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 keep 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 chieftan, 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).


tirsdag den 26. juli 2016

How to spell Nahuatl? Nawatl? Nauatl?

My last blog post was about how the Nahua people wrote before the arrival of Europeans with their alphabetic writing system. But almost all Nahuatl texts from the colonial period onwards are of course written in alphabetic writing. In this blog post, I describe the many different conventions for writing Nahuatl using the Latin script.

For the past 80 years, Nahuatl scholars have argued about how to standardize Nahuatl orthography and what conventions to use. Different groups of scholars and activists have recommended  and supported different systems. Sometimes scholars and Nahauatl activists seem to be spending more time arguing about how to write Nahuatl than they do on actually writing it. There are even cases where a single community has two different lanugage revitalization projects that refuse to cooperate because they use different spelling systems!

In this post, I try to describe the different types of writing conventions that are in use for Nahuatl, and to show their relation to different schools of thought within Nahuatl scholarship.

Roughly we can classify Nahuatl orthographies into two main types, each of which has a bunch of variatoins. One group we can call "Classical orthographies", because they base their orthographic choices on the conventions used by the Spanish speaking friars who wrote the first alphabetic texts in the early 16th century. The other group we can call "Modern orthographies" because they were introduced by academic linguists working to find the most linguistically efficient ways to represent the Nahuatl language in writing in the early 20th century. Both types of orthographies can be used to represent colonial Nahuatl as well as contemporary varieties.

For the current purpose we can define the two types of orthographies in this way:

  • Classical Orthographies: are those that value continuity with the colonial tradition of nahuatl writing - and which adopt colonial conventions because of the value they have as connectors with that tradition.
  • Modern Orthographies: are those that value linguistic efficiency and which aim to represent the Nahuatl language in ways that are either easier to learn or which facilitate a higher analytical precision by representing linguistic elements (phonemes, morphemes) in ways that are minimally variable and maximally efficient.
In practice most orthographies include elements of both "classical" and "modern" principles. 

Classical Orthographies: 

Sometimes people talk about "classical orthography" as if it is a single well-established standard. Really it is not, and it never was. In the 16th century when Nahuatl was first written alphabetically, the idea of a standardized orthography didn't even exist - and there was no established orthography for any of the spoken main languages such as English or Spanish (as anyone trying to read Shakespeare or Cortés' letters will realize). Authors writing in any of these languages simply used the writing conventions they learned from their teachers and put them to the best possible use to get their points across in the easiest way. They tended to write these languages as they were spoken, representing the sounds more or less as they pronounced them. And when they began writing Nahuatl they did the same, tried to use the conventions they knew from writing Spanish to represent the sounds of Nahuatl. This is why the only thing that is really shared by all "classical orthographies" is the fact that they represent the sounds that exist both in Nahuatl and in Spanish using the letters that were most commonly used in Spanish to represent these sounds. For example, Spanish had adopted the Latin convention of writing the sound [k] with the letter <c> before the vowels [a] and [o] but with the letters <qu> before the vowels [i] and [e]. Luckily, actually most of the sounds in Nahuatl are also found in Spanish, which meant that this method was fairly succesful. And in fact in the 16th century, Spanish phonology was even more similar to that of Nahuatl - because at that time Spanish didnt have the harsh j-sound (like in scottish Loch), but instead had a soft sh-sound as in fish which also exists in Nahuatl. They wrote this sound with the letter <x>, because that is how they generally wrote the sh-sound in Spanish. Only over the next century did Spanish gradually change the sh-sound to the harsh j-sound (and eventually began writing it with a j). (This, incidentally, is why the x is pronounced harshly in words like Mexico/Mejico, Oaxaca and Xalapa/Jalapa - but not in the corresponding Nahuatl versions which are pronounced meshi'ko, washakak and shalapan).

However there are some sounds that are found in Nahuatl that do not exist in Spanish: Primarily, the Nahuatl signature sound the tl (written in the International Phonetic Alphabet as  [t͡ɬ]), but this turned out to be easy to write with the letter combination <tl>. The sound [kw]  (as in queen )likewise turned out to be easy to write, since this sound also existed in Spanish as (although in Spanish it is a combination of k and u, and not a single consonant sound) so they wrote it <qu> or <cu>. The Nahuatl consonant [ t͡s] also didnt exist in Spanoish, but the Friars knew the sound from Hebrew and wrote it in the same way they would when transliterating the scripture using the letter combination <tz>. Nahuatl also had the consonant sound [w] (as in "wat?") which was not found in Spanish - friars couldn't quite decide on how to write this one, but usually they simply represented it with the vowel letter <u> - sometimes combined with a consonant letter such as <hu> or <gu> (More about this below, under Canger's orthography).

But the most difficult sounds to write were the glottal stop (or h) neither of which existed in Spanish; and the distinction between long and short vowel duration. At first most friars didn't even realize that these sounds actually existed in Nahuatl, so they simply didnt write them! This is the main difference between the orthographies of the Franciscan friars and the Jesuits.

