The "Useless" MADRID Codex
The Source of the Gregorian Trecena
By D. M. Urquidi
 |
| VEYTIA calendar 1551 |
Astronomy class at Teotihuacàn
I am of the opinion that in order to understand any calculation, calendar or ordinary mathemtics, one must go to the source. Such a process is slow and labrous, but in the end, it can prevent errors made from assuming an equation that does not exist.
Floyd Lounsbury's whole premise for the Maya calendar in his 1976 calculations w
Floyd Lounsbury's whole premise for the Maya calendar in his 1976 calculations w
When it fact, it is only half a year of 26 weeks. Two x haab = 52 weeks
which was never used in the old Maya calendars. The problem is that there were no month designations in the
360 calendar.
The Maya astronomers then decided to use the older 360 day year for their own comfort and to help the older generations to understand the Christian changes that were emerging.
They decided to create a Distance Number for the descrepances between the solar/lunar cycles that came about when the destructive comet soared across the skies; henceforth. making it easier for the uneducated to accept such changes in their life style.
Such Distance Numbers were then used to revise many of the old dedicatory inscriptions. It may well be the reason that broken stelae were, at times, buried under a temple or palace structure.
Since the Maya New Year was created by the Gregorian, as an aid for the European Conquistadores to understand the Maya Calendar, 1-Imix became the equivalent to 8 February while 0 Pop corresponded to July 26. The Gregorian was then given to the Meso-American tribes in 1584, some thirty [slow] years after its creator Diego de Landa, died in 1551.
As a result, many are searching for the original 0 Pop [4 Ahaw, 8 Cumku] thinking the month was invented by the Native Maya, when, in fact, it was part of the post-Conquest, laws and restrictions put upon Meso-Americans by the Church.
No year was given; only that it was the second journey of the sun in the Latitude 19 degrees and 42 minutes. In that way, the seasons were finally restored to their proper sky locations for the astronomer-priests and the farmers.
* * * * * * * *
Here, however, here the Serpent Pages have a different role. It shows us just how the Maya really counted their days in their calendars.: Four, five or even six down and the necessary day glyphs across to complete the twenty days of the first set; slip the top glyph of the second set of days to the bottom of each column [as shown after the first green line in the top section above]; repeating the transfer of the top glyph to the bottom of each column for every 20 day-month. In this manner each month changes at the same time but no column passes any information to its neighbors. It recreates a repeating ring of glyphs in each column and in that manner fill out the necessary 360 day calendar but only if the count of days are noted as 5 weeks x 6 days a week or even the reverse 6 weeks x 5 days per week.
The caveat here is that each subsequent 20 day column reacts like the one-armed bandits "cherry rings" of Reno or any other gambling establishment. The columns put the top glyph at the bottom, until the first glyph (Ik) ends at the bottom its own column in the fourth set of twenty days.
The four, five,or six glyphs of each column set will then begin the whole process all over again.
It is a very difficult thing to learn after being so accustomed to doing the count of the days the easy way. The Trecena has continued in our own calendars since the Gregorian calendar was created. All one has to do is count one to thirteen for every Saturday in even our regular calendar and it works out as 13 weeks per season, only adding one week when our 375-day year is a leap year.
When the week is split into two months, then the week carrying the number thirteen belongs to the Saturday, not to the Sunday of that week, even if it is part of the next week, month or even the next year, as often happens after the Leap year.
With the decision of the astronomer-priests to retain their 360 day/year calendar system, every effort was made to have the new 365 day calendar comparable to their own 360-day calendar. In order to do that, they apparently shaved one or two days off the bottom of their calendar to fill in the new 52 weeks schedule. But they failed, as can be seen on the last section above. The two Kimis [in yellow] found there, was probably their way of telling others that the 52 week calendar failed to function.
The question will be does one only add one day per week, or was it more than five days to the Native pre-conquest weeks. Six days would work very well for the 360-day year.Floyd Lounsbury's Trecena
Above is a paste-up of the eight Serpent calendar pages in the Madrid Codex, which I believe to be of the real "native" Codex, which, starts not ends, at page 112 since the Madrid begins with the presence of the great star of Sahagùn and continues on to tell the story of the "rain or even of resin" [or "of turpentine"] together with the story of the wooden manikins. It continues to relate more of the Popol Vuh. The calendar itself was a complete failure, as a Gregorian example, but does show how the Maya used their own calendar systems.
