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Madrid pages 77 and 78
The following informal reports are based on certain observations while studying the Madrid Codex. The understanding of the Maya has been undergoing constant revision over the last 70 years. It is an exciting time to have an interest in this dynamic culture, both past and present.
A basic knowledge of the structure of the almanacs within the codices would be necessary to understand the reports. Visit www.mayacodices.org for an introduction to the structure of the almanacs. To view the codices, visit www.famsi.org.The codices may appear to be a daunting task at first glance. But once you get the basics, they are a fun challenge to explore.
The reports are as follows:
A Proposed Maya Lunar Almanac, December 2014
Observations on a Proposed Almanac Structure and a Possible Connection to Mars Concerning Pages 77-78 of the Madrid Codex, January 2016
Observations Regarding Almanac Introductory Columns Found within the Madrid Codex, November 2016
Observations on Madrid Codex Pages 2b and 3b, July 2019
A Proposed Maya Lunar Almanac
The Maya belief of time and space was of a repetitive, cyclical nature. It developed its calendars, astronomical tables and ritual almanacs to conform to this belief. This report is the result of the study of one such almanac found in the Madrid Codex, and known as M12b-18b.
This almanac, M12b-M18b which is laid out in grid form, contains all 260 days of the ritual Tzolkin, and has been termed an in extenso almanac. Well, it was probably intended that way but due to scribal error the final form is 52 days short. At any event, the physical layout of the Tzolkin has allowed for Venus and solar calculations to be plotted out upon it. Whether this was the intention or not of the original authors will never be known, but some modern researchers have found it a useful tool to do so.
Following the example of these researchers I was intrigued to see if lunar cycles could be tracked upon the grid. Experiments have led to the formulation of the following proposed lunar almanac.
As has been well demonstrated, the Maya used an alternating pattern of a 29 day interval followed by a 30 day interval to track the lunar cycles. Modern calculations determine the actual lunar cycle at 29.5304 days. As the Maya did not use fractions, they compensated for this by developing long tables and almanacs to reach an end day that mathematically works out the fractional discrepancies, or inserted a new base day at an appropriate point.
The proposed lunar almanac as developed uses an arbitrary Tzolkin day of 13 Ahau as a start/end day. In practice, any Tzolkin day and coefficient can be used. This day however, works well with the almanac on M12b-18b as the last day of the almanac, if completed, would be an Ahau day, and some researchers have assigned it a coefficient of 13. Using that day as the start day and counting 29 days to the completion of the first lunation on the grid leads to a day 3 Muluc. The next lunation completion would be 30 days later and takes one to a day 7 Cauac.
From these two alternating base points subsequent lunation completions can then be plotted out for each successive 29 and 30 day period. The data was entered into a table format, and arranged into groups of ten lunation periods. The process continued until the 13 Ahau Tzolkin day was again encountered. This procedure resulted in a total of 520 Tzolkin day named lunation cycles.
Among the interesting observations is that each of the two individual base day groups regresses one day per lunation cycle, and the coefficients change in a patterned order. Each individual day of the 260 day Tzolkin is represented once, and only once, as a lunation cycle date in each of the two alternating base day groups, accounting for the 520 day names.
Another and perhaps more important observation is that there seems to be a commensuration between the lunar almanac and a known solar/Tzolkin correlation. The 520 lunation almanac is equal to 15,340 days (29.5 x 520). This number is equal (within hours) to 42 solar years (365.2422 x 42 = 15,340.172), and 59 Tzolkins (59 x 260 = 15,340).
Like the Venus Table in the Dresden Codex the absence of fractions leads to errors that are compounded over time in the proposed lunar almanac. The Venus Table has a correction sequence that prefaces the table. One has yet to be devised for the proposed lunar almanac, though it is accurate to within a 3 day station window for nearly 8 years (example: waxing moon, full moon, waning moon).
The proposed lunar almanac could have been a very useful tool for the Maya elite to time or predict certain ceremonies and events. The almanac has a symmetry and simplicity that they would certainly have appreciated.
Steve Mellard December, 2014
OBSERVATIONS REGARDING ALMANAC INTRODUCTORY
COLUMNS FOUND WITHIN THE MADRID CODEX
This informal report relates to certain observations regarding the Introductory column day groups that appear at the beginning of the almanacs found in the surviving codices. It is the belief of this author that these introductory columns constitute the very foundation on which the divinatory almanacs are based, and that the numeral day groups reached within the almanacs are arrived at by a subsequent manipulation of the intervallic (distance) numbers to reach the proper prognostications.
The almanacs appear throughout the few codices that remain from the Spanish Conquest. These are mostly divinatory in nature, making up a good portion of the codices, and are the ones that concern this report.
