THE SUPPLEMENTARY AND LUNAR GLYPHS

Sandwiched between the Tzolkin glyph block, here at A4, and the Haab glyph block at A7, are what is known as the SUPPLEMENTARY AND LUNAR GLYPHS; 8 of these were labeled by Morley as glyphs A, B, X, C, D, E, F and G (Teeple, 1930  p43); at some later time, two additional Lunar glyphs were found and added, Y and Z. All 10 of these glyphs need not appear in any particular inscription, and more than one glyphs is often conflated into one glyph block. The labeling of these Supplementary Glyphs is rather arbitrary, and there is some logic and convenience in grouping these by twos, and in this order: G and F,  Z and Y,  D and E,C and X,B and A. These 5 groups are recognized as Lords of Night, unknown, Moon Age, Lunation Number, Moon Type. (For historical completeness, the Mayanist Morgan, in 1915, working with the then known 7 Lunar Glyphs, labeled then A, B, C, D, E, F and G, and rearranged them backwards, in which order they still are (Schele, 1992, p56). The Supplementary and Lunar Glyphs begin to appear on Pre-Classic Maya recordings as early as 199 A.D. (08.07.19.10.19) (Justeson 198x, p79); this predates the appearance of the first Long Count Dates on Maya monuments.

 THE LORDS OF THE NIGHT

                   GLYPHS G and F

  The glyphs at B4 are called "Supplemental"; Glyph G, 1st part, its element being a stylized shell, is another immutable part of the day calendrics; it is known as a "Lord of the Night Glyph". Supplemental Glyphs "G", of which there are 9, are appropriately named "G1", "G2" ... "G9" and represent the ruling deity of the day.

  The 9 Lords of the Night Glyphs fit in with the rest of the dates the same as the 7 days of the week do for us: Monday through Sunday keep rotating through regardless of the date, Which Lord of the Night is ruling on any particular Long Count Date may be readily figured out (Frumker, 1993); all L.C. dates ending in 0.0 (Winal and Kin) are G9; endings in 0.1 are G1, 0.2 are G2, ... 0.8 are G8. With a great number of stelae and monumental dates being erected at K’atun (20 year), Lahuntun (1/2 K’atun = 10 years) and Hotun (1/4 K’atun = 5 years) and Tun (1 year) end dates, and therefore being 0.0, we have a superabundance of examples of Lords of the Night G9! Because Winal X Kin is 360 days (18 X 20), and since 360 is divisible by 9 with no remainder, the relationship repeats continually. In our example, A3 and B3, 2 Winals and 4 Kins total 44 days (2 X 20 +4); 44 days is 36 with 8 remainder: the ruling Lord of the Night is G8. Another relationship which did not escape the Maya, is that effected by the Tzolkin; because the Tzolkin is 260 days, and 260 is 261 (which is exactly divisible by 9) -1, the same Lord of the Night will rule on the next day, one Tzolkin Year later. In general, days with Ruling Lords G1 and G2 and G7 were regarded as bad luck days, with the remaining Ruling Lords promoting good and very good days.

  Part 2, also imbedded in Glyph at B4, is Glyph F; says Mr. Teeple (Teeple, 1930, p61): "Glyph F has no specific meaning for us; .. an introductory character which notifies us that Moon Age and Number  .. follow". By the way, I am anxious to locate a paper on what or part of the day the Maya considered the end of one day and the beginning of the next day; middle of the night? some Midnight? Sunset? Sunrise? what? How do the daily "Lords of the Night" fit in?

  GLYPHS Z and Y

  The glyph block at A5 contains glyph Z and Y; these are understood to be lunar glyphs, but to date have not been deciphered. Note that the prefix to Z is a bar, indicating 5 of something; also note that two elements of A5 match two elements of B5, these being the 5-dot quincunx with, below it, a small face. According to Thompson, "Glyph Y and Glyph Z appear to indicate dawn or night ... Glyph Z is same as the "bix glyph" (Thompson, 1960, p243). According to Justeson (Justeson, 198x, p78), Glyph Z is merely the numeral prefix + the grammatical suffix "bis" ("bix") of Glyph Y.

