Mga kalendaryo ng Mesoamerica

Time as a living thing

In ancient Mesoamerica a day was not an empty box to be filled. Each one arrived with a number, a name and a presiding power, and those three together decided whether it was a good day to plant, marry, travel, go to war or be born. The Olmec, Zapotec, Maya, Mixtec and Aztec (Mexica) spoke unrelated languages and fought one another for centuries, yet they all kept time with the same two interlocking counts: a sacred cycle of 260 days and a solar year of 365. Where Babylonian and Hellenistic astrology read destiny from the positions of planets against the stars, Mesoamerican daykeepers read it from the calendar itself. The sky mattered, and their astronomers tracked Venus and eclipses with remarkable accuracy, but the first question about any moment was which day it was.

The earliest evidence

The calendar is older than writing in the region. Large ceremonial platforms at Aguada Fénix in Tabasco and at Ceibal in Guatemala, built around 1000 BCE, are laid out as E-Groups: a western pyramid facing a long eastern platform, arranged so that an observer could watch the sunrise move along the horizon through the year. The name comes from Group E at Uaxactun, where the pattern was first recognised. A 2023 survey of Olmec and early Maya sites by Ivan Šprajc, Takeshi Inomata and Anthony Aveni found that many of these complexes face sunrises on dates separated by multiples of 13 and 20 days, often by 260, which suggests the builders already worked with the sacred count.

The written record starts in the first millennium BCE. Monument 3 at San José Mogote in Oaxaca, a carved captive usually dated to around 600 BCE, carries a day name between its feet, read as "1 Earthquake" or "1 Eye". It is the earliest example of a practice that lasted two thousand years: people were named after the day of their birth. At San Bartolo in Guatemala, fragments of a painted wall dated to between 300 and 200 BCE show the day "7 Deer", written with a bar-and-dot seven over a deer's head. Published in 2022, it is the oldest secure Maya calendar notation. Classic Maya scribes later wrote the same day sign as a hand, so the San Bartolo deer shows an earlier, more pictorial stage of the same system.

The 260-day count

The sacred calendar is built from two wheels turning together: the numbers 1 to 13 and a sequence of 20 named days. Each day advances both wheels by one step. Starting from 1 Imix, the Maya count runs 2 Ik', 3 Ak'bal, 4 K'an and so on up to 13 B'en; the next day the numbers start again but the names do not, giving 1 Ix. Because 13 and 20 share no common factor, the same pairing of number and name comes back only after 13 × 20 = 260 days.

The Aztec called this count the tōnalpōhualli, the counting of days. Its best-known Maya name, Tzolk'in, is a modern coinage by the scholar William Gates in 1921; the K'iche' Maya of highland Guatemala, who still keep it, call it the Chol Q'ij, the ordering of days. Nobody knows for certain why the cycle is 260 days long. Three explanations are commonly offered, and they are not exclusive: 260 days is close to the length of human pregnancy, highland Maya midwives and daykeepers make that connection themselves; near 15° north, the latitude of Izapa and Copán, the sun passes directly overhead on two dates that divide the year into spans of roughly 105 and 260 days; and 260 days approximates the maize growing season in parts of the region.

The twenty day signs carry closely related meanings across the whole region, even where the names differ:

The Aztec also divided the 260 days into twenty groups of thirteen, now called trecenas, each under a patron deity whose character coloured all thirteen of its days. Painted almanacs such as the Codex Borbonicus open with these patrons, and a priest reading a birth or a marriage consulted the trecena as well as the day.

The 365-day year

The solar calendar, the Haab' of the Maya and the xiuhpōhualli of the Aztec, had eighteen periods of twenty days, 360 days in all, followed by five extra days. The Maya called those five the Wayeb'; the Aztec called them the nēmontēmi, the days that fill up in vain. They belonged to no god and were feared as unlucky, a time to stay at home, avoid quarrels and start nothing new. The Maya month names run Pop, Wo', Sip, Sotz', Sek, Xul, Yaxk'in, Mol, Ch'en, Yax, Sak', Keh, Mak, K'ank'in, Muwan, Pax, K'ayab and Kumk'u. Maya scribes numbered the days of each month from 0 to 19, with day 0 written as the "seating" of the month.