Franciscan style orthographies:

In the 16th century the most widely used Nahuatl orthographies were those developed by the Franciscans. The Franciscans had a highly practical approach to evangelizing, without too many theoretical considerations - they just did whatever seemed to work (which sometimes got them on the wrong side of other ecclesiastic orders such as the more orthodox Dominicans). The same approach worked in the area of orthography, where the Franciscans never pined much about being consistent or about how best to write. This pragmatic approach was probably partly what allowed the Franciscans friars and their indigenous aides to author the most extensive documentation of  any Indigenous language in the colonial Americas. The 16th century saw major Nahuatl works like Andres de Olmos' Nahuatl grammar, Bernardino de Sahagún's 12 volume encyclopedia about Indigenous Nahua culture (now called the Florentine Codex) and Alonso de Molina's vocabularies. None of these works represented the saltillo or the vowel length distinction, and they were extremely inconsistent in representing sounds like [w] and [j]  - and even so they worked fine and thousands of Nahuas learned to write using these loose conventions. Apparently they didn't loose much sleep worrying about the fact that the representation of some minimal pairs was ambiguous (e.g. [tla:tia] "to hide" and [tlatia] "to burn" both of which was written <tlatia>, or [paʔti] "to become well" or [pa:ti] "to melt" both of which were written <pati>, and even the difference between plural and singular of verbs in the present tense as [kochi] "he sleeps" and [kochiʔ] "they sleep" were both written <cochi>). When Franciscans sometimes heard the saltillo (they only ever seem to have heard it bwhen it occurred before another consonant) and decided to write it, they used the letter <h> giving <pahti> "to cure", <pati> "to melt". 

Other than these conventions Franciscans (and the vast majority of colonial 
Nahuatl authors) were very unruly in their orthographies - for example they used the letters u and o interchangeably for the vowels [o] and [o:], they used the letters <i> and <j> and <y> interchangeably both for the vowel [i] and the consonant [j], they used <hu>, <u> and <o> intechangeably for the consonant [w] and used the letters <z>, <c>  and <ç> for the sound [s]. '

Really, by modern standards the Franciscan orthography was a mess - and yet we are fully able to read it today just as they were back in the 16th century. This tells me that consistency and standardization of orthographies is vastly overrated. 

Jesuit style orthographies: 

Page from Carochi's 1645 grammar which uses macron to show long vowels
and circumflex accent to show wordfinal saltillo.
Among the catholic orders the Jesuits have a reputation for being studious and academically inclined. The jesuit orthographic tradition for Nahuatl embodies this reputation for thoughtfulness, and Jesuits were among the first scholars to have theoretical insights about how the Nahuatl language differed from Spanish and other well known languages and how this ought to influence the way the language was written. Nonetheless, most of the honor for these insights should probably be given to the first Nahuatl grammarian who was also a Nahua person and a Nahuatl native speaker: the jesuit priest Antonio del Rincon. He wrote a short grammar in which he noted the existence of the saltillo and vowel length distinction and to suggest marking it in writing to represent the language more faithfully. His suggestions were taken up a fifty years later by fellow Jesuit Horacio Carochi who introduced a fully developed system for marking vowel length and saltillo systematically. Following Rincon, Carochi used diacritical marks to show these distinctions and he marked the saltillo with an accent (grave, or circumflex) and vowel length with a macron.

Hence the words "to cure" and "to melt" he wrote <pàti> and <pāti> respectively and the difference between "he sleeps" and "they sleep" he wrote <cochi> and <cochî>. Sometimes he marked short vowels with a breve sign <ă>, but he did not do this consistently (since it is redundant to mark both long and short, he only marked short vowels when a long vowel would change the meaning).

The Andrews-Campbell-Karttunen orthography:
Karttunen's dictionary which has
popularized the ACK orthography.
In the mid-twentieth century American historians discovered the rich trove of Nahuatl language writings and began working with them. Among the earliest historians looking at these works were Arthur Anderson and Charles Dibble who translated Sahagun's Florentine Codex into English. Another scholar to take up the study of Nahuatl was the grammarian  J. Richard Andrews, who published his grammar of the "classical" language in 1975. He chose an orthography that was linguistically accurate marking all the phonemes including the vowel length distinction and the saltillo - and which combined aspects of the Franciscan and Jesuit tradition. Specifically he adopted Carochi's use of macron for marking long vowels, and the tradition penchant for marking the saltillo with <h>. He conventionalized the use of <hu> to write the sound <w> before a vowel and <uh> syllable-finally

Andrews' orthography was in turn adopted and conventionalized further by R. Joe Campbell and Frances Karttunen in their Foundation Course and in Campbell's morphological dictionary, and the important dictionary of Frances Karttunen (the first full Nahuatl-English dictionary, and the first to consistently mark the vowel length distinction). This orthography was further adopted by the school of historians trained by James Lockhart who collaborated with Karttunen in the 1970s. Today, almost all new editions of colonial Nahuatl texts adopt the Andrews-Campbell-Karttunen orthography as the standard (although many of them choose not to mark vowel length). 

One problematic feature of the ACK orthography (thanks to John Sullivan for introducing this term which i stole from one of his facebook statuses) is that it uses the letter <h> in three distinct functions - as the saltillo and as a part of the <hu>-digraph used to write [w] and as part of the <ch> digraph. This gives spellings with two consecutive h's such as  michhuacan [mit͡ʃwaʔka:n] (name of the state Michoacan - "Place of Fishowners"), or ohhui [oʔwi]"difficult". And it also creates near-ambiguity in cases where a [k] sound written with <c> precedes a [w] written with <hu>  over a syllable boundary (e.g. cachuia "to provide someone with sandals" where the reader has to realize that the <ch> is pronounced as [kw] and not [ch].) From the point of view of a proponent of a modern "efficiency based" orthography, clusters like <hhu>, <chhu> and <chu> where the letter <h> has a different value, comes across as unelegant and unnecessary - even though it is not technically ambiguous.

