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:—

1.	Kan.	6.	Muluc.	11.	Ix.	16.	Cauac.
2.	Chicchan.	7.	Oc.	12.	Men.	17.	Ahau.
3.	Cimi.	8.	Chuen.	13.	Cib.	18.	Imix.
4.	Manik.	9.	Eb.	14.	Caban.	19.	Ik.
5.	Lamat.	10.	Ben.	15.	Eɔnab.	20.	Akbal.

The months, in the Mayan calendar in their order, were:—

1.	Pop.
2.	Uo.
3.	Zip.
4.	Zoɔ.
5.	Zeec.
6.	Xul.
7.	Ɔe-yaxkin.
8.	Mol.
9.	Chen.
10.	Yaax.
11.	Zac.
12.	Ceh.
13.	Mac.
14.	Kankin.
15.	Moan.
16.	Pax.
17.	Kayab.
18.	Cumku.

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.

[53]

	1st year.	14th year.	27th year.	40th year
1	Kan	Muluc	Ix	Cauac
2	Muluc	Ix	Cauac	Kan
3	Ix	Cauac	Kan	Muluc
4	Cauac	Kan	Muluc	Ix
5	Kan	Muluc	Ix	Cauac
6	Muluc	Ix	Cauac	Kan
7	Ix	Cauac	Kan	Muluc
8	Cauac	Kan	Muluc	Ix
9	Kan	Muluc	Ix	Cauac
10	Muluc	Ix	Cauac	Kan
11	Ix	Cauac	Kan	Muluc
12	Cauac	Kan	Muluc	Ix
13	Kan	Muluc	Ix	Cauac.

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 at, 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.

Mayan Languages

Mayan Languages.

Compared with many American languages, the Mayan languages are simple in construction. It is analytic rather than synthetic; most of its roots are monosyllables or dissyllables, and the order of their arrangement is very similar to that in English. It has been observed that foreigners, coming to Yucatan, ignorant of both Spanish and Maya, acquire a conversational knowledge of the latter more readily than of the former.

An examination of the Mayan languages explains this. Neither nouns nor adjectives undergo any change for gender, number or case. Before animate nouns the gender may be indicated by the prefixes ah and ix, equivalent to the English he and she in such expressions as he-bear, she-bear. The plural particle is ob, which can be suffixed to animate nouns, but is in fact the third person plural of the personal pronoun.

In the Maya Languages the conjugations of the verbs are four in number. All passives and neuters end in l, and also a certain number of active verbs; these form the first conjugation, while the remaining three are of active verbs only. The time-forms of the verb are three, the present, the aorist, and the future. Taking the verb nacal, to ascend, these forms are nacal, naci,nacac. The present indicative in the Mayan Languages are:—

[29]

Nacal in cah,	I ascend.
Nacal á cah,	thou ascendest.
Nacal ú cah,	he ascends.
Nacal c cah,	we ascend.
Nacal a cah ex,	you ascend.
Nacal u cah ob,	they ascend.

When this form is analyzed in the Maya languages, we discover that in, á, ú, c, a-ex, u-ob, are personal possessive pronouns, my, thy, his, our, your, their; and that nacal and cah are in fact verbal nouns standing in apposition. Cah, which is the sign of the present tense, means the doing, making, being occupied or busy at something. Hence nacal in cah, I ascend, is literally “the ascent, my being occupied with.” The imperfect tense is merely the present with the additional verbal noun cuchi added, as—

Nacal in cah cuchi,	I was ascending.
Nacal á cah cuchi,	Thou wast ascending.
	etc.

Cuchi means, in the Maya language carrying on, bearing along, and the imperfect may thus be rendered:—

“The ascent, my being occupied with, carrying on.”

This is what has been called by Friedrich Müller the “possessive conjugation,” the pronoun [30]used being not in the nominative but in the possessive form.

The aorist presents a different mode of formation:—

Nac-en, (i.e. Naci-en)	I ascended.
Nac-ech,	Thou ascended.
Naci,	He ascended.
Nac-on,	We ascended.
Nac-ex,	You ascended.
Nac-ob,	They ascended.

Here en, ech, on, ex, are apparently the simple personal pronouns I, thou, we, you, and are used predicatively. The future is also conjugated in this form by the use of the verbal bin, binel, to go:

Bin nacac en,	I am going to ascend.
Bin nacac ech,	Thou art going to ascend.
	etc.

The present of all the active verbs in the Maya languages usee this predicative form, while their aorists and futures employ possessive forms. Thus:—

Ten cambezic,	I teach him.
Tech cambezic,	Thou teaches him.
Lay cambezic,	He teaches him.

