Katun Quarters in the 12 Lamat Eclipse Correlation. (01/08/2001)

When Maya astronomers set the zero base-day ( 4 Ahau 8 Cumku) for the Long Count notation at some particular point in time in their own mytho-historical past, they also necessarily chose the temporal locations of every subsequent quarter-Katun position in their calendrical structure. This is true, and inescapable, because 4 Ahau 8 Cumku is a Katun-ending position itself, where every subsequent quarter-Katun marker after it falls 1,800 days later in an unbroken sequence through the entire length of the LC notation. Most scholars view this structure as being chronological, as opposed to astronomical, because 1,800 days does not seem to reflect any apparent interval of time that is, or might be, consistent with an astronomical periodicity. One reason this view of quarter-Katun positions has persisted for so many years in Eurocentric scholarship about Maya calendrical astronomy concerns the fact that no single explanation for the astronomical intent of 1,800 days can be expressed. In other words, no single astronomical interval known to European astronomers can be said to account for the fact that Maya astronomers during the Classic period chose to fashion a calendar based on the use of this interval as a means of counting the passage of time with respect to any known conceptualization of celestial motion.

As Anthony F. Aveni has pointed out, certain kinds of directional orientations built into the architecture of Maya ceremonial centers (at Copan, Honduras, for instance) make it impossible to "ignore the fact that the Venus and solar orientations in the architecture fit together in a way that evokes not only the most vital period of the agricultural season but also the very type of calendar (counting by twenties relative to solar zenith passage) that we know the ancient Maya once practiced and that their descendants continue to employ" ("The Real Venus-Kulkulkan in the Maya Inscriptions and Alignments," The Sixth Palenque Round Table, 1986, ed. M. G. Robertson [Norman, 1991], p. 320). The orientations Aveni refers to here were marked at Copan along the western horizon of the ceremonial center to target exactly the setting position of the sun (and planets as well) when it (and they) reached an azimuth of +278*25'00". This particular orientation was created by the placement of a window in the western-facing wall of Temple 22 in the central acropolis of the ceremonial center, where the mid-line of that window exactly measures that azimuth line. Hence, when the sun sets at that orientation, it is visible in the middle of the window of Temple 22. This only happens twice in every solar year: once 20 days after vernal equinox and 20 days before solar zenith passage in the Spring; and again 20 days after solar zenith passage and 20 days before autumnal equinox in the Fall (See Anthony F. Aveni, "Concepts of Positional Astronomy Employed in Ancient Mesoamerican Architecture," in Native American Astronomy, ed. Anthony F. Aveni [Austin, 1977], 3-19, pp. 9-14). A secondary orientation was also established from this same vantage point relative to the placement of Stela 10 on the western ridge of the Copan valley at an azimuth of 276*45'00". The sun reached this position four days before it crossed the central axis line of the window in the Spring and four days after that same position in the Fall. A second Stela (#12) was positioned on the eastern ridge of the valley at the ceremonial center and marked a baseline consistent with the sun's setting azimuth as it crossed the central axis of the window in Temple 22. What this means is that two astronomers, one positioned at Stela 12 looking west at Stela 10 and the other at the window inside Temple 22, would be able to observe simultaneously the sun's setting orientation as it disappeared behind Stela 10 on the western horizon. Given the complexity of the architectural structure at Copan, where two independent but simultaneous observations of the same event were always possible, one can argue that the astronomers at Copan were absolutely determined to fix the exact days, year to year, on which the sun reached its setting azimuth at +278*25'00", a position that always occurred 20 days after vernal equinox in the Spring and 20 days before autumnal equinox in the Fall, and the same number of days before and after solar zenith passage, respectively, as well.

Since it is also true, by virtue of cause and effect relationships, as Anthony Aveni suggests, that the calendrical system used by the Maya came into existence in order to count the 20-day intervals between equinoxes, setting orientation azimuths, and solar zenith passages, one must assume that those orientations were observed and known by the astronomers prior to the earliest contemporaneous use of the day-name system that counted and preserved those intervals and orientations. This is true simply because the effect, counting the intervals in a calendrical system, cannot come before the cause, observing the intervals that separate the solar events being counted. Some Maya dates, ones that were recorded on stone monuments during the Classic period, were clearly perceived in retrospect and were not recorded as contemporaneous events. The zero base-day, for instance, occurred so early in Maya mytho-history that there is no chance at all that anyone who could be called Maya observed any event that might be associated with 4 Ahau 8 Cumku.

