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HORUS VOL III. Issue 1
Ring Counters and Calendrical Cycles
|Day Names||The Tonalpohualli and Tzolkim|
|IX or HIX||1||8||2||9||3||10||4||11||5||12||6||13||7|
The results are summarized in Table 2 which lists all combinations of the 13 numbers and the 20 day-names, reading vertically in columns, from 1 Imix to 13 Ahau. Starting with 1 Imix, successive days are 2 Ik, 3 Akbal, 4 Kan, etc. After 13 Ben, the numerical sequence repeats, the next day being 1 lx. The last date is 13 Ahau - the completion of a 260-day cycle.
The glyphs in Figure 4 are the same throughout Mesoamerica, regardless of language or dialect, much as Chinese characters are in China.The names for the 20 days depend on the language. Scholars of Mayan calendrics use the Yucatec day-names and often refer to the 260-day cycle as the Tzolkin. The Nahuatal-speaking Aztecs called it the Tonalpohualli.
Why the 260-day cycle? The factors four and five in the count of 20, along with the count of 13 are fundamental throughout planetary astronomy and calendrics. In round numbers, for eight revolutions of the Earth around the Sun, there are 13 revolutions of Venus, which overtakes the Earth five times. Also, there are 13 revolutions of the Moon about the Earth (sidereal months) in a year, and conjunctions of Jupiter and Saturn occur at 20 year intervals. These are just a few typical examples.
Going along with the Pythagoreans, who were concerned with form (rather than matter) which was expressed in numbers, it would seem natural to construct a model which embodied the essential numbers in a form easy to memorize and use for computation. The Mesoamerican 260-day cycle could be the result of such an effort.
The astronomical nature of the 260-day cycle is revealed when we note that a double cycle of 520 days is very close to three eclipse half-years (3 X 171.31 = 519.93 days), the actual appearance interval of Venus is 263 days on the average, and Mars' synodic period is 3 X 260days. The idea that the numbers 20 and 13 were chosen because the Mayans went barefoot and counted on their fingers and toes has no merit.
The Mayan calendar system also included a 365-day calendar which consisted of eighteen 20-day periods (or "months"), and one five-day period. The 365-day count and the 260-day cycle are combined in another double cycle, which is illustrated as a table rather than a ring counter (Table 3). The names of the months are shown across the top of Table 3, and the days of the months, which are numbered from 0 to 19, are given in the column on the right. (Since the days of each month are numbered sequentially as in our calendar, a ring counter is not shown.) Since any day was not counted until it was completed, the first day is zero, which indicates completion of a previous cycle. The body of Table 3 gives the numbers of the 260-day cycle. It is read vertically in columns from left to right in contrast to our calendar, which is read across in rows. The first day is 1 Ik, 0 Pop, and the last in the first column is 7 Imfix, 19 Pop. Going to the top of the next column, the next day is 8 1k, 0 Uo.
Names of the Months
|Names of the Days||Pop||Uo||Zip||Zotz||Tzec||Xul||Yaxkin||Mol||Chen||Yax||Zac||Keh||Mac||Kankin||Muan||Pax||Kayab||Cumhu||Uayeb||Day of the Month|
|IX or HIX||13||7||1||8||2||9||3||10||4||11||5||12||6||13||7||1||8||2||12|
First Year of the Calendar Round (the year 1 Ik).
The first day of the year is Ik 0 Pop, and the last day is 1 Kimi 4 Uyaeb. The last day of the month Cumhu is 9 Imix Cumhu.
The last day of the year is 1 Kimi, 4 Uayab. The first day of the next year is 6 Manik, 5 Pop, and the following years start on 11 Eb and 3 Caban, respectively, after which the cycle is repeated. These dates are known as the Year Bearers. With three more tables like Table 3 for each of the other Year Bearers one would have a perpetual calendar.
In this case we get the number of possible combinations by dividing 260 by the common factor of 5, which is multiplied by 365:
(260 / 5) X 365 = 52 X 365
Leaving the answer in this form, we can see that the count repeats itself every 52 years of 365 days. This 52-year cycle, which occurred throughout Mesoamerica, is referred to as the Calendar Round by scholars. There is solid evidence for widespread use of the 260-day and 365-day cycles as early as 500 B.C., and indications that this calendar system may have originated with the Olmecs much earlier.
The day count was continued without interruption, even though the Calendar Round came up 12.6 days short of 52 solar years. (Astronomers today use a strict day count called the Julian Period, not to be confused with the Julian year.) The error continued to accumulate amounting to a full solar year every 29 calendar rounds. The 365-day count was also adhered to in Egypt, even after the Canopus Decree ordered an additional day every four years to prevent the festivals from drifting through the seasons. This correction was introduced into the Roman Empire by Julius Caesar, and is thus called the Julian year.
Why was the 365-day year, often called the vague year, clung to so tenaciously, even though the Calendar Round or New Year drifted through the seasons? The 365-day year seems to be made to order for Venus, since the number of days in eight vague years falls between those in five synodic and 13 sidereal revolutions of Venus:
|5 X 583.92||= 2919.6|
|8 X 365||= 2920|
|13 X 224.7||= 2921.1|
For the Julian year we get:
|8 X 36515||= 2922|
With one day of error in 8 X 365 = 2920 days, Venus makes 13 revolutions about the Sun, and passes Earth five times. Note that eight vague years fall two days short of eight Julian years. Velikovsky has shown that the Greek version of the Canopus Decree speaks of Venus and its relation to Sothis (Sirius). [see Peoples of the Sea, p. 205 ff.1 By observing the helical risings of Venus relative to Sirius, the return of the heliacal rising of Venus to its starting point in the seasonal year could be determined.
Showing historically that the "Sothic" cycle pertained to Venus, exposed a major flaw in the current scheme of Egyptian chronology. It also showed clearly that scholars of both Egyptian and Mesoamerican cultures remain ignorant of the fact that both had a 365-day year related to Venus.
Especially curious is that in a recent study, Mesoamerican scholar Vincent Malmstrom came to the conclusion that the 260 and 365-day cycles were linked to initiate the Calendar Round about 235 B.C., without noting also that the Canopus Decree was issued in 238 B.C.
Efficient computation requires number systems which fit the problem. The decimal system, which has become second nature to us, is often not the best, and at times ill-suited. Planetary and lunar cycles were the kind that ring counters were used for in vacuum tube digital computers. This is only one example of the If rediscovery" of long forgotten calculation techniques brought about by new tools.
The 20-day month, which was at the heart of the Mesoamerican calendar, calls for further investigation. We used quotes when we introduced it above, since "month" actually refers to a synodic month of 29.53 days, which is the time required for the Moon to go through a complete set of phases. However, some of the Maya are known to have also referred to the 20-day period as a month, and the glyph for "twenty" is the Moon sign [Velikovsky suggested evidence that the 20-day month reflects a system much older than the 360-day system].
We showed above that the Calendar Round was a 52-year cycle which was specifically related to Venus. The termination of a Calendar Round was marked by the New Fire Ceremony, another subject worthy of further exploration. We shall return to these and related subjects in future issues of HORUS.