The almanacs each contain introductory columns of days that are arranged in very specific groups of Maya day names. The day groups incorporate paired color and cardinal directions which played a great role in Maya ritual. They also contain a numerical coefficient which could have had ritual, calendrical or astronomical associations.
This report will focus on one of the codices known as the Madrid Codex. This codex contains a vast number of divinatory almanacs, and provides a broad scope of Maya activities that the shamans/priests would have been relied upon to make their prognostications.
I am only referencing basic divinatory almanacs, including those with repetitive intervals, and not those specially related to year bearers, planetary tables or other specific calendric or astronomical events.
The day groups reached within the almanacs through the intervallic structure are often equally represented, and for ritual purposes that would seem logical. It is also evident that the day groups that make up the introductory columns are not equally represented, and it would appear that there may be reasons for this.
I refer to day groups, as opposed to individual days, in that the days do not appear randomly, but are in well-defined groups in more than 99% of the recognizable divinatory almanacs, which themselves are based upon the 260 day ritual Tzolkin. In the 5 x 52 almanac structures there are four unique groups of 5 days, and in the 4 x 65 almanac structures there are five unique groups of 4 days. Some of these almanacs have what would be considered more than one day group in the introductory column, so I will be referring to the total number of day groups that appear in the Introductory columns, as opposed to the total number of individual almanacs.
A review of the Madrid codex shows approximately 248 day groups that appear in the introductory columns of divinatory almanacs that can be read with a degree of certainty. Of these, 207 are composed of 5 x 52 almanacs, and 41 of the 4 x 65 almanacs.
As the vast majority of divinatory almanacs follow the 5 x 52 formula (83%), this is the group I will focus on. Of these 207 day groups, 86 contain the day group Ahaw-Eb-Kan-Kib-Lamat, representing the majority. The next largest group, Ik-Ix-Kimi-Etznab-Oc is represented 59 times. Together these total 145 of the 201 identified day groups (70%). The remainder is split nearly evenly between the other two day groups: Imix, Chichan, Muloc, Ben, Caban 32 times; and Akbal, Manik, Chuwen, Men, Kauac 30 times.
The fact that a sizeable majority of these day groups belong to just two groups seems to indicate that there was a specific reason for them to be chosen. As each individual day group consists of days that are associated with the same referent color and cardinal direction this could be relevant. The coefficient numeral that accompanies them could also be of importance. Also, and perhaps more importantly, these two groups have been connected with Venus stations as shown in the Venus Table of the Dresden Codex.
The days Ahaw-Eb-Kan-Kib-Lamat are associated with helical rise of Venus. In practice any of these days can begin as the first day of an almanac, though the day Ahaw appears most often. This day is paired with the coefficient 4 in 17 of the 44 identifiable day groups that start with Ahaw, or 39% of the total. The next largest Ahaw start day is 1 Ahaw which occurs 4 times, or 9%, together totaling 48% of the total. The remainder is distributed unevenly between the other 11 possible coefficient numerals.
As the helical rise of Venus was considered of great ritual importance to the Maya, it would seem to be reasonable to think that these days would provide a meaningful base day upon which to begin a divinatory almanac. Also, the two days, 1 Ahaw and 4 Ahaw, have highly significant mythological connotations and would in themselves be a desirable start date for any divinatory almanac.
A review of modern astronomical tables reveals that there was a helical rise of Venus on or about 4 Ahaw (13 Kej), April 15, 1419 CE, and a 1 Ahaw (13 Kej) helical rise of Venus on or about April 22, 1403 CE. These dates, though slightly earlier than the time frame put forward as to when the Madrid Codex may have been assembled, could have acted as a contemporary reference, especially as the 1 Ahaw date is considered the start/end of the Venus Table, and its 104 year span would also incorporate the mid to late 15th century date for the codex.
The second largest representative day group, Ik-Ix-Kimi-Etznab-Oc, is associated with cosmic rise of Venus. This would attract almost as much attention as helical rise, and provide a good reason why it is often paired with the Ahaw-Eb-Kan-Kib-Lamat group as an Introductory column group. This paired grouping appears as an Introductory column at least 29 times throughout the Madrid. With one possible exception (M64b), they are never paired with either of the other two day groups in an Introductory column (except when all four day groups are represented), though the other two day groups appear together at least 12 times.
Another interesting observation on the Madrid is that in the hunting almanacs, pages M38-49, the two day groups discussed above appear in 38 out of 42 identified introductory groups (90%). There would certainly seem to appear to be a connection between these two day groups and hunting rituals which may be brought to light through the ethno-historical record, perhaps involving Venus as well.
