onsdag den 26. april 2017

The Aztecs did not need a leap year: Introducing the Nuttall-Ochoa model for the Aztec Calendar

This blogpost is inspired by a recent blogpost by Itztli Ehecatl at Calmecac Anahuac, in which he lays out the different calendar correlations between the Aztec/Mexica calendar and the gregorian one, and in which he argues in favor of the correlation recently made by Rubén Ochoa. I agree that Ochoa’s correlation is the best available, and in this blogpost, I describe why that is – recycling some of the arguments from Itztli Ehecatl’s blogpost and adding others.

Depiction of the Celebration of the feast of Tlacaxipehualiztli
during the Spring Equinox in the Codex Borgia (folio 34)

 A recurring question in the study of Aztec calendrics has been whether the Aztec calendar did or did not correct for leap years. Generally the question has been answered in the negative (see e.g. 
Sprajc 2000). Archaeoastronomer and expert in Mesoamerican calendars Anthony Aveni (2016:110), in his recent chapter on calendars in the  Oxford Handbook of the Aztecs, concludes that “there is little evidence that the Aztecs employed a leap-year correction”, but that the question is open.
Rather, I think the question is wrongly posed - who says the Aztec calendar even needed a leap year correction the first place?

The basic problem is that there is little explicit evidence that the Aztecs used an intercalary leap year in their xiuhpohualli solar year count, but also it seems that the monthly feasts, many of which were related to an agricultural cycle and themes were usually celebrated at the appropriate time of year for a given agricultural event. This poses a basic question of how to reconcile the idea of calendric agricultural rituals with a calendar count that cannot be fixed in relation to the tropical year.

But as I see it the question can be resolved quite simply by recognizing, as several scholars have, that the beginning of the Aztec year was fixed by the vernal equinox and that the nemontemi are simply the days between the end of the 360-day cycle and the beginning of the next. This would make the question of leap year moot for the Aztec calendar since the equinox/new year would automatically fix the calendar to the tropical year every year, and the need to have an explicit principle for intercalating days or months due to the increasing disjuncture between the astronomical and calendric year would never arise.

Currently, none of the most widely accepted correlations between the Aztec calendar and the Gregorian adopt this solution to the leap year problem. But the solution emerges naturally from the argument that the vernal equinox marked the beginning of the Aztec year.

Today, the most scholars use one of two correlations – Caso’s or Tena’s.  Alfonso Caso’s correlation does not correct for the bissextile year and so does not begin on a specific day relative to the Gregorian calendar, it would result in the Aztec year starting on a different day each year with the monthly ceremonies gradually changing their position relative to the tropical year.  Rafael Tena’s model, in turn, does correct for leap year, but he argues the year begins on February 26th with the veintena of Atlcahualo. 

Oddly, as noted by Itztli Ehecatl, neither Caso nor Tena cites Nuttall’s 1894 paper or her 1904 article in American Anthropologist in response to Eduard Seler. The argument against the intercalation of an extra day to correct for leap year is that some scholars find that it disrupts the ongoing count of the other calendrical cycles – the 260 day tonalpohualli and the lunar and venus counts. The argument for an intercalary day has mostly been the seemingly correct correspondence with sowing and fertility rituals in the spring months and the harvest rituals in the fall. Some scholars (e.g. Graulich 2002) have argued that the agricultural associations of the monthly feasts were so vague that they didn't really require being performed at a specific time of year (which is debatable), and that farmers don't need a calendar to tell them when to sow and harvest (which is right). 

Nuttall was the first to propose the equinox as marking the end and beginning of the Aztec solar year. Her proposal however has been echoed also by Lopez Luján (2005), who argues, based on the astronomical alignment of the Templo Mayor, and in accordance with Nuttall, that Tlacaxipehualiztli was the first 20-day month of the Aztec year and that its beginning was fixed by the equinox. 

Recently, Rubén Ochoa has verified that Nuttall’s correlation is consistent with the evidence from prehispanic calendric codices, and that the length of the nemontemi must have varied so as to gradually adjust to the tropical year. He notes that the addition of a day is evident in the relation between the two most securely dated events in Aztec history:  the arrival of Cortés in Tenochtitlan on November 8th 1519 (2 quecholli/8 ehecatl) and the fall of Tenochtitlan on August 13th 1521 (15 miccailhuitontli/1 coatl). He notes that counting from the first date to the second requires at least one intercalary day, which he supposes would have extended the nemontemi of one of the two interceding years with one day from 5 to 6 days.  The explanation of Ochoa’s model and the evidence from the codices can be found here and the evidence showing how the model works for the known dates around 1519-1521 is found here.

Nuttall however, followed the colonial chronicler De La Serna in believing that there was a 13-day intercalary trecena every 52 years, when the New Fire ceremony was celebrated. But as noted by Hassig, this would have had the effect of throwing the correlation between the agricultural year and the calendric year off so much that it would be impractical as an agricultural calendar. Hassig proposes that rather than resetting directly to the astronomical year, the New Fire Ceremony reset the year to 7 days earlier than the exact match, which would mean that the total variance between the agricultural year and the calendar would vary over the 52-year period, but without becoming greater than about 7 days which is agriculturally tolerable. The main problem with Hassig’s explanation is that it is entirely conjectural.

