The tzolkʼin (, formerly and commonly tzolkin) is the 260-day
Mesoamerican calendar used by the
Maya civilization
The Maya civilization () was a Mesoamerican civilization that existed from antiquity to the early modern period. It is known by its ancient temples and glyphs (script). The Maya script is the most sophisticated and highly developed writin ...
of
pre-Columbian
In the history of the Americas, the pre-Columbian era, also known as the pre-contact era, or as the pre-Cabraline era specifically in Brazil, spans from the initial peopling of the Americas in the Upper Paleolithic to the onset of European col ...
Mesoamerica
Mesoamerica is a historical region and cultural area that begins in the southern part of North America and extends to the Pacific coast of Central America, thus comprising the lands of central and southern Mexico, all of Belize, Guatemala, El S ...
.
The tzolkʼin, the basic cycle of the
Maya calendar
The Maya calendar is a system of calendars used in Pre-Columbian era, pre-Columbian Mesoamerica and in many modern communities in the Guatemalan highlands, Veracruz, Oaxaca and Chiapas, Mexico.
The essentials of the Maya calendar are based upon ...
, is a preeminent component in the society and rituals of the ancient and the modern Maya. The tzolkʼin is still used by several
Maya
Maya may refer to:
Ethnic groups
* Maya peoples, of southern Mexico and northern Central America
** Maya civilization, the historical civilization of the Maya peoples
** Mayan languages, the languages of the Maya peoples
* Maya (East Africa), a p ...
communities in the
Guatemala
Guatemala, officially the Republic of Guatemala, is a country in Central America. It is bordered to the north and west by Mexico, to the northeast by Belize, to the east by Honduras, and to the southeast by El Salvador. It is hydrologically b ...
n highlands. While its use has been spreading in this region, this practice is opposed by
Evangelical
Evangelicalism (), also called evangelical Christianity or evangelical Protestantism, is a worldwide, interdenominational movement within Protestantism, Protestant Christianity that emphasizes evangelism, or the preaching and spreading of th ...
Christian converts in some Maya communities.
The word ''tzolkʼin'', meaning "division of days", is a western
coinage in
Yucatec Maya
Yucatec Maya ( ; referred to by its speakers as or ) is a Mayan languages, Mayan language spoken in the Yucatán Peninsula, including part of northern Belize. There is also a significant diasporic community of Yucatec Maya speakers in San Fra ...
. Contemporary Maya groups who have maintained an unbroken count for over 500 years in the tzolk'in use other terms in their languages. For instance, the
Kʼicheʼ use the term ''Aj Ilabal Qʼij''
χ ilaɓal qʼiχor ''Raj Ilabal Qʼij''
�aχ ilaɓal qʼiχ 'the sense of the day' or 'the round of the days' and the
Kaqchikel use the term ''Chol Qʼij''
͡ʃol qʼiχ 'the organization of time'. The names of this calendar among the pre-Columbian Maya are not widely known. The corresponding Postclassic
Aztec
The Aztecs ( ) were a Mesoamerican civilization that flourished in central Mexico in the Post-Classic stage, post-classic period from 1300 to 1521. The Aztec people included different Indigenous peoples of Mexico, ethnic groups of central ...
calendar was called ''
tonalpohualli'' in the
Nahuatl language
Nahuatl ( ; ), Aztec, or Mexicano is a language or, by some definitions, a group of languages of the Uto-Aztecan language family. Varieties of Nahuatl are spoken by about Nahuas, most of whom live mainly in Central Mexico and have smaller popul ...
.
The twenty day names
The tzolkʼin calendar combines a cycle of twenty named days with another cycle of thirteen numbers (the ''
trecena
A trecena (From Spanish: trece) is a 13-day period used in pre-Columbian Mesoamerican calendars. The 260-day Mayan calendar (the '' tonalpohualli'') was divided into 20 trecenas. Trecena is derived from the Spanish chroniclers and translates to ...
