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THE CORRELATION QUESTION
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Qurigua Stela C
Records Creation date
The long counts recorded on monuments from the Classical period of Maya civilization mark off the time since creation of the world.  Most Classical long counts fall in baktun 9, as reckoned by the scribes.  The baktun is a period of 144,000 days, about 400 years. Thus Classical civilization was at its height some 3600 years after the putative date of creation. 

The Classical period is now believed to date roughly from 200 to 900 AD.  This time frame is based in part on radio-carbon and other standard archaeological dating methods. These techniques are not accurate enough to precisely date the events recorded in the inscriptions, but since the monuments bear long counts, the details of  Maya history can be fixed in time by correlating the long count with the European calendar.


See an on-line Mayan Archaeological Timeline  with European and long count dates. See also A note on radiocarbon dates

The most widely accepted correlation is a variation on the oldest effort to match the long count to the European calendar. In 1897, Joseph Goodman (an American journalist who was Mark Twain's first editor), proposed that the Maya creation date, the zero long count, was in 3114 BC. Goodman's correlation was supported by the work of a Yucatecan scholar, Juan Martinez, but other correlations were more popular until  J. Eric Thompson revived interest in Goodman's correlation in 1927. His work was supported by the astronomical discoveries of J.E. Teeple in 1930. Thompson reviewed the evidence again in an influential study of the question in 1937. He was able to narrow down the range of possible base dates to three days. The correlation he proposed is now usually referred to as the Goodman-Martinez-Thompson (GMT) correlation. The base dates he identified are correlation constants used to convert long counts to European calendar dates:

11 August 3114 BC (Gregorian)   6 September 3114 BC (Julian) 
12 August 3114 BC (Gregorian)   7 September 3114 BC (Julian) 
13 August 3114 BC (Gregorian)   8 September 3114 BC (Julian)

Each correlation constant is also expressed as a Julian Day Number (JDN). See below

The choice between these three dates is still hotly debated, but almost all Mayanists accept one of the versions of the GMT correlation.

Nothing, as they say, is certain except death and taxes. But the GMT correlation seems nearly as certain as any deduction from the available evidence can be. Its wide acceptance survived even the drastic revision of Maya scholarship when Thompson's intellectual hold on the field was broken by a new generation of scholars. The alternatives have few supporters among Mayanists. Yet when I searched the web for information on the correlation question, I failed to turn up any account of the arguments supporting the GMT correlation.  I did, however, find defenses of at least eight alternative correlations. In the result, I fear it is all too easy for new students of the Maya to get the impression that the GMT correlation is dubious, or worse, an example of academic myopia. Some internet savants even hint darkly at conspiracy.

Of course,  no one should accept anything merely because it is favoured by tenured professors. It is for just this reason that I have put this web document together. It sets out the reasons why the GMT correlation has been widely accepted as definitive.  The arguments are unavoidably technical  and complicated in places, but I have tried to make my account as readable as possible.
 

The correlation problem

In principle, all that is required to correlate the long count with the European calendar is a single long count date with a known equivalent in the European calendar. This would, of course, allow us to calibrate the relationship between the calendars. Unfortunately, the Maya of the post-Classical period (900 -1519 AD) gave up the practice of recording long counts of contemporary events. We do not have even one complete long count for an event that occurred after the arrival of Europeans in the Yucatan.

The correlation must therefore be deduced from incomplete and inconclusive information. Goodman  relied primarily on  sources from shortly after the Spanish conquest.  At the time of the conquest, the Maya still kept both the calendar round, a cycle of about 52 years, and the ukahlay katunob, the "count of the katuns", a cycle of about 256 years. Colonial sources give us the European equivalents of a few calendar round dates, and the year in which at least one katun ended. These are not enough in themselves to correlate the calendars, but long count dates on Classical monuments include the calendar round date and a count of katuns. The GMT correlation was deduced from  "incomplete" conquest era dates, using arguments based on the structure of the Maya calendar.

Astronomy did not play a  role in arriving at the GMT correlation, but Thompson and Teeple turned to astronomy to confirm it. Classical monuments sometimes give the long count dates of astronomical events. The Dresden Codex, a post-Classical  glyph book, assigns long counts to a table of eclipses and a table of the apparitions of Venus. Floyd Lounsbury, one of the leaders of the generation of scholars who "broke the code" of Maya hieroglyphs, reviewed the astronomical evidence in detail in an important contribution to Maya calendrics in 1978. He agreed with Thompson that the astronomy in the inscriptions and the Codex is compatible with the GMT correlation.

However, astronomy does not provide the kind of unequivocal evidence many had hoped for, and most competitors to the GMT correlation have been based on interpretations of Maya astronomy. Some of these are on the remotest fringes of scholarship, or worse. Others, such as the Bohm and Wells-Fuls correlations, are based on reasoned arguments.  But there is an inherent  problem in any correlation theory that depends primarily on astronomy. Maya astronomy was concerned with augury, ritual, and mythology. There are still gaps in our understanding of the way the scribes used astronomy. Astronomical evidence is important, but must be used cautiously and carefully when discussing the correlation problem.

Perhaps the greatest strength of the GMT correlation is the fact that it was deduced from the structure of the Maya calendar, and independently confirmed by astronomy.  Although some of the individual pieces of evidence have weaknesses, converging lines of argument support it. Unlike some of its competitors, it is not a "house of cards" that will collapse if any one of the pieces of evidence marshaled in its favour proves to be mistaken.
 
 

Introductory Glyph
9 Baktun
16 Katun
Zero Tun
2 Winal
Zero K'in
3 Ahaw (Tzolk'in)
13 Yaxk'in (Haab)
The Maya Calendar: Long Count and Calendar Round

The long count marks off the time from creation in multiples of five periods 

k'in = day
winal = 20 day month
tun =  360 day long count year (18 winal)
katun = 7200 days (20 tun)
baktun = 144,000 days (20 katun)
The example here can written (bakun to k'in) as 9.16.0.2.0  It counts: 

(9 x 144,000) + (16 x 7200) + (0 x 360) + (2 x 20) +  (0 x 1) = 1411240 days 

The long count  is  followed by the calendar round date. It is actually two dates---  the day in the tzolk'in cycle of 260 days (designated by one of 13 day numbers  and one of 20 day names), and the date in a 365 day year, the haab, which is divided into 18 months of 20 days, plus 5 days at year end. 

See Note on the Maya Calendar at this web site for further information.

Bishop Landa and the u kahlay katunob: A starting point

The katun is 7200 days, about 20 years, in length. Rituals were performed on katun end dates, which were often recorded in Classical inscriptions. A little calendrical math will show that the tzolk'in day name on any katun end is always Ahaw.  For example the tzolk'in date of the katun end 9.3.0.0.0  was 2 Ahaw. Calculation will also show that the day number of katun  ends advances by 11 days through the cycle of 13 day numbers from katun to katun.  Thus the next katun end was 9.4.0.0.0 13 Ahaw. For Maya scribes, relationships such as these were keys  unlocking the meaning of the cycles of time tracked by their calendar.
 