The use of <h> for saltillo also has the problem that it makes it impossible to distinguish in writing between varieties that pronounce the saltillo as a glottal stop, and those that pronounce it as an [h] - and it also somewhat implies that the h-pronunciation is the norm, when in fact we know that the normative pronunciation in the Nahua capital of Tenochtitlan was the glottal stop. 

The main advantages of the ACK orthography is that 1. it is very similar to the ortography used for most colonial texts and makes the transition from the study of the grammars (using Andrews and Karttunen's works) to the reading of colonial texts very easy, 2. it marks each Nahuatl phoneme with a single letter (or letter combination) and uses only symbols found on a standard American keyboard. 

Launey's orthography

About the same time that Andrews was working in the US, a French linguist was also working on a major analysis of the Nahuatl language based on the Florentine Codex and on Carochi's grammar. Michel Launey published a full didactic grammar of Nahuatl in French in 1979. He chose to use Carochi's conventions for marking saltillo with diacritic marks, standardizing them, and getting rid of the breve accent on short vowels. Since Launey's work was first published only in French and Spanish, (and a somewhat inadequate English translation in 2011) it mostly gained currency in Europe and Mexico, and among linguists more than among historians. His main work, the 1986 thèse d'etat, still exists only in French. It is to my mind the single best grammar of colonial Nahuatl written - surpassing the work of Andrews, and that of Carochi (francophone readers can check it out here). 

The Carochi-Launey orthography has the advantage that because the saltillo is marked as a diacritic it avoids the collisions of digraphs that are found in the ACK orthography, and it avoids implicitly suggesting the pronunciation <h> as the way to pronounce the saltillo.

Canger's orthography

Una Canger is a Danish linguist (and my first Nahuatl teacher) and writes in many different orthographies - this is because she works with many contemporary varieties and adopt the conventions that work best with the variety and its speakers and her own linguistic sensibilities. For the writing of Nahuatl she has made one important proposal. 

In a 2011 article, Canger described the how it happened that Nahuatl grammarians ended up writing the sound [w] with the letter combination <hu>. She shows that the tradition originates with the Franciscan Andres de Olmos - but she also shows that he did not always write the phoneme [w] as <hu> or <uh> - in fact he mostly did this when the [w] followed a consonant or preceded a word boundary or a consonant in the subsequent syllable. When the u was For example he wrote the word [siwatl] "woman" as <çiuatl>, but the word [yeʔwatl] "he/she/it" he writes <yehuatl> and the word "my wife" [nosiwaw] he writes <noçiuauh>. This leads Canger to suggest that what Olmos was doing was that he was using the <h> to show to the reader that the <w> is pronounced differently when it occurs wordfinally or before or after a consonant than when it occurs between two vowels. In fact drawing on her knowledge of contemporary Nahuatl, Canger suggests that it is exactly the aspiration that often accompanies the devoiced variant of <w> that Olmos was representing with the h (this argument is also strengthened by the fact that Olmos also writes h after the letter l in the same positions - since l also devoices under those conditions). Canger then shows that subsequent grammarians adopted Olmos convention of using hu without understanding the way that he used it, and instead of writing only devoiced w with h they used it across the board. This confusion is the ultimate reason for the problematic digraphs found in the ACK orthography and other orthographies that use the <hu> convention. Instead, Canger suggests returning to Olmos original principle - representing the [w] sound with the vowel letter <u>. Hence Canger does not write "nahuatl" but nauatl (as did Olmos and many colonial authors) or else nawatl writing the [w] as <w>. 

While it seems that Canger would prefer a more modern orthography using k and w and s instead of c/qu and u and z/c, she suggests that also scholars who prefer a classical style of orthography ought to return to writing [w] as <u>. Canger's proposal shares all the advantages of the ACK and Launey orthographies - and avoids the problematic digraphs combination found in both of them. The main drawback is that the other orthographies are already in wide usage and that by now it will be quite hard to get people to start writing Nauatl instead of Nahuatl.

Comparison of "Classical orthographies":

”we do it”

Modern orthographies: 

"Modern" orthographies also differ among themselves - but they share the principle that they aim for maximal efficiency rather than maximal continuity with colonial writing traditions. But efficiency can be measured in different ways that are not always compatible. One criterion of efficience might be simple graphic efficiency to have the smallest and most parsimonious array of graphic units  - for example following the principle of "one phoneme - one letter". This kind of "phonemic efficiency" would prefer to remove all the digraphic letters (tl, tz, ch, kw) so that no letter is used to represent two different phonemes and no phoneme is represented by two distinct typographic units. Another kind of efficiency would be to make sure that the orthography is maximally easy to learn - a kind of "pedagogical efficiency". Another kind of efficiency is to make sure that the orthography is maximally accessible to linguists - for example by using symbols for sound values that are internationally established in the linguistic community (e.g. in the same values as in the International Phonetic alphabet, or the Americanist Phonetic Alphabet). 