''), to produce 260 unique days (20 × 13 = 260). Each successive named day is numbered from 1 to 13, and then starting again at 1.
The 20 individual named days are the following:
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.
Each of the twenty days has its specific primary association connected to the day name's meaning.
*Imix : 'Crocodile' – the reptilian body of the planet earth, or world
*Ik : 'Wind' – breath, life. Also violence.
*Akbal : 'Night-house' – darkness, the underworld, realm of the nocturnal jaguar-sun.
*Kan : 'Maize' – sign of the young maize lord who brings abundance, ripeness. Also lizard, net.
*Chicchan : 'Snake' – the celestial serpent
*Cimi : 'Death'
*Manik : 'Deer' – sign of the Lord of the Hunt
*Lamat : 'Rabbit' – sign of what is also known as the planet Venus, sunset. The glyph may depict four grains of maize. Invoked by the feminine name "Ixqʼanil" by
Xquic.
*Muluc : 'Water' – symbolised by jade, an aspect of the water deities; fish. Invoked by the feminine name "Ixtoj" by
Xquic.
*Oc : 'Dog' – who guides the night sun through the underworld.
*Chuen : 'Monkey' – the great craftsman, patron of arts and knowledge. Also thread.
*Eb : 'Grass' or 'Point' – associated with rain and storms.
*Ben : 'Reed' – who fosters the growth of corn, cane, and man.
*Ix : 'Jaguar' – the night sun. Also maize. Associated with the goddess
Ixchel
Ixchel or Ix Chel is the 16th-century name of the aged jaguar goddess of midwifery and medicine in ancient Maya culture.
She corresponds to Toci, an Aztec earth goddess inhabiting the sweatbath. She is related to another Aztec goddess invo ...
.
*Men : 'Eagle' – the wise one, bird, moon
*Cib : 'Owl/Vulture' – death-birds of night and day. Also wax, soul, insect.
*Caban : 'Earthquake' – formidable power. Also season, thought.
*Etzʼnab : 'Knife' – the obsidian sacrificial blade.
*Cauac : 'Rain' or 'Storm' – the celestial dragon serpents and the ''chacs,'' gods of thunder and lightning.
*Ahau : 'Lord' – the radiant sun god. Also associated with the
Mayan hero twins.
The variant names and associations below are common to three post-conquest Guatemalan highland calendars. Their interpretations are based primarily on an 1854 manuscript by
Hernandez Spina.
*Imox is a bad day, associated with the insane, on which the priests of the sun pray that harm may come to their enemies through evil spirits.
*Iq is a bad day, symbolic in the same way of the destructive forces of nature; that power is localized in stone idols, who are honored with incense, roses, candles, pine needles, and
aguardiente
( Portuguese) or ( Spanish) (; ; ) is a type of distilled alcoholic spirit that contains between 29% and 60% alcohol by volume (ABV). It is a somewhat generic term that can refer to liquors made from various foods. It originates from and is t ...
. Tumours and painful swellings are attributed to the influence of this day.
*Aqabal is a bad day, on which the priests of the sun go to shrines to pray against their enemies. The day is symbolic of evil in general and of slanderers, in particular.
*Kat is a bad day in the same sense as Aqabal, symbolic of evil in general.
*Kan is a bad day. It brings sickness and is symbolic of the arbitrary cruelty of nature.
*Kame is recorded as a bad day by one 19th-century source and as a good day by one 20th-century source,
Ruth Leah Bunzel. It is symbolic of the ultimate dissolution by death of everything good and everything evil. It is a good day to confess one's evil deeds, and ask for pardon.
*Keej is a good day on which wishes are made. It is a good day to ask favors and to commemorate ancestors.
*Qanil is a good day, sacred to fertility gods, associated with human nourishment, the growth of crops, the cycle of death and rebirth, and of the
milpa. After the harvest is completed, thanksgiving is made on Qanil.
*Toj is a bad day, symbolized by sickness, and anyone born on it will be perverse. It is a good day to wish sickness upon an enemy.