Here, however, here the Serpent Pages have a different role. It shows us just how the Maya really counted their days in their calendars.: Four, five or even six down and the necessary day glyphs across to complete the twenty days of the first set; slip the top glyph of the second set of days to the bottom of each column [as shown after the first green line in the top section above]; repeating the transfer of the top glyph to the bottom of each column for every 20 day-month. In this manner each month changes at the same time but no column passes any information to its neighbors. It recreates a repeating ring of glyphs in each column and in that manner fill out the necessary 360 day calendar but only if the count of days are noted as 5 weeks x 6 days a week or even the reverse 6 weeks x 5 days per week.
The caveat here is that each subsequent 20 day column reacts like the one-armed bandits "cherry rings" of Reno or any other gambling establishment. The columns put the top glyph at the bottom, until the first glyph (Ik) ends at the bottom its own column in the fourth set of twenty days.
The four, five,or six glyphs of each column set will then begin the whole process all over again.
It is a very difficult thing to learn after being so accustomed to doing the count of the days the easy way. The Trecena has continued in our own calendars since the Gregorian calendar was created. All one has to do is count one to thirteen for every Saturday in even our regular calendar and it works out as 13 weeks per season, only adding one week when our 375-day year is a leap year.
When the week is split into two months, then the week carrying the number thirteen belongs to the Saturday, not to the Sunday of that week, even if it is part of the next week, month or even the next year, as often happens after the Leap year.
With the decision of the astronomer-priests to retain their 360 day/year calendar system, every effort was made to have the new 365 day calendar comparable to their own 360-day calendar. In order to do that, they apparently shaved one or two days off the bottom of their calendar to fill in the new 52 weeks schedule. But they failed, as can be seen on the last section above. The two Kimis [in yellow] found there, was probably their way of telling others that the 52 week calendar failed to function.
The question will be does one only add one day per week, or was it more than five days to the Native pre-conquest weeks. Six days would work very well for the 360-day year.Floyd Lounsbury's Trecena
tr The trecena or 12 weeks, [not 13 as reported] having 4 days per week for 20-days each month for 52 weeks in a Haab. Such a process was NEVER used by the older Maya calendars. [Four days per week did not work to complete a 52 week cycle. (See historical note about Fra Francisco de la Nava under Veytia Calendar 1975 edition of HMAI, IV, III p. 230.)
v The veintena.
Or the twenty day count should begin with Ik, and end with Imix
since Imix was the GREGORIAN adjustment as the FIRST DAY of the first month
called 0 POP that Rome inserted into the Maya calendar, and began in Mexico in 1593-4.
since Imix was the GREGORIAN adjustment as the FIRST DAY of the first month
called 0 POP that Rome inserted into the Maya calendar, and began in Mexico in 1593-4.
Ik (1), Akbal (2), Kan
(3), Chicchán (4), Cimi (5),
Manik
(6), Lamat (7), Muluc (8), Oc (9), Chuen (10), Eb (11), Ben (12),
Ix
(13), Men (14), Cib (15), Cabán (16), Eznab (17), Cauac (18), Ahaw (19),
Imix
(20)
tz A day of the tzolkin
which equals 13 weeks per season.
[I have separated the thirteen count into three year-segments of four-day columns. It is the year count
not the Trecena count as assumed by some. This just creates a proper agricultural process of: plant
the first year and leave the last two years to follow the first As years to leave the mila as fallow
ground. The last row of the Trecena just allows the three assumed years to repeat itself. Nevertheless ,
this attempt of four days per week failed to create a 52 week calendar, as stated above.]
[I have separated the thirteen count into three year-segments of four-day columns. It is the year count
not the Trecena count as assumed by some. This just creates a proper agricultural process of: plant
the first year and leave the last two years to follow the first As years to leave the mila as fallow
ground. The last row of the Trecena just allows the three assumed years to repeat itself. Nevertheless ,
this attempt of four days per week failed to create a 52 week calendar, as stated above.]
