| 20 | kin (days) | = | 1 | chuen (month). |
| 18 | chuen.. | = | 1 | ahau (year) 360 days. |
| 20 | ahaus.. | = | 1 | katun (20 years or 7,200 days) |
| 20 | katuns.. | = | 1 | cycle (400 years or 144,000 days) |
| 13 | cycles.. | = | 1 | great cycle (5,200 years or 1,872,000 days). |
| 73 | great cycles | = | 1 | era. |
It will be noticed that the Mayan year fell short of the Solar Year by five days five hours 48 minutes 49·7 seconds. This was made up by adding five days to the completion of each year, and these are known as "intercalary" days, thus making a year of 365 days, which the Mayans called haar. But although the Mayans knew how to count up to twenty, they did not always use this as a time-count. The year was divided up into weeks of 13 days, which were arranged irrespective of the twenty day-names, which were as follows: (1) Kan, (2) Chicchan, (3) Cimi, (4) Manik, (5) Lamat, (6) Muluc, (7) Oc, (8) Chuen, (9) Eb, (10) Ben, (11) Ix, (12) Min, (13) Cib, (14) Caban, (15) Ezenab, (16) Cauac, (17) Ahau, (18) Imix, (19) Ik, (20) Akbal. Thus it would seem that if the week began with Kan, it would finish with the 13th day Cib, and a new week would start with the 14th month-day Caban as the first day. This cutting up of the year, irrespective of the months, into "weeks" of thirteen days involved further difficulties at the end of the year. At the end of an ahau (360 days) there would have been twenty-seven of these 13-day weeks with an odd nine days. Again, after the "interlacery" days had been added and the solar year was complete, there would be twenty-eight 13-day weeks and one odd day.
To further complicate matters these Mayan time-counts disclose yet another week of five days; but this works in with the 20-day months, the ahau (360 days), and the solar year accurately, so that it is easier to understand. From these generally accepted statements we draw up the following table, showing the days and months as they would appear to make up the solar year.
| Names of Months. | Pop. | Uo. | Zip. | Zes. | Zeec. | Xul. | Yaxkin. | Mol. | Chen. | Yax. | Zac. | Ceh. | Mac. | Kankin. | Moan. | Pax. | Kayab. | Cunku. | Number of Days. |
| Number of Months. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |
| Names of Days. | |||||||||||||||||||
| Kan | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 1 |
| Chicchan | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 2 |
| Cimi | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 3 |
| Manik | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 4 |
| Lamat | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 5 |
| Muluc | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 6 |
| Oc.. | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 7 |
| Chuen | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 8 |
| Eb.. | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 9 |
| Ben | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 10 |
| Ix.. | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 11 |
| Men | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 12 |
| Cib.. | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 13 |
| Caban | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 14 |
| Ezenab | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 15 |
| Cauac | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 16 |
| Ahau | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 17 |
| Ymix | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 18 |
| Ik.. | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 19 |
| Akbal | 7 | 1 | 8 | 2 | 9 | 3 | 10 | 4 | 11 | 5 | 12 | 6 | 13 | 7 | 1 | 8 | 2 | 9 | 20 |
| Intercalated Days to complete the year of 365 days | Kan.... Chicchan.. Cimi.... Manik.... Lamat.... | 10 11 12 13 1 | 1 2 3 4 5 | ||||||||||||||||
We have followed the generally accepted view and begun the year with the day Kan, though some students follow Mr. J. T. Goodman in his belief that Ik represents the first day. Whoever is right, it is certain that the year can begin with its first day-name only once every four years. If a year begins with Kan, it must, as shown in our table, inevitably finish with the day Lamat. Thus the following day, the first in the New Year, would be Muluc. In the same way the second year will finish with Ben and the third year will commence with Ix. This will finish with Ezenab and the new one would commence with Cauac and finish with Akbal, when Kan would again begin the year. In Goodman's theory these days would change. The beginning days would be Ik, Manik, Eb, and Caban; while the last days of the year would be respectively Cimi, Chuen, Cib, and Imix.
One of the things that the Mexicans seem to have adopted from the Mayans was the twenty-day period. The double meaning of the days of the two countries often is seen in the Zapotec country, where it would seem the knowledge of the Maya Calendar had not entirely died out through the invasion of the Aztec, "unless," says Dr. Seler, "we ought to accept the theory that the Zapotecs or their kindred were those among whom the calendar was invented, and by whom the knowledge of it was originally communicated to both the Mexicans and the Mayas" (Bureau of American Ethnology Report, Bulletin 28, p. 274).
Day Signs
