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This article is part of a series on the
Maya civilization
Drawing of a Mayan stone carving with elaborate decoration.
History
Spanish conquest of the Maya

The Maya calendar is a system of calendars used in pre-Columbian Mesoamerica, and in many modern communities in the Guatemalan highlands,[1] Veracruz, Oaxaca and Chiapas, Mexico.[2]

The essentials of the Maya calendar are based upon a system which had been in common use throughout the region, dating back to at least the 5th century BCE. It shares many aspects with calendars employed by other earlier Mesoamerican civilizations, such as the Zapotec and Olmec, and contemporary or later ones such as the Mixtec and Aztec calendars.[3]

By the Maya mythological tradition, as documented in Colonial Yucatec accounts and reconstructed from Late Classic and Postclassic inscriptions, the deity Itzamna is frequently credited with bringing the knowledge of the calendar system to the ancestral Maya, along with writing in general and other foundational aspects of Maya culture.[4]

Overview

The Maya calendar consists of several cycles or counts of different lengths. The 260-day count is known to scholars as the Tzolkin, or Tzolk'in.[5] The Tzolkin was combined with a 365-day vague solar year known as the Haab' to form a synchronized cycle lasting for 52 Haab', called the Calendar Round. The Calendar Round is still in use by many groups in the Guatemalan highlands.[6]

A different calendar was used to track longer periods of time, and for the inscription of calendar dates (i.e., identifying when one event occurred in relation to others). This is the Long Count. It is a count of days since a mythological starting-point.[7] According to the correlation between the Long Count and Western calendars accepted by the great majority of Maya researchers (known as the Goodman-Martinez-Thompson, or GMT, correlation), this starting-point is equivalent to August 11, 3114 BCE in the proleptic Gregorian calendar or 6 September in the Julian calendar (−3113 astronomical). The GMT correlation was chosen by John Eric Sydney Thompson in 1935 on the basis of earlier correlations by Joseph Goodman in 1905 (August 11), Juan Martínez Hernández in 1926 (August 12), and Thompson himself in 1927 (August 13).[8] By its linear nature, the Long Count was capable of being extended to refer to any date far into the past or future. This calendar involved the use of a positional notation system, in which each position signified an increasing multiple of the number of days. The Maya numeral system was essentially vigesimal (i.e., base-20), and each unit of a given position represented 20 times the unit of the position which preceded it. An important exception was made for the second-order place value, which instead represented 18 × 20, or 360 days, more closely approximating the solar year than would 20 × 20 = 400 days. It should be noted however that the cycles of the Long Count are independent of the solar year.

Many Maya Long Count inscriptions contain a supplementary series, which provides information on the lunar phase, number of the current lunation in a series of six and which of the nine Lords of the Night rules.

Less-prevalent or poorly understood cycles, combinations and calendar progressions were also tracked. An 819-day Count is attested in a few inscriptions. Repeating sets of 9 days (see below "Nine lords of the night")[9] associated with different groups of deities, animals, and other significant concepts are also known.

Tzolk'in

Main article: Tzolk'in

The tzolk'in (in modern Maya orthography; also commonly written tzolkin) is the name commonly employed by Mayanist researchers for the Maya Sacred Round or 260-day calendar. The word tzolk'in is a neologism coined in Yucatec Maya, to mean "count of days" (Coe 1992). The various names of this calendar as used by precolumbian Maya peoples are still debated by scholars. The Aztec calendar equivalent was called Tonalpohualli, in the Nahuatl language.

The tzolk'in calendar combines twenty day names with the thirteen day numbers to produce 260 unique days. It is used to determine the time of religious and ceremonial events and for divination. Each successive day is numbered from 1 up to 13 and then starting again at 1. Separately from this, every day is given a name in sequence from a list of 20 day names:

Tzolk'in calendar: named days and associated glyphs
Seq.
Num. 1 		Day
Name 2 		Glyph
example 3 		16th-c.
Yucatec 4 		reconstructed
Classic Maya 5 		Seq.
Num. 1 		Day
Name 2 		Glyph
example 3 		16th-c.
Yucatec 4 		reconstructed
Classic Maya 5
01 Imix' Imix Imix (?) / Ha' (?) 11 Chuwen Chuen (unknown)
02 Ik' Ik Ik' 12 Eb' Eb (unknown)
03 Ak'b'al Akbal Ak'b'al (?) 13 B'en Ben C'klab
04 K'an Kan K'an (?) 14 Ix Ix Hix (?)
05 Chikchan Chicchan (unknown) 15 Men Men (unknown)
06 Kimi Cimi Cham (?) 16 K'ib' Cib (unknown)
07 Manik' Manik Manich' (?) 17 Kab'an Caban Chab' (?)
08 Lamat Lamat Ek' (?) 18 Etz'nab' Etznab (unknown)
09 Muluk Muluc (unknown) 19 Kawak Cauac (unknown)
10 Ok Oc (unknown) 20 Ajaw Ahau Ajaw
NOTES:
  1. The sequence number of the named day in the Tzolk'in calendar
  2. Day name, in the standardized and revised orthography of the Guatemalan Academia de Lenguas Mayas[5][10]
  3. An example glyph (logogram) for the named day. Note that for most of these several different forms are recorded; the ones shown here are typical of carved monumental inscriptions (these are "cartouche" versions)
  4. Day name, as recorded from 16th-century Yukatek Maya accounts, principally Diego de Landa; this orthography has (until recently) been widely used[10]
  5. In most cases, the actual day name as spoken in the time of the Classic Period (c. 200–900) when most inscriptions were made is not known. The versions given here (in Classic Maya, the main language of the inscriptions) are reconstructed on the basis of phonological evidence, if available; a '?' symbol indicates the reconstruction is tentative.[11]

Some systems started the count with 1 Imix', followed by 2 Ik', 3 Ak'b'al, etc. up to 13 B'en. The day numbers then start again at 1 while the named-day sequence continues onwards, so the next days in the sequence are 1 Ix, 2 Men, 3 K'ib', 4 Kab'an, 5 Etz'nab', 6 Kawak, and 7 Ajaw. With all twenty named days used, these now began to repeat the cycle while the number sequence continues, so the next day after 7 Ajaw is 8 Imix'. The repetition of these interlocking 13- and 20-day cycles therefore takes 260 days to complete (that is, for every possible combination of number/named day to occur once).

Haab'

Haab' months: names and glyphs[12] in sequence
Seq.
Num. 		Yucatec
name 		Hieroglyph
 Meaning of glyph
[13] 		Seq.
Num. 		Yucatec
name 		Hieroglyph
 Meaning of glyph
1 Pop 𝋠 10 Yax 𝋠 green[14]
2 Wo' 𝋠 11 Sak' 𝋠 white [14]
3 Sip 𝋠 12 Keh 𝋠 red [14]
4 Sotz' 𝋠 13 Mak 𝋠
5 Sek 𝋠 14 K'ank'in 𝋠
6 Xul 𝋠 15 Muwan' 𝋠
7 Yaxk'in' 𝋠 16 Pax 𝋠
8 Mol 𝋠 17 K'ayab 𝋠
9 Ch'en 𝋠 black[14] 18 Kumk'u 𝋠
19 Wayeb' 𝋠 five unlucky days
Main article: Haab'

The Haab' was made up of eighteen months of twenty days each plus a period of five days ("nameless days") at the end of the year known as Wayeb' (or Uayeb in 16th-century orthography). The five days of Wayeb' were thought to be a dangerous time. Foster (2002) writes, "During Wayeb, portals between the mortal realm and the Underworld dissolved. No boundaries prevented the ill-intending deities from causing disasters." To ward off these evil spirits, the Maya had customs and rituals they practiced during Wayeb'. For example, people avoided leaving their houses and washing or combing their hair. Bricker (1982) estimates that the Haab' was first used around 550 BCE with a starting point of the winter solstice.[15]

The Haab' month names are known today by their corresponding names in colonial-era Yukatek Maya, as transcribed by 16th-century sources (in particular, Diego de Landa and books such as the Chilam Balam of Chumayel). Phonemic analyses of Haab' glyph names in pre-Columbian Maya inscriptions have demonstrated that the names for these twenty-day periods varied considerably from region to region and from period to period, reflecting differences in the base language(s) and usage in the Classic and Postclassic eras predating their recording by Spanish sources.[16]

Each day in the Haab' calendar was identified by a day number in the month followed by the name of the month. Day numbers began with a glyph translated as the "seating of" a named month, which is usually regarded as day 0 of that month, although a minority treat it as day 20 of the month preceding the named month. In the latter case, the seating of Pop is day 5 of Wayeb'. For the majority, the first day of the year was 0 Pop (the seating of Pop). This was followed by 1 Pop, 2 Pop as far as 19 Pop then 0 Wo, 1 Wo and so on.