The full calendar round date of  long count  0.0.0.0.0  is 4 Ahaw 8 K'umku. (This can be verified by counting back from any Classical long count date. When 0.0.0.0.0 is reached, the calendar round will stand at 4 Ahaw 8 K'umku). The first katun after creation ended on  0.1.0.0.0 2 Ahaw. This is 7200 = 360 x 20 days since creation. Since there are 20 day names,  a katun includes 360 complete cycles through the 20 day names, returning again to a day Ahaw at katun end. 

There are 13 day numbers. 553 full cycles of day numbers occur in the katun, with 11 days left over to  make up the 7200 days in a katun (553 x 13 = 7189). Thus 11 days before the first katun end, the day number reached 4 again, and at katun end, the day number was 11 + 4 = 15,  which must be reduced into the range of 1 to 13,  giving 15-13 = 2. Haab dates need not concern us for the moment.

The mathematics of period end dates is particularly important because it is the link between the Classical long count and the post-Classical  u kahlay katunob. At the time of the conquest, katuns were named by their tzolk'in  end date rather than their long count position. The katun names cycle through the 13 day numbers in this order:  2 Ahaw, 13 Ahaw, 11 Ahaw, 9 Ahaw, 7 Ahaw, 5 Ahaw, 3 Ahaw, 1 Ahaw, 12 Ahaw, 10 Ahaw, 8 Ahaw, 6 Ahaw, 4 Ahaw.  The U kahlay katunob is a full cycle of 13 katuns. It is 13 x 20 = 260 tuns, about 256 years in the European calendar.

The u kahlay katunob was a long enough time frame for practical purposes. The long count was used primarily to allow kings of the Classical period to link the events of their reigns to the mythological past. In the post-Classical period, political power was welded by aristocratic lineages that had little need for the expansive time frame provided by the long count.

Diego de Landa, a missionary brother who later became Bishop of Merida, described the u kahlay katunob in his Relacion de las Cosas de Yucatan, written in about 1566, and illustrated it with a katun wheel that was likely adapted from a Maya glyph book. Similar wheels can be found in post-conquest native manuscripts.

Landa reported that
 

It was easy for the old man [who told him of the fall of Mayapan and other events before the Conquest] to recall events which he said had taken place 300 years years before. Had I not known of this calculation, I should not have believed it possible to recall after such a period.

More important for present purposes, Landa also reported that
 

The indians say that the Spaniards finally reached the city of Merida in the year of Our Lord's birth 1541, which is exactly the first year of the era Buluc (11) Ahau, which is in that block [of the katun wheel] in which the cross stands. . . . 

The katun which preceded katun 11 Ahaw  was katun13 Ahaw. Thus if Landa's information is correct, the katun end  X.X.0.0.0 13 Ahaw occurred sometime in 1541, or if he meant that 1541 was the first year wholly in the new katun, in 1540. For the moment, it is enough to fix the katun end to a date near 1540  The last known long count date recorded on a monument is a katun end, 10.4.0.0.0 12 Ahaw, from Tonina. In the northern Yucatan, the territory familiar to Landa's informants, Chichen Itza recorded its last long count in 10.3.8.14.4. These dates mark the end of the Classical period.  Obviously, the conquest of the Yucatan by the Spanish, the long count position of 1540 AD,  must be later. The end dates of 13 Ahaw katuns after 10.4.0.0.0 are possible candidates. These dates, each 256 years apart, and the number of years each falls after the end of  the Classical era in 10.4.0.0.0, are listed below.

10.10.0.0.0  13 Ahaw  13 Mol  ---118 years
11.3.0.0.0  13 Ahaw  13 Pax  --- 374 years
11.16.0.0.0 13 Ahaw  8 Xul  --- 630 years
12.9.0.0.0 13 Ahaw  8 K'ank'in --- 886 years
 

The Books of Chilam Balam: A rough correlation 

Chichen Itza continued to flourish into the post-Classical period, long after it recorded its last long count, and was eventually superseded by Mayapan as the leading centre in the northern Yucatan. According to Landa's informants, Mayapan was abandoned about 120 years before he wrote. If the conquest correlates to 10.10.0.0.0,  there would be no room for the  post-Classical history of Chichen Itza and Mayapan. The archaeological evidence suggests that the post-Classical period  lasted several centuries, but 12.9.0.0.0 is almost certainly too late to correspond to the time of the Conquest.

The choice between the intermediate dates is more difficult, but here we can get some assistance from native traditions. After the conquest,  augury and history were recorded in Maya towns by the Chilam Balam, "Spokesman of the Jaguar". Books of Chilam Balam from eleven towns, written in Yucatec using the Latin script, survive.  Several of the Books give an account  of  the history of the Yucatan from the arrival of the Itzas, the post-Classical rulers of Chichen Itza, to the time of the Conquest, and record the katun dates of the events they recount. The Books report that the Itzas settled in Chichen Itza in katunAhaw. The "League of Mayapan" was founded in the next katun,Ahaw, only about 20 years later.But Chichen Itza remained the dominant  power in the Yucatan  until it was conquered by Hunac Ceel, the ruler of Mayapan, in katun 8 Ahaw. This was 11 katuns, about 220 years after the Itzas had arrived. Mayapan was destroyed, according to the Books, a full cycle of the u kahlay katunob, about 256 years, later, in the next katun Ahaw. If, as Landa was told, and the Books confirmthe Spanish Conquest was about a century later, the entire post-Classical era lasted about 600 years. This makes 11.16.0.0.0 13 Ahaw the most probable long count date correlating to 1540 AD. 

If we tentatively place 11.16.0.0.0  13 Ahaw in 1540, the base date of the long count is 11 baktuns and 16 katuns (about 4652 years) earlier.  The base date of the long count would then correlate to about 3113/3114 BC.  This is a plausible deduction, but more evidence is obviously required before it can be accepted.
 
 

Confirmation from Juan Xiu and the Chronicle of Oxkutzcab

In 1685, Juan Xiu, a Maya of noble lineage, copied out a page "from an ancient book", and added it to the Xiu family papers, which have come to be known as  the Chronicle of Oxkutzcab.  The document records events by the year in the European calendar, and also gives both the calendar round date of  first day of the haab and of the tun end that occurred in each year.
 


The entries of particular interest read: 

1540 11 Ix on 1 Pop [new year]. 
 13 Ahau the tun on 7 Xul ..
..
1541  12 Cauac on 1 Pop
 9 Ahau the tun on 2 Xul

1542 13 Kan on 1 Pop
when the Spaniards founded the city of Ti-Hoo [Merida]  when they settled, and the tributes first began through those of Mani, and the province was established. 5 Ahau on 16 Tzec.
 