                                                                        GLYPHS D and E

The story goes that Teeple, a chemical engineer with apparently a penchant for things Maya, and for solving puzzles, spent a considerable amount of time while on train travels, unraveling the puzzle of the Moon Glyphs. Armed with somewhat less than 200 date inscriptions, he resolved a great deal of their meaning and values almost single-handedly. These are described at length in a couple of brilliant monograms (Teeple, 1925 and 1930). The Moon Age is glyph D at B5; its value here, a bar and two dots, is 7, meaning that this date, 9.0.19.2.4 is seven days after new moon, or day 7 into the current lunation, kind of like "First Quarter Moon". We can check on the correctness of this value with a little mathematical manipulation, which unfortunately is a too lengthy for this short paper. A method, well described by Christopher Jones (C Jones, 1984, p48), is based on Quiriguá Stela E which records a Moon Age of Zero, and a Moon Number of 2 on a base date 9.17.0.0.0 (see also Kelley, 1977, p63); the method then casts out whole lunations of 29.53059 on the difference between that date and the date being checked; the remainder (or 29.53059 minus the remainder if the date is earlier than the base date) should come close to the inscribed moon age, say within 1 or 2 days.

Glyph E, when present, adds 20 to the Moon Age value of Glyph D; on our example of 9.0.19.2.4, Glyph E is not present (Teeple 1930, p50, C Jones 1984, p60, Schele 1988, p54, T Jones, 1986, p14) or present (Coe, 1992, p131), the interpretation depending on whether or not the moon element representing the value "20 days" is at Glyph Block B5. The "20 days" element is variedly drawn as a complete moon sign with a dot or circle in the center (Thompson, 1960, p239), or the complete moon sign with three dots, sometimes at a diagonal (T Jones, 1986, p14). Perhaps of crucial importance, to have a value increased by 20, Glyph E must precede Glyph D. Glyph D will have a prefix value from  zero to 19; Moon Age values from 20 to 29 will have both Glyph E, meaning "add 20 days", and Glyph D with an appropriate prefix. Stated another way, for example "To record a moon age of 23 days,... the Lunar Series is initiated by an "E" Glyph prefixed by a 3 and followed immediately by the "D" Glyph ... the coefficient of "E" never exceeds 9 (T & C Jones, 1993, p34).

                                                                    THE MOON NUMBER

                                                                         GLYPH C and X

Glyph C, the Moon Number, here at A6, represent the lunation number, which in this case is 3. The lunation number goes from 1 to 5 or 6; it is obviously counted from a base lunation of zero, and cycles through to 5 or 6, then back to 1, implying that the base lunation is related to an eclipse season. Teeple denies that there is any relationship between eclipse seasons on the ground that he finds as many groups of 5 as groups of six lunations (Teeple 1925, p548, where he also notes that 9.17.0.0.0 is an eclipse syzygy). Recall that some form of Solar and Lunar Eclipse, no matter how paltry or grandiose, occurs somewhere on Earth every 6th, sometimes 5th lunar month, at the rate of 3 to 7 per year (Ottewell, p39).

Now, eclipse prediction for a stone age culture, while significant and important, has to be elusive. Consider that, while there is about an equal number of solar as well as lunar eclipses, probably only about 1/3 of all eclipses are visible at any one location on Earth, and that furthermore, of these, only one out of ten will be solar. Not only that, but studies have shown that these few visible eclipses do not show up at regular intervals, but rather tend to appear and bunch up in groups (Smither, 1986, p99). The point that I would like to make is that, like most other cultures, the Maya apparently attempted to link specific lunations to eclipses for prediction purposes, and apparently were not always successful.