The Americanist orthography

The Americanist orthography stems from the earliest studies of contemporary spoken Nahuatl by American and Mexican US-trained linguists in the first half of the 20th century. They tended to use a phonetic notatoin system now known as APA (Americanist Phonetic Alphabet), which aimed towards being strictly phonemic and based on the principle of one letter per phoneme. Hence they used single letter symbols for all of the sounds that the "classical" orthographies represented with digraphs -

APA style transcription key:
  • tl = ƛ
  • tz = ¢ (or sometimes c)
  • cu/qua = kw (or sometimes q)
  • ch = č
  • x = š
  • c/qu = k
  • hu/uh = w
  • h = h
  • ʔ = '
Americanist orthography is really very efficient in this way - except that it requires a bunch fo special symbols not found on ordinary keyboards. Hence many linguists taking a practical approach retained tl, ts, ch and x avoiding unnecessary additional signs apart from those already on a standard keyboard.

Such a modified Americanist orthography was in fact adopted as the official standard by the participants in the first Aztec Congress which was held in Milpa Alta in 1940 and attended by many native speakers. They stated that they prefered this orthography exactly because it didnt use the Spanish-style digraphs que/qui ce/za etc. In this way the choice of a "modern" and "scientific" orthography was a political move towards decolonization. Today a variant of this orthography (without the special symbols, but with k and w) is used by most Nahuatl speakers in the Zongolica region where the linguist Andrés Hasler has promoted it for several decades. 

SEP and SIL's orthographies

Example of the SEP/SIL orthography from a textbook.
It uses the letter j to represent the h sound.
In the 1940s an American missionary organization called Instituto Linguistico de Verano (Summer Institute of Linguistics or SIL) began collaborating with the Mexican Ministry of Education (SEP) to develop educational materials in indigenous languages. Because the government wanted indigenous peoples to learn Spanish and primarily wanted to use indigenous language education as a way to teach Spanish, they considered that the orthographies should only use letters already found in Spanish. They developed many different orthographies for different Nahuan varieties - some of which used the "classical" Spanish digraphs, and others which used k and w (although most use hu or simply u for [w]).  The only common denominator seems to be that they use the letter j for the saltillo when it is pronounced as an [h]. This presumably is because the letter <h> is "mute" in Spanish which migh confuse the children during the gradual transition from Nahuatl to Spanish. Today SIL still consider the ease of acquisition for students who are already literate in Spanish as the main criteria for efficiency. Most SEP/SIl orthographies do not mark vowel length, because most Nahuatl speakers are not actually aware of this feature of their language, and vowel length is not very important in distinguishing words from eachother. Some of them however do and when they do they tend to use either double vowels (aa/ee/ii/oo)  or underlining (a, e, i, o) to mark long vowels.

SEP and SIL style orthographies are extremely influential in Mexico and those Nahuatl speakers who have been lucky enough to have classes in their languages in school are likely to have learned them. Also most Nahuatl language authors tend to use these orthographies (because most of them are trained as bilingual teachers through SEP). Many SEP and SIL orthographies also do not write the double [ll] sound which is very common in Nahuatl but instead writes it as a single l. This is of course because Mexican Spanish pronounces the double l as the [j] sound (which is written with y in Nahuatl).

The drawback of using <j> to write the sound [h] is that it often causes non-Nahuatl speakers to erroneously pronounce it as the harsh Spanish j-sound and not as a soft h-sound. Writing the double l as a single-l is problematic from a grammatical viewpoint because the double-l is what happens when the absolutive suffix -tli occurs after a root ending in -l. So by writing only a single l, the grammatical structure of the language is obscured making it harder to teach the grammar. 

"Intuitive orthographies"

Example of intuitive orthpography form a kindergarten in Hueyapan. It says
"xi nech ate ki an xinech pojpua nochipan kion kual le ni koponis"
which usually would be written as
"xinechateki an xinechpojpoa nochipan kion kualle nikoponis"
which means
"Water me and weed me, that way I will always bloom"
Most Nahuatl speakers have not received any education in Nahuatl and many have never even been aware that their language can be written down. Usually Mexican schools teach only Spanish. This means that they have to invent new conventions almost from scratch (or based on Spanish) when they start writing their language since they havent been taught any of the existing orthographic conventions. These new Nahuatl-writers tend to adopt ways of writing that are intuitive to them based on their knowledge of Spanish and sometimes English orthography. Such intuitive orthographies can be seen on the internet where Nahuatl speakers sometimes converse in writing withouth ever having been taught how to write their language. These orthographies are often  sinmilar to the SEP orthographies (using j for h) - but two new features that are not used in any of the established orthographies are often found in intuitive Nahuatl writing. One is that they often use <sh> instead of the traditional <x> to write the sh-sound. This is probably because most Mexicans are associate this sound with English, and know that it is written sh in the English orthography. The second is that they often write grammatical prefixes as separate words, instead of fusing them together as Nahuatl grammarians do. This is probably because they often think in Spanish when they write in Nahuatl translating from Spanish into Nahuatl and therefore isolating elements of meaning the way it is done in Spanish.