Recognition of this fact does not mean, however, that Classic period astronomers were not able to say precisely what kinds of events occurred on, and in proximity to, the zero base-day they established for their calendrical system. This assertion can be sustained by taking note of the fact that the 260-day almanac, whose essential structure maintains a system of counting day-names in intervals of twenty, where 13 x 20 = 260, expresses an interval exactly equal to the true length of the solar year (at 365.2422 days each) every time 59 turns of its cycle (at 15,340 days exactly) are counted, where 42 x 365.2422 = 15,340.172 days. Since the setting azimuths of the sun marked by the architectural orientations at Copan are determined by the true length of the solar year, at 365.2422 days of separation between them, those events must occur on the same almanac day-name every time 42 years and 59 almanacs have passed. True also is the fact that the differential between one thing and the other is so brief (at 0.172 days) that this system of calendrical counting can be used for a total of 252 years (6 x 42 = 252 and 6 x 0.172 = 1.032) before a single whole day of regression occurs in the day-name that marks the solar event. While other reasons for the adoption of the 260-day interval in the Maya calendrical system can be cited (its natural propensity to predict eclipses at 46 turns of its cycle, after 11,960 days have passed, in the Dresden Codex eclipse table, for instance), its expression of the true length of the solar year and its capacity to name the day of the sun's setting azimuth as it crosses the mid-line of the window in Temple 22 at Copan, which also establishes the days of equinox and solar zenith passage simultaneously, probably reflects the primary cause for its choice as the foundation of the Maya calendrical system.

What makes this even more probable is the fact that, over the course of the duration of the Long Count notation itself, from 4 Ahau 8 Cumku to 4 Ahau 3 Kankin 1,872,000 days later, exactly 20 days of regression occur in the day-names marking these solar events from the beginning to the end of the Maya calendrical interval. In the 12 Lamat Eclipse correlation, for instance, vernal equinox fell 12 days prior to the zero base-day at 5 Lamat 16 Kayab (April 17, 3171 B. C.-Julian Day #563322) when the sun reached a declination of +00*00'01" at 10:21:00 AM. Eight days after the zero base-day, and hence 20 days after vernal equinox, at 12 Lamat 16 Cumku (May 7, 3171 B. C.-Julian Day #563342), the sun reached a setting azimuth of 278*15'15" and was just nine minutes and forty-five seconds of circular arc from the orientation of the mid-line of the window in Temple 22 at Copan. Since there are 122 intervals of 15,340 days each, with an additional 520 days as a remainder, in the interval of the Long Count notation, vernal equinox 512 days prior to 4 Ahau 3 Kankin (August 14, 1955-Julian Day #2435334) should occur at 12 Lamat 16 Xul, which fell on March 20, 1954 (Julian Day #2434822), where, in fact, the sun reached a declination of -00*03'32" at sunset and would have crossed the celestial equator 3.5 hours later 21:50:00 PM on that day. The regression here, of course, shifts the solar event from the orientation of the sun's setting azimuth at the mid-line of the window in Copan in the ancient sequence (12 Lamat 16 Cumku) to the actual day of vernal equinox (12 Lamat 16 Xul) in the modern one at the end of the LC notational interval. This is clearly the way in which the calendrical structure was designed to function and explains why the LC notation was designed to count exactly 1,872,000 days. The terminal point itself at 4 Ahau 3 Kankin marks the day of solar zenith passage 40 days prior to autumnal equinox at 5 Ahau 3 Pax on September 23, 1955 A. D. (Julian Day #2435374) when the sun reached its equatorial passage into the southern sky with a declination of -00*00'01" at 13:41:00 PM on that day.