Conversely, in the bee keeping related almanacs, pages M103-112, these two groups appear in only 7 out of 27 identified introductory columns (26%). Clearly these day groups were not as important to this particular activity.
These observations reveal a possible pattern that could explain why certain day groups appear in the Introductory day columns of the divinatory almanacs, and would suggest a closer relationship between these introductory day groups and the activities/rituals contained within the almanacs themselves. I would think a more detailed study of the Introductory day columns in the codices would reveal more connections to their importance as the actual base from which divinatory almanacs were devised.
Steve Mellard November 2016
Revised May 2020
Madrid page 101 registers a-c (register d not shown)
Observations on a Proposed Almanac Structure
and a Possible Connection to Mars Concerning
Pages 77-78 of the Madrid Codex
This informal report will describe certain observations regarding an almanac found on two full pages, pages 77 and 78, of the Madrid Codex. Experimentations and deductions have resulted in a proposed extended almanac structure containing an inherent design to the synodic cycle of Mars, and other astronomical phenomena.
This almanac has received scant attention in the published record. What has been reported is that the almanac has been termed a trecena almanac and follows an in extenso format. It shows day names, directional glyphs, deities, and offerings set up in 13 columns incorporating 10 rows. Four of the rows contain numbers in two different formats.
The two pages are in reverse order in the Codex. An unusual situation, but one in which some researchers have contended that it can be used with the in extenso almanac that appears on the obverse of the Codex, pages 12b-18b.
If these two pages are indeed an almanac, then it would need to exhibit a structural form characteristic of others found throughout the rest of the Codex. Nearly all of these are arranged around the 260-day ritual cycle known as the Tzolkin, and are structured in a 10 x 26, 5 x 52, 4 x 65, or 1 x 260- day format. In these formats certain days are named, while others are inferred. Only in the 1 x 260 day format, the in extenso almanac, are all the days named. The Tzolkin consists of the twenty day names, complemented by a rotating cycle of the numbers 1-13, with each of the 260 days being paired with a number (coefficient), the exact pairing appearing only once. As an example, the first day of the Tzolkin is generally 1 Imix, and the last day 13 Ahau (Think of January 1, and December 31).
The top row of the almanac contains the first thirteen days of the Tzolkin with accompanying coefficients of 1 through 13, signifying that the days are to be read in the order that they appear (1 Imix, 2 Ik, 3 Akbal, 4 Kan, 5 Chicchan, and so on). This unique structure of showing the thirteen days is what has led researchers to the conclusion that the almanac is based on an in extenso format (1 x 260 days). There does not seem to be any recognizable interval numbers present, but as an in extenso almanac it would not be necessary.
Directly below each 13 day-name column appears either a directional or a possible earth related glyph. There is a pattern to these glyphs that has led to the establishment of a proposed structure for the almanac. The key to this is the thirteenth day which has what appears to be a directional glyph for South that informs the reader on how it is to be further developed.
The first twelve day-name columns have the associated glyphs:
The last day (day 13, Ben) includes the glyph:
These days form a patterned series; the four directional glyphs followed by the two earth related glyphs. To complete this structure from the presumed South glyph, associated with the last day of the almanac, it would need to be followed by five other glyphs; three of them being directional and two of them the earth related glyphs. It would then be necessary to continue forward an additional six days, starting with the directional glyph North, thereby completing the four directions and finishing with a similar glyph pattern series as described above. The Maya were sticklers when it came to mathematical structure and almanac sequences, and this layout is a very plausible scenario.
A proposed completion of the directional pattern series then brings the total to 24 days, and a completed row would finish like this:
In keeping with the in extenso nature of the almanac, the 24th day would be a day named Kan. As Kan does not lead directly to Imix, the start day of the Tzolkin, the structure must continue until it reaches a day Ahau, the last day of the Tzolkin and the day that precedes Imix. (Example: Sunday comes before Monday.). When completed through the Ahaw end day the run would total 120 days (5 rows of 24 days each) with a start date of 1 Imix and an end date of 3 Ahau, and complete what I would term a module.
The first column of the module would be a 5 day-name group; Imix-Chicchan-Muluc-Ben-Caban, a recognized grouping of days found in a 5 x 52 Tzolkin format, followed by the three other known day groups, the day groups each repeating six times.
However, 3 Ahau does not lead directly to 1 Imix in an in extenso almanac. It must end in 13 Ahau. Therefore, it is necessary to continue the 120-day modules until a 13 Ahau end day of a module is reached, and the entire almanac sequence is allowed to recycle. This is accomplished after 12 additional modules are completed and the 13 Ahau end date reached, a total of 13 modules. Each module is similar in content with the days remaining exactly the same, and the coefficients advancing in a patterned order. The total amount of days included in the almanac is 1,560 days.
