Elements of the Day Count.
There is reason to believe that the Mayas had first a lunar-solar calendar of twelve months of thirty days each, making a year of 360 days, and that they reduced the number of days in the formal month to 20 and raised the number of months in the year from 12 to 18. These changes permitted a close adjustment of the units of time with their vigesimal system of counting. With a truer knowledge of the length of the year an extra five day month was added to make a year of 365 days. Beyond this the “leap year” error was calculated but not interpolated. As proof that the lunar month of thirty days preceded the formal month of twenty days, it need only be pointed out that the name for this period, uinal, seems to be connected with the name for moon, u, and that the hieroglyph for moon has the value, twenty, in the inscriptions and ancient books.
Fig. 40. The Twenty Day Signs. The first example in each case is taken from the inscriptions and the second from the codices.
Before entering into a fuller discussion of the astronomical and notational facts let us turn for a moment to the third fact, the permutation system. The origin of the cycle[1] known by the Mayan name tzolkin and the Aztecan name tonalamatl, book of the days, has never been satisfactorily explained. It is a permutation system with two factors, 13 and 20. The former is a series of numbers (1-13) and the latter a series of twenty names as follows:—
1. Imix 2. Ik 3. Akbal 4. Kan 5. Chicchan 6. Cimi 7. Manik 8. Lamat 9. Muluc 10. Oc 11. Chuen 12. Eb 13. Ben 14. Ix 15. Men 16. Cib 17. Caban 18. Eznab 19. Cauac 20. Ahau
These two series revolve upon each other like two wheels, one with thirteen and the other with twenty cogs. The smaller wheel of numbers makes twenty revolutions while the larger wheel of days is making thirteen revolutions, and after this the number cog and name cog with which the experiment began are again in combination. Thus, a day with the same number and the same name recurs every 13 × 20 or 260 days.
This 260 day cycle corresponds to no natural time period and is an invention pure and simple. It is the most fundamental feature of the Mayan time count and of the time counts of other nations in Mexico and Central America. We may perhaps assume that the twenty names were originally those of the twenty days in the modified lunar months. But the thirteen numbers have no recognized prototype. The formal book of days generally was considered to begin with 1 Imix for the Mayas and with a corresponding day for the other Mexican and Central American nations. But it can be made to begin anywhere and proceed to an equivalent station that is always 260 days removed.