Here, however, I must note a difference of ]opinion between eminent grammatical critics. Friedrich Müller considers all such forms as—

Nac-en,

I ascended,

to exhibit “the predicative power of the true verb,” basing his opinion on the analogy of such expressions as—

Ten batab en,

I (am) a chief.

M. Lucien Adam, on the other hand, says:—“The intransitive preterit nac-en may seem morphologically the same as the Aryan ás-mi; but here again, nac is a verbal noun, as is demonstrated by the plural of the third person nac-ob, ‘the ascenders.’ Nac-en comes to mean ‘ascender [formerly] me.’”

I am inclined to think that the French critic is right, and that, in fact, there is no true verb in the Maya language, but merely verbal nouns, nomina actionis, to which the pronouns stand either in the possessive or objective relations, or, more remotely, in the possessive relation to another verbal noun in apposition, as cah, cuchi, etc. The importance of this point in estimating the structure of the language will be appreciated by those who have paid any attention to the science of linguistics.

[The objective form of the conjugation is composed of the simple personal pronouns of both persons, together with the possessive of the agent and the particle ci, which conveys the accessory notion of present action towards. Thus, from moc, to tie:—

Ten c in moc ech,	I tie thee,
literally,	I my present tying thee.

These refinements of analysis have, of course, nothing to do with the convenience of the Maya language for practical purposes. As it has no dual, no inclusive and exclusive plurals, no articles nor substantive verb, no transitions, and few irregular verbs, its forms are quickly learned. It is not polysynthetic, at any rate, not more so than French, and its words undergo no such alteration by agglutination as in Aztec and Algonkin. Syncopated forms are indeed common, but to no greater extent than in colloquial English. The unit of the tongue remains the word, not the sentence, and we find no immeasurable words, expressing in themselves a whole paragraph, such as grammarians like to quote from the Eskimo, Aztec, Qquichua and other highly synthetic languages.

The position of words in a sentence is not dissimilar from that in English. The adjective ]precedes the noun it qualifies, and sentences usually follow the formula, subject—verbal—object. Thus:—

Hemac	cu	yacuntic	Diose,		utz	uinic.
He	who	loves	God,	[is]	good	man.

But transposition is allowable, as—

Taachili	u tzicic	u	yum	uinic.
Generally	obeys	his	father,	a man.

As shown in this last example, the genitive relation is indicated by the possessive pronoun, as it sometimes was in English, “John, his book;” but the Maya is “his book John,” u huun Juan.

Another method which is used for indicating the genitive and ablative relations is the termination il. This is called “the determinative ending,” and denotes whose is the object named, or of what. It is occasionally varied to al and el, to correspond to the last preceding vowel, but this “vocalic echo” is not common in the Maya language. While it denotes use, it does not convey the idea of ownership. Thus, u cħeen in yum, my father’s well, means the well that belongs to my father; but cħenel in yum, my father’s well, means the well from which he obtains water, but in which he has no proprietorship. Material used is indicated by [34]this ending, as xanil na, a house of straw (xan, straw, na, house).

Compound words are frequent, but except occasional syncope, the members of the compound undergo no change. There is little resembling the incapsulation (emboitement) that one sees in most American languages. Thus, midnight, chumucakab, is merely a union of chumuc, middle, and akab, night; dawn, ahalcab, is ahal, to awaken, cab, the world.

While from the above brief sketch it will be seen that the Maya is free from many of the difficulties which present themselves in most American tongues, it is by no means devoid of others.

In its phonetics, it possesses six elements which to the Spaniards were new. They are represented by the signs:

cħ,

k,

pp,

tħ,

tz,

ɔ.

Of these the cħ resembles dch, pronounced forcibly; the ɔ is as dz; the pp is a forcible double p; and in the tħ the two letters are to be pronounced separately and forcibly. There remains the k which is the most difficult of all. It is a sort of palato-guttural, the only one in the language, and its sound can only be acquired by long practice.

]The particles are very numerous, and make up the life of the Maya language. By them are expressed the relations of space and time, and all the finer shades of meaning. Probably no one not to the manor born could render correctly their full force. Buenaventura, in his Grammar, enumerates sixteen different significations of the particle il.

The elliptical and obscure style adopted by most native writers, partly from ignorance of the art of composition, partly because they imitated the mystery in expression affected by their priests, forms a serious obstacle even to those fairly acquainted with the current language. Moreover, the older manuscripts contain both words and forms unfamiliar to a cultivated Yucatecan of to-day.