Any effort undertaken to prove that the astronomy marked by quarter-Katun positions in this, or any other correlation proposal, must necessarily fall short of achieving a high level of certainty by virtue of the fact that the Maya during the Classic period never expressed in any way understood now what those positions were intended to designate from an astronomical point of view. Since there are 1,040 quarter-Katun positions in the duration of the LC notation itself, it is reasonable to suppose that some, even many, of them must have designated recognizable astronomical configurations as a matter of course with respect to any fixed position one might choose for the zero base-day in the Julian Day List. With that obvious logical constriction in mind, however, it is still worth the effort to evaluate a few quarter-Katun positions as they fall out over the course of their use during the Classic period in the 12 Lamat eclipse correlation. In the following table, those positions from 11 Ahau 3 Pax (November 17, 220 A. D.-Julian Day #1801734) to 5 Ahau 3 Kayab (July 17, 792 A. D.-Julian Day #2010534) are listed. While there are a few recorded dates prior to 11 Ahau 3 Pax, which probably are contemporaneous, and a few more after 5 Ahau 3 Kayab, which fall under the same category, the vast majority of Classic period notations recorded in monumental inscriptions fall between these two Katun-ending designations. The numbers preceding each group of four dates records the position of the quarter following it from the first position at the zero base-day in a continuous sequence.

Maya Long Count Notation
Julian Day Number
Universal Date
#1 4 Ahau 8 Cumku
April 29, 3171 B. C.
#688 11 Ahau 3 Pax
November 17, 220 A. D. 4 Ahau 18 Kankin
October 22, 225 A. D. 10 Ahau 13 Mac
September 26, 230 A. D. 3 Ahau 8 Ceh
August 31, 235 A. D.
#692 9 Ahau 3 Zac
August 5, 240 A. D. 2 Ahau 18 Ch'en
July 10, 245 A. D. 8 Ahau 13 Mol
June 13, 250 A. D. 1 Ahau 8 Yaxkin
May 18, 255 A. D.
#696 7 Ahau 3 Xul
April 22, 260 A. D. 13 Ahau 18 Zotz
March 26, 265 A. D. 6 Ahau 13 Zip
February, 28, 270 A. D. 12 Ahau 8 Uo
February 2, 275 A. D.
#700 5 Ahau 3 Pop
January 7, 280 A. D. 11 Ahau 3 Cumku
December 11, 284 A. D. 4 Ahau 18 Pax
November 15, 289 A. D. 10 Ahau 13 Muan
October 20, 294 A. D.
#704 3 Ahau 8 Kankin
September 24, 299 A. D. 9 Ahau 3 Mac
August 28, 304 A. D. 2 Ahau 18 Zac
August 2, 309 A. D. 8 Ahau 13 Yax
July 7, 314 A. D.
#708 1 Ahau 8 Ch'en
June 10, 319 A. D. 7 Ahau 3 Mol
May 15, 324 A. D. 13 Ahau 18 Xul
April 19, 329 A. D. 6 Ahau 13 Zec
March 24, 334 A. D.
#712 12 Ahau 8 Zotz
February 26, 339 A. D. 5 Ahau 3 Zip
January 31, 344 A. D. 11 Ahau 18 Pop
January 4, 349 A. D. 4 Ahau 18 Cumku
December 9, 353 A. D.
#716 10 Ahau 13 Kayab
November 13, 358 A. D. 3 Ahau 8 Pax
October 18, 363 A. D. 9 Ahau 3 Muan
September 21, 368 A. D. 2 Ahau 18 Mac
August 26, 373 A. D.
#720 8 Ahau 13 Ceh
July 31, 378 A. D. 1 Ahau 8 Zac
July 5, 383 A. D. 7 Ahau 3 Yax
June 8, 388 A. D. 13 Ahau 18 Mol
May 13, 393 A. D.
#724 6 Ahau 13 Yaxkin
April 17, 398 A. D. 12 Ahau 8 Xul
March 22, 403 A. D. 5 Ahau 3 Zec
February 28, 408 A. D. 11 Ahau 18 Zip
January 28, 413 A. D.
#728 4 Ahau 13 Uo
January 2, 418 A. D. 10 Ahau 8 Pop
December 7, 422 A. D. 3 Ahau 8 Cumku
November 11, 427 A. D. 9 Ahau 3 Kayab
October 15, 432 A. D.
#732 2 Ahau 18 Muan
September 19, 437 A. D. 8 Ahau 13 Kankin
August 24, 442 A. D. 1 Ahau 8 Mac
July 29, 447 A. D. 7 Ahau 3 Ceh
July 2, 452 A. D.
