The Tzolk’in — Sacred 260-Day Calendar of the Maya

The Tzolk’in is the 260-day sacred almanac that, together with the 365-day Haab’ and the Long Count, forms the heart of the Maya calendar system. Its name derives from the Yukatek Maya tzol (to count) and k’in (day), and colonial Yukatek sources render it ch’ol k’ij, “the ordering of days.” Twenty named day-signs paired with a numerical coefficient running 1 through 13 generate a 260-day cycle, after which the same combinations begin again. The Tzolk’in has no month, no year, and no astronomical anchor; it is, in the strict sense, a divinatory almanac. A daykeeper consulting it for a birth, a marriage, a planting, or a royal accession could identify the day-sign, the trecena, the veyene, and the presiding spirit, and from these determine the character of the day.

This page describes the structure of the Tzolk’in, its twenty day-names, its subdivision into named periods, and the way the cycle was used in Classic-period inscriptions and in modern living Maya practice.

The mathematical structure

The cycle arises from the coprimality of 13 and 20. Each day advances both the numerical coefficient (mod 13) and the day-sign (mod 20). Because 13 and 20 are coprime, the cycle has length 13 × 20 = 260 days, and no shorter sub-cycle returns to the same combination of name and number. A given day-sign appears 13 times per 260-day cycle, and any given day-sign-and-coefficient combination — for example, 1 Ajaw, the most sacred seat in the cycle — appears only once per cycle.

The Tzolk’in is sometimes compared to a perpetual calendar with 20 weekday-names that march through a 13-position numerical odometer; the visual analogy is exact, and the cycle length is 260 because that is the smallest number at which both wheels return to their starting position simultaneously.

The twenty day-names

The 20 Tzolk’in day-names are the load-bearing glyphs of the almanac. Listed in their canonical order, they are:

Imix — water-lily, primordial pond, the female generative principle
Ik’ — wind, breath, life force, the soul-substance
Ak’bal — darkness, the house of night, the interior of the earth
K’an — yellow maize ear, abundance, the yaxche’ tree
Chikchan — celestial serpent, the sky-band, the rainbow
Kimi — death, the closed bundle, the ancestor
Manik’ — the deer’s foreleg, the hunter’s hand
Lamat — the rabbit, the planet Venus, the young leaf
Muluk — water, the rains, the ch’ulel (animating essence) of water
Ok — the dog, the storm, the leg of the journey
Chuwen — the monkey, the trickster-artisan, the spinning bat
Eb’ — the road, the rough path, the ch’ol (broom)
Ben — the reed, the cosmic axis, the mat-reed
Hix — the jaguar, the night sun, the spotted one
Men — the moon, the elder of the sky, the wise lunar deity
K’ib’ — the vulture, the transformed soul, the foul-smelling
Kab’an — the earth, the earthquake, the bent-stone
Etz’nab’ — the flint, the mirror, the obsidian blade
Kawak — the storm, the K’awill (storm-god), the rain-bringing serpent
Ajaw — the lord, the sun, the king, the K’uhul Ajaw (Holy Lord)

The order is fixed and universal across the Maya area. The same sequence appears in the Classic-period inscriptions at Palenque, Copán, Tikal, Quiriguá, and the highland codices. Modern highland daykeepers in the K’iche’ and Kaqchikel communities use the same sequence under K’iche’an names, and the Yukatek Chilam Balam books preserve the same order in colonial orthography.

The thirteen numerical coefficients

The numerical coefficient is a number from 1 to 13. After 13 the count returns to 1. The pairing of number and day-sign produces 260 unique combinations; a particular day-sign repeats with a particular number 13 times in the cycle, and the same number appears with each day-sign in turn. The most sacred combination is 1 Ajaw, which in the Long Count corresponds to the base date 4 Ajaw 8 Kumk’u. 13 Ajaw is the close of any 260-day almanac.

The numbers themselves are not merely ordinal; they are charged with directional and color associations. Each number has a preferred direction, a preferred color, and a presiding deity. The daykeeper reading a child’s birth on, say, 8 K’an, would note that 8 is the cardinal number of the West (in some traditions) and that K’an is the maize sign; the child’s path would be read from the combined meaning.

Trecenas and veyenes

The 260-day cycle is divided into 20 named periods in two ways:

Trecenas (ch’ol k’ij in some sources, trecena in colonial Yucatec): 13-day periods each beginning with 1 of a day-sign. There are 20 trecenas in the cycle. The 13 days of a trecena form a sequence of omens, with the 13th day — the Ajaw position of the trecena — bearing the principal message. Classic-period almanac pages typically lay out one trecena at a time, with the glyphs of the 13 days and a short prophetic text for each.
Veyenes (or veintenas): 20-day periods each beginning with a day-sign. There are 13 veyenes in the cycle. Each veyene has a presiding spirit and a set of prognostications. The Books of Chilam Balam preserve the 13 veyenes in their colonial spelling, and some modern highland daykeepers continue to read the 13 veyenes as ritual texts.

