From the heading (§8), “Of the Great Cycle of 312 years, or Ahau Katunes,” as well as of the text just quoted, it is apparent that Señor Perez intended to establish the fact that the ancient Maya cycles were composed of 24 and 312 years respectively. He does so in manifest contradiction to the prevalent opinion that they consisted of 20 and 260 years. We do not understand the reasons why he should have come to this conclusion. It grew out neither from the facts alleged nor from the connection into which he wove them together. The peculiar circumstance of having, in his commentary references, four years intercalated in succession to the usual cycle of twenty years, and included in a square, to serve as a “pedestal” to the former, is not capable of shedding new light upon the question and causing us to distrust authorities on which we were accustomed to rely. The other reason, which stands second in his order of forming premises for his conclusion, is said to be the undeniable fact, that those periods took their name of Ahau Katun, because they began to be counted from the day Ahau, which was the second day of those years that began in Cavac. Of this incontrovertible fact the readers are not elsewhere informed. The information, however, which we are able to give is that according to all we have been able to gather on the Maya Calendar, a period, or a single year, commencing with a day named Ahau, has never existed in their system of counting. They always commenced it with the words Kan, Muluc, Hix, Cavac. If there existed any exceptional ground for changing an old established method of dating, the reason should have been stated, for it is preposterous to assume that the first day of a great cyclical period should have taken its name from any other day of the year’s calendar than from the four above named. Nor do we understand the reason why, just here, the topic of the succession of the numbers 13, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2, was introduced. Could it have been with the intention of showing that this singular enumeration of alternating Ahaues, which we shall hereafter speak of, occurred only in cycles of 24 years, and that therefrom a proof might be derived for establishing the pretended cycle of 24 and 312 years? Evidence of this should have been given by a table showing the series, and by still another table in which should be shown that such an alternating succession did not occur in cycles composed of 20 years. Not one single fact can be detected in Señor Perez’s text, by which the long established assumption of a 20 years’ cycle has been disproved.
Nevertheless, the data which we possess of the ancient Maya Calendar are not so complete as to disprove emphatically that a cycle of 24 and 312 years respectively was never used by the Maya chronologers.
Without doubt, Yucatan owed its ancient greatness to the success of uniting a rude and scattered population around a number of theocratical centres, where similar forms of worship were maintained. Though the ancient records are wanting, this feature of the Maya system stands out upon the background of dim traditions with great distinctness. After this concentration of tribes, and with the view of regulating worship, a uniform calendar would have been introduced, the main features of which would probably have been a solar year of 365 days, the division of the year into 20 months, and a cyclical period of 20 and 260 years respectively. In the middle of the 11th century great tribal revolutions took place on the high plateaus of Anahuac, by which the lowlands of Yucatan were also affected. An adventurous tribe of the Nahuatl stock possessed itself of one of the principal towns of Yucatan and established its influence and power. Mayapan became the centre of Nahuatl worship. The calendar the invaders brought with them must have been the old honored division of the years into 365 days, with 20 months, and their cyclical period of not 20 but 52 years, and it is also known that about the year 1450, the political union of the Mayas was broken into several smaller divisions, some of which presumably would have held to the ancient cycle of 20 years; others may have adopted the Nahuatl cycle of 52 years, and possibly, may have introduced the cycle of 24 years spoken of by Señor Perez. Political schism was likely to have generated also a hierarchical one, and each newly formed body of priests, in whose hands the custody and composition of annals fell, would have sought to distinguish themselves from their predecessors by innovations, if only of a formal character. Such changes we also observe among the Nahuatls in Anahuac. The period of 52 years, however, seems to have constantly prevailed among them, and also the divisions of the 365 days into 18 months of 20 days each.
We find, for instance, that one of the Nahuatl tribes begins its annals with December 9, another selects December 26, another January 9, and others January 12, February 4, and February 22. We also know that a different calculation prevailed among these tribes in beginning their annals. The State of Colhuacan began its chronology with a year 1 Calli, the State of Mexico with 2 Acatl, others with 1 Tochtli, and seemingly the most ancient calculation began with the year 1 Tecpatl. Thus we have a historical basis for our assertion that the Nahuatl as well as the Maya tribes did not conform to a uniform rule in beginning their first year’s date, in their chronological epochs, or in the division of their cyclical epochs.
In spite of this diversity, so perplexing to modern chronologists, the Aztecs and the Mayas were both governed by the same general principle in arranging their calendars. Both nations recognized the fact that in the past their solar year had numbered only 360 days; and they preserved in the words nemotemi and xona-kaba-kin, the remembrance of a not to be forgotten effort exerted by their ancestors to correct the primordial solar year of 360 days into one of 365 days. Both nations conscientiously kept on dividing the year into 18 months, and each of the months into 20 days, and with both the number 13 returns as a basis governing the calendar of years as well as that of periods.[[35]]
We notice, moreover, that both nations omit to count the 20 days of the month in the succession of the figures 1–20, but after the thirteenth day they again begin with the number 1, and the 20th day therefore was figured with the number 7, and also that the Mexicans counted their smallest period with 13 years, the so-called tlapilli, and upon its quadruple the cycle of 52 years was based. The lesser Maya or Ahau period is 20 years, while the greater or Ahau Katun is 260 years or 13 times the smaller. Señor Perez’s lesser period of 24, and the greater one of 312 years show the same method and calculation (13 × 24 = 312).
This conformity between the early calendars of Central America should not escape the observation of the future historical enquirer. He will be compelled to adopt a very remote period of time when both nations, differing so entirely in their language, dwelt in peace, connected by the strong bands of a hierarchical power. One of these two nations, it is clear, must have invented it. Hence the question arises, was it original with the immigrating Nahuatl tribes who came from the higher northern countries as is reported, and did they succeed in forming such a consolidation with the Maya races as to mingle both under the same hierarchical government, or did the contrary take place? The most prevalent opinion makes the Nahuas the inventors of the general system of chronology, but later students begin to express themselves in favor of its Maya origin. On a more fitting occasion we are desirous to present our reasons for taking the latter view.
Before passing from these chronological speculations to the discussion of the Maya Manuscript, we wish to state briefly our idea of the origin of the system of reckoning by alternating Ahaues. [See page [66]]. We promised to return to this subject, and shall now endeavor to give a solution to this chronological problem differing from that of Señor Perez. A passage in Bishop Landa’s work, determined our decision. After a previous and positive assertion that the lesser Ahau period consisted of 20 years, Landa continues, ... “The order in which they computed their dates and made their prophecies by the aid of this computation (of 20 years) was arrived at by having two idols, dedicated to two of these characters (Ahaues). To the first idol, which stands with a cross marked above the circle, they paid homage by making him offerings and sacrifices, in order to obtain an immunity from the calamities to come in these 20 years, but after ten of these years had passed they offered nothing but incense and worship. When the twenty years of the first were fully passed they began to occupy themselves with the presages of their second idol and to offer sacrifices to him, having taken away their first idol to replace it by the second, in order to worship it in the coming ten years.”[[36]]
AHAU KATUN.
[Above we give a reproduction of a Maya Ahau Katun wheel taken from that in Landa’s “Las cosas de Yucatan,” § XL., in order that his explanation may be understood.]