Maya Lunar Supplementary Series

The Lunar Supplementary Series is part of in the Maya calendar and Glyph A, C, D/E, G, X and Z are implemented in the ARCHAEOCOSMO package. These glyphs need a few assumptions to work (and these assumption are not fully known [yet]):

Comparing glyphs with calculations

An inventory of some 175 Lunar Supplementary Series (around 75 from Period 1 (Independent); 60 from Period 2 (Unity); and 40 from Period 3 (Revolt)) has been evaluated (taken from Teeple and Linden's articles) and compared with calculations, for some100 to 160 for each of the glyphs A, D/E, C and X. This comparing gives a difference distribution.

If one uses: the 18 month lunar synodic calendar proposed by Linden [18Month length]; a Moon's Age of 22 at Maya Creation Date (which looks to be the norm according to Linden); and the Copan synodic period [Base cres. and SMType:1]: it gives a difference distributions for Glyph A, C and X of around zero, but for the D/E glyphs there is an offset (around 1.6 days):

        of difference with MoonAge at of 22 days

Coba Stela 1 has a D/E glyph of 23 [Base cres. and SMType:6], so this is different from Teeple's norm value of 22 or 24:
With Moon's
        Age at at 23 days

Remark: The above difference distribution was made with month length determine by taking the average of first and last crescent at beginning of month and at beginning of next month. So you can see that the 18 month lunar synodic calendar provides a better match for Glyph A.

If one uses the Palenque Moon's Age of 24 days at Maya Creation Date [Base cres. and SMType:5], but still using Copan synodic period; the D/E glyphs get a difference distribution with a mean of around zero:

Distribution of difference with
        MoonAge at of 24 days

Remark: using the Palenque synodic period [29.53086 days] does not produce such distribution with mean around zero!

So it looks that the Moon's Age at Maya Creation Date could be the reason for the non-zero mean of the difference distribution. Should it be close to zero or not?
So what is this Moon's Age at Maya Creation Date and how sure are we about its value?

Variation depending on date

Teeple [1928] recognises three periods: Period 1 (Independence), Period 2 (Unity) and Period 3 (Revolt).
If one puts all the differences between glyph and calculation in a graph, one can determine if the differences change over time:

Time line of Maya calendar dates with
        their glyphs
Using a Moon's Age of 22 at Maya Creation Date makes the Glyph D/E difference value below zero (~-1.6 days)

Time line of Maya calendar dates with
        their glyphs (24 D/E)
Using a Moon's Age of 24 at Maya Creation Date makes the Glyph D/E difference value closer to zero (~0.2 days).

Period 2 indeed seems to have somewhat less variations (as expected for the Unity period), but it is not that significant. In the below figure the 1 sigma of the differences has been calculate over groups of 10 dates, and one can see there is no significant reduction of this variation around Period 2:
1 sigma of the differences

In general the above behaviour of  this Moon's Age at Maya Creation Date (using Copan/Palenque's Moon's Age or Synodic period) does not change when only looking at Period 2 glyphs: for the Unity period a Moon's Age of 24 at Maya Creation Date make the difference distribution still close to zero. This could be expected as the Moon's Age of 24 is linked to Palenque, which was the centre of Unity.


The following parameters are chosen to calculate the best mapping on actual Glyph notations:
No decision could be taken around the Correlation. This will be investigated as part of future evaluation of lunar/solar eclipse notations.


I would like to thank the following people for their help and constructive feedback: David Stuart and all other unmentioned people. Any remaining errors in methodology or results are my responsibility of course!!! If you want to provide constructive feedback, let me know.


John E. Teeple. "Maya Inscriptions: Glyphs C, D and E of Supplementary Series." American Anthropologist 27, no. 1 (1925): 108-15.
John E. Teeple. "Maya Inscriptions VI: The lunar calendar and its relation to Maya history." American Anthropologist 30, no. 3 (1928): 391-407.
John E. Teeple. Maya astronomy. Vol. I-4, Contributions to American archaeology. Washington: Carnegie Institution of Washington, 1931.
John Linden. "Glyph X of the Maya lunar series: An Eighteen-Month Lunar Synodic Calendar." American Antiquity 51, no. 1 (1986).
John Linden. "The deity head variants of Glyph C." Paper presented at the Eighth Palenque Round Table, San Francisco, 1993.
Mark Van Stone. 2012: Science and Prophecy of the Ancient Maya: Tlacaelel Press, 2010.

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Major content related changes: Sept. 5, 2012