Xultun Number A and the 819-Day Count

by Barbara MacLeod and Hutch Kinsman

Within a few hours of the publication in the 11 May, 2012 issue of Science of “Ancient Maya Astronomical Tables from Xultun, Guatemala”, by William Saturno, David Stuart, Anthony Aveni and Franco Rossi, Hutch Kinsman contacted colleagues who regularly correspond by email, pointing out that Number A—1,195,740—is evenly divisible by 819. It is the only one of the four which contains this factor. He also noted that the coefficient of the tzolk’in day at the top of the column is 1. Since all tzolk’in dates which are stations in the 819-Day Count have a coefficient of 1, this was further evidence that the purpose of the interval was to commensurate the 819 (2.4.19)-Day Count with the Calendar Round.

Figure 1. Number array from north wall, Structure 10K-2, Xultun, Guatemala. (Preliminary drawing by David Stuart)

For anyone not familiar with this cycle, 819 is the product of 7, 13, and 9—numbers of ritual and calendric significance to the Maya. Following the Initial Series, the count appears as a short distance number leading to the previous station–one of four which are 819 days apart. These are associated with the cardinal directions and their corresponding colors. A verb meaning ‘stand still’ or ‘stop’ appears along with several regular protagonists. Yaxchilan and Palenque are noteworthy in having multiple monuments featuring the 819-Day Count. J. Eric S. Thompson (1950:214) and his contemporaries offered early suggestions about its purpose. Heinrich Berlin and David Kelley (1961) first described the structural similarity between the Dresden New Year pages and the color/direction symbolism of the 819-Day Count. Given the formula [4 x 819] = [9 x 364] one may add nine days to the latter to complete nine haabs. Michael Grofe (personal communication, May, 2012) suggests that it is an idealized system for tracking the sidereal position of eclipses.

Figure 2. Example of 819-day count record from Yaxchilan, Lintel 30. (Drawing by Ian Graham)

The interval of Xultun Number A—1,195,740 days– is [63 x 18,980] and [4 x 819 x 365]. It is also [9 x 365 x 364], which brings to mind the [9 x 364] = [4 x 819] formula mentioned above. The unit of 364 days is the Maya “computing year” discussed by Thompson (1950:256). The interval of Xultun Number A is also the smallest unit which commensurates the 819-Day Count with the Calendar Round.

Thompson (cited above) wrote: “as only once in every 63 times will a day with a coefficient of 1 also mark the start of the 819-day cycle, the fact that this first day before ( 4 Ajaw 8 Cumku is a base in the 819-day cycle argues strongly for that count’s being primarily ritualistic”.

The day 1 Kaban before the Era Base 4 Ajaw 8 Kumk’u, per a discussion Carl Callaway and Barbara MacLeod had several years ago, is an 819-Day Count station in the east quadrant—the quadrant in which, for several reasons, we concluded that the count should begin. From this datum, counts both forward and back might reach other stations in the cycle; thus the pre-era date 1 Kaban 5 Kumk’u need not be the earliest documented station. The earliest station known, 1 Chikchan 18 Ch’en, recorded on the Palenque Temple XIX bench, is therefore not the base date but rather a distant-past station reached from it.

At the 1974 Segunda Mesa Redonda de Palenque, Floyd Lounsbury presented a meticulous analysis of the pre-era initial date of the Tablet of the Cross at Palenque. This paper is well worth reading and is available on Mesoweb:


Per Lounsbury’s work, the Palenque interval is 1,359,540 days, or [4 x 819 x 415]. While it is not an even multiple of the 18,980-day Calendar Round, it is [5229 x 260] and [1734 x 780] and [3735 x 364]. It demonstrates the application to dynastic mythological narrative of large multiples of [4 x 819] by Maya scribes in deep-time calculations.

Saturno et. al. note that the tzolk’in day at the top of Column A is either 1 Kawak or 1 Kaban. We suggest that it is 1 Kaban—the tzolk’in position of the base date of the 819-Day Count. This in turn sheds light on the function of the other three tzolk’in dates. We tentatively suggest that the 9 K’an date atop Column B is that of the Dresden Codex Serpent Base 9 K’an 12 K’ayab. More will be said about the other three numbers in the near future.

References Cited

Berlin, Heinrich, and David H. Kelley. 1961. The 819-day Count and Color-direction Symbolism among the Classic Maya. Middle American Research Institute Publication 26.

Lounsbury, Floyd G. 1976 A Rationale for the Initial Date of the Temple of the Cross at Palenque. Second Palenque Roundtable, 1974. The Art, Iconography & Dynastic History of Palenque, Part III, edited by Merle Greene Robertson. Pebble Beach, California: Pre-Columbian Art Research, The Robert Louis Stevenson School.

Saturno, William, David Stuart, Anthony Aveni and Franco Rossi. 2012. Ancient Maya Astronomical Tables from Xultun, Guatemala. Science 336, 714.

Thompson, J. Eric S. 1950. Maya Hieroglyphic Writing: An Introduction. University of Oklahoma Press, Norman.

8 thoughts on “Xultun Number A and the 819-Day Count

  1. David Stuart June 11, 2012 / 3:06 PM

    Very nice observation on the connection of number A with the 819-day count — something I had missed entirely. I just wanted to mention that while working with the scans last year, and squinting at the tiny glyphs in situ last March, Bill, Franco and I agreed that 1 Kaban was the likely reading of the header glyph in A. We felt it was too damaged to warrant a firm i.d. in the Science article, but I’m glad to see that it all fits.

  2. Timothy Alan February 24, 2017 / 8:47 AM

    I’ve been working with this number 1195740 and found the following…

    365 x 260 x 819 x 584 = 45390290400 = 1195740 x 37960
    260 x 365 x 819 = 77723100 = 1195740 x 65
    819 x 780 x 584 = 3539939040 = 1195740 x 296
    260 x 584 x 819 = 124356960 = 1195740 x 104

    Timothy Alan 2017.