Xiu Family Tree  (Chronicle of Oxkutzcab)
The Chronicle does not record katun ends, so it cannot be used to deduce a correlation. But katun end dates are also tun ends. It is likely that the tun end in 1540, which occurred on the tzolk'in day 13 Ahaw, was  the katun end referred to by Landa.  Despite minor discrepancies,  the Chronicle would appear to confirm that katun 13 Ahaw began sometime around 1540.

The Chronicle of Oxkutzcab also provides evidence confirming that Landa's katun 13 Ahaw corresponds to 11.16.0.0.0 rather than an earlier or later long count position. The Chronicle gives the haab date 7 Xul  for the tun end in 1540.  As will be explained below, it appears that a one-day shift in the calendar round occurred shortly before the Spanish conquest. Thus 13 Ahaw 7 Xul in the post-conquest calendar is equivalent to 13 Ahaw 8 Xul in the Classical calendar. This is the full calendar round date of the Classical katun end 11.16.0.0.0. Thus the Chronicle confirms that the long count of the conquest era katun 13 Ahaw was 11.16.0.0.0.
 

Landa and the Wayeb festival: A more precise correlation

Landa supplies one more bit of useful information, which turns out to be the key to a more precise correlation. He gives a lengthy description of rituals the Spanish frairs witnessed during the Wayeb, the last days of the haab, the Maya year. He followed this with a sort of Maya ecclesiastical calendar for a complete year, beginning on the first day of the haab, 1 Pop. He also recorded the tzolk'in date of this day,  12 K'an, which he tells us was Sunday, July 16. During the time Landa was in the Yucatan,  July 16 fell on Sunday only in 1553. Since we have  established that 11.16.0.0.0 13 Ahaw 7 Xul (according to the post-conquest Calendar round) was sometime around 1540,  if Landa's information is correct, it is only necessary to count  back from 12 K'an 1 Pop on July 16, 1553  to 13 Ahaw 7 Xul to fix the exact date of the long count position 11.16.0.0.0.  The katun end occurred  5004 days before 12 K'an 1 Pop.  This gives us a date of Nov 3, 1539 for 11.16.0.0.0 13 Ahaw 7 Xul.  The calculated base date of the long count will then be September 7, 3114 BC in the Julian Calendar in use when Landa wrote, or August 12, 3114 BC in the reformed Gregorian Calendar.

But is Landa's correlation between the Maya new year and the European calendar correct? There are in fact inconsistencies between Landa's date and dates from other colonial sources. For example, if we count forward from 13 K'an 1 Pop, listed as the new year calendar round date in 1542 in the Chronicle of Oxkutzcab, we reach Landa's 12 K'an 1 Pop in 1554, not 1553. However, these inconsistencies are more apparent than real. The key to understanding them was discovered by careful study of the Books of Chilam Balam.

According to the Books, the beginning of the European year was fixed to July 16 by the Maya. There appear to have been two reasons for this practice. First, the Maya understood that the European year of 365.25 days is a true solar year. Their own measurement of the solar year began in mid-July, when the sun reaches the zenith in the Yucatan. Second, it chanced that the beginning of the haab fell on July 16 shortly after the conquest. Of course, since the haab makes no allowance for leap year, the haab new year fell on July 16 for only four years, but one of these appears to be the year in which Landa witnessed the festival welcoming the new haab.  If we assume that the Chronicle of Oxkutzcab fixes the beginning of the European year to July 16, it confirms Landa's correlation of  July 16, 1553 to 12 K'an 1 Pop.
 

The Books of Chilam Balam are difficult to interpret, in part because they were recopied and reworked from the 16th to at least the late 18th Century.  As the traditional calendar fell into disuse in the Yucatan, even the copyists failed to understand the texts.  Some of the calendar round dates in the Books are not possible combinations of tzolk'in and haab dates in either the Classical or post-Classical count. 

Unfortunately, Landa's 13 K'an 1 Pop is the only complete calendar round date equated to a European calendar date we have that was definitely unaltered since the 16th Century.  Fortunately, we can be quite sure that it is a real date, not merely contrived by Landa as an example. If it were contrived, he might well have chosen a day Kan since this is the first year bearer (see below), but he would likely have not assigned the specific day number 11, which varies from year to year,  to it.  Nor would he have also assigned the dominical letter A  (used by the Church in calendrical calculations) to the date, which indicates that July 16 fell on Sunday.

The Year-bearers: Three possible correlations
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The crucial 12 K'an 1 Pop date in Landa's manuscript is a post-conquest calendar round date. It  is not compatible with the dates recorded on Classical monuments. According to Classical inscriptions, the long count began on the calendar round date 4 Ahaw 8 Kumk'u. Counting forward from 0.0.0.0.0 4 Ahaw 8 Kumk'u will never reach a calendar round date that combines 12 K'an  and 1 Pop.  All post- conquest calendar round dates are similarly incompatible with Classical dates. It would appear that a slip in the alignment of the tzolk'in and haab occurred sometime before the conquest. 

The shift in the calendar has to do with the "year bearers", the tzolk'in day names on the beginning of the haab.

Because the length of the haab is five days longer than a whole multiple of the twenty tzolk'in day names, the day name of  new year advances by five places each year. If this year began on a day K'an, next year will begin on a day Muluk. This will be followed by new year on Ix, and the fourth new year in succession will begin on Kawak. On the fifth year, the day name will return to K'an. These four day names are the year bearers.  According to Landa, the rituals performed at new year were dictated by the year bearer, which also determined whether the year would bring good or ill.  Landa reported the year bearers as K'an, Muluk, Ix, and Kawak. These are also the day names of new years in the Chronicle of Oxkutzcab.

Relationship between tzolk'in and haab dates, assuming that  New Year falls on 0 Pop, and the tzolk'in  day name at New Year must always be one of the Classical "Tikal" year bearers, Ik, Manik, Eb, and Kaban.

The beginning of the long count on 4 Ahaw 8 Kumk'u was in the last full 20-day month of the haab. The new year 1 Pop arrived only 17 days later, on 9 Etz'nab 1 Pop. Etz'nab is not a post-Classical year bearer. The next day, however, was a day Kawak, which is a post-Classical year bearer. Thus the change between the pre-conquest and post-conquest calendars appears to have been a change in the year-bearers, which produced a one day shift in the alignment of tzolk'in and haab.