#736 13 Ahau 18 Yax
June 6, 457 A. D. 6 Ahau 13 Ch'en
May 11, 462 A. D. 12 Ahau 8 Mol
April 15, 467 A. D. 5 Ahau 3 Yaxkin
March 19, 472 A. D.
#740 11 Ahau 18 Zec
February 21, 477 A. D. 4 Ahau 13 Zotz
January 26, 482 A. D. 10 Ahau 8 Zip
December 31, 486 A. D. 3 Ahau 3 Uo
December 5, 491 A. D.
#744 9 Ahau 3 Uayeb
November 8, 496 A. D. 2 Ahau 18 Kayab
October 13, 501 A. D. 8 Ahau 13 Pax
September 17, 506 A. D. 1 Ahau 8 Muan
August 22, 511 A. D.
#748 7 Ahau 3 Kankin
July 26, 516 A. D. 13 Ahau 18 Ceh
June 30, 521 A. D. 6 Ahau 13 Zac
June 4, 526 A. D. 12 Ahau 8 Yax
May 9, 531 A. D.
#752 5 Ahau 3 Ch'en
April 12, 536 A. D. 11 Ahau 18 Yaxkin
March 17, 541 A. D. 4 Ahau 13 Xul
February 19, 546 A. D. 10 Ahau 8 Zec
January 24, 551 A. D.
#756 3 Ahau 3 Zotz
December 29, 555 A. D. 9 Ahau 18 Uo
December 2, 560 A. D. 2 Ahau 13 Pop
November 6, 565 A. D. 8 Ahau 13 Cumku
October 11, 570 A. D.
#760 1 Ahau 8 Kayab
September 15, 575 A. D. 7 Ahau 3 Pax
August 19, 580 A. D. 13 Ahau 18 Kankin
July 24, 585 A. D. 6 Ahau 13 Mac
June 28, 590 A. D.
#764 12 Ahau 8 Ceh
June 2, 595 A. D. 5 Ahau 3 Zac
May 6, 600 A. D. 11 Ahau 18 Ch'en
April 10, 605 A. D. 4 Ahau 13 Mol
March 15, 610 A. D.
#768 10 Ahau 8 Yaxkin
February 17, 615 A. D. 3 Ahau 3 Xul
January 22, 620 A. D. 9 Ahau 18 Zotz
December 26, 624 A. D. 2 Ahau 13 Zip
November 30, 629 A. D.
#772 8 Ahau 8 Uo
November 4, 634 A. D. 1 Ahau 3 Pop
October 9, 639 A. D. 7 Ahau 3 Cumku
September 12, 644 A. D. 13 Ahau 18 Pax
August 17, 649 A. D.
#776 6 Ahau 13 Muan
July 22, 654 A. D. 12 Ahau 8 Kankin
June 26, 659 A. D. 5 Ahau 3 Mac
May 30, 664 A. D. 11 Ahau 18 Zac
May 4, 669 A. D.
#780 4 Ahau 13 Yax
April 8, 674 A. D. 10 Ahau 8 Ch'en
March 13, 679 A. D. 3 Ahau 3 Mol
February 15, 684 A. D. 9 Ahau 18 Xul
January 19, 689 A. D.
#784 2 Ahau 13 Zec
December 24, 693 A. D. 8 Ahau 8 Zotz
November 28, 698 A. D. 1 Ahau 3 Zip
November 2, 703 A. D. 7 Ahau 18 Pop
October 6, 708 A. D.
#788 13 Ahau 18 Cumku
September 10, 713 A. D. 6 Ahau 13 Kayab
August 15, 718 A. D. 12 Ahau 8 Pax
July 20, 723 A. D. 5 Ahau 3 Muan
June 23, 728 A. D.
#792 11 Ahau 18 Mac
May 28, 733 A. D. 4 Ahau 13 Ceh
May 2, 738 A. D. 10 Ahau 8 Zac
April 6, 743 A. D. 3 Ahau 3 Yax
March 10. 748 A. D.