Ik (1),
Manik (6), Eb (11), Cabán (16), Ik (1
+1),
Manik (2),
Eb (2), Cabán (2), Ik (2), Manik (2+1)
Eb (3),
Cabán (3), Ik (3), Manik (3) Eb (3+1)
Cabán (4), Ik (4), Manik (4),
Eb (4), Cabán (4+1)
Ik (5),
Manik (5), Eb (5), Cabán (5), Ik (5 +1),
Manik (6),
Eb (6), Cabán (6),
Ik (6), Manik (6+1)
Eb (7),
Cabán (7), Ik (7), Manik (7), Eb (7+1)
Cabán (8), Ik (8), Manik (8),
Eb (8), Cabán (8+1)
Ik (9),
Manik (9), Eb (9), Cabán (9), Ik (9 +1),
Manik (10),
Eb (10), Cabán (10),
Ik (10), Manik (10+1)
Eb (11),
Cabán (11), Ik (11), Manik (11), Eb
(11+1)
Cabán (12), Ik (12), Manik (12), Eb (12),
Cabán (12+1)
Ik (13), Manik (13), Eb
(13), Cabán (13), Ik (13 +1) for a "loop" formula
M Calendrical
month any one of 18 months. [Again, 0 POP and all other months
was a Gregorian adjustment by Rome for the Maya calendar year ]
was a Gregorian adjustment by Rome for the Maya calendar year ]
Pop (1), Uo
(2), Zip (3), Zotz (4), Tzep (5), Xul (6), Yaxkin (7), Mol
(8),
Ch'en (9),
Yax (10), Sac (11), Ceh (12), Mac
(13), Kankin (14), Moan (15),
Pax (16),
Kayeb (17), Cumhu (18),
[Wayeb (19) Floyd's Text],
(If month has only n1, n2, n3, n4, and
n5, for the
number of days in
that month, If the year has 365 days, use Wayeb)],
d day
of the month, any one of the twenty days. Mod 19, i.e. of
20 days in
five weeks
of four days each, [as found in the Madrid Codex on the Serpent
Pages.]
Pages.]
This list is different
from the normal sequence.
Ik (1),
Akbal (2), Kan (3), Chicсhán
(4), Cimi (5) Manik (6), Lamat (7),
Muluc (8),
Oc (9), Chuen (10), Eb (11), Ben (12), Ix (13), Men (14),
Cib (15),
Cabán (16), Eznab (17), Cauac
(18), Ahau (19), Imix (20),
h days
of two haabs = 52 weeks = mod 360 days, [if 365, then Mod 365 +1=
every 6th year = 366]
every 6th year = 366]
cr day
of calendar-round expressed in terms of coordinates tr, v, and h.
[For example
“6 Etznab 11 Yax”. Floyd's original text]
{For
pre-split mountain event found in the Bodley Codex, a 360 day-year
calculation is necessary for the pre-first mountain and for the post-mountain
one needs 365.25-day year.]
calculation is necessary for the pre-first mountain and for the post-mountain
one needs 365.25-day year.]
lc date
in the long count: expressed in Maya numerals, usually of five
places, of
the following:
the following:
n5, n4, n3, n2, n1,
where n1 is the number of days in
the kin position, n2
the
number of winals, n3 the number of tuns; n4 the number of katuns, and n5
the number of baktuns.
number of winals, n3 the number of tuns; n4 the number of katuns, and n5
the number of baktuns.
dn distance
number: (positive or negative) to be added to a give cr or lc or both;
expressed as a Maya numeral, of any number of pieces.
expressed as a Maya numeral, of any number of pieces.
[The above definitions are just suggested changes to Floyd Lounsbury's original calculus statements
which indicate a 52-year cycle. This makes his calculated data a bit out of sync with the natural measurements of orbital time of the world.]
A conclusion reached, is that, without searching for the beginnings of any theory, one should never assume such unknown numbers are useful, until all data pertaining to such artificial dating methods can be used in all phases of their calendar calculations.
[See the Borgia Codex Calendar for the 364 day-year which included the 260-day count for the Trecena in the middle.]