Comparison of Modern Orthographies:

”we do it”
tic chiua
shi tsecuini

Note that the SEP1 and SEP2 and the "intuitive" orthography are just possible examples, but many different combinations of the different choices exist.

So Which One Should You Use?

There is no objective answer. Each orthography comes from different ideas about what is important, and is used by certain communities working within specific genealogies and traditions.

That fact of the matter is that regardless of which orthography you use someone will inevitably tell you that you are using the wrong one. I think the best approach is to learn to read all of them and to use one consistently. But really as I noted consistency is overrated. Shakespeare and Chaucer and Cervantes were able to found their national literatures without using standardized orthographies. Molina and Sahagun were able to found Nahuatl literature without one. The important part is that we keep writing and reading in Nahuatl.

Now I have told how one writes in the Nahuatl language
aʃka:n onikiɁtoɁ ke:nin se:  t͡ɬakwilo:s i:ka nawat͡ɬaɁtolli
aška:n oniki’to’ ke:nin se: ƛa’kwilo:s i:ka nawaƛa’tolli
axcan oniquito quenin ce tlacuiloz ica nahuatlahtolli
axcān oniquìtô quēnin cē tlàcuilōz īca nahuatlàtolli
axcān oniquihtoh quēnin cē tlahcuilōz īca nahuatlahtolli

axcan oniquijtoj quenin se tlajcuilos ica nahuatlajtoli

axkan onikijtoj kenin se tlajkuilos ika nahuatlahtoli
axkan onikihtoh kenin se tlahkuilos ika nawatlahtolli
ashkan onik itoh kenin se tlacuilos ica nahua tlajtoli

(Note: This post was edited on July 31st 2016 to make some minor corrections to the section on the ACK orthography based on comments from Frances Karttunen on the Nahuatl-l listserver)

onsdag den 8. juni 2016

Aztec Writing: How does it really work?

I have never written on this blog about colonial or precolonial Nahua iconography or glyphic writing. This is partly because I tend to find codices boring, prefering to work with spoken language, and partly because other people are much more knowledgeable about these things than I am. Recently, however, I have started reading up on this, and had some talks with some specialists in Nahua writing. So here comes my attempt to describe the current debates within the field of Nahua writing studies.

First of all perhaps we need to point out what we mean by Nahua glyphic writing - most Nahua texts are of course written in Latin letters - but here we mean texts written with non-European signs. In the codices this kind of writing abounds, mostly used to write personal names and the names of places.

The name of Acamapichtli "handful of reeds",
ruler of Tenochtitlan,  written with
glyphs  and Latin letters.
The glyphs shows a hand holding
a bunch of reeds.

The name of the town of Xochimilco "Flower field place" written with Nahua glyphs:
The squares on the bottom represent a "field" - representing the root MIL- in Nahuatl
and the flowers on top represent the root XOCHI "flower" in Nahuatl.

As can be seen from the examples, we have a pretty good idea about how to read Nahua glyphs (because almost all glyphic texts are accompanied by writing in Latin letters), and generally we know what the say. But there is still some discussion about the principles based on which the Nahua wrote. Scholars have for example discussed if the Nahua simply depicted concepts with pictures, or whether their signs actually represent words and sounds? Today we know that Nahuas seem to have definitely used their signs to represent spoken words and sounds, but specialists are still discussing the technicalities of how the Nahua writing system worked.

Aztec Writing: Logographic? Phonetic? Semasiographic? Rebus-writing? 

The decipherment of Aztec writing is not really the classic kind of situation where we have a lot of long monolingual texts that we are unable to read because we don't know the language or the principles they used to write with, and where a bilingual text (such as the Rosetta stone for Egyptian hieroglyhs, or Landa's syllabary for Maya hieroglyphs) can provide the clues to finally crack the code. On the contrary, we know that Aztec glyphic texts were written in Nahuatl, and they supply us both with the glyphic script, and with a transliteration in to the Latin alphabet, and they often even with a Spanish translation. So most of the time the question is not what the glyphs mean, the question is how they work to give that meaning. Furthermore, most texts written in Aztec glyphs are short, and consist mostly of names of places and people.

Nonetheless, the decipherment of Aztec writing did have to pass through some phases of confusion. Particularly, a phase in which scholars didn't consider it to be a script at all, but just drawings that could only be read non-linguistically. In some sources we can still find the claim that the Aztecs did not have "true writing". The concept of "true writing" in this sense is used to describe the fact that it does not seem the Nahuas wrote long narrative texts using their script. Rather they wrote stories using sequences of pictures, and used the script to name the persons and places who participated in the stories.