#796 9 Ahau 18 Mol
February 12, 753 A. D. 2 Ahau 13 Yaxkin
January 17, 758 A. D. 8 Ahau 8 Xul
December 22, 762 A. D. 1 Ahau 3 Zec
November 26, 767 A. D.
#800 7 Ahau 18 Zip
October 30, 772 A. D. 13 Ahau 13 Uo
October 4, 777 A. D. 6 Ahau 8 Pop
September 8, 782 A. D. 12 Ahau 8 Cumku
August 13, 787 A. D.
#804 5 Ahau 3 Kayab
July 17, 792 A. D.
#1040 4 Ahau 3 Kankin
August 14, 1955 A. D.

An obvious point to begin this discussion appears at the 794th quarter after the zero base-day at 10 Ahau 8 Zac on April 6, 743 A. D. (Julian Day #1992534). On the day in question, the sun reached a setting azimuth equivalent to +278*17'39" which placed it well within the necessary limits to qualify as the orientation of the mid-line of the window in Temple 22 at Copan. Also significant here is the fact that vernal equinox, 20 days earlier, fell at 3 Ahau 8 Yax on March 17, 743 A. D. (Julian Day #1992514), a position in the Maya calendar that fell exactly midway between two formal positions in the Dresden Codex Venus table. The first came at 12 Cib 4 Yax on March 13, 743 A. D. (Julian Day #1992510) after the addition of the 250-day interval in that Maya table in the 46th synodic period of the planet after the base-day at 1 Ahau 18 Kayab (September 1, 669 A. D.). The second position occurred 8 days later at 7 Kan 12 Yax on March 21, 743 A. D. (Julian Day #1992518). Since the Maya would have been aware of this convergence between the Venus table, solar orientations, and the half-Katun marker at, it seems reasonable to suppose that these various aspects of their calendrical astronomy were integrated with one another in the way Classic period astronomers watched and recorded celestial motion. Also true here is the fact that after every 3.5 Katuns have been counted the quarter position falls in close proximity to the orientation markers built into the architectural alignments at Copan. Hence, at 4 Ahau 13 Yax on April 8, 674 A. D. (Julian Day #1967334), the sun reached its orientation at the window in Temple 22 at Copan two days before the Katun-ending date at 2 Etz'nab 11 Yax on April 6, 674 A. D. with an azimuth of +278*14'06". At 11 Ahau 18 Ch'en (April 10, 605 A. D.-Julian Day #1942134), the sun's orientation at the mid-line of the window in Temple 22 at Copan occurred three days earlier at 8 Caban 15 Ch'en on April 7, 605 A. D., which clearly establishes a pattern susceptible to prediction in the relationship between Katun quarters and solar orientations in the Maya calendrical system. With the more precise methodology for determining their day-names explicitly expressed in the 15,340-day interval of the almanac, actual temporal locations relative to the quarter-Katun markers would have been obvious.

Two other quarter-Katun positions are directly relevant to this discussion because they were inscribed on Stela 12 at Copan and were the only dates recorded on that monument. The first fell at 6 Ahau 13 Mac on June 28, 590 A. D. (Julian Day #1936734). The second date was recorded at 12 Ahau 8 Ceh on June 2, 595 A. D. (Julian Day #1938534). This date sequence is somewhat unusual, since sequential Katun-quarters, with no other dates before, after, or between, them, do not occur on any other monument in the Maya area. There is a third date associated with the Copan baseline, recorded at 3 Ahau 8 Yaxkin on February 22, 595 A. D. (Julian Day #1938434), which was inscribed on Stela 10. In a general context, quarter-Katun markers were used by the Maya to specify the day on which various kinds of dated monuments were dedicated. Again, generally speaking, the day of a public ritual commemorated by a monument, say the birth, accession, or death, of a ceremonial center's ruler, was listed in the text and was then followed by the quarter-Katun position that comes in closest proximity to it, where that second date specifies when the monument was dedicated. In the case of Stela 12, 6 Ahau 13 Mac would have been the date of the public ritual and 12 Ahau 8 Ceh would have functioned as the date the monument was dedicated. The problem with that interpretation, however, is that no indication exists in the text to suggest that 6 Ahau 13 Mac was meant to mark a public ritual associated with the ruling dynasty at Copan. The date on Stela 10, 3 Ahau 8 Yaxkin, does not seem to be the day of a public ritual either and there is no period ending date at a quarter-Katun position recorded on it at the same time, which might suggest that the period ending date for Stela 10 was the same as the one for Stela 12 at 12 Ahau 8 Ceh. Since these two stelae mark the setting orientation of the sun when it also crosses the central axis line of the window in Temple 22, it seems reasonable to suppose that these dates somehow commemorate an important solar passage in the history of Copan. Another observation that must be made here is that these dates cannot specify the first time in Maya history that these orientations were employed to mark the 20-day intervals associated with vernal and autumnal equinoxes, window orientations, and solar zenith passages, because the orientations themselves had to be known prior to the establishment of the architectural monuments that mark them.

