Monday, March 26, 2012

The Mayan Calendar Explained

The Mayan Calendar.
The Mayan Calendar
The system of computing time adopted by the Maya calendar is a subject too extensive to be treated here in detail, but it is indispensable, for the proper understanding of their annals, that the outlines of their chronological scheme be explained.
Within the Mayan calendar, the year, haab, was intended to begin on the day of the transit of the sun by the zenith, and was counted from July 16th. It was divided into eighteen months, u (u, month, moon), of twenty days, kin (sun, day, time), each. The days of the Maya calendar were divided into groups of five, as follows:—
The months, in the Mayan calendar in their order, were:—
As the Maya calendar year was of 365 days, and as 18 months of 20 days each counted only 360 days, there were five days intervening between the last of the month Cumku and the first day of the following year. These were called “days without names,” xma kaba kin (xma, without, kaba, names, kin, days), an expression not quite correct, as they were named in regular order, only they were not counted in any month.
It will be seen, by glancing at the list of days of the Mayan calendar, that this arrangement brought at the beginning of each year, the days Kan, Muluc, Ix and Cauac in turn, and that no other days could begin the year. These days were therefore called cuch haab, “the bearers of the years” (cuch, to bear, carry, haab, year), and years were distinguished as “a year Kan,” “a year Muluc,” etc., as they began with one or another of these “year bearers.”
But the Mayan calendar was not so simple as this. The days were not counted from one to twenty, and then beginning at one again, and so on, but by periods of 13 days each. Thus, in the first month, beginning with 1 Kan, the 14th day of that month begins a new “week,” as it has been called, and is named 1 Caban. Twenty-eight of these weeks make 364 days, thus leaving one day to complete the year. When the number of these odd days amounted to 13, in other words when thirteen years had elapsed, this formed a period which was called “the katun of days,” kin katun, and by Spanish writers an “indiction.”
It will be readily observed by an inspection of the following table, that four of these indictions, in other words 52 years, will elapse before a “year bearer” of the same name and number recommences a year.
 1st year.14th year.27th year.40th year
A cycle of 52 years was thus obtained in a manner almost identical with that of the Aztecs calendar, Tarascos and other nations.
But the Maya calendar took an important step in advance of all their contemporaries in arranging a much longer cycle.
This long cycle was an application of the vigesimal system to their reckoning of time. Twenty days were a month, u or uinal; twenty years was a cycle, katun. To ask one’s age the question was put haypel u katunil? How many katuns have you? And the answer was, hunpel katun, one katun (twenty years), or, hopel in katunil, I am five katuns, or a hundred years old, as the case might be.
The division of the katuns was on the principle [54]of the Beltran system of numeration 
xel u ca katun,thirty years.
xel u yox katun,fifty years.
Literally these expressions are, “dividing the second katun,” “dividing the third katun,” xel meaning to cut in pieces, to divide as with a knife. They may be compared to the Germandritthalb, two and a half, or “the third a half.”
The Katun of 20 years was divided into five lesser divisions of 4 years each, called tzuc, a word with a signification something like the English “bunch,” and which came to be used as a numeral particle in counting parts, divisions, paragraphs, reasons, groups of towns, etc.
[These tzuc were called by the Spaniards lustros, from the Latin lustrum, although that was a period five years. Cogolludo says: “They counted their eras and ages, which they entered in their books, by periods of 20 years each, and by lustros of four years each. The first year they placed in the East [that is, on the Katun-wheel, and in the figures in their books], calling it cuch haab; the second in the West, called Hijx; the third in the South, Cavac; and the fourth, Muluc, in the North, and this served them for the Dominical letter. When five of the lustros had passed, that is 20 years, they called it a Katun, and they placed one carved stone upon another, cemented with lime and sand, in the walls of their temples, or in the houses of their priests.”
The historian is wrong in saying that the first year was called cuchhaab; that was the name applied to all the Dominical days, and as I have said, means “year bearer.” The first year was called Kan, from the first day of its first month.
This is but one of many illustrations of how cautious we must be in accepting any statement of the early Spanish writers about the usages of the natives.
[There is, however, some obscurity about the length of the Katun. All the older Spanish writers, without exception, and most of the native manuscripts, speak of it distinctly as a period of twenty years. Yet there are three manuscripts of high authority in the Maya which state that it embraced twenty-four years, although the last four were not reckoned. This theory was adopted and warmly advocated by Pio Perez, in his essay on the ancient chronology of Yucatan, and is also borne out by calculations which have been made on the hieroglyphic Codex Troano, by M. Delaporte, in France, and Professor Cyrus Thomas, in the United States.