For the Aztec, each twenty-day period, called a veintena by Spanish chroniclers, was a public festival with its own gods and rites. The sequence below follows the Florentine Codex of Bernardino de Sahagún; other sources start the year at a different point and disagree on some details.

Neither calendar had a leap day, so the 365-day year slipped against the true solar year by about a day every four years. Mesoamerican astronomers knew this, but they never altered the count. They tracked the drift in their tables instead, which kept every date since the beginning of the system in one unbroken sequence.

The Calendar Round and the year bearers

Run together, the two calendars give every day a double name, such as the Maya 4 Ajaw 8 Kumk'u. The same combination returns only after the least common multiple of 260 and 365: 18,980 days, which is 52 years of 365 days and 73 cycles of 260. This 52-year span, the Calendar Round, was the "century" of Mesoamerica, and a person rarely saw a given Calendar Round date twice.

The arithmetic has a neat consequence. Because 365 leaves a remainder of 5 when divided by 20, each new year begins five day signs later than the last, so only four of the twenty signs can ever open a year. These are the year bearers, and each year took the name of its bearer and number. Because 365 leaves a remainder of 1 when divided by 13, the number rises by one each year: the Aztec sequence runs 1 Reed, 2 Flint, 3 House, 4 Rabbit, 5 Reed, and so on through four sets of thirteen years.

Different peoples used different bearers, because they anchored the year on different days:

• Aztec and Mixtec: Reed, Flint, House and Rabbit.
• Classic Maya: Ik', Manik', Eb' and Kab'an, the days that fall on the seating of Pop.
• Postclassic Yucatec Maya, as recorded by Diego de Landa: K'an, Muluk, Ix and Kawak.
• Highland Maya today: the K'iche' and other highland peoples still use Iq', Kej, E and No'j, the direct continuation of the Classic set.

The New Fire

The end of a Calendar Round was the most dangerous moment the Aztec knew. If the sun did not rise on the first day of the new cycle, the tzitzimimeh, star demons of the dark, would come down and devour the world. In the last days of the old cycle households put out their fires, broke or threw away their hearthstones and cooking pots, and cast their household images of the gods into the water. Pregnant women were shut away in granaries, wearing masks of maguey leaves, so that they would not turn into beasts, and children were kept awake so that they would not become mice.

At midnight the priests on the Hill of the Star, Huixachtlan, near modern Iztapalapa, watched the Pleiades. If the cluster crossed the meridian, the world would continue. A new fire was drilled on the chest of a sacrificed captive, and runners carried it to the Templo Mayor and from there to every temple and hearth. The rite was called the binding of the years, xiuhmolpilli, and it was held in the year 2 Reed rather than 1 Rabbit, a change the Aztec made in their own history. The last one took place in 1507 and is painted on page 34 of the Codex Borbonicus.

The Long Count

The Calendar Round could fix a date within a lifetime but not across history, since every date recurred after 52 years. The Long Count solved this with a running total of days from a fixed starting point, written in a modified base-20 system:

The third place uses 18 rather than 20 so that the tun approximates the year. Every place above it goes back to twenty. Scholars have also named higher units, the piktun (2,880,000 days), kalabtun, k'inchiltun and alawtun (23,040,000,000 days), but these names are modern conventions. The Maya did write such units: Stela 1 at Cobá fills the places above the b'ak'tun with the number thirteen, a span of time many times the age of the universe.

A Long Count date is written as five numbers, such as 9.12.11.5.18, counting b'ak'tuns, k'atuns, tuns, winals and k'ins. The zero point of the current era is written 13.0.0.0.0 4 Ajaw 8 Kumk'u. On Stela C at Quiriguá it is the day the gods set the three stones of creation, the cosmic hearth, at the Lying-Down Sky. At Palenque, the Cross Group temples dedicated by K'inich Kan Bahlam II in 692 CE record the births of gods before the era began, tying the king's own reign to that mythic past.

The oldest surviving Long Count dates are not Maya at all. Stela 2 at Chiapa de Corzo gives a date equivalent to 36 BCE, Stela C at Tres Zapotes one in 32 BCE, and Stela 1 at El Baúl one in 37 CE. The earliest Maya example in the lowlands is Stela 29 at Tikal, dated 8.12.14.8.15, which falls in 292 CE.

