What Is a Katun in Maya Timekeeping?

A katun is a 7,200-day period of the Long Count, roughly 19.71 tropical years. It is the second-largest standard period in the Maya day-count, smaller only than the 144,000-day baktun and larger than the 360-day tun and the 20-day uinal. The katun is the principal political timekeeper of the Classic-period Maya: the close of a katun (k’atun b’ate’ in the colonial Yukatek spelling) was marked by a monument, by an accession ceremony, or by the burning of the old k’atun book and the installation of a new one. The katun was, in essence, the political “year” of the Classic Maya court, and the Tikal, Palenque, Copán, and Quiriguá inscriptions record over a hundred katun-endings from the 5th through the 10th centuries AD.

This page describes the mathematics of the katun, the names given to individual katuns, the ceremonies that marked their close, the role of the k’atun-b’atab’ (the katun-keeper), and the katun prophecies preserved in the colonial-era Books of Chilam Balam and in modern highland K’iche’ practice.

The mathematics of the katun

The katun is 7,200 days, exactly 20 tuns of 360 days each, or 360 uinal of 20 days each, or 7,200 kin of 1 day each. The katun is also 7,200 ÷ 260 = 27.69 Tzolkin cycles (with a remainder of 180 days), and 7,200 ÷ 365 = 19.73 Haab’ years (with a remainder of 125 days). The katun does not return to the same Calendar Round position; the Tzolkin position advances by 180 days (8 trecenas) and the Haab’ position advances by 125 days, or 6 months and 5 days, between successive katun-endings.

The katun is exactly 7,200 days, and the katun-ending is the day on which the katun position of the Long Count reaches 0. For example, the Long Count position 9.4.0.0.0 has a katun position of 0, and the day is the close of the 4th katun of the 9th baktun. The position 9.14.0.0.0 is the close of the 14th katun of the 9th baktun, and so on.

The 13-katun cycle is a 93,600-day period, or 13 × 7,200 = 93,600 days, or roughly 256 solar years. The 13-katun cycle is, in the Books of Chilam Balam, the basis of the Maya historical periodization, with the 13-katun cycle being a “century” of Maya time. The 13-katun cycle is tied to the 13-trecena sequence of the Tzolkin: the Tzolkin position of a katun-ending advances by 8 trecenas (180 days) every katun, and 13 × 180 = 2,340 days = 9 complete Tzolkin cycles. After 13 katuns, the katun-ending returns to the same Tzolkin position.

The names of the katuns

Each katun is named by the Tzolkin position of the katun-ending day. The names follow a fixed sequence:

13 Ajaw
11 Ajaw
9 Ajaw
7 Ajaw
5 Ajaw
3 Ajaw
1 Ajaw
12 Ajaw
10 Ajaw
8 Ajaw
6 Ajaw
4 Ajaw
2 Ajaw

The sequence of 13 katun names cycles, with 13 katuns forming a complete round and the next 13 katuns repeating the same names. The sequence is tied to the Tzolkin cycle: a katun-ending at 1 Ajaw is followed, 7,200 days later, by a katun-ending at 8 Ajaw (the next 1-day Treceña would be at the 1+180 mod 260 = 1+180 = 181 position, which is 1 + 13 × 13 = 1 + 169 = 170 days, but 180 days is 8 trecenas, so the next Ajaw position is 1 + 8 × 13 = 105, hmm — actually the formula is more subtle; the next Ajaw position is 180 days later, which corresponds to 8 trecenas forward, or 180 ÷ 13 = 13.85, so the coefficient of the next Ajaw position is 1 + 180 mod 13 = 1 + 11 = 12, and the day-sign is Ajaw, giving 12 Ajaw). The sequence 1, 12, 10, 8, 6, 4, 2, 13, 11, 9, 7, 5, 3, 1 — and so on, with each katun the coefficient advancing by 11 (mod 13).

In the colonial-era Books of Chilam Balam, the katun sequence is given in the same order, with each katun named by its Ajaw position. The Books of Chilam Balam also give a character to each katun, with the k’atun 4 Ajaw being the “katun of battles,” the k’atun 8 Ajaw being the “katun of the book,” and so on.

The katun-ending ceremonies

The k’atun b’ate’ (katun-ending) was, in the Classic-period Maya and in the colonial-era Yukatek communities, a major ritual occasion. The k’atun b’ate’ was marked by:

The erection of a stela or a monument.
The accession of a new ruler, often a son of the previous ruler, who would be installed on the same day.
The burning of the old k’atun book (a wooden codex with the prognostications of the closing katun) and the installation of a new k’atun book.
The performance of ritual bloodletting, autosacrifice, and the offering of captives.
The consultation of the daykeeper (ah k’in) and the elder men and women of the community.
The recitation of the almanac texts for the new katun.

The k’atun b’ate’ is documented in the inscriptions of Tikal (where 9.0.0.0.0 and 10.0.0.0.0 are major events), Copán (where 9.4.0.0.0 and 9.14.0.0.0 are major events), Quiriguá (where 9.17.0.0.0 and others are recorded), and Palenque (where the accession of K’inich Janaab’ Pakal in AD 615 is a katun-ending event).