What is interesting to note here is that 1,560 days is equal to two Mars synodic periods of 780 days each, and equal to six Tzolkins. Also, the 120 day periods as produced by each of the modules have been shown by researchers to be related to certain planetary stations, such as a synodic station of Mars from helical set to helical rise, and the mean retrograde period of Jupiter. It is also nearly equal to 9 eclipse half-years (173.31 x 9 = 1,559.79 days).
The modules of 120 days could be useful in demonstrating that the almanac might be oriented to the Tun, wherein 3 of the modules would be equal to 360 days/1 Tun. Recycling the entire almanac three times (4,680 days) would be equal to 13 Tuns (the May Cycle); 18 Tzolkins; and 6 synodic cycles of Mars, a time frame that has been recognized by researchers for its importance in Classic period Maya inscriptions. As has been reported, this number is also close to 8 Venus synodic cycles (583.9 x 8 = 4,671.2 days); and 40 synodic cycles of Mercury (40 x 115.9 = 4636). The almanac therefore may have acted as a device to mesh the synodic cycles of the three planets with the Tun and the Tzolkin, as well as with 27 eclipse half-years (27 x 173.31 = 4,679.37).
Two different deities appear in each Tzolkin day name column. Both have been shown to have astronomical associations. God K has been linked strongly with Jupiter, and God C has been identified with Venus as morning star, and possibly with Mars. As mentioned earlier, the four rows of numbers appear in two distinct formats. The upper two rows seem to measure tangibles while the lower two rows may relate to day counts, the day counts being between 22 and 39. It would be interesting to see if the lower series of numbers might represent actual celestial observations of some sort. Of interest as well would be the function that the earth related glyphs play.
The trecena almanac as it is shown contains days, numbers, directions, deities, and offerings. What it does not have are glyphs that would relate it as a strictly divinatory almanac with the associated prognostications. The almanac then appears to be astronomical/calendrical in nature containing ritually timed offerings.
The existing codices do not seem to show a 5 x 24 format, and it is an unusual structure for an almanac. The dangling thirteenth directional glyph however, has led to this proposed structure, which in turn produced the above observations. With this in mind it is hoped that researchers will look at this almanac with a renewed interest, leading to new interpretations, new directions, and tease still further information from this most interesting codex.
Steve Mellard January 2016
Madrid Codex pages 13-18
OBSERVATIONS ON MADRID CODEX PAGES 2b & 3b
This informal report is based upon certain observations regarding a partial almanac within the Madrid Codex. The codex contains 112 pages in its current form. It appears to be missing a number of the pages that start/end the codex as the codex itself is written on both sides. The codex is comprised mostly of divinatory almanacs that rulers and priests used to help govern their daily lives. Often times these almanacs are spread out over several pages.
The purpose of this report is to propose a further understanding of the structure and imagery of one of these almanacs that appears on pages 2 and 3 of the codex, and labeled by researchers as 2b and 3b. The reasoning is that very little information has been reported on this particular almanac, and it is hoped others will re-exam it.
The page now numbered Page 1 is totally effaced with no information available. The next page, Page 2, is partially effaced, though much of the information is discernable. The numbering system of the codex sub-divides each page into horizontal registers (a,b,c,d) that are clearly delimited by the original authors (scribes).
The top half of page 2 contains two related registers which researchers have combined and identified as 2a. The lower half on page 2 contains an almanac page that has been numbered as 2b.
Page 3 is similarly divided into separate registers with the lower half of the page, 3b, being very similar in content to 2b, and is considered to be part of the same almanac. These almanac pages display a common theme having a central figure along with glyphs, numbers and related iconography.
The central figure on each page is shown to be the Rain God, Chaac, and he is depicted holding an axe and torch. Above him are glyphs for the cardinal directions and an additional glyphic compound, while rain is indicated behind him. In front of Chaac is a type of altar topped with glyphs that have been reported to each represent 20, and may be related to offerings as opposed to measuring distance or time.
Above the altar glyphs are a series of numbers and glyphs that are of interest to this report. While these are similar on each page, they differ in their exactness, so each will be examined separately.
The numbers that appear on page 2b are all written in bar-dot-shell form. The upper left-hand corner has the number 73 written in red. Below this number is a day name glyph and coefficient number in black, which combined is termed a Tzolkin day. The coefficient number is 5, and the day name is partially obscured from making an exact determination, but is identified here as the day Chuwen as will be discussed later.