Setting Maya dates on our calendar

To convert a Long Count date to a European one, scholars need the Julian Day Number of the zero date. The value most use is 584,283, called the GMT correlation after Joseph Goodman, Juan Martínez Hernández and J. Eric S. Thompson, who established it between 1905 and 1950. It places 13.0.0.0.0 on 11 August 3114 BCE in the proleptic Gregorian calendar, which is 6 September 3114 BCE in the Julian. A close rival, 584,285, moves every date two days later. The GMT family is supported by colonial records that tie Maya dates to Spanish ones, by eclipse and Venus tables that only fit the sky under it, and by radiocarbon dating of carved wooden lintels from Tikal, published in 2013.

The same correlation placed the end of the thirteenth b'ak'tun, 13.0.0.0.0 4 Ajaw 3 K'ank'in, on 21 December 2012. The only Classic text that mentions that date, Monument 6 at Tortuguero, speaks of a god's descent, not of the end of the world, and the Long Count simply rolls on into the fourteenth b'ak'tun.

Lords of the Night and the moon

Classic Maya inscriptions usually follow a Long Count date with a Supplementary Series of further glyphs. The first names one of nine Lords of the Night, a nine-day cycle that ran alongside the other counts. Mayanists call them G1 to G9, since most of their Maya names are unknown. The Aztec kept the same cycle, and the Codex Borbonicus lists their nine Lords of the Night in order: Xiuhtecuhtli, Itztli, Piltzintecuhtli, Centeotl, Mictlantecuhtli, Chalchiuhtlicue, Tlazolteotl, Tepeyollotl and Tlaloc. Because nine does not divide 260, the same day name falls under a different night lord each time it returns, adding another layer to its reading.

The Lunar Series that follows records the moon: how many days had passed since the new moon, where the current lunation stood in a group of six, and whether the month had 29 or 30 days. Glyph C, which counts the lunation, carries one of three rotating deity heads. Groups of six lunations are the building blocks of eclipse prediction, which is why this record was worth carving in stone.

Venus, eclipses and the planets

Venus was the most closely watched planet in Mesoamerica, and its first dawn rising as the morning star was feared. The Annals of Cuauhtitlan describe the Aztec Venus god Tlahuizcalpantecuhtli spearing different kinds of victims depending on the day of that rising, from the old to the young to the rulers. The Maya called the planet Chak Ek', Great Star. They set its synodic period, the time from one morning rising to the next, at 584 days, against a true mean of 583.92. Five such periods make 2,920 days, exactly eight years of 365 days, and 65 periods make 37,960 days, exactly two Calendar Rounds and 146 sacred counts. After these 104 years all three cycles return together.

The Venus pages of the Dresden Codex, page 24 and pages 46 to 50, run through five Venus cycles and build in small corrections so that the table stays accurate over centuries. The Maya Codex of Mexico, long known as the Grolier Codex, is another Venus almanac, radiocarbon-dated to between about 1021 and 1154 CE and authenticated in 2018. It is the oldest surviving book of the Americas.

Ang mga pahina 51 hanggang 58 ng Dresden Codex ay naglalaman ng talahanayan ng eklipse na sumasaklaw sa 11,960 na araw, na eksaktong 46 na sagradong bilang at halos eksaktong 405 na buwan sa kalendaryong lunar. Nangyayari lamang ang mga eklipse kapag ang bagong buwan o kabilugan ng buwan ay pumatak malapit sa mga node ng orbit ng buwan, at nauulit ang mga ganoong panahon sa pagitan ng anim na lunasyon, na nasa halos 177 o 178 na araw, na may paminsan-minsang lima, 148 na araw. Pinagsasama-sama ng talahanayan ang mga pagitang ito upang mamarkahan ang mga kahabaan ng 260 na araw na bilang kung saan posibleng magkaroon ng eklipse. Walang nakadepende rito mula sa mga gawa ng mga Babylonian o Griyego; isa itong malayang solusyon sa parehong problema.