What we find is that sometimes different Maya City-States agreed on which lunation to start counting the Moon Number from, and sometimes they did not. Teeple found this out when he puzzled out the Moon Number. Previous to 9.12.15.0.0 (687 A.D.), differing Maya city-states had differing Moon Number Base, a period which he calls, "of independence"; at about 9.12.15.0.0 a period of agreement was reached, and all Maya City-States counted Moon Numbers from the same base lunation, and furthermore, they all cycled through 6 lunations and never 5; this is especially evident in at least the city-states of Piedras Negras, Yaxchilán, Copán, Naranjo and Quiriguá (Teeple 1930, p54);  this he called the "Period of Uniformity". After 9.16.5.0.0 (765 A.D.), varying City-States, beginning with Copán, which began inserting an occasional 5-lunations cycle (148 days) and which probably was the leading city intellectually, gradually dropped out of uniformity, into a period known as the "2nd change".

(Justeson notes that an eclipse, Lunar or Solar, occurs somewhere every 176, 177 or 178 and occasionally 148 days, or every 6th and occasionally 5th lunation; the Saros eclipse cycle follows the pattern 47 +41 +47 +41 +47 lunations; 47 is 7x6 + 1x5 lunations, and 41 is 6x6 + 1x5 lunations).  Justeson expounds on eclipse predictions (Justeson 198x, pp83-91), with postulated lunation number, and the postulated last month of a moon number beginning on a solar eclipse possibility; however, as enlightening as it is, its too lengthy to present here.

Glyph X, here recorded at the left half of Glyph Block B6, has been known to be closely related to Glyph C, but no one knows its significance; note for instance the skull which appears in both glyphs, over the hand in Glyph C, under the crossed legs in Glyph X. Recently, Linda Schele made a breakthrough in patterning the differing "X" glyphs (Schele, 1992, p58); the pattern is that one of three elements: a skull, or a young moon goddess, or a jaguar, co-varies with the Moon Number (the prefix of Glyph C). Aveni notes that often, when the "crossed legs" appear in Glyph X, the prefix of C is 3 (Aveni, 1980, p165).

THE MOON TYPE GLYPH

GLYPH B and A

The Moon Type Glyph, Glyph A, here at the right half of B6, identifies the current lunation as being either 29 days or 30 days in length; it is the length of the current lunation; since the average lunation is a bit over 29 days (29.530588 days), by alternating between a "29" A and a "30" A, the calendar keepers managed to stay in synch with the observed lengths of the Lunar Month.  Glyph A is typically represented with an element for the moon, here several concentric circles and three dots, and a number suffix either being 9 or 10, here it being 9; the moon element is understood to stand for the value of 20 days. (A similar element is typically used for Glyph E above, when it is needed to express and add "20 days"). Aveni states that when Glyph C prefix is even, Glyph A usually shows 29 days, and when C is odd, A is usually 30 days (Aveni, 1980, p165); this is not the case in our example. (A study of an 800-year span, 1600 A.D. to 2400 A.D., shows the Lunation time variation to range from as little as 29 days 6 hours 31 minutes, or 29.271527 days to as long as 29 days 19 hours 59 minutes, or 29.834097 days; this is a variation of .572570 day or near a half day about the average of 29.530588 days! (Sinnott, 1993, p76). 

Glyph B, when present, identifies or names the 29 or 30 day lunation; Schele calls Glyph B its "Sprout Name" (the "Sprout Name" of Glyph A); in our example, Glyph B is not present.

 In summary, we can see that Glyphs E/D, C, A, these representing Moon Age, Moon Number and Moon Type, show a fairly sophisticated way to express a Lunar Calendar; perhaps in the future, we will be able to prove or disprove that their lunar calendar was also rigorously tied to eclipse predictions. In general, while the accuracy of this calendar is one expected from the observational data of a stone age culture, we have no problems using modern methods to authenticate the basic correctness of at least the Moon Age values. We can also see that the ancient Maya managed to mesh their exact day count with the lunar calendar for some two thousand years (today, there are still Maya Calendar Keepers in remote villages of the Yucatan Peninsula). As exemplified by over 170 Maya inscriptions, the date almost always show the calendric order of "LONG COUNT",  "TZOLKIN",  "LORDS OF THE NIGHT",  "LUNAR GLYPHS F - Z  - Y - E/D - C  - X - B - A", and "HAAB'.

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