Page 58 of the *Dresden Codex *contains in its right-most columns (Figure 1) the heading of a computational table that follows the manuscript’s noted eclipse tables. The nature of the table on pages 58-59 is complex and subject to some debate, and here I will happily put aside any in-depth discussion of its numerology in order to simply point out an unusual paleographical feature of a day sign (13 Muluk) written in the page’s final column.

The numbers shown provide anchors or base dates for the calculations that follow on page 59, many of which are multiples of 780 days that fall on the day 13 Muluk. For example, we see in the first column two integrated Ring Numbers (RN), 1.7.11 and, added in red, 12.11. These calculate the intervals backwards before 13.0.0.0.0 to the intended base dates:

RN Base 1: 12.19.18.10.9 13 Muluk 2 Sak

RN Base 2: 12.19.19.5.9 13 Muluk 17 Tzek

13 Muluk 2 Sak is the primary of the two dates. It is recorded as the header of the two glyph columns on page 58 and as the CR at the lower right of the page, next to 4 Ahaw 8 Kumk’u.

The two intervals given on the right coloumn are so-called Long Reckonings, or a special type of Distance Number from the pre-era base date to reach a new base for the table. The first of these numbers is 9.18.2.2.0, which when added to the 12.19.18.10.9 13 Muluk 2 Sak results in 9.18.0.12.9 13 Muluk 2 Mol. The other LR record below it is 9.12.11.11.0 can also be added to the secondary base date (13 Muluk 17 Tzek), thereby reaching 9.12.10.16.9 13 Muluk 2 Sip. There is a bit of ambiguity in what gets added to what here, but the important point to stress here is that adding these LRs to either pre-era base date will always result in a 13 Muluk.

The day shown between the two LR numbers is obviously a Muluk, but different from others by two unusual features: it lacks a number coefficient and is surrounded by a red edging around the conventional black border (not shown in the Villacorta tracing, as it happens). Perusing the Dresden, I can find no other day sign with similar marking, even though red cartouches were common for painted day signs throughout the Classic period, and as far early as the Late Preclassic. No such red borders were ever used in the Dresden, however, and in light of the scribal style and practice employed in the Dresden I doubt that this red border is meant to be a decorative or without meaning.

The absence of the number prefix leads me to suspect that the red line around the Muluk is an unusual and playful means of indicating a 13 day coefficient — the fullest number possible that can accompany Muluk or any day sign in the 260-day tzolk’in. Perhaps the idea was that the number 13 has in some sense “come full circle.” It might be worth recalling that all number coefficients on tzolk’in dates are painted in red as well.

Admittedly this interpretation hinges on the assumption of highly unconventional scribal practice. But there are other examples of “odd” numbers in the Dresden. For example, phonetic spellings of the numbers three (*ox*, **o-xo**) and eleven (*buluk*, **bu-lu-ku**) with day signs in the Dresden are also well outside of normal conventions, never seen elsewhere. I’ll therefore put forward this idea of the circular 13 as a tentative hunch, hoping it explains the “missing” number on the day sign.

ablumeAugust 28, 2012 / 10:27 PMWonderful to see this kind of observation David since it brings us right to the edge of a Maya scribe thinking something as in a kind of whisper. The zero signs are by an large written in red in the Dresden. Do you have any thoughts about why that may be?

David StuartAugust 29, 2012 / 4:10 PMIt’s true that the zero signs are pretty much always in red in the Dresden, but I can’t say I have an explanation. I’m reminded of the practice of writing whole LC dates in red, as we see on K1440. It’s a different pattern, but I wonder if some common general rationale underlies both.

carlos@dresdencodex.comSeptember 4, 2012 / 12:53 PMAs a matter of fact, the highest possible value of any cyclical pattern becomes zero when it is expressed as a residual.

Please consider what happens 7 days before the New Year record 9.17.0.0.7

On 9.17.0.0.7, the tzolk’in coefficient = tzolk’in day sign value = G(F) value = Z(Y) value = moon age value = tzolk’in day position = 7

Therefore, when we subtract 7 days from the above components, we obtain a value of zero for all of them, which means that on the date 9.17.0.0.0:

The tzolk’in coefficient was 13 (its highest possible value); the tzolk’in day sign value was 20 (Ahaw); the ninth lord of the night was ruling [i.e. G(F) = 9], Z(Y) = 7; the moon age was 29 or 30 days [i.e. it was new moon; as a matter of fact it was a solar eclipse]; and it was the 260th day of the tzolk’in [13 Ahaw].

Anna VanichkinAugust 29, 2012 / 2:46 AMHello, Dr Stuart,

If we were to determine the position of 13 Muluk in a sequence of 260 days starting with 1 Imix, it would be the 169th day of the tzolk’in. And 169 is 13 squared. “Full circle” indeed.

Anna Vanichkin

David StuartAugust 29, 2012 / 4:17 PMInteresting observation. I like the notion of thirteen 13s!

Carlos Barrera AtuestaSeptember 4, 2012 / 1:47 PMWe can find those thirteen 13s on page 52-a [column D] of the Dresden Codex.

I suspect that they were used to calculate the same lunar phase [full moon] that occurred on the dates 9.18.0.4.0 [i.e. 9.18.0.12.9 – 13 x 13 days], 9.15.7.17.9 [i.e. 9.18.0.12.9 – 1 Calendar Round of 18980 days], as well as the opposite lunar phase [new moon] that ocurred on 9.17.0.0.0 [i.e. 9.18.0.4.0 – 4 x 1820 days].

This assumption is based on the fact that every 4 years, 13 days must be subtracted to obtain integer multiples of lunations.

In one Calendar Round there are 13 quadrennials, so it is necessary to subtract thirteen 13s [169 days] from 18980 days to obtain 637 lunations of 29.5306 days on average.

Please note also that 13 tuns after 9.18.0.4.0, on the date 9.18.13.4.0, a solar eclipse occurred. This is due to the fact that [4 x 1820 + 13 x 360] days = [7280 + 4680] days = 11960 days [Dresden Codex lunar cycle], so:

9.17.0.0.0 [solar eclipse] + 11960 days = 9.18.13.4.0 [solar eclipse]

Stephen HoustonAugust 31, 2012 / 12:21 PMA thought: could the red outline be taken at its word (so to speak) and record Chak, “great” or “large”? Thus, the highest possible coefficient for a day sign?