The Classic Maya Calendrical System
The ancient Mayan people were precise in their construction of time, and they seemed to have applied the same exactitude in other realms of life. They dedicated themselves to accuracy in mathematics, the passage of time, and the calendrical cycles. Using the concept of zero in their calculations, they established an incredibly accurate calendar. They studied the stars, and successfully deduced many mathematical facts concerning the concept of time and planets. They calculated that one Earth year was a little more than 365 days, an estimate that differs by only .002 of a day from today's modern estimation of a year. Their obsession with time and accuracy relative to the planet Venus allowed them to calculate a Venetian year to be 489 days, accurate to within two days of the modern estimate. Venus, the brightest star in the world could foretell of war and the prediction of its place in the cosmos was essential.
The Maya calendar kept track of time through the use of three intertwined and inter-related cycles:
the tzolkin of 260 days
the tun of 360 days
the haab of 365 days
The tzolkin cycle was itself composed of two separate subsidiary cycles, a cycle of numbers (1 to 13) and a cycle of 20 day names used in a constant order (Imix, Ik, Akbal, Kan, Chicchan, Cimi, Manik, Lamat, Muluc, Oc, Chuen, Eb, Ben, Ix, Men, Cib, Caban, Edznab, Cauac, Ahau). The full tzolkin date was actually a combination of a day number and day name; the first such permutation in the tzolkin cycle of 260 days was the day "1 Imix", the second was 2 Ik, the thirteenth was 13 Ben, the fourteenth was 1 Ix, etc.
The tun was composed of 18 months or uinals of 20 days each; 20 tuns made up a unit of time called a katun, and 20 katuns made up a baktum. (Eighteen months of 20 days each equally 360 days. To reach the katun you have 20 tuns (360 year periods) to account for a total of 7,200 days. The reach the baktum level of time, the Mayan were actually working with 144,000 days - 20 katuns (each with 7,200 days.)
The haab consisted of 18 months each having 20 days (Pop, Uo, Zip, Zodz, Tzec, Xul, Yaxkin, Mol, Ch'en, Yax, Zac, Ceh, Mac, Kankin, Muan, Pax, Kayab, Cumku) plus a short intercalary month, Uayeb, having only 5 days. This was the way the Mayan viewed the 365 day year. The main platform temple at Chitzen Itza has four stepped sides with 91 steps each. Adding the top step of the platform, you have 365 - the number of days in one haab. The 20 days in each regular month were numbered from 0 to 19; those in Uayeb were numbered from 0 to 4. The haab thus started with a day 0 Pop, followed by 1 Pop, 2 Pop, etc., and ended with a day 4 Uayeb.
Information about the place of a given day in all three of the major calendrical cycles was sometimes given in the following form:
9.16.4.10.8 12 Lamat 1 Muan
The first part of this expression, the long-count date, states that the following temporal units of the current calendrical era have been completed: 9 baktuns (out of a possible 13, numbered 0 or 13 to 12), 16 katuns (of 20, numbered 0 to 19), 4 tuns (of 20, numbered 0 to 19), 10 uinals (of 18, numbered 0 to 17), and 8 kins or days (of 20, numbered 0 to 19). The second part of the expression is the tzolkin date, the 168th day of the 260-day cycle. The third part of the expression is the haab date, the 2nd day of the 15th month since one day has already been counted.