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 26^th 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 8^th 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).

Bibliography:

• Aveni, A. F. (2016). The Measure, Meaning, and Transformation of Aztec Time and Calendars. In The Oxford Handbook of the Aztecs (p. 107). Oxford University Press.
• Caso, A. (1967). Los calendarios prehispánicos (Vol. 6). Universidad Nacional Autónoma de México.
• Graulich, M. (2002). Acerca del” Problema de ajustes del año Calendárico mesoamericano al año trópico”. Estudios de Cultura Náhuatl, 33(033).
• Hassig, R. (2001). Time, History, and Belief in Aztec and Colonial Mexico. University of Texas Press.
• Lopez Luján, L. (2005). The offerings of the Templo Mayor of Tenochtitlan. UNM Press.
• Nuttall,Zelia. 1894. Note on the Ancient Mexican Calendar System. Communicated to theTenth International Congress of Americanists in Stockholm. Bruno Schulze.Dresden.
• Nuttall, Z. (1904). The periodical adjustments of the ancient Mexican calendar. American Anthropologist, 6(4), 486-500.
• Sprajc, I. (2000, January).Problema de ajustes del año calendárico mesoamericano al año trópico. In Anales de Antropología (Vol. 34, pp. 133-160). UniversidadNacional Autonoma de Mexico, Instituto de Investigaciones Antropologicas.
• Tena, R. (1987). El calendario mexica y la cronografía (Vol. 161). Instituto Nacional de Antropología e Historia.

Quetzalcoatl: Precious Twin?

It is commonly asserted that a possible meaning of the name of the deity Quetzalcoatl is "precious twin". Sometimes it is even claimed that this is the real meaning and that the more commonly given meaning "Feathered Serpent" is false. In this blogpost I take a look at the history of this claim and its validity.

The claim is found in many different places: 

Historian Enrique Florescano states in his 2002 "The Myth of Quetzalcoatl" that "Uniting into one single entity the attributes of the serpent and the bird, metaphorically combining both the germinating powers of the earth and the creative powers of the sky, the Plumed Serpent became synonymous with the Precious Twin" (p. 147) 

Nahuatl translator John Bierhorst states in his 1974 "Four Masterworks of American Indian Literature" takes it as an example of the multifaceted meanings of Nahuatl metaphors: "The name Quetzalcoatl means literally "plumed serpent" from quetzalli, feather of the precious green quetzal, and coatl , a snake". ... A particularly ingenious reinterpretation, involving a double pun, transforms "bird-snake" into "precious twin", an epithet of the morning star considered the twin of the evening star (quetzal = "quetzal" or "precious", coatl = "snake" or "twin")" (p. 4)

The idea is not new either, in 1908 anthropologist H. Beyer published an article about the "symbolic meaning of the dog in ancient Mexico" in which he stated that  "Xolotl is the twin-brother of Quetzalcoatl, and vice versa. Therefore Xolotl became the 'god of the twins', and Quetzalcoatl’s name can be translated not only as 'plumed serpent' but also as 'precious twin'.”

And in the more extreme form denying the meaning "plumed serpent" it is found in discussion fora on the internet:  "Another lie. Quetzalcoatl was not white, he made no prophecy, he didn’t promise to return, and his name does not mean ‘feathered serpent.’ The name means ‘precious twin’. The myth that Quetzalcoalt promised to return is a total fabrication--a post-conquest myth contrived by Spanish missionaries to facilitate their conversion of Indians." (2012 discussion forum)

So lets look a bit at what the evidence for this secondary meaning actually is.

Everyone agrees that the name Quetzalcoatl is composed of two roots quetzalli /ketzal-li/ and coatl /ko:wa-tl/.  What is less clear is what exactly the meanings of those two words are.

Related to the verb quetza /ketza/ "to stand/put upright", the meaning of the word quetzalli is given by Molina as "pluma rica, larga y verde" (Long, green, rich feather). The relation probably refers to the way that feathers stand up from the skin of the bird. In the Florentine Codex we find sentences such as "in quetzalli īhuān in nepapan tlazohihhuitl " (the quetzalli and the other precious feathers),  or the description of the feather seller at the market "quināmaca in quetzalli in chīlchōtic, in tzicoliuhqui, in pilihhuitl"  (he sells the quetzalli, the chili-green-colored, the curved, the young feathers) and "ca ixachi inin tōtōtl īquetzallo" (they are huge that bird's feathers) (I have the examples from the Florentine from Wimmer's dictionary under the entry "quetzalli"). This should show adequately that the meaning is primarily related to a particular kind of long green feather which is highly valuable for decorative purposes.  According to Sahagun the metaphorical usages of the word quetzalli were as a reference to an unborn child, and as a form of address when addressing the Tlatoani "Quetzallé!". This does suggest that it was used to express feelings of deep appreciation similar to calling somone "my treasure" or "my jewel". However I have found no examples of usages of "quetzalli" as modifier with the meaning "precious". In compounds it always seems to refer directly to the quetzal feather itself , e.g. quetzalcomitl "a recipient for holding feathers" or quetzalcopilli "feathered headdress" (one possible exception is the word quetzalitztli, describing a kind of precious stone, but I wonder if we can assume that quetzal- necessarily means "precious" in the Nahuatl word, it might well refer to some other property of the stone, perhaps a green color - or to the original literal meaning of quetzalli as "something that stands upright"). 