A trecena begins on a 1-day and ends on a 13-day; a veyene begins on a day-sign and ends on the next occurrence of the same day-sign 20 days later. The two systems mesh: the 1st, 8th, and 15th days of any 26-day span, for example, are all the same day-sign, and the daykeeper can read either sub-structure as a way of fragmenting the cycle for almanac consultation.

The role of the aj q’ij in modern practice

In modern K’iche’, Kaqchikel, and Tz’utujil communities of highland Guatemala, the aj q’ij (literally “he of the day,” the equivalent of the Classic ah k’in) maintains a 260-day ch’ol k’ij on a wooden board with seeds or pegs. The board is laid out at the family altar, and the aj q’ij consults it before naming a child, scheduling a marriage, or selecting a planting day. Modern highland aj q’ij sometimes keep a k’ex (change) day count to track the rotation, and they preserve almanac texts in K’iche’an orthography in small Maya codices that survive in family libraries.

The highland daykeepers trace their tradition to pre-conquest practice and reject the use of the day-names as “Maya zodiac” in popular Western almanacs. The day-names are spirits, not constellations, and the cycle is a way of structuring ritual life, not of dividing the sky.

Tzolk’in day-names in the inscriptions

Every Classic-period Long Count date is followed in the inscription by a Tzolk’in position. The standard format is Coefficient Day-Sign, e.g., 9 Ik’ 5 K’an, read as “9 Ik’, the 5 K’an.” This is the daykeeper’s k’in (the sun, the day) and is the binding element between the Long Count and the divinatory almanac.

The most sacred seat in the almanac is 1 Ajaw, the only position in the cycle that does not appear as a Long Count base date for a 13-baktun completion; the base date 4 Ajaw 8 Kumk’u corresponds to 1 Ajaw’s fourth occurrence in a 260-day cycle. The 1 Ajaw day is the day on which the Hero Twins, in the Popol Vuh creation account, were celebrated in their ascent to the sun and the moon, and it is the day of royal accessions, with Tikal Stela 29, Copán Stela N, and a number of Palenque panels recording the king’s accession on 1 Ajaw.

Tzolk’in positions and the k’atun names

In colonial Yukatek sources, the k’atun names are derived from the Tzolk’in positions of the k’atun-ending days. The k’atun ending on 13 Ajaw is, for example, called 13 Ajaw k’atun; the next k’atun, 7,200 days later, is 11 Ajaw k’atun (because 260 days later, the next Ajaw position in the cycle is 11). The k’atun 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 — is the basis of the katun prophecies in the Books of Chilam Balam.

The numerology of the sequence is exact: because the k’atun is 7,200 days, and 7,200 = 27 × 260 + 180, the Tzolk’in position of the k’atun ending advances by 180 days, or 8 trecenas, each time. After 13 k’atun endings, the position has advanced by 13 × 180 = 2,340 days, or 9 complete 260-day cycles, returning the k’atun-ending day to its starting Tzolk’in position.

The almanac in the codices

The Dresden Codex preserves 65 almanac pages, each presenting a trecena of 13 days with a prognostic text and a deity image. The almanacs include the 1 Lamat, 1 Ben, 1 Etz’nab’, 1 Ajaw, 1 Imix, 1 K’an, 1 Kawak, 1 K’ib’, 1 Chikchan, 1 Men, 1 Ok, 1 Hix, 1 Kab’an, 1 Ak’bal, 1 Muluk, 1 Eb’, 1 Manik’, 1 Chuwen, 1 Kimi, and 1 K’awill sequences. Each almanac is a self-contained text: the daykeeper opens the almanac to the relevant trecena and reads the prognostic for the day in question.

The Madrid Codex contains similar almanacs in its “Maya almanac” section, and the Paris Codex preserves a series of 11 trecenas on its surviving pages. The Grolier Codex (also called the Maya Codex of Mexico) is heavily damaged but its almanac content is consistent with the Dresden and Madrid.

The 260-day cycle and the agricultural year

The exact origin of the 260-day length is debated. Several hypotheses have been proposed:

The nine-month human gestation period (260 = 9 × 29 + 13, an approximation to a gestation of 38 weeks).
The interval between zenith-passage days at Copán (where the two passages are 260 days apart, although the calculation is approximate).
The minimum number of days required to fit a 13 and a 20 coprime.
The period of the K’awill cycle tied to the storm-god ritual.