Because the calendar round was kept by peoples throughout Mesoamerica, all of them were aquainted with the year bearer system,  and several sets of year bearers are known. The K'an, Muluk, Ix, and Kawak set is referred to as the "Mayapan year bearers". Assuming that the Classical new year was celebrated on 1 Pop, the Classical year bearers would have been Akbal, Lamat, Ben and Etz'nab. These are called the "Campeche year bearers". However, in the inscriptions, the first day of each month begins with the "seating" (chum) of the month, and is followed by days numbered 1-19. This is equivalent to numbering the days of the month from 0 to 19. Chum Pop can be interpreted as either the last day of the old year or the first of the new. If new year was celebrated on chum Pop, the Classical year bearers would have been Ik, Manik, Eb, and Kaban, the "Tikal year bearers". The Tikal set is used in the Paris Codex. The Dresden Codex lists both the Tikal and Campeche sets; which marks the beginning of the year is uncertain.
 

The relationship between the tzolk'in and  haab places other constraints on possible dates. Note that in a K'an year, K'an will fall on the first day of each of the 20-day months in the haab. But because the 5 day Wayeb intervenes at year end, in the next year, it retreats 5 days, to the 16th of each month. It retreats by 5 days in each year of the cycle until on the 5th year it again falls on the 1st of the month.  Thus K'an can be associated only will four days of the month.  Each of the day names is similarly fixed to four possible positions in each month. Thus, for example, in the Mayapan calendar, a day Ahaw can fall only on the 2nd, 7th, 12th, or 17th of the month. The date 13 Ahaw 7 Xulin the Chronicle of Oxkutzcab is compatible with this calendar. In the Tikal calendar, a day Ahaw can fall only on the 3rd, 8th, 13th, or 18th. The Classical period end  11.16.0.0.0 13 Ahaw  8 Xul is compatible with the Tikal calendar.

We do not know precisely when or why the year bearer system was changed in the Yucatan. The Dresden and Paris Codices, which were almost certainly produced in the post-Classical period, retain the Classical year bearers. On the other hand, cities in the Puuc hills of the western Yucatan abandoned the Classical year bearers during the last phase of the Classical period. This change may have resulted from Mexican influence in the western Yucatan. Munro Edmonston believes that an obscure passage in the Book of Chilam Balam of Tzimin records a calendrical compromise between the eastern and western Yucatan just before the conquest that led to adoption of the Mayapan calendar.
 

"As the Mexican people had signs and prophecies of the coming of the Spaniards . . . so also did those of Yucatan. Some years before they were conquered by Admiral Montejo, in the district of Mani, in the province of Tutul Xiu, an Indian named Ah cambal, filling the office of Chilan . . .  told publicly that they would soon shift to fresh calendar bearers, [and] be ruled by a foreign race who would preach a [new] God . . .". 

Landa, Relacion de las Cosas de Yucatan


More about year bearers at Peter Meyer's Maya Calendar site 

For our purposes, the important question is not when or why, but how.  The realignment could have occurred in several ways. The possibilities are perhaps easiest to understood by considering what might have been done on the katun end 13 Ahaw to convert the date from 13 Ahaw 8 Xul to 13 Ahaw 7 Xul. Assuming  no more than a one day slip, there are three possibilities:

1. If  November 3, 1539 was the Classical katun end 13 Ahaw 8 Xul,  the tzolk'in date could have been left unchanged, and a day subtracted from the haab, so that this date became 13 Ahaw 7 Xul.  This preserves the base date deduced above, August 12, 3114 BC.

2. If November 3 was 12 Kawak 7 Xul,  the the day before the Classical katun end, the tzolk'in date could have been reset on this day to 13 Ahaw without changing the haab date. Since in this case, the Classical katun end fell on  November 4, 1539,  the long count base date must have been a day later than calculated above, August 13, 3114 BC.

3. If, November 3 was the day after the Classical katun end, both tzolk'in and haab would have needed to be reset. The classical date on November 3 would have been 1 Imix 9 Xul. The tzolk'in date could have been reset by one day to 13 Ahaw, and the the haab date adjusted by two days to 7 Xul. Since in this case the classical katun end would have fallen on November 2, the long count base would have been on August 11, 3114 BC.
 

Calendrical calculations are usually made using Julian day numbers, a system of numbering days consecutively used by astronomers to calculate the "days between dates".  The correlation constant used to convert long counts to European calendar dates is usually stated as the Julian day number of the base date of the long count. The three GMT correlation constants derived above are:

JDN   584283   11 August 3114 BC (Gregorian)   6 September 3114 BC (Julian) [-3113]
JDN   584284   12 August 3114 BC (Gregorian)   7 September 3114 BC (Julian) [-3113]
JDN   584285   13 August 3114 BC (Gregorian)   8 September 3114 BC (Julian) [-3113]

The correlation constants are often referred to informally as '83, '84, and '85.

Note also that there is no year zero between AD and BC, which complicates calculations. Astronomers avoid the problem by recording dates before the common era  as negative numbers rather than dates BC.  Thus 3114 BC = -3113 in the astronomers' system. Surprisingly, some older authorities make the error of reporting the  long count base date as "3113 BC".

 


For an on-line discussion of Julian day numbers and European calendrical calculations see What is the Julian Period?

These three possibilities were all discussed by Thompson. For a time, August 12 was most popular with Mayanists. It seems to require the least destructive change in the calendar, leaving both the long count and the tzolk'in unchanged. The long count had fallen into disuse before the calendrical slip occurred, so its preservation may not have been an important consideration. However, the tzolk'in is another matter. It is a sacred almanac, used to time rituals and make auguries. The change in the haab could have been  a consequence of  the shift to  numbering the days of the month from 1 to 20 instead of 0 to 19. But the truth is that we can only speculate about the motives for the change in the calendar.

August 13 is now more popular with Mayanists. It was revived by Floyd Lounsbury, and adopted by Linda Schele, David Freidel, and Vincent Malmström among others. Lounsbury based his conclusion primarily on astronomical considerations (which will be discussed below).  Astronomy lends considerable support to the GMT correlation, but whether it favours the August 13, 3114 BC version is more debatable.

Logically, August 11 seems least likely because it involves changes in both haab and tzolk'in. However, the Quiche of highland Guatemala still keep the tzolk'in (ch'olk'ij in Quiche).  Barbara Tedlock, who studied the calendar of Quiche "day keepers", reports that the Quiche count of days coincides with Classical tzolk'in dates only if the long count base date was August 11, 3114 BC. Likewise, Alfonso Caso's widely accepted correlation between the Central Mexican calendar round and the European calendar coincides with the Classical Maya calendar round only if the August 11 correlation is adopted. Munro Edmonston, after an extensive review of Mesoamerican calendars, concluded that "no other solution [than the August 11 correlation]  is  ethnohistorically possible without postulating a break in the  continuity and uniformity of the universal Middle American day count". This correlation has many supporters among anthropologists, including Victoria Bricker and Dennis Tedlock.  It is also favoured by writers, like John Major Jenkins, who believe that Maya calendrical prophecy has modern relevance. But it is of course possible that a break in calendrical traditions did occur, or that the Classical Maya calendar was simply the the "odd man out" among Mesoamerican calendars.
 

