 1st cycle in the Calendar Round calendar.
Note that the total combinations of Calendar Round dates is 260
(Tzolkin days) times 365 (Haab days), which comes to 94,900. But
the two calendars repeat after every 18,980 days, which is exactly 1/5
of the total combinations. So only 1 in 5 combinations are
actually possible, the others are invalid combinations.
ACCURACY OF THE MAYAN CALENDAR
The Mayan calendar is said to be more accurate than the Gregorian
calendar, but the argument for this is a bit flakey.Here is how the
calculation is done
A solar year has been accurately measured to be 365.24218 days.
Now we need to calculate the average number of days in the Gregorian
calendar and in the Mayan calendar, and compare them to this value.
A Gregorian year bounces around as leap years come and go, but after
cycling 400 years we can calculate the average number of days per year
Total number of days =
+ 100 leap days for years divisible by 4
- 3 leap day for years not divisible by 400
= 14,6000 + 100 - 3 = 14,6097
Average number of days per year =
= 14,6097 / 400 = 365.24250
Now to compute the average number of days per year in the Mayan
Calendar Round. The round count repeats every 52 Haab years of
365 days or 73 Tolzim years of 260 days, which corresonds to 18,980
days. Just how many Mayan years that corresponds to is hard to
say since there is really no concept of a Mayan year.
But if we wait for 29 of these round-count cycles, we get 18,980 * 29 =
550,420 days. This is 29 * 52 = 1,508 Haab years, although we
have cycled through the seasons 1,507 times (550,420 / 365.24218 =
1507.00009). So if we call this period 1,507 years, we get the
average number of days per year to be 550,420 / 1,507 =
365.24220. And this is closer to the true value of 365.24218 than
is the Gregorian value of 365.24250.
Another (and perhaps simpler) way of looking at it is as follows.
After each Haab year (365 days) the earth drifts 0.24218 days relative
to the seasons. That means it will drift an entire year relative
to the seasons in 365.24218 / 0.24218 = 1508.14 Haab years.
During this time we will have made 1507 cycles through the
seasons. Dividing the total number of days in 1508 Haab years by
1507 season changes gives 1508 * 365 / 1507 = 365.24220 days per season
Of course we could have made the same argument for the Gregorian
calendar, and the correction is even more dramatic. After each
Gregorian year (365.24250 days) the earth drifts 365.24250 - 365.24218
= .00032 days relative to the seasons. That means it will
drift an entire year relative to the seasons in 365.24218 / 0.00032 =
1,141,381.8 Gregorian years. During this time we will have made
1,141,383 cycles through the seasons. Dividing the total number
of days in 1,141,382 Gregorian years by 1,141,383 season changes gives
1,141,382 * 365.24250 / 1,141,383 = 365.24218 days per season change.
So the bottom line is that the corrected Mayan year of 365.24220 days
is closer to the true value of 365.24218 days than is the Gregorian
year of 365.24250 days. But if the same correction is made to the
Gregorian calendar, we get closer yet to the true value. That is
why I started by saying that the argument about the Mayan calendar
being more accurate than the Gregorian calendar is flakey.
NEGATIVE YEAR NUMBERS
Before I explain negative year numbers, I need to introduce some
terminology. You are probably familiar with the terms BC (before
Christ) and AD (Anno Domino). These terms are
very religion specific, so I will use religion-neutral terms
instead. The religion neutral equivalents are BCE (before the
era) and CE (common era). Year numbers in both systems are
the same -- it is just the terminology that changed.
Recall that the origin of the Long-Count calendar corresponds to 11
August -3113. You might think that that corresponds to 3113 BCE,
but that is not quite correct. The problem is that the BCE/CE
numbering system doesn't have a year zero. The year before 1 CE
was not zero but instead was 1 BCE. That is, the years go from 2
BCE to 1 BCE to 1 CE to 2 CE etc. The correspondence between the
signed years and the BCE/CE years is as follows:
year 4 = 4 CE
year 3 = 3 CE
year 2 = 2 CE
year 1 = 1 CE
year 0 = 1 BCE
year -1 = 2 BCE
year -2 = 3 BCE
year -3 = 4 BCE
So now it's clear that year -3113 is in reality 3114 BCE.