*Tzi is a bad day, symbolized by sexual depravity. No ceremonies must ever be held on this day.
*Batz is a bad day, symbolized by paralysis. According to some, it is a good day, symbolic of the ancestors.
*E is a good day, symbolized by destiny, fortune, and the essential characteristics of one's personality. It is a day on which marriages may be held, and sacrifices to benign deities may be made.
*Aj is a good day, consecrated to fertility gods, herdsmen, and domesticated animals. The day is symbolic of one's destiny as embodied in one's
nagual.
*Ix is a good day, sacred to the mountain and forest spirits. On this day, protection may be sought from wolves and wild predators, in favor of flocks and animals. The day is symbolic of the creative force in general, and of the earth itself.
*Tzikin is the most excellent day of all. Double offerings are made at shrines, in forests, and in caves. It is a day on which wishes may be made, forgiveness may be sought, and important matters may be finalized.
*Ajmaq is also a very good day, one sacred to the spirits that preside over good health.
*Noj is an auspicious day, on which good judgement may be prayed for. The day is symbolic both of humanity's amoral and moral qualities.
*Tijax is a good day. It is a day of verbal arguments, and a good day to confess sins.
*Kawoq is recognized as an indifferent day or a bad day. It is symbolic of the malice of the dead.
*Junapu or Ajpu is an indifferent day, neither a bad or good portent, on which the power of the ancestors is embodied by the house itself.
Uses
The tzolkʼin was extensively used in Mayan inscriptions and codices. Symbolism related to the tzolkʼin is also observed in the
Popol Vuh
''Popol Vuh'' (also ''Popul Vuh'' or ''Pop Vuj'') is a text recounting the mythology and history of the Kʼicheʼ people of Guatemala, one of the Maya peoples who also inhabit the Mexican states of Chiapas, Campeche, Yucatan and Quintana Roo, ...
(which, though written in the early post-conquest period, is probably based on older texts). For instance, when
Xmucane has set an impossible task for
Xquic of collecting a netful of corn from one stalk and Xquic successfully completes it, she leaves the imprint of her net in the ground, and the day "net" is the opening of the
Venus cycle which follows "ahau" ("ajpu" in Kʼicheʼ), just as her child is the heir of Hun Hunajpu.
The uses to which the ancient Maya applied the calendar are unknown, nonetheless modern Maya communities employ the calendar as follows:
* For
Maize
Maize (; ''Zea mays''), also known as corn in North American English, is a tall stout grass that produces cereal grain. It was domesticated by indigenous peoples in southern Mexico about 9,000 years ago from wild teosinte. Native American ...
cultivation.(The
zenith
The zenith (, ) is the imaginary point on the celestial sphere directly "above" a particular location. "Above" means in the vertical direction (Vertical and horizontal, plumb line) opposite to the gravity direction at that location (nadir). The z ...
transit days may have been significant for agriculture along the south coast of
Guatemala
Guatemala, officially the Republic of Guatemala, is a country in Central America. It is bordered to the north and west by Mexico, to the northeast by Belize, to the east by Honduras, and to the southeast by El Salvador. It is hydrologically b ...
because April 30 occurs just before the rainy season. Modern Maya plant their corn at the end of April or early in May. In the August 13
zenith
The zenith (, ) is the imaginary point on the celestial sphere directly "above" a particular location. "Above" means in the vertical direction (Vertical and horizontal, plumb line) opposite to the gravity direction at that location (nadir). The z ...
transit the Maya initiate its current era in this day', approximating the harvest of the dried corn.
* For modern
Guatemala
Guatemala, officially the Republic of Guatemala, is a country in Central America. It is bordered to the north and west by Mexico, to the northeast by Belize, to the east by Honduras, and to the southeast by El Salvador. It is hydrologically b ...
n highlanders, the 260 days are employed in training the Aj Kʼij, or 'calendar diviner'. Nine months after commencing training in divination, the novice is "reborn" and initiated into office. The tzolkʼin is explainable, in principle, as a calendar of midwives, since it counts 260 days from the 20 day period of the conception, from when the heart of the fetus starts to beat, until birth.