The word coatl /ko:wa:tl/ (with the plural form cocoua /ko:ko:waʔ/) however clearly has two meanings, "snake" and "twin". Molina gives it in several instances both in the Spanish and Nahuatl parts of his vocabulario: 
- Geminos,hermanos nacidos de vn vientre. - Cocoua.

- Mellizo - coatl

- Cocoa - culebras o mellizos.

- Coatl.- culebra,mellizo,o lombriz del estomago
The usage of "twin" lives on in Mexican Spanish as cuate "twin/close friend".

So half the translation holds, Quetzalcoatl could be translated as "feather twin", which would not be weird given the fact that he is described as being the twin of the dog-deity xolotl, and that he was related to the planet venus which was considered a twin-star with different twins appearing in the evening and the morning.

But where does the "precious" aspect come into play? How and when was it suggested that the word for "precious feather" could be used to mean simply "precious".

Here we have to go even further back in the literature. 

Jacques Lafaye in his "Quetzalcoatl and Guadalupe" points us to a manuscript called El Fénix de Occidente: Santo Tomas descubierto con el nombre de Quetzalcoatl written by the Jesuit Manuel Duarte in the second half of the 17th century (Lafaye argues that it was not written by Carlos Sigüenza y Góngora to whom the text is usually attributed).  In this manuscript Duarte was determined to demonstrate that the native people of New Spain were not strangers to the Christian Gospel. Many friars had a hard time believing that God could have left an entire hemisphere devoid of his word for 1500 years, and they looked for signs to suggest that  they had in fact been subject to evangelization which they had then subsequently forgotten.

Duarte was convinced that Saint Thomas the apostle, who was known to have preached in India, had also reached the West Indies, and converted the natives to Christianity and he looked for all the evidence that he could find for this thesis. In the myths of Quetzalcoatl he found exactly what he was looking for. The idea that Quetzalcoatl was in fact St. Thomas had already circulated among the Franciscans and Dominicans (e.g. Diego Durán)  as a quiet heresy, but Duarte made it explicit. He argued that apart from the ways that the figure of Quetzalcoatl as bringer of knowledge and light, and his relations to the human prince called Topiltzin suggested that the myth had its origin in the figure of of a religious man, the very name of Quetzalcoatl was indeed the same as St. Thomas. He derived the name Thomas from the Greek form of the Aramaic name תָּאוֹמָא (Ta'oma') which means "twin", corresponding also to the greek didymus "twin".  Here was a clear correspondence between the two! But what about the Quetzal part? What did that respond to?  It seems that Duarte in his eagerness to make the two parts fit, considered quetzalli with its connotations of appreciation and value corresponded to the title "Santo" (Saint/Holy). Quite a stretch when you think about it. 

The idea of Quetzalcoatl being a European Christian missionary is also found in the work of Bartolomé de las Casas, who nonetheless does not give the translation "precious twin" or suggest that it wa specifically St. Thomas. Rather Las Casas states that Quetzalcoatl refers to a certain kind of snake which has a feather on top of its head, and which is mostly found in the tropical province of Xicalango.

So no, Quetzalcoatl, cannot and does not translate to "precious twin", 

The idea behind this translation can be traced back to the millenarian heresy of the Franciscans (which is also the origin of the erroneous ideas that Quetzalcoatl was blonde, and that he promised to return and that the Aztecs thought that Cortés was the returning Quetzalcoatl/St. Thomas). It is extremely unlikely that any native Nahuatl speaker in the 16th or 17th century would have considered Duarte's etymology to make any sense. They might have accepted the idea of coatl as a double entendre connoting subtly his status as a twin, but it is unlikely that they would ever consider quetzalli to mean anything other than "precious green feather". So indeed they must have thought of the deity Quetzalcoatl as being characterized by plumage, and to have the dual aspect of a twin and a snake. 

Thus it is not surprising to look at the way Quetzalcoatl was depicted in the codices, either as a snake or a man, but in both cases decorated by long, rich green feathers.

[Thanks to the readers of the Nahuat-l listserv 

who responded to a query of mine regarding this issue, 

and pointed me on the way towards the facts. 
I have also made some corrections in 
response to comments from the list.]

Quetzalcoatl as Snake in Codex Telleriano Remensis

Quetzalcoatl as human in Codex Telleriano Remensis