The role of the k’atun-b’atab’

The k’atun-b’atab’ (katun-keeper) was the specialist responsible for maintaining the k’atun book and the k’atun prophecies. The k’atun-b’atab’ was a hereditary office, and the k’atun book was passed from one generation to the next. The k’atun-b’atab’ would consult the almanacs, the Tzolkin, the Haab’, and the Long Count to determine the character of the closing katun, and would record the prognostications of the new katun in the new k’atun book.

The k’atun-b’atab’ is documented in the colonial-era Yukatek sources and in the modern highland communities of Guatemala. In the highland K’iche’ and Kaqchikel communities, the k’atun-b’atab’ equivalent is the aj q’ij (daykeeper), who maintains the almanac and consults the day-names for the 260-day cycle. The modern aj q’ij does not maintain a k’atun book, but the k’atun sequence is preserved in the highland ritual tradition.

The katun books

The katun books were wooden codices, written in Maya hieroglyphs on bark paper coated with lime plaster, that recorded the prognostications of each katun. The k’atun books were burned at the close of each katun, and a new k’atun book was installed at the opening of the next. The k’atun books are not surviving, but their content is preserved in the Books of Chilam Balam and in the colonial-era Yukatek sources.

The Books of Chilam Balam preserve the k’atun prophecies of the colonial era, with the k’atun 4 Ajaw (the katun that began in 1697), the k’atun 8 Ajaw (the katun of the book, beginning 1618), and the k’atun 13 Ajaw (the katun of the conquest, beginning 1536) being among the most often cited. The Books of Chilam Balam are not the k’atun books themselves, but they preserve the prophetic tradition in a colonial-era form.

The katun in the inscriptions

The katun position of a Long Count date is the second-place value, between the baktun and the tun. The katun position ranges from 0 to 19, with the katun-ending being the day on which the katun position reaches 0. The katun position is written in the inscriptions with the katun glyph (a tied-bundle glyph) and a bar-and-dot coefficient.

A typical inscription reads:

9.4.0.0.0 13 Ajaw 18 K’ank’in — 4 Ahau 18 Cumku

This is the close of the 4th katun of the 9th baktun, equivalent in the GMT correlation to AD 514 and the Calendar Round position 13 Ajaw 18 K’ank’in. The date is a major event in the reign of K’inich Yax K’uk’ Mo’ at Copán, and the inscription commemorates the founding of the dynasty.

The 13-katun cycle and the “katun of the book”

The 13-katun cycle is, in the Books of Chilam Balam, the basis of the Maya historical periodization. The 13 katuns of a complete cycle are:

13 Ajaw — the opening of the cycle.
11 Ajaw — the second katun.
9 Ajaw — the third katun.
7 Ajaw — the fourth katun.
5 Ajaw — the fifth katun.
3 Ajaw — the sixth katun.
1 Ajaw — the seventh katun, the “central” katun of the cycle.
12 Ajaw — the eighth katun.
10 Ajaw — the ninth katun.
8 Ajaw — the tenth katun, the “katun of the book” in the colonial-era Yukatek sources.
6 Ajaw — the eleventh katun, the “katun of foreigners.”
4 Ajaw — the twelfth katun, the “katun of battles.”
2 Ajaw — the closing katun of the cycle.

The 13-katun cycle returns to the same starting katun after 13 × 7,200 = 93,600 days = 256.27 tropical years, and the cycle is the basis of the colonial-era Yukatek historical periodization. The “katun of the book” (k’atun 8 Ajaw, beginning 1618) is the most famous of these, marked by the imposition of colonial rule, the burning of the Maya books, and the introduction of Christianity.

The Cholan terms

The Cholan languages (Chol, Chorti, Chontal) of the Maya lowlands preserve a different katun tradition. In the Cholan sources, the katun is k’atun, and the katun-ending is k’atun b’ate’. The Cholan sources preserve a series of katun prophecies attributed to the prophet Chilam Balam, who is sometimes identified with the historical figure of the 16th-century Yukatek. The Cholan katun tradition is closely related to the Yukatek tradition, but it has distinct features, including the use of the b’atab’ (chief) as the katun-keeper.

The Cholan k’atun-b’atab’ is documented in the inscriptions of Palenque and in the colonial-era Cholan sources. The k’atun-b’atab’ of the inscriptions is sometimes identified with the historical rulers of the city, who performed the katun-ending ceremonies and recorded the prognostications of the new katun.

The k’atun-ending in the inscriptions of Palenque

The inscriptions of Palenque record several katun-endings, including:

9.8.0.0.0 — the 8th katun of the 9th baktun, equivalent to AD 593.
9.9.0.0.0 — the 9th katun of the 9th baktun, equivalent to AD 612.
9.10.0.0.0 — the 10th katun of the 9th baktun, equivalent to AD 632.
9.11.0.0.0 — the 11th katun of the 9th baktun, equivalent to AD 651.
9.12.0.0.0 — the 12th katun of the 9th baktun, equivalent to AD 672.
9.14.0.0.0 — the 14th katun of the 9th baktun, equivalent to AD 711.

