Mayan Calendrics

The KIHN and the 260 and 365 Day Cycles

Gunthar Hartwig

Archaeology, Prehistory, and the Evolution of Technology

Professor Joanne Mack

December 12, 1991

The Maya were a people obsessed with the notion of time and its relationship to the spatial reality that they perceived around them. It is impossible to launch into a study of Mayan chronology and calendrics without incorporating not only astronomy and mathematics, areas of obvious relevance to any calender system, but also religion, folk history, linguistics, writing systems, architecture, and social structure. Their acheivements in all of these areas are impressive even by modern standards. For the sake of simplicity, however, I will herin concentrate on three elements of the Mayan system: the 260 day cycle, the 365 day year, and the notion of "kihn,' or sun/day/time, with a brief description of Mayan mathematics.

In the field of mathematics alone, the Mayans were far more advanced than any other contemporary civilization. By the third century A.D., Mayan scholars had discovered the mathemetical concept of the zero, an idea not to be considered in the Old World until it was explored by Hindustani thinkers five hundred years later (the zero would not arrive in Europe for several more centuries) and a positional, vigesimal counting system (both Leon-Portilla, p.1) that enabled the Mayans to make highly accurate calculations of astronomical and temporal periods. The counting system was based upon fives and twenties, evidence indicates that the Maya used multiplication and division, as well as addition and subtraction [Sanchez], p.21]. Numbers were written using a dot to represent one and a bar to represent five. They were written both vertically and horizontally, with the dots for ones being either to the left or on top, respectively. The numbers one through thirteen also had representative glyphs that could be used either individually or in conjunction with the dot-dash system.

The 260-day cycle, or Tzolkin, was the calendar of day-to-day life for the Maya. The days were composed of twenty day names combined with thirteen numbers, each of which, depending upon the name and number, had its own unique character. The day names correspond to the god who ruled the day. The character of each day was a representation of the god and the attached number, the two were inseparable, although the name carried more weight than the number [Thompson, p. 66]. Throughout the cycle, no two days were exactly alike, as the days and numbers continued in succession and each combination would not be repeated until the end of 260 days. For example, when the number thirteen was reached, the sequence starts up again at one, regardless of the name. Therefore, although Ix is the fourteenth name from the beginning of the cycle, the day would be "1 Ix." The first name of the cycle, Imix, would be "8 Imix" (as opposed to "21 Imix") on its second appearance.

The day names are, in order: Imix, Ik, Akbal, Kan, Chicchan, Cimi, Manik, Lamat, Muluc, OC, Chuen, Eb, Ben, Ix, Man, Cib, Caban, Etz’nab, Cauac, Ahau. A complete discription of the character of each is impossible in a treatise of this length, but a brief summary of some of the more prominent ones is possible.

"Imix" represents the earth and abundance. In glyph form this name often takes the shape of the great earth crocodile, on whose back rests the surface of the earth. The water lily was the symbol of the earth monster, and he brought abundance to the land.

"Cimi" is connected with death. Anyone falling ill upon this day wll surely die, although at the same time various Mayan peoples attributed, ironically, good luck to this day.

"Ix" is the day of the jaguar god. The jaguar permeates Maya mythology as an being of great power, and this day is seen as an excellent occasion to pray for rain, good crops and well-being.
"Ahau" means chief or lord in a number of Mayan languages. This is the day of the sun god, and as the sun was an integral part of the Mayan conception of the universe, it held great significance [all Thompson, pp. 69-88].

What each day held depended also on the number as well. One through thirteen carry many of the attributes of the primary god with which they are associated. Evidence suggests that these were those from Caban to Muluc. As the Tzolkin progressed, the numbers would fall upon the names with which they were connected. These days held particular power. Perhaps the luckiest of numbers was 9; it was at any rate, the most popular, and eagerly anticipated. It is very difficult, however, to determine what exactly it was that made some combinations better than others as a great deal of information about many Mayan beliefs has been lost.

Mayan scholars understood, of course, that the solar year lasted a great deal longer than 260 days. The Tzolkin was used for religious and ceremonial purpses, but more pragmantic matters required a different form of chronology. The 365 day calendar was broken down in to eighteen months of twenty days each. The five days remaining at the end of the period were not a part of any month, and were considered extremely unlucky. Each month had a name and a patron, who corresponded to the month in a way similiar to days and their names, but not nearly as strongly. The months, from beginning to end of the cycle, with the patron following, are: Pop, the jaguar; Uo, jaguar of the underworld; Zip, a deer; Zotz, the xoc fish; Zec, sky and earth, Xul, a canine god; Yaxkin, sun god; Mol, patron unknown; Ch’en, the moon; Yax, Venus; Zac, the frog constellation; Ceh, sky god; Mac, God of the number 3; Kankin, the Earth Monster; Muan, the Moan Bird; Pax, Jaguar or puma; Kayab, Moon Goddess; Cumku, a crocodile; and Uayeb, the five ending days.

Although Mayan astronomers had calculated the year to a high degree of accuracy -- they new it to be 365.2422 days -- they did not incorporate this into the calendar itself. They did, however, make careful calculations and records of the error that occured with reference to the seasonal cyvle. Leap days were not incorporated because of the importance of the coincidence of the various days of each cycle. This stretched beyond a simple correspondence between the two "yearly" cycles however. The mayan imagination stretched far back and far forward into time. Mayan scholars wished to know how certain celestial events, say the rising of Venus, would correspond within their system for centuries to come. The incorporation of the occasional leap year might throw the whole system, and their philophical beliefs, into dissarray.

Finally, whe reach the subject of "kihn," the Mayan term which can alternately mean sun, day, or time. The word kihn, while larger in scope, is related to the word kin, which forms a part of the long term system the Mayans used for marking period of time. 1 kin = 1 day. 20 kins = 1 uinal (1 365 day calendar month). 18 uinals = 1 tun (the 360 day year). 20 tuns = 1 katun (7,200 days). 20 katuns = 1 cycle (144,000 days). 400 cycles = 1 great cycle (2,880,000 days). [Morley, p.62].

Kihn describes the notion of the sun and its relationship to the unaltering reality of the universe. The sun defines this reality; in the Popol Vuh, the great Mayan story of the creation of the world, the rising of the sun is the dawn of humanity. The pattern of the suns movement across the sky is constant. It forever rises from up from Xibalba (the Mayan underworld) to cross the sky and be devoured in the west, but only to rise again. The passing of each successive day brings forth a new, clearly defined world -- the day name and number defines what will be. The concept of time is an inexctricable part of this process, the sun forever being consumed and returned once again. Thus Sun/day/time. By combining the two calendric cycles, a conception of the nature of the world at any point in the past or future was possible. The Maya, be he peasant or priest, could rest assured that by following these patterns he could understand the universe about him.


Morley, Sylvanus Griswold
Maya Hieroglyphs, 1975, Dover Publications, New York, New York

Sanchez, George I.
Arithmetic in Maya, 1961, independently published, Austin Texas

Linda Schele and David Freidal
A Forest of Kings, the Untold Story of the Maya, 1990, William Morrow and Company, Inc. New York, New York.

Thompson, J. Eric S.
Maya Hieroglyphic Writing, 1950, Carnegie Institution of Washington, Washington, D.C.>