The tzolkʼin[1] (Mayan pronunciation: [t͡sol ˈkʼin], formerly and commonly tzolkin) is the 260-day Mesoamerican calendar used by the Maya civilization of pre-Columbian Mesoamerica.
The tzolkʼin does not have a generally recognized start and end, although there are specific references in the books of Chilam Balam to 1 Imix as the beginning day.
Symbolism related to the tzolkʼin is also observed in the Popol Vuh (which, though written in the early post-conquest period, is probably based on older texts).
[7] The earliest evidence of this calendar comes from a possible day sign with a dot numeral coefficient in an Olmec-like inscription in Oxtotitlán cave dated to 800-500 BCE.
[8] Some of the next oldest calendric inscriptions are from early strata of Zapotec in the Oaxacan highlands at sites such as Monte Albán, dating from mid-1st millennium BCE.
A few earlier-dated inscriptions and artifacts have what appear to be calendric glyphs, such as at San José Mogote and in the Olmec Gulf Coast region.
[9] The earliest unequivocal written record is a 7 Deer day sign found in mural paintings at the central lowland Maya site of San Bartolo, Guatemala, dated to the 3rd century BCE,[10] but it is now obvious that the origin of the 260-day is much earlier.
An archaeoastronomical study has shown that a number of architectural complexes built in the late second and early first millennia BCE in the area along the southern Gulf coast in Mexico are oriented to the Sun's positions on the horizon on certain dates, separated by multiples of 13 and 20 days.
Aveni notes that "the average duration between successive halves of the eclipse season, at 173 ½ days, fits into the tzolkin in the ratio of 3 to 2.
According to this hypothesis, the 260-day cycle originated in the narrow latitudinal band (14°42′N to 15°N) in which the sun is vertically overhead about 12–13 August and again 260 days later about 30 April – 1 May (Malmström identifies the proto-Classic Izapan culture as one suitable candidate at this latitude).
However, others object to this conception, noting that while the 260-day calendar runs continuously the interval between autumn-spring and spring-autumn positions alternates between 260 and 105 days, and that the earliest-known calendric inscriptions are from considerably farther north of this zone.
[20] In 1998, composer Michael John Wiley discovered mathematical and aesthetic correlations between the tzolk'in vigesimal count and the naturally occurring overtone series found in music, yielding the composition Tzolkin in C Major", which was premiered by the Tokyo Philharmonic Orchestra in Japan, 2002, taking 3rd Prize at the prestigious Toru Takemitsu Composition Award, and subsequently developed into a Tzolkin Cultural Meditation, an audio/visual presentation of the 260 day calendar and timing matrix.