Aztec Calendar

The Aztec calendar is perhaps the best known Mesoamerican calendar today due to the famous Aztec monument in Mexico, the Piedra del Sol which means the Stone of the Sun. The text under Aztec calendar offers a new solution to it, including its starting point (October 23, 4004 BCE).

The Aztec calendar

This below was taken from Z.A. Simon (1984: 9-31) by permission, in a condensed form. Some of it is disputed by mainstream scholars of ancient Mesoamerica.

1) Proof of the nonexistence of intercalary days in the Aztec calendar, verifying Professor Michael Coe's theory.

2) Establishment of an exact starting date of the calendar (day, month, and year), which was unknown until 1984.

3) Solution of the contradictory interpretations of the ancient chroniclers: Sahagún and Diego Durán.

4) Mathematical proven evidence of the pre-Columbian contacts between the Mesoamerican and some West-European cultures.

Most of our largest libraries have a few dozen books on the history of Mexico, but these books usually interpret the Aztec calendar very briefly. Besides this, they often emphasize only those scientific achievements that are important for their authors. The wide range of different opinions can be illustrated by one example. A well-known expert on Mexican culture remembers Antonio de León y Gama (1736-1802), who has been called the first Mexican archaeologist. He states that the most important of León y Gama's books on archaeology is the "Descripción histórica y cronológica de las dos piedras." The sculptures of the title are two famous monoliths. Bernal adds that one of them is the Stone of the Sun, and falls into the error of attributing to the stone a calendrical significance, though he never claims that it was used as a calendar. In this situation, despite the correct but brief information of the encyclopeadias, the reader might get easily confused.

In addition to this, some sources introduced certain new terms without proper consistency. Other denominations were superseded, including a few calendrical miscalculations of amateur writers. Due to the apparent lack of coherence, the new results of some interesting papers have been neglected or ignored by the editors of many popular books. Therefore, a detailed description of the Mexican (Aztec) calendar is necessary for a complete understanding of the question. Therefore we will give that description before examining what experts have said about the problems. It will be concluded with the author's solution and its implications.

It is well-known that the Mayas and Aztecs had a highly developed calendar system. The two basic time cycles that governed Mesoamerican life were the solar calendar and the ritual calendar. In other words, the Mexican calendar is twofold, and comprises a ritual calendar, with a round of 260 days, which was employed in divination and in fixing "movable feasts"; and a solar year, with a round of 365 days, according to which the seasonal feasts were held (Muser, 1978:17 and Joyce, 1970:59).

The solar calendar of 365 days, called the Vague Year (or Civil Year), was composed of 18 months of 20 days each, with a period of 5 days added at the end. The 360-day period was called "xíhuitl" by Aztecs, and "haab" or "tun" by the Maya. The final unlucky days were called "Nemontemi" in Nahuath, and "Uayeb" in Mayan.

Each month had its own special name, and the days were numbered from zero to nineteen. The days of the last month, Uayeb, were numbered from zero to four. In this calendar the Maya counted the days starting from zero rather than from one (Ivanoff, 1971: 87).

This solar calendar was inseparable from the Sacred Round, or Sacred Almanac. The priests used this ritual calendar of 260 days, called [Tonalpohualli]]by the Aztecs and tzolkin by the Maya, primarily for divinatory purposes. The concurrent permutation of the solar and ritual calendars produced the Calendar Round. An exclusively lowland Classic Maya calendar achievement was the Long Count, which permitted an infinite computation of time, backward or forward, from an established starting point (Muser, 1978: 17). By the passing centuries, this simplified system may have became dominant, but we want to know its original form.

As we have already mentioned, in both solar and ritual calendars, time elapsed in parallel fashion, simultaneously and continuously. Peter Tompkins (1976: 290) states that each day of the tzolkin was governed by a deity who was thought to influence that day for good or evil, each separate day being regarded by the Maya as an individual god, whose glyph was a stylized portrait of his attributes. The numbers 1 to 13 were also personized as the heads of the gods they represented.

The use of this 260-day calendar was in no way arbitrary. The Mesoamericans possessed the correct knowledge that 260 x 18 was the same as 360 x 13, that 260 x 7 was the same as 364 x 5, that 260 x 73 was the same as 365 x 52, and that 260 x 1461 (like the Egyptian Sothic cycle!) was the same as 365.25 x 1040. Tompkins adds that to these calendars, which all fell into the 260-day pattern, were added more refinements, in order to calculate the synodic returns of the moon and the planets.