The Haab' year had exactly 365 days, and ignored the extra quarter of day (approximately) in the actual tropical year. This meant that the seasons moved with respect to the calendar year by a quarter of a day each year, so that the calendar months named after particular seasons no longer corresponded to these seasons after a few centuries.

Calendar Round

A Calendar Round date is a date that gives both the Tzolk'in and Haab'. This date will repeat after 52 Haab' years or 18,980 days, a Calendar Round. For example, the current creation started on 4 Ahau 8 Kumk'u. When this date recurs it is known as a Calendar Round completion.

Arithmetically, the duration of the Calendar Round is the least common multiple of 260 and 365; 18,980 is 73 × 260 Tzolk’in days and 52 × 365 Haab’ days.[17]

Not every possible combination of Tzolk'in and Haab' can occur. For Tzolk'in days Imix, Kimi, Chwen and Kib', the Haab' day can only be 4, 9, 14 or 19; for Ik', Manik', Eb' and Kab'an, the Haab' day can only be 0, 5, 10 or 15; for Akb'al', Lamat, B'en and Etz'nab', the Haab' day can only be 1, 6, 11 or 16; for K'an, Muluk, Ix and Kawak, the Haab' day can only be 2, 7, 12 or 17; and for Chikchan, Ok, Men and Ajaw, the Haab' day can only be 3, 8, 13 or 18.

Year Bearer

A "Year Bearer" is a Tzolk'in day name that occurs on the first day of the Haab'. If the first day of the Haab' is 0 Pop, then each 0 Pop will coincide with a Tzolk'in date, for example, 1 Ik'  0 Pop. Since there are twenty Tzolk'in day names and the Haab' year has 365 days (20*18 + 5), the Tzolk'in name for each succeeding Haab' zero day will be incremented by 5 in the cycle of day names like this:

1 Ik'   0 Pop
2 Manik'   0 Pop
3 Eb'   0 Pop
4 Kab'an   0 Pop
5 Ik'   0 Pop...

Only these four of the Tzolk'in day names can coincide with 0 Pop, and these four are called the "Year Bearers".

"Year Bearer" literally translates a Mayan concept.[18] Its importance resides in two facts. For one, the four years headed by the Year Bearers are named after them and share their characteristics; therefore, they also have their own prognostications and patron deities.[19] Moreover, since the Year Bearers are geographically identified with boundary markers or mountains, they help define the local community.[20]

The classic system of Year Bearers described above is found at Tikal and in the Dresden Codex. During the Late Classic period a different set of Year Bearers was in use in Campeche. In this system, the Year Bearers were the Tzolk'in that coincided with 1 Pop. These were Ak'b'al, Lamat, B'en and Edz'nab. During the Post-Classic period in Yucatán a third system was in use. In this system the Year Bearers were the days that coincided with 2 Pop: K'an, Muluc, Ix and Kawak. This system is found in the Chronicle of Oxkutzcab. In addition, just before the Spanish conquest in Mayapan the Maya began to number the days of the Haab' from 1 to 20. In this system the Year Bearers are the same as in the 1 Pop – Campeche system. The Classic Year Bearer system is still in use in the Guatemalan highlands[21] and in Veracruz, Oaxaca and Chiapas, Mexico.[22]

Long Count

East side of stela C, Quirigua with the mythical creation date of 13 baktuns, 0 katuns, 0 tuns, 0 uinals, 0 kins, 4 Ahau 8 Cumku – August 11, 3114 BCE in the proleptic Gregorian calendar.
Main article: Mesoamerican Long Count calendar

Since Calendar Round dates repeat every 18,980 days, approximately 52 solar years, the cycle repeats roughly once each lifetime, so a more refined method of dating was needed if history was to be recorded accurately. To specify dates over periods longer than 52 years, Mesoamericans used the Long Count calendar.