Given the fact that these two quarter-Katun dates may mark the dedication dates of Stelae 10 and 12 at Copan, on the one hand, it is also important to note that both position fall in close proximity to summer solstice, on the other, where the first one (6 Ahau 13 Mac) occurs eight days after it on June 28, 590 A. D., while the second one (12 Ahau 8 Ceh) falls 18 days before it on June 2, 595 A. D. This may be significant because summer solstice always marks the mid-point in the sun's transition between vernal and autumnal equinox, where the baseline between the two stelae always mark the 20-day intervals that form the ground on which Maya calendrical conceptualizations were based. This rather benign observation can be said to conceal a much more significant reality in the short-term history of Maya calendrical science in as much as the Katun-ending position at foreshadows its own third quarter marker, at 4 Ahau 13 Mol on March 15, 610 A. D. (Julian Day #1943934), which also designates a position exactly 1 Katun (20 x 360 = 7,200 days) after the other date on Stela 12 at 6 Ahau 13 Mac. The reason this matters is that the LC notation for 4 Ahau 13 Mol ( counts exactly 1,380,600 days after the zero base-day at 4 Ahau 8 Cumku. This interval, of course, is a multiple of 260 days because both positions are marked by 4 Ahau in the almanac's day-name sequence. In fact, this interval is equivalent to 90 x 59 x 260 days exactly. Since 90 is also a multiple of 6 (6 x 15 = 90), the day of vernal equinox in closest proximity to must necessarily fall exactly 15 days after the almanac day-name that marked that same position in closest proximity to the zero base-day itself. In fact, vernal equinox in 610 A. D. fell on March 18, when the sun reached +00*00'01" of declination one minute and thirty-nine seconds after sunrise (06:12:00) on that day. In Maya notation that day was designated at 7 Akbal 16 Mol. Fifteen days earlier, the count reached 5 Lamat 1 Mol on March 3, 610 A. D. (Julian Day #1943922). This position, of course, is 12 days prior to the Katun-quarter at 4 Ahau 13 Mol. As noted earlier, vernal equinox, 12 days prior to the zero base-day, fell at 5 Lamat 16 Kayab on April 17, 3171 B. C. (Julian Day #563322). The point to be taken here is not that Maya prediction technology is more or less accurate over long periods of time but rather that certain kinds of calendrical structures inherent in their system are as close to absolutely precise as anything can possibly be. Given the fact that the sun crossed the celestial equator one minute and thirty-nine seconds after it rose across the eastern horizon at Palenque, Chiapas, Mexico, on March 18, 610 A. D., 1,380,600 days after the zero base-day of their calendar, certainly suggests, if not absolutely confirms, precisely how they were able to fix the position, relative to the Julian Day List, that initiated the Classic period Long Count notation so that this configuration would appear in the due course of the count of the days. Palenque matters in this context because 5 Lamat 1 Mol is the Calendar Round anniversary of the accession of its most notable ruler-Pacal II, who acceded to Palenque's throne at 5 Lamat 1 Mol on March 16, 558 A. D. (Julian Day #1924942), exactly 18,980 + 12 days prior to the Katun-quarter at 4 Ahau 13 Mol. To say that Pacal II anticipated this astronomical structure in his choice of the day for his accession ritual is to say simply that Maya astronomers were aware of the full implications of their own calendrical system. We, on the other hand, at the start of the 21st Century, mere children in comparison to any Maya astronomer, are just beginning to comprehend what that system envisions and what it is able to express over the long course of its use during the Classic period.