Lumalabas lamang ang isang pambihirang siklo sa mga Classic na monumento sa Palenque, Copán, Yaxchilan at ilang iba pang lungsod: ang 819 na araw na bilang. Nakatalaga ang bawat bilang sa isa sa apat na direksyon at kulay—silangan at pula, hilaga at puti, kanluran at itim, timog at dilaw—at iniuugnay sa diyos na si K'awil. Ang numero ay 7 × 9 × 13, na tatlong sagradong numero na pinarami (multiplied). Noong 2023, ipinakita nina John Linden at Gerardo Aldana na ang bilang ay akma rin sa mga nakikitang planeta: ang 819 na araw ay eksaktong pitong synodic period ng Mercury, anim na bilang ang katumbas ng labintatlo para sa Saturn, labinsiyam na bilang ang katumbas ng tatlumpu't siyam para sa Jupiter, at dalawampung bilang, 16,380 araw, ang katumbas sa dalawampu't isa ng Mars.

Space, prophecy and the k'atun wheel

For Mesoamerican thinkers, days came from somewhere. Page 1 of the Codex Fejérváry-Mayer draws the world as a cross with a tree, a bird and a pair of gods in each of the four directions, and the fire god Xiuhtecuhtli at the centre. The 260 days run around the frame, so that each direction owns a share of time and the passing of days becomes a journey around the world.

In the Yucatán after the collapse of the Classic cities, the Long Count fell out of use. People kept a shorter count of k'atuns instead, each named after the day Ajaw on which it ended. Because each k'atun is 7,200 days long, the number of its closing Ajaw drops by two each time: 11 Ajaw, 9 Ajaw, 7 Ajaw and on down, then 13 Ajaw after 2 Ajaw, a round of thirteen k'atuns lasting about 256 years. The colonial Books of Chilam Balam treat this round as a wheel of prophecy: whatever happened under a k'atun would happen again when it came back. K'atun 8 Ajaw was remembered for the fall of great cities and the scattering of peoples. When the Itza of Tayasal, the last independent Maya kingdom, finally gave up their capital in 1697, it was again a k'atun 8 Ajaw, and their own prophecies had long pointed to that k'atun as a time of change.

A calendar that never stopped

The Spanish conquest ended the public festivals of the 365-day year, but the 260-day count went underground and survived. In 1704 colonial authorities in the Villa Alta district of Oaxaca confiscated 103 booklets from Zapotec communities. The historian David Tavárez found that 99 of them contain copies of the 260-day calendar, still used for divination and naming nearly two centuries after the fall of Tenochtitlan.

In the Guatemalan highlands the count has never been broken. K'iche', Kaqchikel, Ixil and Mam daykeepers, ajq'ijab' in K'iche', keep the Chol Q'ij in step with the Classic calendar to the day, and among the Mixe of Oaxaca a version of it survives as well. A K'iche' daykeeper answers a question by laying out a handful of red tz'ite' seeds, from the coral tree, together with small crystals, sorting them into small piles and counting through the days one pile at a time. The day each pile lands on speaks to the question. Communities still celebrate Waqxaqi' B'atz', 8 Monkey, as the day new daykeepers are initiated and the calendar is honoured.

How to read this section

Sinusundan ng mga card sa itaas ang kalendaryong Mesoamerica mula sa unang paglitaw nito sa arkitektura hanggang sa mga daykeeper ngayon. Sinasaklaw ng mga ito ang dalawang batayang bilang, ang Calendar Round na nabuo mula rito, ang mga ritwal na nagmarka sa pagtatapos nito, ang Long Count at ang mga karagdagang siklo nito, ang astronomiyang itinala sa mga codex, ang propetikong gulong ng k'atun at ang buhay na tradisyon sa mga kabundukan. Ang mga taong nakalista pagkatapos ng mga ito ay mga pinuno, mga prayle at mga iskolar kung saan ipinamana sa atin ang kalendaryo. Tulad ng bawat tradisyon sa mga pahinang ito, inilalahad ito bilang isang historikal at kultural na gawain. Inilalarawan ng isang day sign o isang petsa ng kapanganakan ang isang paraan ng pag-iisip tungkol sa oras at karakter; hindi nito pinagdedesisyunan kung ano ang gagawin ng isang tao o nagbibigay-garantiya sa anumang kalalabasan.