None of these hypotheses is decisive. The 260-day cycle is attested in Zapotec, Mixtec, and Aztec ritual practice as well, and the cycle appears to be a pan-Mesoamerican institution by the Late Preclassic. The Maya Tzolk’in, however, is the most elaborately developed form of the cycle in the surviving record.

Tzolk’in positions and the 819-day cycle

The 819-day cycle (819 = 3 × 273 = 7 × 117) returns to the same Tzolk’in position only after 819 days, not 260. The 819-day cycle is a “super-Tzolk’in” that rotates through the four cardinals and four colors three times, and it is attested in the inscriptions of Caracol, Naranjo, and a handful of other Late Classic sites. The 819-day cycle is mathematically tied to the 260-day cycle: 819 ÷ 260 = 3.15, and 3 × 260 = 780, with 39 days of correction to complete the rotation.

The 20 named day-signs in the Popol Vuh and the inscriptions

The 20 day-signs appear as characters in the Popol Vuh creation account. The Hero Twins’ ascent to the sky occurs on 1 Ajaw; their defeat of the Xibalba lords is dated to specific days; the maize is created on a specific day-sign that is read in the same almanac. The 20 day-names are not interchangeable, and the choice of day-sign in a narrative is theologically significant.

In the Classic-period inscriptions, the 20 day-signs are written with full glyphs that are nearly identical to the almanac glyphs in the codices. The glyphs are: a water-lily for Imix, a T-shape for Ik’, a half-darkened glyph for Ak’bal, a yellow maize-ear for K’an, a serpent-head for Chikchan, a death’s-head for Kimi, a deer’s-leg for Manik’, a rabbit’s-head for Lamat, a water-shell for Muluk, a dog’s-head for Ok, a monkey’s-head for Chuwen, an open road for Eb’, a reed-bundle for Ben, a jaguar’s-head for Hix, an elder’s-face for Men, a vulture’s-head for K’ib’, an earth-face for Kab’an, a flint-blade for Etz’nab’, a storm-face for Kawak, and a king’s-face for Ajaw.

The sacred character of the day-names

The day-names are not just labels; they are spirits, deities, and ancestors. The daykeeper reading a child’s birth on 5 K’an (the fifth of the 13 days of a K’an trecena) would note that K’an is the maize spirit, the patron of abundance, the bringer of green growth, and that the 5 indicates a particular cardinal and color. The child would be named accordingly, with a day-name (sometimes the Tzolk’in day itself, sometimes a K’iche’-style compound) that would function as a personal name for life.

The 13-trecena sequence is the basic unit of almanac reading. Each trecena has a presiding spirit, a color, a direction, a deity, and a set of prognostications. The first day of the trecena is 1 of a day-sign; the 13th is 13 of the same day-sign, and the 13th is the most important position. The 13-day cycle is itself 13 days because the coefficient odometer returns to 1 every 13 days.

The Tzolk’in and the eclipse tables

The Tzolk’in positions are used as column headers in the Dresden eclipse table. The 405-lunar-month table (11,960 days) divides into 46 6-month eclipse half-years, and each entry in the table is keyed to a Tzolk’in position that allows the daykeeper to determine whether a given eclipse is solar or lunar, visible or invisible, dangerous or routine. The Tzolk’in is the indexing system of the entire astronomical apparatus.

The Tzolk’in and the 52-year cycle

The 18,980-day Calendar Round — the cycle of the combined Haab’-Tzolk’in — is 73 Tzolk’in cycles long. A given 18,980-day span contains exactly 73 complete Tzolk’in cycles and 52 Haab’ years. The 52-year cycle is the smallest time after which a given combined Calendar Round position (Haab’ day + Tzolk’in day) recurs, and the Tzolk’in’s role as the indexing system of the Calendar Round makes it the binding element of the entire 18,980-day rhythm.

The 260-day cycle and modern festival calendars

The 260-day cycle continues to structure modern highland ritual life. The 1 Ajaw day, falling roughly every 260 days, is marked in some highland communities with a community ceremony and the consultation of the aj q’ij. The 13-day trecenas are sometimes mapped onto the Christian liturgical calendar (with the trecena starting on 1 Imix aligned to a feast of the Virgin, for example), and the modern syncretic calendar is a complex system in which the Tzolk’in remains the dominant cycle. The daykeepers’ councils in the highland communities have, since the late twentieth century, coordinated a unified Tzolk’in calendar for the highland communities of Guatemala, with the result that the modern aj q’ij calendar is one of the most consistent ritual timekeeping systems in the world.

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