To the right of the Tzolkin day is the number 13 in black. Above that number is some iconography that may be a type of offering. It is also to be noted that the glyph for the direction West is recorded in the uppermost glyph band. Preceding the glyph for West are two other glyphs that may represent night and day. As they are joined together it could indicate a period of elapsed time. The imagery then could depict Chaac being ritually placed in the West for a set period of time beginning on 5 Chuwen.
The numbers that appear on page 3b are similar. The upper left-hand corner has the same number 73 in red. Below this is also a day name and coefficient number in black. This day name, however, is clearly identified as the day name Kib, and also has a coefficient of 5. To the right of the Tzolkin day is the number 17 in black, with similar iconography above it as is found on page 2b. The glyph for the direction South and the night/day glyph compound are recorded. The imagery here could indicate the ritual placement of Chaac in the South on 5 Cib for a set time period. On both pages the set time period would be 65 days, as is explained below.
The structure of almanacs that appear in the Madrid Codex come in several forms, but they are nearly all built around the sacred cycle (Tzolkin) of 260 days. There are different multiples of 260 that have been used: 1 x 260; 4 x 65; 5 x 52; 10 x 26.
When one looks at the almanac on pages 2b and 3b the question then becomes: What is the possible structure of this almanac that would have fit into a 260-day sacred cycle? There are two useful items that would be helpful: the two cardinal directions, and the two Tzolkin days.
The two named cardinal directions would seem to imply that there are two missing pages with directions representing East and North. These would need to be included to incorporate the four directions that were extremely important to the Maya, and which appear together in many of the other almanacs. This format could indicate an almanac structure of 4 x 65, with each page covering a time span of 65 days.
On page 3b there is the clearly defined Tzolkin day of 5 Kib. If one were to calculate backwards 65 days in the Maya calendar the day reached would be 5 Chuwen. The glyph for the day name on page 2b is partially effaced, but enough remains that would not disqualify this interpretation. The coefficient of 5 is clearly visible.
Simple arithmetic would identify the two missing Tzolkin days as 5 Kimi and 5 Imix, all four together a known grouping that appears throughout the Madrid Codex. This would also incorporate the missing directions, and would suggest at least two missing pages of the codex. The almanac structure would be complete and read as such: 5 Imix (+ 65 days to), 5 Kimi (+ 65 days to), 5 Chuwen (+ 65 days to), 5 Kib (+ 65 days back to), 5 Imix, a 260- day Tzolkin, though the distance number of "65” is implied rather than numerically indicated.
The number 73 that appears in red has some known correlations that are worth mentioning. It is a whole fraction of both the Venus cycle (584 days) and the Maya Haab (365 days), which could possibly indicate a type of correlation between the two. Alternately it may collectively refer to one-half of a Venus cycle (4 x 73 = 292 days) with its relation to the Rain God Chaac and the rainy season, as the first eleven pages of the codex appear to be devoted to Chaac and rain. With the upper register on page 2, 2a, apparently associated with Mars and the rainy season, this is entirely possible.
The red number 73 is also a divisor of the Calendar Round (52 Haabs) in conjunction with the Tzolkin (73 x 260 = 18,980 days/52 Haabs). If it’s one thing the Maya loved, it was the meshing of numbers and cycles.
The two numbers that appear in black, 13 and 17, are a bit more ambiguous. However, if 5 Kib, associated with the number 17 were to be positioned in the seventeenth month of the Maya calendar (Kayab), then 5 Chuwen would appear within the thirteenth month (Mak). The iconography above the numbers may indicate a certain offering associated with those months. Why these apparent months would not just be identified by their glyphic name is unresolved at the moment.
This possible pairing of a Tzolkin day and month into what is known as a Calendar Round date may help, along with the other previously identified calendar round dates, to place the Madrid Codex in real time. Some relevant dates reached are identified below, and fall within the time frames offered by other researchers.
5 Chuwen (19) Mak - 22.214.171.124.11 – May 10 1420
5 Kib (4) Kayab - 126.96.36.199.16.- July 14 1420
5 Chuwen (19) Mak – 188.8.131.52.11 - April 27 1472
5 Kib (4) Kayab – 184.108.40.206.16 – July 1 1472
The proposed structure of this almanac would be unique within the codex, in that the almanac only incorporates four named days, with each day apparently having its own page. The imagery could depict Chaac being ritually placed in each of the four directions for a specified time. Nonetheless, this could possibly help researchers draw out further information on the relationships between certain time frames, seasonal rain, Venus, Mars, and lunar cycles. It could also be a possible foundation for completion of the partial almanac that appears above on page 2a.
Steve Mellard July, 2019 revised April, 2021
Madrid page 2