I should admit that my personal preference is the '83 correlation, even though I've used the slightly more popular '85 correlation in these pages on Maya astronomy.  It seems to me that the "ethnohistorical" argument --- the match between the '83 correlation and the Quiche and Aztec counts--- makes a very strong  prima facie case for '83.  The '85 correlation is a bit more easily reconciled with Maya astronomical records, but it is easier for an advocate of '83 to explain this away than for an advocate of the '85 to explain away the Quiche day count.  Below, I try to show that astronomy alone cannot solve the correlation problem --- Thus I am suspicious of Lounsbury's revival of the '85 correlation, replacing the choice that otherwise makes the most sense, purely on astronomical grounds. 

The Age of the Moon and the correlation problem
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In 1930, John Teeple demonstrated that long counts in the inscriptions are often followed by the age of the moon, the number of days elapsed since new moon. Thompson used Teeple's discovery to confirm the GMT correlation. Many of the lunar ages on the monuments are those predicted by the GMT correlation. For example, a monument from Qurigua dated 9.18.5.0.0 4 Ahaw 13 Keh correlates to September 15, 795 AD (Gregorian) if the '85 version of the GMT correlation is used. The inscription gives the age of the moon as 23 days, the value calculated using modern methods.

Moon age 27 days

See lunar astronomy in the inscriptions  for a full description of the "lunar series" glyphs on Classical monuments 

There are also frequent discrepancies between lunar ages and their predicted correlations, but most result from errors in the inscriptions themselves.  By studying sequences of lunar dates on monuments from Copan and Palenque, Teeple showed that the lunar ages recorded by the scribes were often based on calculation rather than observation. For example, it appears that the scribes sometimes used the formula 6 lunar months = 177 days to date new moon from earlier observations.  Since 6 lunar months is actually 177.18 days, this calculation accumulates an error of about 1 day over  3 years.  Although the scribes also knew more accurate approximation formulas, we cannot expect all the lunar ages they recorded to agree exactly with the GMT or any other correlation.  What is possible is a statistical check on the GMT correlation.  The average error if the GMT correlation is correct to about 3 days, about as close as could be expected.
 

The statistical fit between the lunar ages recorded on the inscriptions and the ages predicted using the GMT correlation is actually better than the bald statement that the mean error is about than 3 days. Consider, for example, the 18 lunar series inscriptions with readable Classical period long counts from Palenque and Naranjo. The mean error if the '85 version of the GMT is adopted is 3.566 days. However, the average is distorted by two rather large errors in the nine Palenque dates of 8.4 and 8.1 days. Thus the lunar ages cluster closer to the correct values than the mean error may suggest. In fact, 13 of the 18 lunar ages are correct to within one standard deviation (1.9 days).  At Naranjo, the maximum error is only 2.5 days, and the mean error is only 1.577 days. 

It should also be noted that there is doubt about how the scribes defined "new moon".  The astronomical new moon occurs when the sun and moon are in conjunction, but this moment cannot be observed directly. We do not know if Maya astronomers recorded the new moon at the moment the crescent moon first became visible after conjunction, or tried to interpolate the moment of new moon between the time it disappeared and reappeared. Depending on the acuity of the observer and atmospheric conditions, the recorded date of new moon may differ from astronomical new moon by 2 -3 days.

The problem of the definition of "new moon" makes it virtually impossible to use lunar series dates to choose between the three versions of the GMT correlation. The calculation above used the '85 version and  astronomical new moon. But if the '83 constant is adopted and new moon is assumed to occur when the crescent moon appeared 2 days after astronomical new moon, the results of the calculation would be similar. 

The Dresden Codex elipse table

The Dresden Codex eclipse table has provided both advocates and critics of the GMT correlation with ammunition. The table counts the days between "eclipse warning stations". The intervals between the warning stations are eclipse cycles, intervals at which eclipses reoccur. Similar cycles were used by Greek and Babylonian astronomers. They predict only the possibility of eclipses, however. The reoccurrence of an eclipse after lapse of an eclipse cycle may not be visible to the observer who recorded the first eclipse. In addition, cumulative error in approximations of eclipse cycles is an inherent problem in any table of eclipses based on the cycles. Nevertheless, the eclipse table is an impressive achievement.


For a detailed description of the eclipse table see The Dresden Codex Eclipse Table at this web site
Page from the eclipse table
There are  three long count entry points into the table. The principle entry date appears to be 9.16.4.10.8 12 Lamat, November 12,  755 AD if the the '85 correlation is used. The second long count is 15 days later. If  9.16.4.10.8 12 Lamat was used to predict solar eclipses, the second date would  fall at full moon, and could be used as an entry point for predicting lunar eclipses. The third date is 15 days later still, and might be a secondary entry point for predicting solar eclipses. These entry points work reasonably well if the GMT correlation is correct. Harvey and Victoria Bricker have shown that all 77 solar eclipses (including many not visible in the Yucatan) in the 33 year run of the table from 9.16.4.10.8 12 Lamat occurred close to the warning stations.(If the '85 version of the GMT 
correlation is used, the mean error is .08 days).  Aveni has shown that the lunar eclipse entry date works almost as well. 51 of the 69 lunar eclipses in the 33 year life of the table are close to warning stations. 

However, as might be expected, there are problems in interpreting the table.  In particular, the status of the 9.16.4.10.8 12 Lamat entry date is uncertain.  The Codex was written in the post-Classical period, likely no earlier than 1200 AD, long after 9.16.4.10.8 12 Lamat if the GMT correlation is correct. Moreover, 9.16.4.10.8 12 Lamat is not the best choice for an entry date if it correlates to November 12, 755 AD.  A new moon occurred on that date, but the moon was about 15 days from its orbital node. An eclipse cannot occur if the moon is not close to the node. No eclipse occurred on Nov 12, 755 AD. A  lunar eclipse did occur 15 days later, and a partial solar eclipse about 30 days later, but neither was visible in the Yucatan. Most of the solar eclipses in the 33 years after 755 AD occurred on days reached from the secondary solar eclipse predicting entry date rather than from the primary 12 Lamat entry date.

The less than ideal performance of  Nov 12, 755 AD as an entry point has been used by critics of the GMT to propose alternatives. Smiley, for example deduced a correlation by moving 9.16.4.10.8 back in time in order to match it with a date on which an eclipse occurred near the node. Vollemaere moves the long count forward in time for much the same reason. Advocates of the GMT correlation regard exercises such as these as arbitrary. There are many 12 Lamat tzolk'in dates in the span of Maya history on which the new moon was close to an orbital node. If the game is merely to match 9.16.4.10.8 12 Lamat with such a date, there are many choices.