In Mesoamerica the planet Venus looms in the dawn sky with extraordinary brilliance. Both the Maya and the Nahua astronomers devoted special attention to the planet, and particularly to its heliacal rising. Venus revolves around the sun every 224.7 days, but since the earth is moving along its own orbit, the planet appears at the same place in the sky in 584 days, called synodic period. As 5 x 584 is equal to 8 x 365, the Maya considered five Venus years equal to eight solar years. And as 365 x 104 is equal to both 146 x 260 and 65 x 584, the sacred, the solar, and the venus calendars become coincident every 37,960 days, or 104 years. That is, two Mesoamerican "centuries" of 52 years. (Actually, the Maya knew the Venus cycle to be 583.92 days, instead of a round 584, so they dropped four days every sixty-one Venus years, in order to compensate for the discrepancy and make a round number divisible by 260.)

As astronomers are quick to point out, such an accurate knowledge of the cycle of Venus, whose revolutions are by no means regular, points to a long and careful observation.

Furthermore, the Mesoamericans devised a lunar calendar that would fit with the others. Calculating that 405 lunations or 11,960 days was exactly divisible by 260 (or, 260 x 46), they obtained a lunar period of 29.53 days which is practically the same what we know today. This would give them a lunar calendar accurate within a day over a period of 300 years.

Returning to the ritual and the solar calendars, the method of naming the individual days was the same for both, and consisted in the combination of twenty pictorial signs, with the numbers one to thirteen. The signs, according to the four cardinal points, were as follows:

E(ast)... 1 Cipactli (alligator, crocodila, aquatic monster)

N(orth).. 2 Éhecatl (wind, wind god)

W(est)... 3 Calli (house)

S(outh).. 4 Cuetzpalin (lizard)

E...........5 Cóatl (serpent, snake)

N..........6 Miquiztli (death)

W..........7 Mázatl (deer)

S...........8 Tochtli (rabbit)

E...........9 Atl (water)

N.........10 Itzcuintli (dog)

W.........11 Ozomatli (monkey)

S..........12 Malinalli (dead grass

E..........13 Ácatl (reed)

N.........14 Océlotl (ocelot, jaguar)

W.........15 Quauhtli (eagle)

S..........16 Cozcaquauhtli (king buzzard, vulture)

E..........17 Ollin (motion, earthquake)

N.........18 Técpatl (flint, flint knife)

W.........19 Quiáhuitl (rain)

S..........20 Xóchitl (flower)

By combining both series, one gets 1 Alligator as the name of the first day; of the second, 2 Wind; of the third, 3 House, until we reach the day 13 Reed. The following day is called 1 Jaguar; the nex is 2 Eagle, and so on. When the day Flower is reached, it is necessary to start counting the day Alligator over again, with its corresponding number. This calendar was essentially the basis for all other calendrical computations, such as the Mayan, the Zapotec, the Mixtec, the Totonac, the Huaxtec, the Teotihuacán, the Toltec and the Aztec. (Caso, 1958: 66)

Joyce (1970: 61-62) states that these signs ran consecutively in the order given above, one being assigned to each day, and the series was repeated ad infinitum. Conjointly with them were repeated the numerals one to thirteen, e.g., 1 Cipactli, 2 Eecatl, 3 Calli, and so on to 13 Acatle, which was followed by 1 Ocelotl, 2 Quauhtli, etc. There being no common factor to the numbers 13 and 20, a period of 13 x 20 days, or 260, would elapse before the sign 1 Cipactli would recur. This period of 260 days constituted the divinatory or ritual calendar, known as tonalamatl. The tonalamatl was subdivided in various ways; in some manuscripts each of the twenty 13-day periods, or weeks, is shown separately, together with the figure of a god who was especially associated with the first day, but whose influence was supposed to extend over the whole "week". In some manuscripts the tonalamatl is arranged on a different system: in five long horizontal rows of 52 days each. Each row, and each vertical column of five days, is provided with a presiding deity symbol, the influence of which must be assessed.

The Mexicans reckoned 365 days to the solar year, which they divided into 18 months of twenty days each, and a nineteenth period of five days, considered extremely unlucky, at the end of the year. As the days were known by their tonalamatl names, it is obvious that the first 105 days of the year recurred at the end, after the 260-day period. However, it was possible to distinguish between two days of the same name which fell in the same year, owing to the fact that each day was associated with one of a series of nine deities, called lords of the night, a series also repeated ad infinitum, except no "lord" was assigned to any of the five unlucky days at the end of the year, which were called nemontemi or "useless days." Thus, since the number 260 is not divisible by 9, it was possible to differenciate between two days of the same name falling in one year. And since 9 goes into 360 without a remainder, the commencement of the year coincided with the beginning of the series of "lords of the night."

Nor is this all; a corresponding series of thirteen "lords of day," which, however, is not similarly composed in all manuscripts, accompanied the days (except the nemontemi), and the influences of the day- and night-lord assigned to each day respectively constituted two additional features for the consideration of the would-be interpreter of the tonalamatl.