* For rituals performed every 260 days. Most famous of these is the "Initiation" celebration of 8 Chuwen, ''Waxakibʼ Bʼatz'', in the
Kʼiche town of
Santa Cruz del Quiche.
* For days which are suitable for certain actions. For instance, a low-numbered Akʼabʼal or Bʼen would be a good day for a wedding, whereas Kʼan would be a good day for building or maintaining a house.
* For
divination
Divination () is the attempt to gain insight into a question or situation by way of an occultic ritual or practice. Using various methods throughout history, diviners ascertain their interpretations of how a should proceed by reading signs, ...
based on
casting lots and counting forward through the calendar from the current 'year bearer' to arrive at a day which is then interpreted. This is not pure
cleromancy
Cleromancy is a form of sortition (casting of lots) in which an outcome is determined by means that normally would be considered random, such as the rolling of dice ( astragalomancy), but that are sometimes believed to reveal the will of a deit ...
because somatic twitches of "blood lightning" can either be specifically consulted or arise spontaneously during the process.
* For traditional Mayan names, which are based on calendar days, often birthdays.
* Somewhat analogous to
astrology
Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions ...
, personal characteristics are believed to be influenced by the name of the day on which a person was born, and the success of some particular types of endeavor depend on carrying them out on a day whose name is auspicious for those actions.
Origins
The 260-day calendar spread throughout the Mesoamerican cultural region and is regarded as the oldest and most important of the calendar systems, with an origin predating its first appearances in Maya inscriptions. The earliest evidence of this calendar comes from a possible day sign with a dot numeral coefficient in an Olmec-like inscription in
Oxtotitlán
Oxtotitlán is a natural rock shelter and archaeological site in Chilapa de Álvarez, Mexican state of Guerrero that contains murals linked to the Olmec motifs and iconography. Along with the nearby Juxtlahuaca cave, the Oxtotitlán rock pa ...
cave dated to 800-500 BCE. Some of the next oldest calendric inscriptions are from early strata of
Zapotec in the
Oaxaca
Oaxaca, officially the Free and Sovereign State of Oaxaca, is one of the 32 states that compose the political divisions of Mexico, Federative Entities of the Mexico, United Mexican States. It is divided into municipalities of Oaxaca, 570 munici ...
n highlands at sites such as
Monte Albán
Monte Albán is a large pre-Columbian archaeological site in the Santa Cruz Xoxocotlán Municipality in the southern Mexico, Mexican state of Oaxaca (17.043° N, 96.767°W). The site is located on a low mountainous range rising above the plain i ...
, 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
San José Mogote is a pre-Columbian archaeological site of the Zapotec civilization, Zapotec, a Mesoamerican culture that flourished in the region of what is now the Mexico, Mexican States of Mexico, state of Oaxaca. A forerunner to the better- ...
and in the
Olmec
The Olmecs () or Olmec were an early known major Mesoamerican civilization, flourishing in the modern-day Mexican states of Veracruz and Tabasco from roughly 1200 to 400 Before the Common Era, BCE during Mesoamerica's Mesoamerican chronolog ...
Gulf Coast
The Gulf Coast of the United States, also known as the Gulf South or the South Coast, is the coastline along the Southern United States where they meet the Gulf of Mexico. The coastal states that have a shoreline on the Gulf of Mexico are Tex ...
region. However, either the dating method or the calendric nature of the glyphs are disputed by scholars. 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, 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. Since these were elementary periods of the 260-day cycle, the orientations marking these intervals can only be explained in association with this calendar. The dating of the earliest constructions indicates that it was in use by 1100 BCE.