We simply do not know enough about how the eclipse table was used in practice to assume that 9.16.4.10.8 12 Lamat need be the best possible entry point.  It may be, as Harvey and Victoria Bricker argue, that a Classical eclipse table using 9.16.4.10.8 12 Lamat was actually used for solar eclipse prediction, and copied into later codices. Anthony Aveni notes that the moon was almost at the node at the lunar eclipse entry date, 15 days after 9.16.4.10.8 12 Lamat. He speculates that the table was designed primarily to predict lunar eclipses. Floyd Lounsbury suspected that  9.16.4.10.8 12 Lamat was never used as a practical base date for either solar or lunar eclipse prediction. He argued that it is throw back, calculated by subtracting multiples of the table length from a later, more accurate, base date. Cumulative error in projecting the eclipse cycles back several centuries would explain why 9.16.4.10.8 12 Lamat is only a marginally acceptable entry date.

But whether 9.16.4.10.8 12 Lamat was a practical entry point or a throw back from a more useful entry date, the fact remains that the eclipse table does do a reasonably good job of  warning of eclipses if the GMT correlation is correct. The very nature of the table prevents it from doing much more, what ever entry date is chosen. Unlike correlations based on astronomy, the GMT correlation is not contrived to force a fit with the eclipse table or other astronomical data. Thus the eclipse table offers an independent check on the GMT correlation. The eclipse table does not unequivocally prove the GMT correlation is correct, but if it was based on mistaken premises, we could hardly expect Nov 12, 755 AD to be as good as entry point into the table as it is in fact.
 

The Venus table problem

The Dresden Codex Venus table has generated even more controversy than the eclipse table. The Venus table tracks dates of the apparitions of Venus, beginning with heliacal rise (first appearance of Venus in the morning sky before sunrise). The synodic period of Venus (the time from heliacal rise to heliacal rise) is recorded at 584 day intervals in the table. This is very close to the modern figure of  583.92 days.

Like the eclipse table, the Venus table provides long counts that appear to be entry dates. The latest of these long counts is 9.9.9.16.0  1 Ahaw 18 K'ayab, February 9, 623 AD if the '85 version of the GMT correlation is used. This date has been seized upon by critics of the GMT correlation because Venus was 16 days from heliacal rise on the date. The Bohm correlation, the most ambitious recent effort to depose the GMT correlation, was motivated in part by the assumption that 9.9.9.16.0 1 Ahaw 18 K'ayab should be close to heliacal rise. Once again, however, much depends on the status of this date.


For a detailed description of the Venus table see the Dresden Codex Venus table at this web site.

There is clearly important ritual significance in the putative heliacal rise date 1 Ahaw.  Hun (1) Ahaw is the name of one of the "hero twins" who defeated the Lords of the Underworldand made creation of the present world possible. Dennis Tedlock, translator of the Quiche Popol Vuh, which includes the story of the twins, inteprets the myth cycle as an account of the apparitions of Venus. Since heliacal rise occurs only once every 584 days, it rarely matches a day 1 Ahaw in the tzolk'in cycle, but the scribes may have had strong incentive to do so. Matching a full calendar round date is even more difficult. Lounsbury found that there is only one 1 Ahaw18 K'ayab  in the Classical or post-Classical  periods which was a heliacal rise date of Venus if the GMT correlation is correct.  On 10.5.6.4.0 1 Ahaw 18 Kayeb = 25 November 934 AD ('85 correlation constant), Venus was within 0.1 day of heliacal rise.  Equally important, this date is exactly 196 Venus cycles of 584 days after the 9.9.9.16.0 entry date recorded in the codex.  Lounsbury suggests that this was a "unique event in historical time". He believes it was the date on which the Venus table was inaugurated. If he is correct, 9.9.9.16.0 1 Ahaw 18 K'ayab was a throw back, calculated by subtracting multiples of the 584 day Venus period from the heliacal rise date 10.5.6.4.0 1 Ahaw 18 K'ayeb  to reach an earlier calendar round date of  1 Ahaw 18 K'ayeb. Since the Venus period is actually 593.92 days, a cumulative error resulted from projection of the table this far back in time.  Thus the scribes'  long-range calculation failed to reach a true heliacal rise date.

If the GMT correlation is not correct, it must be mere coincidence that the long count base date of the table is an exact number of  Venus cycles earlier than the heliacal rise date discovered by Lounsbury.  Lounsbury's explanation of  9.9.9.16.0 1 Ahaw 18 K'ayab may be too circumstantial to prove that the GMT correlation is definately correct, but it is certainly strong enough to make it very difficult to argue that the Venus table makes the GMT correlation untenable. Unfortunately, the nature of Maya astronomy makes it unlikely that any correlation can be based on astronomy alone. At best astronomy can confirm or deny  the plausibility of a correlation, but must be used cautiously even for that purpose.
 

More evidence from the inscriptions

Great strides in deciphering the Maya script have been made in the last 25 years . Some critics of the GMT correlation argue that if the GMT correlation is sound, decipherment should have produced evidence that unequivocally verified it.  But while absolute proof is still elusive, decipherment, particularly of astronomical references on Classical monuments, has in fact produced considerable new support for the GMT correlation.

Perhaps the most remarkable example is found in the glyphic record of the dedication ceremonies of the temples of the Cross Group at Palenque. These rituals fell within a four day period commencing 9.12.18.5.16 2 Kib 14 Mol , July  23 690 AD if the GMT correlation is correct.  On this date,  Mars, Jupiter, Saturn and the Moon were separated by intervals of less than 5 degrees. According to Dutting and Aveni,  "[On 23 July 690 AD] all four planets were close together (a quadruple conjunction) in the same constellation, Scorpio, and they must have made quite a spectacle with bright red Antares shining but a few degrees south of the group as they straddled the high ridge that forms the southern horizon at Palenque".  This astronomical event appears to be recorded in the inscription, which recounts that the wayob (spirit companions) of  the gods known as the Palanque triad  were "in conjunction" on 9.12.18.5.16 2 Kib 14 Mol.

Right: "His way in conjunction, GIII".  GIII is one of the gods of the Palenque triad. Conjunction is marked by the glyph inset with "crossed bands". The number three before this glyph may represent the  conjunction of Mars, Jupiter and Saturn.  This text begins with an account of Creation, the birth of First Mother and First Father, and of their sons, the gods of the Palenque triad. Schele and Freidel suggested that the alignment of these  planets with the Moon on 23 July 690 was interpreted by Palenque scribes as the symbolic re-uniting of First Mother (the moon) and her three sons.

'83, '84 or '85: A smoking gun?

The limited power of astronomy to unequivocally settle the correlation question has not prevented it from being used to erect alternative correlation theories.  Nor has it prevented advocates of the GMT correlation from attempting to use astronomical data to choose between the three GMT correlation constants. What is needed is a "smoking gun", a unique astronomical event with a clear long count date. But the smoking gun is difficult to find.