What sets apart Ochoa’s solution from those of de la Serna, Nuttall and Hassig is that when following the principle of beginning the calendar year on the day after the observable equionox, no explicit intercalation is necessary, nor are any calculations or record-keeping of a deep day count.  The intercalation arises naturally as the number of days between the end of the 360- xiuhpohualli and the beginning of the next after the equinox naturally varies between five and six days. For the Aztec commoner, the principle is simply that when the last day of the year is over, the waiting period for the beginning of the new year begins, and the waiting period ends when the priests calls that the sun is in the right position. Calendar priests will be aware that every four years there are six days before the equinox rather than the usual five, but since the nemontemi are already out of count and simply fill up the rest of the year, they do not need to make explicit mention of any “intercalation”, they simply keep counting the tonalpohualli day count and then restart the year count on the equinox. In this way, the Aztecs had a smoothly functioning calendar which could function without significant deviation from the tropical year, and which could be observed in all communities that shared the custom of beginning the new year on the vernal equinox, regardless of what month they used as the first in the year.

The Nuttall-Ochoa model has a number of major advantages over all previous calendar models:
  •  It solves the leap year problem without the necessity of explaining how the intercalation of days was accomplished without further confounding any existing mismatch between local calendar variants.
  •  It requires minimal astronomical knowledge to use since it can be maintained as a self-correcting system through the simple cultural practice of beginning the year count the day after the observable equinox, without the necessity of making calculations into the past or future or keeping records of bissextile years.
  •  It is congruent with the clear cultural relations between the calendar rituals and the agricultural cycle and the close cultural association between the year and the growth period.
  •  It is congruent with the archeologically attested importance of the equinox, and with the use of westward-oriented double temples that allow for ease of observation of the equinox sun between the two temples, and which symbolically divides the year into two deities who then represent the estival and hibernal solstices.
  • It is linguistically plausible based on the literal and cultural meanings of ‘nemontemi’ (“they vainly fill up”), and ‘xihuitl’ (year/herb/green(-stone)/comet).
  •  It is congruent with what we know about the practices surrounding the Maya solar calendar, including the architectural use of E groups as observation points from where the vernal equinox can be observed relative to the main temple structures.
  • It is congruent with the known correlation dates for the arrival of Cortés in Tenochtitlan in 1519 and the fall of Tenochtitlan in 1521.
      To me however the best argument comes from the Templo Mayor and has been used by Leonardo Lopez Luján to argue that the temple was tied to the equinox and to the calendar: If we assume that the Mexica new year started right after observing the spring equinox (usually march 21st in the Gregorian calendar), then the sun would rise exactly in between the two shrines on top of the Templo Mayor. AND: The feast for Huizilopochtli in Panquetzaliztli the sun would fall around the Winter Solstice when the sun would be above the Huitzilopochtli temple, and the feast for Tlaloc in Etzalcualiztli would fall on the summer solstice (during the rainy season in central Mexico).  With Ochoa's model, but not with any of the others, this would be the same year after year, without any need to discuss how to put the calendar back in sync with the sun. 

This image based on the official model of the Templo Mayor at the Museo Templo Mayor, shows how the sun would be observed from the Quetzalcoatl temple on the Equinox, and on the winter solstices - if Ochoa's model is correct.
Can this be a coincidence?

Finally, as a treat, here is a link to  Calmecac Anahuacs "Aztec Date app" which calculates any given date according to the Nuttall-Ochoa correlation. You can use it to find out what date you were born, married in the Aztec calendar.

Update (28/04/2017): Additional Arguments:

I have been encouraged to also mention the main arguments against the Nuttall-Ochoa correlation, so I will do this here. Traditionally it has been believed that the Aztec year was named after the day-sign (in the tonalpohualli ritual calendar) of the first day in the year. If we follow the Nuttall-Ochoa model, the first day of the year however is not the one that defines the year bearer - rather years seem to be named after the thirteenth day of the new year - this does seem a somewhat arbitrary principle, although thirteen is of course an important number.

Also a final argument in favor of the correlation , although a somewhat subjective one, is that in the Nuttall-Ochoa correlation and none of the others, my birthday falls on the Tonalpohualli day 13 Ozomahtli, about which the Florentine codex writes (in Anderson and Dibble's translation): "It was said that anyone who was born upon this day sign became a highly favored person; he succeeded and endured on Earth. He was well respected and recognized; he was famed and honored; hence he was one who prospered, enjoyed glory, was compassionate, and served others. As a chieftain, he was strong, daring in battle, esteemed, intrepid, able, sharp-witted, quick-acting, prudent, sage, learned and discreet; an able talker, and attentive. To everyone he brought happiness, as much as to comfort the afflicted and provide succor. And if such did not befall one, it was said that he himself, by his own doing, neglected and destroyed his day sign through vice, because perchance he took not good heed, perhaps did not perform the penances well.The closing day sign 13 Ozomatli was named Tonacatecutli. And likewise they said that the one then born would become aged; they said that he would finish his work, endure on Earth, and be admired" (Florentine Codex, vol. 4-5:53-54).