MAYAN CALENDAR DESCRIPTION

Stephen P. Morse , San Francisco


INTRODUCTION

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 calendar


MAYAN LONG-COUNT CALENDAR
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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 19.19.19.17.19.  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 12.19.19.17.19.  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 13.0.0.0.0.  Such end of baktuns occur approximately every 400 years, and no cataclysmic event has occurred at the end of the 12 previous baktuns.


MAYAH 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 Tzolkin years (of 365 days) because that is the same number of days as 73 Haab 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 18,980-day 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.


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 common 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
etc.

So now it's clear that year -3113 is in reality 3114 BCE.