The Maya name for a day was k'in. Twenty of these k'ins are known as a winal or uinal. Eighteen winals make one tun. Twenty tuns are known as a k'atun. Twenty k'atuns make a b'ak'tun.

The Long Count calendar identifies a date by counting the number of days from the Mayan creation date 4 Ahaw, 8 Kumk'u (August 11, 3114 BC in the proleptic Gregorian calendar or September 6 in the Julian calendar -3113 astronomical dating). But instead of using a base-10 (decimal) scheme like Western numbering, the Long Count days were tallied in a modified base-20 scheme. Thus 0.0.0.1.5 is equal to 25, and 0.0.0.2.0 is equal to 40. As the winal unit resets after only counting to 18, the Long Count consistently uses base-20 only if the tun is considered the primary unit of measurement, not the k'in; with the k'in and winal units being the number of days in the tun. The Long Count 0.0.1.0.0 represents 360 days, rather than the 400 in a purely base-20 (vigesimal) count.

There are also four rarely used higher-order cycles: piktun, kalabtun, k'inchiltun, and alautun.

Since the Long Count dates are unambiguous, the Long Count was particularly well suited to use on monuments. The monumental inscriptions would not only include the 5 digits of the Long Count, but would also include the two tzolk'in characters followed by the two haab' characters.

Misinterpretation of the Mesoamerican Long Count calendar was the basis for a popular belief that a cataclysm would take place on December 21, 2012. December 21, 2012 was simply the day that the calendar went to the next b'ak'tun, at Long Count 13.0.0.0.0. The date on which the calendar will go to the next piktun (a complete series of 20 b'ak'tuns), at Long Count 1.0.0.0.0.0, will be on October 13, 4772.

Sandra Noble, executive director of the Mesoamerican research organization Foundation for the Advancement of Mesoamerican Studies, Inc. (FAMSI), notes that "for the ancient Maya, it was a huge celebration to make it to the end of a whole cycle". She considers the portrayal of December 2012 as a doomsday or cosmic-shift event to be "a complete fabrication and a chance for a lot of people to cash in."[23]

Table of Long Count units
Long Count
unit		 Long Count
period		 Days Approximate
Solar Years
1 K'in   1  
1 Winal 20 K'in 20  
1 Tun 18 Winal 360 1
1 K'atun 20 Tun 7,200 20
1 B'ak'tun 20 K'atun 144,000 394
1 Piktun 20 B'ak'tun 2,880,000 7,885
1 Kalabtun 20 Piktun 57,600,000 157,704
1 K'inchiltun 20 Kalabtun 1,152,000,000 3,154,071
1 Alautun 20 K'inchiltun 23,040,000,000 63,081,429

Supplementary Series

Many Classic period inscriptions include a series of glyphs known as the Supplementary Series. The operation of this series was largely worked out by John E. Teeple (1874–1931). The Supplementary Series most commonly consists of the following elements:

Lords of the Night

Main article: Lords of the Night

Each night was ruled by one of the nine lords of the underworld. This nine-day cycle was usually written as two glyphs: a glyph that referred to the Nine Lords as a group, followed by a glyph for the lord that would rule the next night.

Lunar Series

A lunar series generally is written as five glyphs that provide information about the current lunation, the number of the lunation in a series of six, the current ruling lunar deity and the length of the current lunation.

Moon age

The Maya counted the number of days in the current lunation. They used two systems for the zero date of the lunar cycle: either the first night they could see the thin crescent moon or the first morning when they could not see the waning moon.[24] The age of the moon was depicted by a set of glyphs that mayanists coined glyphs D and E:

  • A new moon glyph was used for day zero in the lunar cycle.
  • D glyphs were used for lunar ages for days 1 through 19, with the number of days that had passed from the new moon.
  • For lunar ages 20 to 30, an E glyph was used, with the number of days from 20.