Since each "month" consisted of twenty days, and there were twenty day-signs, it is obvious that each month in a given year started with the same sign; but that since the last month was followed by the five unlucky days, each year began with a day-sign five days later than the last. Also since 365 is divisible by 13 with 1 as remainder, it follows equally that each year began wit a day-number one in advance of the last.

Further, since there were 20 day-signs, and 5 (the highest common factor of 365 and 20) goes into twenty exactly four times, the year began with one of the four signs only. The four signs mentioned by T.A. Joyce (1970: 63-65), which gave the names to the years, are the signs Tecpatl, Calli, Tochtli and Acatl, recurring in that order. (It is more than probable that the day-number entering into the name of the year was that of the first day, as held by most authorities.) The years were named successively, 1 Tecpatl, 2 Calli, 3 Tochtli, etc., until, after a period of 52 years (that is, 13 x 4), the same sign recurred with the same number as the name-date of the year. This period of 52 years named xiuhmolpilli (meaning bundle of years) formed the shorter cycle of the Mexicans.

To understand the calculation of a 52-year cycle, imagine two wheels of time rotating simultaneously. On time when recorded days, for which there were 20 names with 13 numbers. The complete name of a day must be accompanied by the appropriate number, such as 4 Reed or 9 Eagle. The other wheel presents a somewhat parallel situation. Eighteen months of 20 days each, to which the dreaded 5-day period of bad luck was added, resulted in a 365-day cycle (18 x 20 plus 5 equals 365), corresponding to our solar year. In order to return to the very same day and month, 52 years would have to elapse. This was the basic computation of time used in Mesoamerica. See the diagrammatic illustration in Michael D. Coe, Mexico and in the books of J. Eric S. Thompson. This Calendar Round enabled unique designation within a 52-year period but difficulties arise when dealing with several cycles: one needs to know to which Calendar Round the date refers. (The Maya Long Count also used the 52-year cycle but avoided confusion by accurately recording lapsed time from an initial starting point in 3113 BCE, according to the Goodman-Martínez-Thompson correlation. Many scholars agree upon that this starting point represents a mythological event, probably the latest creation of man.)

These statements mentioned above require some adjustment. The four signs cited were actually in use during the Spanish Conquest. We should not conclude from this fact alone that this was the original form of all Mesoamerican calendars. Many of those tribes may have used the 52-year Mexican century during their whole history, using it automatically, being incapable of understanding the deeper meaning of the calendar for absolute dates. Regardless of our knowledge of the existence of the supposed infinite version of the calendar using exclusively four year-signs (like part of the Boturini manuscript with its 188 year-signs), we cannot admit that this would be the final solution of the Mesoamerican calendars. This system must have had some kind of starting point and the correct 3113 BCE of the Maya does not fit into the Aztec system. (This is the point where we have to break with the widely accepted theories, and start to build up a more understandable explanation.)

Ignacio Bernal states in The Olmec World that it must have dawned on the Olmecoids that a system in which dates were repeated every 52 years was confusing on the long run. It could be compared to our cryptic way of writing, for instance, '56. Does this refer to 1956, or 1856, or even 156? Of course at the moment of writing we know what it meant, but after many centuries it is not clear. The Long Count system (of the Maya) is far more exact and equates basically to the one that has been followed by many civilized peoples.

Seen this way, the logic behind the system is no longer apparent. Would the Mexicans have been that illogical? Did they just ignore the difficulties and the inaccuracy in such a refined institution? Our answer is definitely no. From all the facts we must not arrive at the conclusion that only 4 signs recur infinitely during the whole history of the Aztecs. Also, although the sequence of these four year signs is correct, we must emphasize that there would not be any particular reason to start with the Tecpatl sign.

If we have a good look at the picture of a conjectural Mexican calendar published by Gemelli Carreri (1645-1700), we arrive at some interesting conclusions. See A history of Mexican archaeology (1980: 55). This circular calendar is surrounded by a serpent, a symbol of both earth and time, according to Irene Nicholson (1975: 27). The orientation of the drawing itself suggests that we have to start to read it at the top. The head of the snake symbolizes the beginning. Fray Diego Durán, Book of the Gods and Rites and The Ancient Calendar refers to ann oddity that "Cipactli, which was the first figure and which means Head of Serpent," observing that "when people called it a head, I think that they understood it to be the beginning of the month, or its first day" (Durán, 1971 reprint: 394). (The English, Spanish, Hungarian and other languages have corresponding cognates for head, principal and chapter.)

We can be certain that the Head of Serpent really means the beginning in this representation. Therefore, we can assume that our count is supposed to progress from the head towards the tail of the snake. Emphasizing the correctness if this explanation, the drawing shows four loops on the serpent's body. These loops indicate the year-bearers, namely Rabbit, Reed, Flint-knife, and House. These four fields are significantly larger than the others on the drawing (altogether 52 year-signs). We can see clearly that the commencing year of a 52-year cycle was the Rabbit sign, at least at that time when the original of the drawing was made.