I must, however, not omit to contradict formally an assertion made by the traveler Waldeck, and often repeated, that the language has undergone such extensive changes that what was written a century ago is unintelligible to a native of to-day. So far is this from the truth that, except for a few obsolete words, the narrative of the Conquest, written more than three hundred years ago, by the chief Pech, which I print in this volume, could be read without much difficulty by any educated native.

Again, as in all Mayan languages largely monosyllabic, there are many significations attached to one word, and these often widely different. Thus kab means, a hand; a handle; a branch; sap; an offence; while cab means the world; a country; strength; honey; a hive; sting of an insect; juice of a plant; and, in composition, promptness. It will be readily understood that cases will occur where the context leaves it doubtful which of these meanings is to be chosen.

These homonyms and paronyms, as they are called by grammarians, offer a fine field for sciolists in philology, wherein to discover analogies between the Maya and other tongues, and they have been vigorously culled out for that purpose. All such efforts are inconsistent with correct methods in linguistics. The folly of the procedure may be illustrated by comparing the English and the Maya. I suppose no one will pretend that these languages, at any rate in their present modern forms, are related. Yet the following are but a few of the many verbal similarities that could be pointed out:—

[37]

Maya Languages.	English.
bateel,	battle.
cħab,	to grab, to take.
hol,	hole.
hun,	one.
lum,	loam.
pol,	poll (head).
potum,	a pot.
pul,	to pull, carry.
tun,	stone.

So with the Latin we could find such similarities as volah=volo, ɔa=dare, etc.

In fact, no relationship of the Mayan language group to any other has been discovered. It contains a number of words borrowed from the Aztec (Nahuatl); and the latter in turn presents many undoubtedly borrowed from the Maya dialects. But this only goes to show that these two great families had long and close relations; and that we already know, from their history, traditions and geographical positions.

Mayan Language Family

The Maya Language Family.

Whatever the primitive meaning and first application of the name Maya, it is now used to signify specifically the aborigines of Yucatan. In a more extended sense, in the expression “the Maya language family,” it is understood to embrace all tribes, wherever found, who speak related dialects presumably derived from the same ancient stock as the Maya proper.

Other names for this extended family have been suggested, as Maya-Kiche, Mam-Huastec, and the like, compounded of the names of two or more of the tribes of the group. But this does not appear to have much advantage over the simple expression I have given, though “Maya-Kiche” may be conveniently employed to prevent confusion.

These affiliated languageof Maya tribes are, according to the investigations of Dr. Carl Hermann Berendt, the following:—

1.	The Maya proper, including the Lacandons.
2.	The Chontals of Tabasco, on and near the coast west of the mouth of the Usumacinta.
3.	The Tzendals, south of the Chontals.
4.	The Zotzils, south of the Tzendals.
5.	The Chaneabals, south of the Zotzils.
[18]6.	The Chols, on the upper Usumacinta.
7.	The Chortis, near Copan.
8.	The Kekchis, and
9.	The Pocomchis, in Vera Paz.
10.	The Pocomams.
11.	The Mams.
12.	The Kiches.
13.	The Ixils.		In or bordering on Guatemala.
14.	The Cakchiquels.
15.	The Tzutuhils.
16.	The Huastecs, on the Panuco river and its tributaries, in Mexico.

The Mayan languages of these do not differ more, in their extremes, than the French, Spanish, Italian and other tongues of the so-called Latin races; while a number resemble each other as closely as the Greek dialects of classic times.

What lends particular importance to the study of this group of Mayan languages is that it is that which was spoken by the race in several respects the most civilized of any found on the American continent. Copan, Uxmal and Palenque are names which at once evoke the most earnest interest in the mind of every one who has ever been attracted to the subject of the archæology of the New World. This race, moreover, possessed [19]an abundant literature, preserved in written books, in characters which were in some degree phonetic. Enough of these remain to whet, though not to satisfy, the curiosity of the student.

The total number of Indians of pure blood speaking the Maya proper may be estimated as nearly or quite 200,000, most of them in the political limits of the department of Yucatan; to these should be added nearly 100,000 of mixed blood, or of European descent, who use the tongue in daily life. For it forms one of the rare examples of American languages possessing vitality enough not only to maintain its own ground, but actually to force itself on European settlers and supplant their native speech. It is no uncommon occurrence in Yucatan, says Dr. Berendt, to find whole families of pure white blood who do not know one word of Spanish, using the Maya exclusively. It has even intruded on literature, and one finds it interlarded in books published in Merida, very [20]much as lady novelists drop into French in their imaginative effusions.

The number speaking the different dialects of the stock are roughly estimated at half a million, which is probably below the mark.