The first scholars to note that the Aztec script in fact has a lot of "phoneticism" (i.e. it represents the sounds of spoken language, and not just ideas), were those 19th century antiquarians who first studied the early colonial codices. One of them was Joseph Marius Alexis Aubin, a young French scholar who accompanied Maximilian of Habsburg who went to Mexico with a contingent of French forces because Napoleon III (no, not Bonaparte) had appointed him the new Emperor of Mexico. Aubin had studied Nahuatl in France, and probably also had help from Maximilian's main Nahuatl specialist the Nahua nobleman Faustino Chimalpopoca who had worked with many of the Nahuatl language codices. Reading Aztec maps and tribute lists Aubin (1849 [1885]) realized that all the Nahua rulers and all the cities in the codices had little name glyphs attached to them, and that these name glyphs consisted depicted concepts or words that were part of the name they represented. For example all the places that had the locative ending -pan in their name, had a little flag in their name glyph. "Flag" in Nahuatl is of course pantli or pamitl - so Aubin realized that the flag represented the ending. Aubin deciphered a number of glyphs in this way, by seeing that they depicted short words that could be used both to signify the word they depicted but also words that sounded similarly (e.g. a stone "tetl" signified the syllable TE, a pot "comitl" signified the syllable KO, etc.). And he noted that there was a good deal of systematicity in the way the word signs were used, going as far as describing the system as an écriture syllabique [a syllabic script]. Aubin was particularly inspired by finding a version of the "Pater Noster" written partly in Aztec script - it was apparently used as a medium with which the friars could better teach the Nahuas the catechism. In the Nahuatl script the title said:

Flag            Stone              Cactus               Stone
PAN(TLI)     TE(TL)        NOCH(TLI)       TE(TL)
pa                  te                   noch                  te  

Aubin realized the flag glyph was /pantli/ "flag" representing the root pan, the second symbol was the stylized symbol for /tetl/ "rock" representing the syllable te, the cactus symbol was /nochtli/ representing the root noch (the tli/tl suffix is not part of the stem). The phonetic reading was PA TE NOCH TE - a fairly close approximation of the Latin "Pater Noster" (remember that colonial Nahuatl has no /r/). This convinced Aubin that the Aztec script operated from a syllabic principle - and he considered that Nahuas were already literate in this script when the friars arrived, which why it made sense for the friars to use it.

However, his argument was not very well received. A number of scholars argued that the phonetic signs were introduced by the friars simply using a rebus principle, and that it didnt represent pre-contact usage. Since all of the known texts using the script were from the early colonial period, this was hard to refute, and for many decades the consensus came to be that the Nahua script was not true writing but a "pictographic" form of primitive picture writing. Some scholars argued that Nahua iconography, and central Mexican indigenous iconography in general, is "semasiographic"in character which means that it does not represent a spoken language directly, but rather offered clues to the "reader" through which they can improvise a narrative in whichever language they happen to speak. Nonetheless a number of works on the principles used in Nahua writing were published, by Barlow & McAfee (1954), Dibble (1971), Prem (1992) and Nicholson (1973) - Nicholson particularly argued that perhaps there was a greater degree of phoneticism in precontact Nahua writing than had previously been thought - but the mainstream view continued to be that pre-conquest Nahuas did not "write".

Lacadena's Syllabary:

Lacadena's 2008 Syllabary,
published in PARI journal 8:(4):p. 23
In 2008 a major event happened in Nahuatl writing studies. Spanish linguist and Epigrapher Alfonso Lacadena published an analysis of Nahuatl writing in which he argued that Aubin had been right to call the script "syllabic". Lacadena had previously participated in the work of deciphering the Maya script, and he argued that the Nahua system was essentially similar - combining a set of logograms representing entire words, with a syllabary that could be used to phonetically spell most of the possible syllables of the language - making the system capable of representing spoken language.

Lacadena had been able to arrange the known phonetic elements of the script into a syllabary similar to the Maya syllabary - showing that Nahuas in fact had syllabic signs for almost all the possible syllables in the language. He argued that several of the already recognized signs that had previously been read as logograms ("whole-word signs") in fact ought to be read as syllabograms ("syllable signs") consisting of only a consonant and a vowel - the flag glyph for example ought to be read pa and not PAN,  the pot glyph ko and not KON, etc. He shows that it is possible to demonstrate that some signs that were originally read as logograms, had to be read as syllabograms in certain words. For example the drum sign which had traditionally been read WEWE, he proposed should be read - at least sometimes - simply as we. And he showed this by demonstrating that it was used to write names such as tohuexiuh /towexiw/ where it only represented one syllable, not two.

A very interesting set of readings provided by Lacadena deal with the syllable /wa/ which he shows can be written either with two parallel lines, with two leaves or with a grasping hand. He argues that the two lines come from the verb wawana "to scratch", that the two leaves are amaranth leaves wawtli (Personally, I think they are more likely from ixwa "leaf" and in one of his examples the glyph actually co-occurs with an IX logogram (the eye), suggesting a dual representation of the ix-syllable - but clearly in many other cases it is only read as wa), and that the grasping hand is a logogram based on the possessor suffix -wa' (e.g. in michhua "fish-possessor" or mazahua "deer-owner"). The two former readings he considers syllabograms, while the third he considers a logogram (inspite of not representing a word, but a grammatical morpheme). These readings are very important and constitute an important move towards the syllabary.

The name of Spanish encomendero Luis Vaca written
in Nahua glyphic writing. The bottom sign is an olote (dry maize stalk) (OLO),
then an eyeball (IXand on top two leaves (wa [or maybe (IXWA]), 
the long plate shaped glyph is probably a plate CAX or ca. Giving the full reading (o)LO-IX-WA-KA(X) 

Lacadena demonstrated that as in the Maya (and Egyptian) scripts often the syllabograms were used as phonetic complements, added to logogram to support a specific reading - or even at times to force one of two phonetically distinct readings of the same logogram.