Lounsbury argued that  10.5.6.4.0 1 Ahaw 18 Kayeb was such an event. It corresponds exactly to the heliacal rise of Venus on November 25, 934 AD only if the '85 correlation is adopted. However, as Aveni has noted, naked-eye observation of heliacal rise is fraught with difficulty. Venus is lost in the glare of sunrise at the instant of heliacal rise. Much depends on atmospheric conditions and the acuity of the observer, but Venus is usually not visible until several days after true heliacal rise, when it is about 10 degrees from the sun. Lounsbury assumed that Venus becomes visible 4 days after true heliacal rise, but if it was glimpsed earlier in 934 AD, the heliacal rise date might match the '83 or '84 correlation rather than the '85 correlation.


For discussion of the problem of timing heliacal rise, Heliacal Rising: Definitions, Calculations, and Some Specific Cases on-line.

An eclipse might seem to be a more likely smoking gun. Unfortunately, however, the eclipse table fails to resolve the issue. Eclipse prediction is difficult. Although the eclipse cycles incorporated into the table are remarkably accurate, they will not always predict an eclipse with an accuracy of less than three days. Thus any conclusion about which the three GMT constants is correct that is based on the eclipse table must be suspect.
 

In fact, the eclipse  table appears to have a 3 day latitude build into it:  Each of the tzolk'in dates at warning stations counted from the 12 Lamat entry point is flanked by the tzolk'in dates of the day before and the day after. This is likely the Classical scribe's equivalent of the modern scientist's "+ or - 1 day". 

However, what may be the single strongest piece of evidence in favour of the '85 constant is an eclipse date. Michael Closs has pointed out that Quirigua Stela E appears to record an eclipse on the katun end date 9.17.0.0.0 13 Ahaw 18 Kumk'u. If the '85 constant is correct, this correlates to January 24, 771 AD, when a partial eclipse was in fact visible in the Yucatan. Closs believes this is the only instance of a eclipse occurring on a katun end in the Classical period, which likely gave it particular significance. Certainly, this eclipse is strong evidence in favour of the GMT correlation. But does it necessarily confirm the '85 constant?  Perhaps the occurrence of an eclipse within  2 days of period end was enough for the scribes at Quirigua to associate the eclipse with the end of the katun.

Other pieces of evidence can be marshaled in support of each of the three GMT correlation constants, but the debate is unresolved. While the GMT correlation is almost certainly valid, it seems unlikely that the choice between the '83, '84, and '85 versions can be definitively resolved on the basis of the available evidence.
 
 
 

                           Correlation Constants............................... 
Smiley JDN 482699 26 Jun 3392 BC  (Gregorian) 
Makemson JDN 489138 11 Feb 3374 BC  (Gregorian)
Spinden JDN 489384 15 Oct 3374 BC  (Gregorian)
GMT (1)  JDN 584283 11 Aug 3114 BC  (Gregorian)
GMT (2) JDN 584284 12 Aug 3114 BC  (Gregorian)
GMT (3) JDN 584285 13 Aug 3114 BC  (Gregorian)
Bohm JDN 622261 4 Aug 3010 BC  (Gregorian)
Kreichgauer JDN 626927 14 Mar 2997 BC  (Gregorian)
Wells-Fuls JDN  660208 27 Jun 2906 BC  (Gregorian)
Hochleitner JDN 674265 22 Dec 2867 BC  (Gregorian)
Esalona Ramos JDN 679108 27 Mar 2854 BC  (Gregorian)
Weitzel/Vollemaere JDN 774078 5 Apr 2594 BC  (Gregorian)


A note on radiocarbon dates: Radiocarbon dates are compatible with GMT correlation. They rule out a very early (Smiley and Spinden) or late (Weitzel/Vollemaere) zero long count position, but are not precise enough to completely rule out correlations such as the Bohm that are close to the GMT.

Ironically,  the first radiocarbon dates from the Classic period, obtained from wooden beams in Yaxchilan temples, seemed to favour the Spinden correlation when the dates were reported in the 1956. These dates are still sometimes quoted to discredit the GMT correlation. However, techniques improved rapidly after 1956.  In 1959, the University of Pennsylvania ran 33  samples from  ten beams in a Tikal temple. The series averaged  out to A.D. 746 A.D.  +/- 34 years. These beams were  carved with a long count equivalent to of  741 A.D.  in the GMT correlation. This is of course a particularly close match. Most radiocarbon dates cluster about those expected from the GMT correlation, but typically have a wider margin of error.

The most critical date for purposes of assessing proposed correlations is the end of the Classical period (10.4.0.0.0 = 909 AD GMT). Samples from sealed Late Classical tombs at Muklebal Tzul in Belize have recently been dated to between 600 and 810 AD. This compares with the GMT dates for the Late Classical of 600-900 AD.


Bibliography

Aldana, Gerardo.  "K'in in the Hieroglyphic Record: Implications of a Pattern of Dates at Copán". On-line at Mesoweb. An interesting recent article suggesting that dates at Copan that seem to refer to equinoxes, solstices, and zenith passages of the sun may be difficult to square with the GMT correlation.

Aveni, Anthony F.  Skywatchers (U. of Texas Press, 2001) The best general introduction to Maya calendrics and astronomy. This is a revised edition of Skywatcers of Ancient Mexico.

------ (ed.). The Sky in Mayan Literature (Oxford University Press, Oxford, 1992)

Baaijens, Thijis.  "The typical 'Landa Year' as the first step in the correlation of the maya and the christian calendar",  Mexicon Vol. XVII, 1995.

Bohm B., Bohm, V. "Calculation of the Correlation of the Mayan and Christian system of Dating", Actes du XIIe Congres International des Sciences Prehistoriques et Protohistoriques. Bratislava, 1-7 Septembre 1991. (on-line version) The Bohm correlation.

Bricker, V. R. and H. M. Bricker.  "Classic Maya prediction of solar eclipses", Current Anthropology, xxiv, 1-23

Paul D. Campbell,  Astronomy and the Maya Calendar Correlation, Mayan Studies Series , No 5 (Aegean Park Press). Another recent alternative to the GMT correlation

Caso, Alfonso. ``Calendrical Systems of Central Mexico,'' in Wauchope (ed.) Handbook of Middle American  Indians (University of Texas Press, Austin, 1965).

------. Los Calendarios Prehispánicos (México,UNAM, 1967).

Closs, Michael P. "Cognative Aspects of Ancient Maya Eclipse Theory", in Anthony F. Aveni, World Archaeoastronomy.
Cambridge, 1989.
.............................. "Some Parallels in the Astronomical Events Recorded in the Maya Codices and Inscriptions", in  Aveni, ed. The Sky in Mayan Literature (Oxford, 1992).