The original purpose of such a calendar, with no obvious relation to any astronomical or geophysical cycle, is not securely known, but there are several theories. One theory is that the calendar came from mathematical operations based on the numbers thirteen and twenty, which were important numbers to the Maya, (Thompson 1950: Maya Hieroglyphic Writing:Introduction). The number twenty was the basis of the Maya counting system, taken from the total number of human digits. (See
Maya numerals
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal (base-20) positional notation, positional numeral system. The numerals are made up of three symbols: Zero number#The ...
). Thirteen symbolized the number of levels in the Upperworld where the gods lived, and is also cited by modern daykeepers as the number of "joints" in the human body (ankles, knees, hips, shoulders, elbows, wrists, and neck). The numbers multiplied together equal 260.
Barbara Tedlock studied this system in the contemporary Kʼiche Maya community of the municipality of
Momostenango in highland Guatemala. She underwent a formal apprenticeship in calendar divination with a local adept, and was initiated as a diviner in 1976. She says: "The Momostecan calendar embraces both the 260-day cycle and the 365-day solar year, with the four Classic Maya Year-bearers, or Mam, systematically linking the two. The 260-day cycle is conceived as linked firmly to worldly or earthly affairs, mirroring no astronomical period but rather the period of human gestation. Past ethnographic accounts of this cycle contain various conflicting opinions as to what its first day is, but a comparison of the present results and those of previous studies indicates that there is no fixed first day."
Anthony Aveni asserts, "Once a Maya genius may have recognized that somewhere deep within the calendar system lay the miraculous union, the magical crossing point of a host of time cycles: 9 moons, 13 times 20, a birth cycle, a planting cycle, a Venus cycle, a sun cycle, an eclipse cycle. The number 260 was tailor made for the Maya". Others have observed that the "Venus Table" in the
Dresden Codex
The ''Dresden Codex'' is a Maya book, which was believed to be the oldest surviving book written in the Americas, dating to the 11th or 12th century. However, in September 2018 it was proven that the Maya Codex of Mexico, previously known as th ...
, is an accurate ephemeris for predicting Venus positions.
Others have also observed a basis for the 260-day cycle in the agricultural cycle of highland
Guatemala
Guatemala, officially the Republic of Guatemala, is a country in Central America. It is bordered to the north and west by Mexico, to the northeast by Belize, to the east by Honduras, and to the southeast by El Salvador. It is hydrologically b ...
, which is also about 260 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." This may seem contrived, but the Maya did employ the tzolkin to predict positions of Venus and eclipses.
Another theory is that the 260-day period is the length of human
pregnancy
Pregnancy is the time during which one or more offspring gestation, gestates inside a woman's uterus. A multiple birth, multiple pregnancy involves more than one offspring, such as with twins.
Conception (biology), Conception usually occurs ...
. This is close to the average number of days between the ''first missed''
menstrual period
The menstrual cycle is a series of natural changes in hormone production and the structures of the uterus and ovaries of the female reproductive system that makes pregnancy possible. The ovarian cycle controls the production and release of eg ...
and birth, unlike
Naegele's rule which is 40 weeks (280 days) between the ''last'' menstrual period and birth. It is postulated that
midwives
A midwife (: midwives) is a health professional who cares for mothers and newborns around childbirth, a specialisation known as midwifery.
The education and training for a midwife concentrates extensively on the care of women throughout their ...
originally developed the calendar to predict babies' expected birth dates.
Vincent Malmström identifies a correlation between the 260-day cycle and the 260-day gap between zenithal passages of the
sun
The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...
. 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
Izapa
Izapa is a very large pre-Columbian archaeological site located in the Mexican state of Chiapas; it is best known for its occupation during the Late Formative period. The site is situated on the Izapa River, a tributary of the Suchiate River, ...
n culture as one suitable candidate at this latitude). This period may have been used for the planting schedule of
maize
Maize (; ''Zea mays''), also known as corn in North American English, is a tall stout grass that produces cereal grain. It was domesticated by indigenous peoples in southern Mexico about 9,000 years ago from wild teosinte. Native American ...
. 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. Consequently, this theory is not widely supported.
It is also possible that the number 260 has multiple sources.