In Lacadena's interpretation the Nahuas had a fully developed logo-syllabic writing system already in the pre-contact period, although he also recognizes that the use of phoneticism may have become more prominent as the Nahua logosyllabic script competed with the Latin alphabet. By setting up the Nahuatl phonetic signs into the syllabary format, Lacadena moved the discussion forward - it was now no longer relevant to discuss the phoneticity itself, from now on the discussion would have to be about the degree of systematicity with which the Nahuas used phonetic symbols.

Whittaker's Challenge:

In 2009, anthropologist and epigrapher Gordon Whittaker challenged Lacadena's vision of how the Aztec script worked. Together with Hanns Prem, Whittaker had studied the phonetic principles of Maya writing for awhile and did not agree with Lacadena's strictly syllabic interpretation. In his paper "Principles of Nahuatl Writing" he proposed that rather than being a strict logo-syllabic script, Nahuatl writing allowed a much wider range of possibilities. For example he argued, most of Lacadena's syllable signs could be read both as syllable signs with a consonant and a vowel, but also as logograms including syllable final consonants; and sometimes polysyllabic logograms could be read as syllable signs, selecting just one of their syllables as their phonetic value. In this way the Nahuatl script included both logograms, syllabograms and bisyllabograms. Whittaker therefore suggests that the way that Nahuas read their texts were not as straightforward as Lacadena suggests - they needed access to a wider array of interpretive processes than simply reading the syllabograms. In the example below, the place name Chipiltepec is written with the syllabogram chi (depicting the edible seed "chian"), the logogram HUIPIL"blouse", the logogram TEPE and the syllabogram te used as a phonetic complement.

chi     (hui)pil     TEPE    te
The interesting part here is that the logogram HUIPIL is not read as a logogram but as a syllabogram, ignoring the first syllable and reading only the second syllable pil. This challenges the strict division Lacadena poses between logograms and consonant-vowel syllable signs.

Whittaker also notes that several of the signs that Lacadena considers syllabograms, can be read both as syllabic Consonant-Vowel (CV) reading, as well as as a Consonant+Vowel+Consonant (CVC) group. For example the "flag" can be read both pa and pan, and the "tooth" can be read both tla and tlan. He seems to consider that the reading with final -n is not a real logogram, because it is not usually used to represent the words "flag" and "tooth", but rather to write the locative endings on place names - locative endings that happen to be homophonous with the words depicted by the logograms, but which have completely different meanings. This is another reason Whittaker considers some of the Nahua signs to be phonetic, but to represent neither CV syllables nor words - but longer sequences such as CVC or even CVCV.

Furthermore, Whittaker implies, it does not seem that Nahuas thought of their phonetic writing as a self-contained closed system in the way that a syllabary is generally thought of. Rather the way he describes the system it is an array of conventions, many of them fairly loose, which the Nahua used in a creative and intuitive way. Whittaker notes for example (in a talk he gave at Yale in May 2016) that the Nahuas used ways of expressing concepts that are unique to the Nahua script. For example they used color of glyphs to convey color words (i.e. the word chichiltepec "red mountain" written as a red mountain where the color of the mountain is used as a logogram).

Whittaker also produces some interesting new readings of specific signs, for example he shows that a worm-shaped glyph can be read COCHIN, based on the word ihcochin "earthworm".  For example the name Tlacochin can be written with a combination of four signs: TLACOCH "javelin", (ih)COCHIN, tla/TLAN "tooth", and co/CON (here I allow for both the possibility of reading these as logograms and as syllabograms, hence the /). Interesting here each syllable (except -in) is spelled phonetically twice - providing no possibility for misreadings. Here, following Lacadena's method, co and tla can be read as syllable signs, and TLACOCH as a logogram. But the worm, spelling syllables COCHIN can neither be a logogram (because the name is likely derived from tlacochtli "spear" and not from ihcochin "earthworm") or a simple syllabogram.

The name Tlacochin written both with Latin letters and with
four Nahua glyphs. It is the wormlike creature on top of the teeth
that Whittaker reads as (ih)COCHIN.

Finally, Whittaker argues, that if the Nahuas indeed thought of their system as a complete syllabary, then it was a very deficient syllabary since there are no known syllabograms for several of the most frequently occurring syllables in the language such as ti, ni, ki, tli, kwa, ya, etc. This would make it impossible to actually represent spoken language using only syllabograms. And this in turn suggests that the Nahuas did not conceive of their phonetic signs as a systematic complete syllabary, but that rather than an organized system the syllabograms formed a repertoire of signs that had grown through accumulation in the course of the Aztec writing tradition. An incipient syllabary perhaps, but not quite there yet.

So, Whittaker and Lacadena agree on considering the Nahua script to be highly phonetic - also in pre-contact times - but they disagree on what kind of system it was, and how Nahua scribes interpreted the phonetic signs. Nonetheless, it doesn't seem that either of the two epigraphers are willing to concede many points to the other. To my knowledge, Lacadena has yet to respond publicly to Whittaker's argument, while Whittaker's papers seem to me to exaggerate some of the differences between the two models (for example the difference between logograms and bisyllabograms isn't very big in practice - it is mostly a question of labeling I think). So where does Nahuatl glyph studies go from here?

My 5 Cents Worth:

While I am not an expert on Nahuatl writing, to conclude I will share my own evaluation of Lacadena's and Whittaker's competing models.