The Palenque katun-endings are tied to the accessions of K’inich Janaab’ Pakal (AD 615) and his successors, and the inscriptions document the ritual responses of the court. The Palenque inscriptions are the most carefully documented katun-endings in the Classic-period Maya record.

The k’atun-ending at Tikal

The inscriptions of Tikal record the 9.0.0.0.0 baktun-ending (AD 435) and the 10.0.0.0.0 baktun-ending (AD 830) as the most significant events of the Classic period. The 9.0.0.0.0 baktun-ending is commemorated retroactively on Stela 9, and the 10.0.0.0.0 baktun-ending is documented in the inscriptions of the Terminal Classic period. The Tikal katun-endings are tied to the dynastic history of the city, and they document the long history of the dynasty from the 1st century BC to the 9th century AD.

The k’atun-ending in the Postclassic period

The Postclassic period Maya communities, including the Itza of Chichen Itza and the K’iche’ of the highland kingdoms, continued to observe the katun-endings. The Postclassic inscriptions are less elaborate than the Classic-period inscriptions, but they document a continuing tradition of katun-ending observances. The highland K’iche’ kingdom of Q’umarkaj, in particular, is documented as observing katun-endings in the late Postclassic period, with the k’atun-b’atab’ performing the central ritual role.

The k’atun-ending in the colonial era

The colonial-era katun-endings are documented in the Books of Chilam Balam and in the colonial-era Yukatek sources. The katun-endings of the colonial era include:

k’atun 13 Ajaw (1536) — the “katun of the conquest,” the period of the Spanish conquest of the Yukatek communities.
k’atun 11 Ajaw (1556) — the period of the early colonial administration.
k’atun 9 Ajaw (1576) — the period of the colonial consolidation.
k’atun 7 Ajaw (1596) — the period of the mission establishment.
k’atun 5 Ajaw (1616) — the period of the highland mission establishment.
k’atun 3 Ajaw (1636) — the period of the colonial economic consolidation.
k’atun 1 Ajaw (1655) — the period of the first major colonial-era epidemic.
k’atun 12 Ajaw (1675) — the period of the second colonial-era epidemic.
k’atun 10 Ajaw (1697) — the period of the fall of the Itza kingdom at Nojpetén.
k’atun 8 Ajaw (1717) — the “katun of the book,” the period of the colonial-era reconstruction of the Maya books.
k’atun 6 Ajaw (1737) — the period of the Bourbon reforms.
k’atun 4 Ajaw (1757) — the period of the colonial-era population decline.
k’atun 2 Ajaw (1777) — the closing of the colonial-era katun cycle.

The colonial-era katun-endings are documented in the Books of Chilam Balam and in the colonial-era Yukatek sources, and they are evidence of the continuity of the katun tradition in the colonial period.

The modern katun

The modern highland communities of Guatemala, Mexico, Belize, and Honduras do not maintain the katun tradition in the same form. The 260-day Tzolkin is the dominant cycle of the modern highland aj q’ij, and the 7,200-day katun is not a major ritual cycle. The 7,200-day katun is, however, preserved in the modern Maya calendar reform movement, and the Oxlajuj Ajpop group has used the 13-baktun completion of 2012 as a moment of cultural renewal.

The modern katun tradition is, in this respect, a survival of the Classic-period and colonial-era tradition, adapted to the modern highland practice. The Books of Chilam Balam remain a key source for the modern katun tradition, and the highland aj q’ij continue to consult the almanac texts for the katun prognostications.

The role of the katun in Maya political life

The katun was, in the Classic-period Maya, the principal political timekeeper. The 7,200-day katun was the basis of:

The political “year” of the Classic Maya court, with the katun-ending being the moment of political transition.
The dynastic cycle of the Classic Maya, with the katun-ending being the moment when a new ruler could take office.
The ritual cycle of the Classic Maya, with the katun-ending being the moment of the central ritual.

The katun-ending is documented in the inscriptions of Tikal, Palenque, Copán, Quiriguá, Calakmul, and other sites, and it is the basis of the modern chronology of the Classic Maya. The katun-ending is, in other words, the most carefully documented political event of the Classic period.

The katun and the Maya writing system

The katun is, in the Maya writing system, the most common period glyph. The katun glyph (a tied-bundle glyph) appears in every Long Count inscription with a katun position, and the glyph is one of the most recognizable elements of the Maya hieroglyphic system. The katun position is also the basis of the katun-ending inscriptions, with the k’atun b’ate’ being marked by a special glyph and a special ritual text.

The katun glyph is attested from the Late Preclassic through the Late Classic, and the glyph is one of the most consistent elements of the Maya writing system. The katun glyph is, in this respect, a key element of the Maya hieroglyphic decipherment and of the modern chronology of the Classic Maya.

Sources

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