David Carrasco discusses the use of multiple calendars among the Maya.
David Carrasco, Religions of Mesoamerica: Cosmovision and Ceremonial Centers (San Francisco: HarperSanFrancisco, 1990), 38-39
One of the most creative religious achievements of the Classic Maya was the long count calendar. Although this calendric system had earlier origins based on intense astronomical observations, it was the Maya who elaborated the cosmological conviction that human life would be most favorable if it mirrored the mathematically expressible cycles of the heavens. As a means of recording important human events and attuning human order to the celestial order, the Maya developed a calendar system with many different counts including the Tzolkin (260-day count related to human gestation), the Haab (365-day count related to solar cycle), the Long count (related to ancestor worship and lineages), the calendar round (a 52-year cycle), the Lord of the Night (nine-day interval, and the lunar cycle. The largest count in this system was the Long Count, which measured each day from the beginning date of the present cosmic era in 3114 BCE and prophesied its end on December 23, 2012. Each day was measured by a system of five subunits and enabled the priest to compute dates in colossal cycles going back t at least nine million years BCE as marked on inscriptions in several ceremonial centers. Mathematicians have pointed out that an understanding of the concept of zero is necessary for such computations. The Maya marked these days so they could be in conscious contact with the sacred forces appearing in the terrestrial world at carefully determined intervals. Unfortunately this calander system largely faded from use, excerpt in scattered parts of Yucatan, after the Classic Maya society collapsed.