The tzolkʼin and the New Age movement
The tzolkʼin is the basis for the modern,
New Age
New Age is a range of Spirituality, spiritual or Religion, religious practices and beliefs that rapidly grew in Western world, Western society during the early 1970s. Its highly eclecticism, eclectic and unsystematic structure makes a precise d ...
invention of the "
Dreamspell" calendar, developed by the esoteric author
José Argüelles
José Argüelles (; born Joseph Anthony Argüelles; January 24, 1939 – March 23, 2011) was an American New Age writer and artist. He was the co-founder, along with Lloydine Argüelles, of the Planet Art Network and the Foundation for the Law of ...
. The Dreamspell calendar is sometimes mistakenly identified as an authentic interpretation or extension of the original Maya calendar, although Argüelles himself acknowledges the Dreamspell calendar is a new and syncretic creation, inspired by elements from Mesoamerican and non-Mesoamerican sources.
In 1987, before the
Harmonic Convergence, inspired by a single paragraph of Argüelles's book "The Mayan Factor" (wherein he refers to each day as a "tone"), singer/songwriter and sound healer, Alyras (aka Mirai), translated the tzolkʼin's harmonic values into sound, with the tutelage of Barbara Hero. Eschewing extensions of the tzolkʼin, Alyras opted for strict mathematical adherence to the tzolkʼin's fundamental structure and sequences, in order to present a truly authentic sonic expression of its inner workings.
In 1995, Maria von Boisse translated the mathematical matrix of the tzolkʼin to musical notes and set them into music. The final version of the work was developed in collaboration with
Hubert Bognermayr in the ''Electronic Försterhaus'' in
Linz
Linz (Pronunciation: , ; ) is the capital of Upper Austria and List of cities and towns in Austria, third-largest city in Austria. Located on the river Danube, the city is in the far north of Austria, south of the border with the Czech Repub ...
,
Austria
Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...
.
"TZOLKIN – the sacred Mayan calendar (Part I. Of Tolteca)"
/ref>
In 1998, compose
Michael John Wiley
discovered mathematical and aesthetic correlations between the tzolk'in vigesimal
A vigesimal ( ) or base-20 (base-score) numeral system is based on 20 (number), twenty (in the same way in which the decimal, decimal numeral system is based on 10 (number), ten). ''wikt:vigesimal#English, Vigesimal'' is derived from the Latin a ...
count and the naturally occurring overtone series
The harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a ''fundamental frequency''.
Pitched musical instruments are often based on an acoustic resonator s ...
found in music, yielding the compositio
Tzolkin in C Major"
which was premiered by the Tokyo Philharmonic Orchestra
The is recognized as the oldest symphony orchestra in Japan. It was founded in 1911 and debuted at the original Matsuzakaya store in Nagoya as the . It relocated to Tokyo in 1938. As of 2024, it has 166 members.
The orchestra plays frequently a ...
in Japan, 2002, taking 3rd Prize at the prestigious Toru Takemitsu Composition Award, and subsequently developed into
Tzolkin Cultural Meditation
an audio/visual presentation of the 260 day calendar and timing matrix.
See also
* Haabʼ
The Haabʼ () is part of the Maya calendar, Maya calendric system. It was a 365-day calendar used by many of the pre-Columbian cultures of Mesoamerica.
Description
The Haabʼ comprises eighteen months of twenty days each, plus an additional per ...
* Mesoamerican calendars
The calendar, calendrical systems devised and used by the pre-Columbian cultures of Mesoamerica, primarily a 260-day year, were used in religious observances and social rituals, such as divination.
These calendars have been dated to early as ca. ...
* Tonalpohualli
Notes
References
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External links
Maya Calendar with Names and color Glyphs
Maya Calendar Round (CR) made of two parts: Ritual (Tzolkʼin) Calendar and the Haab
Red Galáctica
(Tzolkʼin Maya)
{{Maya
Maya calendars
Specific calendars
Maya civilization
zh:瑪雅曆#卓爾金曆