Lacadenas demonstration of pervasive phoneticity of the Nahua script is extremely important, and did inaugurate a new way of looking at the Nahua script. But I am not convinced by the argument that the script can be understood as a strictly logo-syllabic script. Whittaker demonstrates that the script is considerably more flexible than that, including types of signs not known in any other scripts (e.g. the use of color to signify color words), and making more readings available to the reader. I simply dont think that there is a convincing reason to think that Aztec scribes and readers thought of their signs as representing mainly CV syllables rather than for example representing entire word-stems that could e read for their phonetic value as well as as the word-concept they represent. On the other hand I am not sure if Lacadena is actually argueing that the Aztec scribes thought of their script as a syllabary, and that the syllabic interpretation is "psychologically real" - this I think would be a problematic claim. But it is possible, I think, that he simply meant to demonstrate the pervasiveness of syllabic signs in the system to show that it is not as different from the Maya system as it has been claimed. If this is the case I think the point was well-made and Whittaker's argument can simply be considered a demonstration of additional features of the script, that Lacadena did not spend time exploring because his aim was another.

On the other hand, I think Whittaker exaggerates the differences between the two interpretations. Particularly, it seems that Lacadena does allow for many of the readings that Whittaker considers disyllabograms and CVC syllables - he just considers those logograms used according to the rebus principle (Whittaker apparently doesnt like using the word "rebus" for phonetic readings of logograms). This seems to me as a mostly theoretical discussion that doesn't really impinge on our understanding of the script itself. I assume that Lacadena acknowledges that when a logogram can serve the function of expressing another word than the one that is actually depcited, this is indeed a phonetic rather than a logographic reading of the sign.

Some of Lacadena's readings also beg the question about whether each sign really has only one possible reading. For example many of his syllabograms clearly must have originated as logograms, for example the tla- and pa syllabograms which are represented "logographically" with signs that must have been read originally as TLAN and PAN - and which sometimes still are clearly used to write out those exact phonetic sequences with final -n (for example in toponyms). Hence it seems to me that we must concede that these signs are either used sometimes as syllabograms and sometimes as logograms, or that we can simply conclude that the final consonants can sometimes be omitted to produce syllabic readings from logograms. Probably, over time some logograms were conventionalized as being mostly used syllabically, while others kept their double readings. Whittaker produces further evidence for this type of process when he shows that the HUIPIL logogram can be read simply as PIL. And another example would be if I am right that the double leaf symbol was originally and occasionally a logogram IXWA which then became conventionalized as a syllabogram wa. Although the possible alternative  reading of "Luis Vaca" as OLO IX IXWA (where IX is a phonetic complement noting that the leaf sign should be read IXWA and not simply wa), instead of Lacadena's reading OLO IX wa, suggests that maybe two readings continued to coexist).

Where, I think Whittaker's interpretation is strongest is in that it paints a picture of a very different process of writing than Lacadena's  - a process that is highly creative, combining intuitive conventions and a repertoire of established signs with local innovation. I think it is clear that Nahua writing was in many ways unique when compared to other writing systems, for example in being seemingly open-ended, and without many fixed conventions.

In any case, I think any future engagement with Nahua glyphic script needs to take both Lacadena's and Whittakers arguments into account, in order to pick out the important insights of both of them. A question that needs further exploration is how systematic and or flexible the system really was  - what were the limits? Which kinds of readings do we not get that we might? Also additional support for the syllabary could be provided for example if we were to find syllabograms used to spell final consonants in the Maya style (where for example BALAM can be spelled ba-la-ma).

In the end it seems to me that we cannot escape the fact that even though the Nahua script was highly phonetic, and clearly shared principles with the Maya logo-syllabic script, their approach to writing was very different from that of the Maya. Nahuas do not generally seem to have considered it a function of their script to represent spoken language much beyond personal and place names used to label narratives that were represented with pictures. No clear examples of full sentences have been deciphered, and indeed it doesnt seem that the script was even capable of writing such sentences given the lack of syllabograms for such important grammatical morphemes as ni, ti, and ki  which would be necessary to represent almost any slightly complex Nahuatl sentence. [Edit: After publishing this, I was reminded of the long sequences of glyphs found in the Codex Xolotl which may well represent something like full sentences - however I do not believe these have been deciphered yet].


  • Barlow, Robert H. and Byron McAfee. 1949. Diccionario de elementos fonéticos en escritura jeroglífica (Códice Mendocino). Mexico, D.F.: Universidad Nacional Autónoma de México.
  • Dibble, Charles E. 1971. Writing in Central Mexico. in Gordon F. Ekholm and Ignacio Bernal (eds.), Handbook of Middle American Indians: Archaeology of Northern Mesoamerica, Part 1, Vol. 10, pp. 322-332. Austin: University of Texas Press.
  • Nicholson, Henry B. 1973. Phoneticism in the late Pre-Hispanic Central Mexican writing system. in Elizabeth P. Benson (ed.), Mesoamerican Writing Systems, pp. 1-46. Washington: Dumbarton Oaks
  • Prem, Hanns J. 1992. Aztec writing. in Victoria Reifler Bricker (ed.), Handbook of Middle American Indians, Supplement, Vol. 5: Epigraphy, pp. 53-69. Austin: University of Texas Press.