Dutting, Deiter,  and Anthony F. Aveni. "The 2 Cib 14 Mol Event in the Palenque Inscriptions". Zeitschrift fur Ethnologie 107, 1982.

Edmonson, M. S. (transl.). The Ancient Future of the Itza: The Book of Chilam Balam of Tizimin (U. of Texas Press, 1982)

--------. The Book of the Year: Middle American Calendrical Systems (University of Utah Press, 1988). An excellent survey, particularly good on controversial topics such as year bearer systems.

Gates, William. [Transciption and translation with notes of page 66 of the Cronica de Oxkutzcab] in S.G. Morley, Inscriptions at Copan (Carnegie Inst., 1921).

Goodman, J. T. The Archaic Maya Inscriptions (Taylor and Francis, London, 1897). Now only of historical interest, includes the original Goodman correlation.

Justeson, Jonn S.  "Ancient Maya ethnoastronomy: an overview of hieroglyphic sources" in Aveni (ed.), World archaeoastronomy: Selected papers from the 2nd Oxford International Conference on Archaeoastronomy (Cambridge, Cambridge University Press, 1989).

Jenkins, John M.  Tzolkin: Visionary Perspectives and Calendar Studies (Borderland Sciences, 1994). See Jenkin's strong defence of the '83 GMT correlation  online.

Landa, Diego de. Relacion de las cosas de Yucatan (1556), English translation by W. Gates,  Yucatan Before and After the Conquest (Dover Press, 1978). See an on-line translation.

Lounsbury, Floyd: "The Base of the Venus Table of the Dresden Codex and its Significance for the Calendar-Correlation Problem", in Aveni & Brotherston (eds.), Calendars in Mesoamerica and Peru: Native American Computations of Time (BAR International Series, no. 174, Oxford, 1983). Lounsbury's influential defence of the '85 GMT correlation

----. "Maya Numeration, Computation, and Calendrical Astronomy," in Dictionary of Scientific Biography, ed., Charles Coulston, 1976. Lounsbury's influential first paper on the GMT correlation and astronomy

----. "A Derivation of the Mayan-to-Julian Calendar Correlation from the Dresden Codex Venus Chronology," in Aveni (ed.),  The Sky in Mayan Literature (Oxford University Press, Oxford, 1992).

 Makemson, Maud W. The Maya Correlation Problem (Publications of the Vassar College Observatory, No 5, New York 1946). Makemson variously supported the '84 GMT correlation and her own correlation derived from the Dresden eclipse table.

Malmström, Vincent H. Cycles of the Sun, Mysteries of the Moon: The Calendar in Mesoamerican Civilization (University of Texas Press, 1997).

-------. "Astronomical Footnotes", Arqueología 21, Segunda Época, Enero-Junio 1999  (English version on line). Makes the interesting case that the '85 GMT correlation best fits the astronomical data if it is assumed that the Maya began the day at sunset.

Morley, S. G. "Correlation of Maya and Christian Chronology", Amer. J. of Archaeology, 2nd ser., XIV
(1910). An early discussion of the correlation question.

Owen, Nancy K.: "The Use of Eclipse Data to Determine the Maya Correlation Number", in Aveni  (ed.), Archaeoastronomy in Pre-Columbian America (University of Texas Press, 1975). Owen rejects the GMT correlation.

Proskouriakoff, Tatiana A and J. E. S. Thompson.  Maya Calendar Round Dates such as 9 Ahau 17 Mol (Notes on Middle American Archaeology and Ethnology, no. 79, Washington, 1947). Discusses the "slip" in the Maya calendar

Prufer, Keith M. "Analysis and Conservation of a Wooden Figurine Recovered from Xmuqlebal Xheton Cave in Southern Belize, C. A.", Report Submitted to FAMSI, 2001. Discusses some Late Classical radiocarbon dates.

Roys, Ralph L. (transl.). The Book of Chilam Balam of Chumayel (U. of Oklahoma Press, 1967). On-line version at the Sacred Texts web site.

Satterthwaite, Linton. Concepts and Structures of Maya Calendrical Arithmetics (Philadelphia, 1947)

--------.  "Long Count Positions of Maya Dates in the Dresden Codex with Notes on Lunar Positions and the
Correlation Problem". Proc. 35th Int. Cong. Amer. Mexico, 1962.

Smiley, Charles H. "The Solar Eclipse Warning Table in the Dresden Codex", in Aveni, (ed.), Archaeoastronomy in Pre-Columbian America (University of Texas Press, 1975). Smiley is a leading opponent of the GMT correlation.

Smither, R. K.: "The 88 Lunar Month Pattern of Solar and Lunar Eclipses and its Relationship to the Maya Calendars", Archaeoastronomy, Vol. IX (1986).

Spinden, Herbert J.: The Reduction of Mayan Dates (Papers of the Peabody Museum of American Archaeology and Ethnology, Harvard University, vol. 6, no. 4, 1924). The most influentialearly alternative to the GMT correlation.

Stock, Anton. Astronomie der Maya-Kultur - Die Datierung der Finsternistafel aus dem Dresdner-Codex  und das Korrelationsproblem.  Katun Verlag, 1998.  Another alternative to the GMT. See information on-line

Tedlock, Dennis. "Myth, Math, and the Problem of Correlation in Mayan Books", in Anthony F. Aveni, ed. The Sky in Mayan Literature. Oxford, 1992.  Support for the '83 GMT through an analysis of astronomical references in Maya mythology

Tedlock, Barbara. Time and the Highland Maya (U. of New Mexico Press, 1982). Account of the calendar kept by modern Quiche "day keepers".

Teeple, J. E.: "Maya Astronomy", Contributions to American Archaeology (Carnegie Institution of Washington, Vol. 1, 1931).

Thompson, J. Eric S.  A Correlation of the Maya and European Calendars, Field Museum of Natural History , Anthropological Series, Vol. 17, no.1, 1927.

.......... "Maya Chronology: The Correlation Question,", Contributions to American Archaeology, Volume III, Nos. 13 to 19, Carnegie Institution of Washington, No. 14, 1937. Thompson's  influential review of Goodman's correlation, proposing the three versions of the GMT correlation.

-------  "The Introduction of Puuc Style of Dating at Yaxchilan", Notes on Middle American Archaeology and Ethnology No. 110, May 15, 1952.

Wells, Bryan and Fuls, Andreas, Western and Ancient Maya Calendars, ESRS (West) Monograph no. 6 , Berlin 2000. Another recent alternative to the GMT correlation  (see information about this correlation on-line)

Volemaere, Antoon. " La correlación maya-tolteca-azteca", Congreso internacional de americanistas, Amsterdam, 1988. Another alternative to the GMT correlation. (see information about this correlation on-line)


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Michael John Finley   Saskatoon, Saskatchewan,  Canada  May 2002 (revised Dec 2002/Apr 2003/Nov 2003)