The best confirmation for this theory can be found in Miguel León-Portilla, Aztec Thought and Culture (1963: 54-55): The division of time gave rise to the years of the East, of the North, of the West, and of the South. In abstract terms, motion appeared as a consequence of the spatialization of time and of the orientation of the years and the days toward the four directions. Such a conclusion can be drawn from the accounts of Sahagún's Indian informants explaining the tabulation of the year-count, in which the years are spatially oriented:

1. One Rabbit, this is the name of the annual sign, the year-count for the region of the South.

2. Thirteen years it carries, guiding, carrying always on its shoulders each of the thirteen years.

3. And it goes along, guiding, beginning; it introduces all of the signs of the years: reed, flint, house. (Italics added.)

4. Reed is the name given to the sign of the region of light (East)...

5. The third group of years: flint. It is called the sign of the region of the dead... [North]...

8. And the fourth annual sign, house, was called the sign of the region of women... (West).

A close look at the table of the 52 year count preserved by Sahagún shows it to be very similar to the foregoing text, and clearly illustrates that in a Nahuatl century of fifty-two years, for each of the four directions a 13-year period of predominant influence was allotted. In a similar manner, within each year, the days of the tonalámatl or Sacred Calendar were divided into 65-day series of five 13-day "weeks." In a year of 260 days there were four of these 65-day groups, and each carried a sign which related it to one of the four cardinal directions. Jacques Soustelle noted that the most important Indian manuscripts demonstrate a clear distribution of 20 day-signs among the four directions. Thus, not only in each year, but also in each day, the influence of one of the four spatial directions predominated.

William Prescott, The World of the Aztecs states that in the measurement of time, the Aztecs adjusted their civil year by the solar... A month was divided into four weeks of five days each, on the last of which was the public fair or market day. As the year is composed of nearly six hours more than 365 days, there still remained an excess, which, like other nations who have framed a calendar, they provided for by intercalation; not indeed, every fourth year as the Europeans, but at longer intervals, like some of the Asiatics. They waited till the expiration of the fifty-two vague years, when they interposed thirteen days, or rather twelve and a half, this being the number which had fallen in arrear.

Nicholson (1975: 47) repeats that some authors believe that the end of the 52-year cycles an extra or intercalary period, sometimes of twelve and sometimes of thirteen days, brought the calendar into line with the position of the sun among the stars. This is not a widely accepted theory, since its theoretical usefulness is no proof in itself. Joyce is of the following opinion: The employment by the Mexicans of a solar year of 365 days brings us to the question whether they at any time intercalated any day or days to make their year square with real solar time. It is quite obvious that a people, most of whose feasts were connected with agriculture, were bound to notice that their festivals gradually failed to correspond with the seasons, and many conjectures have been made regarding the methods which they might have used to rectify their calendar. It must be confessed that ''there is no direct evidence that days were ever intercalated in the latter, and Seler has shown that at any rate between the year of the conquest (1519) and the date of Sahagún's writing, some forty years, no intercalation had been made.

Peter Tompkins (1976: 289) asserts that Mesoamericans divided their year into 360 days plus 5 extra days on regular years and 6 on leap years or 13 every 52 years. Michael D. Coe of Yale University is categoric in his assertion that "there is no evidence that the Mesoamericans ever intercalated days or leap years." According to him, because the tropical year is 365.2422 days long, the 365-day vague year simply gained on the seasons by a factor of 13 days every 52 vague years. But the fact remains that whatever system the Mesoamericans used, the result was a calendar more accurate than ours, adds Tompkins.

Prof. Coe's theory must be right from another point of view also. Since a pictorial sign was attributed to every single day of the calendar, even to the "useless" nemontemi days, it is incontrovertible that each of these supposed intercalary days would have had its own year-sign too. All the civilized nations of Mexico and Central America seem to have been the most calendar-oriented people, as held by many authorities. Given their way of thinking, no day could have passed without being marked for posterity. If the supposed intercalary days had had their own signs, new signs besides the existing four would have had to be introduced because of the hypothetical shift of 12 or 13 days between the 52-year cycles.

The nonexistence of extra year-signs due to the intercalary days positively implies the nonexistence of an intercalary shift. On the other hand, the lack of intercalary days does not mean new signs could not have been introduced. If the Mexicans possessed 20 different symbols, why they could not have used all of them for their great time-cycles? Why did they keep repeating only four of them? We investigated this mysterious question below.

It is known that the Aztecs and the Maya used very similar systems in their calendars. Keith G. Irwin,