This discrepancy may arise from the custom of counting the katuns by two different systems, ground for which supposition is furnished by various manuscripts; but for purposes of chronology and ordinary life, it will be evident that the writers of the annals in the present volume adopted the Katun of twenty years’ length; while on the other hand the native Pech, in his History of the Conquest, which is the last piece in the volume, gives for the beginning and the end of the Katun the years 1517-1541, and therefore must have had in mind one of twenty-four years’ duration. The solution of these contradictions is not yet at hand.
This Mayan calendars great cycle of 13 × 20=260 years was called an ahau Katun collectively, and each period in it bore the same name.
This name, ahau Katun, deserves careful analysis. Ahau is the ordinary word for chief, king, ruler. It is probably a compound of ah, which is the male prefix and sign of thenomen agentis, and u, collar, a collar of gold or other precious substance, distinguishing the chiefs. Katun has been variously analyzed. Don Pio Perez supposed it was a compound of kat, to ask, and tun, a stone, because at the close of these periods they set up the sculptured stone, which was afterwards referred to in order to fix the dates ofoccurrences. This, however, would certainly require that kat be in the passive, katal or kataan, and would give katantun. Beltran in his Grammar treats the word as an adjective, meaning very long, perpetual. But this is a later, secondary sense. Its usual signification is a body or batallion of war]riors engaged in action. As a verb, it is to fight, to give battle, and thus seems related to the Cakchiquel tresilloat, to cut, or wound, to make prisoner. The series of years, ordered and arranged under a controlling day and date, were like a row of soldiers commanded by a chief, and hence the name ahau katun.
Each of these ahaus or chiefs of the Katuns was represented in the native Mayan calendars by the picture or portrait of a particular personage who in some way was identified with the Katun, and his name was given to it. This has not been dwelt upon nor even mentioned by previous writers on the subject, but I have copies of various native manuscripts which illustrate it, and give the names of each of the rulers of the Katuns.
[59]The thirteen ahau katuns were not numbered from 1 upward, but beginning at the 13th, by the alternate numbers, in the following order:—
13, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2
Various reasons have been assigned for this arrangement. It would be foreign to my purpose to discuss them here, and I shall merely quote the following, from a paper I wrote on the subject, printed in the American Naturalist, Sept., 1881:—
“Gallatin explained them as the numerical characters of the days “Ahau” following the first day of each year called Cauac; Dr. Valentini thinks they refer to the numbers of the various idols worshiped in the different Ahaus; Professor Thomas that they are the number of the year (in the indiction of 52 years) on which the Ahau begins. Each of these statements is true in itself, but each fails to show any practical use of the series; and of the last mentioned it is to be observed that the objection applies to it that at the commencement of an Ahau Katun the numbers would run 1, 12, 10, 8, etc., whereas we know positively that the numbers of the Ahaus began with 13 and continued 11, 9, 7, 5, etc.
“The explanation which I offer is that the number of the Ahau was taken from the last day Cauac preceding the Kan with which the first year of each Ahau began—for, as 24 is divisible by 4, the first year of each Ahau necessarily began with the day Kan. This number was the “ruling number” of the Ahau, and not for any mystical or ceremonial purpose, but for the practical one of at once and easily converting any year designated in the Ahau into its equivalent in the current [60]Kin Katun, or 52 year cycle. All that is necessary to do this is, to add the number of the year in the Ahau to the number of the year Cauac corresponding to this “ruling number.” When the sum exceeds 52, subtract that number.
“Take an example: To what year in the Kin Katun does 10 Ahau XI (the 10th year of the 11th Ahau) correspond?
“On referring to a table, or, as the Mayas did, to a ‘Katun wheel,’ we find the 11th Cauac to be the 24th year of the cycle; add ten to this and we have 34 as the number of the year in the cycle to which 10 Ahau XI corresponds. The great simplicity and convenience of this will be evident without further discussion.”
The important question remains, how closely, by these cycles, did the Mayas approximate to preserving the exact date of an event?
To answer this fairly, we should be sure that we have a perfectly authentic translation of their hieroglyphic annals. It is doubtful that we have. Those I present in this volume are the most perfect, so far as I know, but they certainly do not agree among themselves. Can their discrepancies be explained? I think they can in a measure (1) by the differing length of the katuns, (2) by the era assumed as the commencement of the reckoning.
It must be remembered that there was apparently no common era adopted by the Mayas; each province may have selected its own; and it is quite erroneous to condemn the annals off-hand ]for inaccuracy because they conflict between themselves.