Maya Lunar Supplementary Series
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]):
- Reference for determining the Moon's Age (like: an observed
New Moon; a calculate New moon; a known base from Maya Creation
Date [aka 0.0.0.0.0]).
A few more parameters are needed to determine this further:
- The month's length determination
By observation [some 5 methods are implemented, related to how New Moon was determined] or by the 18
month lunar synodic calendar (Linden , page
- The Correlation
(like GMT) between Maya calendar and Julian Day Number.
In the below no reference is made to the Julian Day Number as
the Maya Creation Date, 0.0.0.0.0, and the Moon's Age at that
date are used, so the Correlation is not important in this case.
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
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):
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:
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:
Remark: using the Palenque synodic period
[29.53086 days] does not produce such distribution with mean
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  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:
Using a Moon's Age of 22 at Maya Creation Date makes the Glyph
D/E difference value below zero (~-1.6 days)
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:
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:
- The Maya Creation Date 0.0.0.0.0 as a reference
- The Copan Synodic period of 29.5302 days; which was also
used during the Unity period (Teeple , page 68)
- The Palenque Moon's Age at Maya Creation Date of 24 days
Somewhat controversial related to the Copan Synodic period
length! If you have feedback, let me
- The 18 month lunar synodic calendar of Linden
- In general this is working for Teeple 's Periods 1,
2 and 3.
No decision could be taken around the Correlation. This will be
investigated as part of future evaluation of lunar/solar eclipse
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
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
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,
Mark Van Stone. 2012: Science and Prophecy of the Ancient
Maya: Tlacaelel Press, 2010.
Major content related
changes: Sept. 5, 2012