[Illustration: Scheme of the Mayan Calendar as presented in the Codex Tro-Cortesianus. In the center is Itzamna, the God of the Sky, and his spouse, under what has been called the celestial tree. The band of hieroglyphs that frames in this picture contains the twenty day signs of the Mayan month. The figures on the outside are arranged in four groups, according to the four directions of the compass. At the top or east we again see Itzamna and his mate. In the north, or right hand quarter, human sacrifice is shown and the Death God sits opposite the God of War. In the east and in the south are also shown pairs of divinities. A series of dots running from one day sign to another covers the _tzolkin_ or 260 day cycle of names and numbers.]
Ik Manik Eb Caban 0 5 10 15 Akbal Lamat Ben Eznab 1 6 11 16 Kan Muluc Ix Cauac 2 7 12 17 Chicchan Oc Men Ahau 3 8 13 18 Imix Cimi Chuen Cib 4 9 14 19
Thus Ik occupies 0 position the first year, 5, the second year, 10 the third, 15 the fourth, and 0 the fifth. While Manik that belongs to the same set has position 5 the first year, 10 the second, etc. It will be noted that Imix, the first day of the formal permutation of the _tzolkin_ is never the first day of a month.
But this assignment of particular day names to particular places in the month does not close the problem. Each day name is associated in the _tzolkin_, or permutation, with a day number. While it is true that each day can occupy only four month positions in as many years, it must be remembered that the day numbers associated with these names can run the whole gamut of 13 changes. Thus, although Ik must always occupy the fifth position in the months during a certain year, nevertheless it will have numbers which fall in the sequence 1, 8, 2, 9, 3, 10, 4, 11, 5, 12, 6, 13, 1, etc. The complete cycle of variations must run through the least common multiple of 260 (the permutation) and 365 (the conventional year) or 18,980 days. This cycle is commonly known as the Calendar Round. A Mayan day fixed in a month, or let us say a calendar round date, has four parts to its name, thus, 11 Ahau 18 Mac. We describe a day as Tuesday, July 4, meaning “Tuesday the third day of the seven day week occupies the fourth position in the month of July.” Similarly the Mayan date 11 Ahau 18 Mac may be read “the day named Ahau as eleventh day in a thirteen day week occupies the eighteenth position in the month Mac.” Owing to leap year corrections the European date given above does not recur at regular intervals, but a Mayan day recurs infallibly in 52 calendar years, never sooner, never later.