Count of Lunations

The Maya counted the lunations. This cycle appears in the lunar series as two glyphs that modern scholars call the 'C' and 'X' glyphs. The C glyph could be prefixed with a number indicating the lunation. No prefixing number meant one, whereas the numbers two through six indicated the other lunations.[25][26] There was also a part of the C glyph that indicated where this fell in a larger cycle of 18 lunations. Accompanying the C glyph was the 'X' glyph that showed a similar pattern of 18 lunations.[27][28]

Lunation length

The present era lunar synodic period is about 29.5305877 mean solar days or about 29 days 12 hours 44 minutes and 2+7/9 seconds. As a whole number, the number of days per lunation will be either 29 or 30 days, with the 30-day intervals necessarily occurring slightly more frequently than the 29-day intervals. The Maya wrote whether the lunar month was 29 or 30 days as two glyphs: a glyph for lunation length followed by either a glyph made up of a moon glyph over a bundle with a suffix of 9 for a 29-day lunation or a moon glyph with a suffix of 10 for a 30-day lunation. Since the Maya didn't use fractions, lunations were approximated by using the formula that there were 149 lunations completed in 4400 days, which yielded a rather short mean month of exactly 4400/149 = 29+79/149 days = 29 days 12 hours 43 minutes and 29+59/149 seconds, or about 29.5302 days.[29]

819-day count

Some Mayan monuments include glyphs that record an 819-day count in their Initial Series. These can also be found in the Dresden codex.[30] This is described in Thompson.[31] More examples of this can be found in Kelley.[32] Each group of 819 days was associated with one of four colors and the cardinal direction with which it was associated — black corresponded to west, red to east, white to north, and yellow to south.

The 819-day count can be described several ways: Most of these are referred to using a "Y" glyph and a number. Many also have a glyph for K'awill — the god with a smoking mirror in his head. K'awill has been suggested as having a link to Jupiter.[33] In the Dresden codex almanac 59 there are Chaacs of the four colors. The accompanying texts begin with a directional glyph and a verb for 819-day-count phrases. Anderson[34] provides a detailed description of the 819-day count.

Short Count

During the late Classic period the Maya began to use an abbreviated short count instead of the Long Count. An example of this can be found on altar 14 at Tikal.[35] In the kingdoms of Postclassic Yucatán, the Short Count was used instead of the Long Count. The cyclical Short Count is a count of 13 k'atuns (or 260 tuns), in which each k'atun was named after its concluding day, Ahau ('Lord'). 1 Imix was selected as the recurrent 'first day' of the cycle, corresponding to 1 Cipactli in the Aztec day count. The cycle was counted from katun 11 Ahau to katun 13 Ahau, with the coefficients of the katuns' concluding days running in the order 11 – 9 – 7 – 5 – 3 – 1 – 12 – 10 – 8 – 6 – 4 – 2 – 13 Ahau (since a division of 20 × 360 days by 13 falls 2 days short). The concluding day 13 Ahau was followed by the re-entering first day 1 Imix. This is the system as found in the colonial Books of Chilam Balam. In characteristic Mesoamerican fashion, these books project the cycle onto the landscape, with 13 Ahauob 'Lordships' dividing the land of Yucatán into 13 'kingdoms'.[36]

See also

Notes

  1. ^ Tedlock, Barbara, Time and the Highland Maya Revised edition (1992 Page 1) "Scores of indigenous Guatemalan communities, principally those speaking the Mayan languages known as Ixil, Mam, Pokomchí, and Quiché, keep the 260-day cycle and (in many cases) the ancient solar cycle as well (chapter 4)."
  2. ^ Miles, Susanna W, "An Analysis of the Modern Middle American Calendars: A Study in Conservation." In Acculturation in the Americas. Edited by Sol Tax, p. 273. Chicago: University of Chicago Press, 1952.
  3. ^ "Maya Calendar Origins: Monuments, Mythistory, and the Materialization of Time".
  4. ^ See entry on Itzamna, in Miller and Taube (1993), pp.99–100.
  5. ^ a b Academia de las Lenguas Mayas de Guatemala (1988). Lenguas Mayas de Guatemala: Documento de referencia para la pronunciación de los nuevos alfabetos oficiales. Guatemala City: Instituto Indigenista Nacional.. For details and notes on adoption among the Mayanist community, see Kettunen & Hemke (2005), p. 5
  6. ^ Tedlock (1992), p. 1
  7. ^ "Mythological" in the sense that when the Long Count was first devised sometime in the Mid- to Late Preclassic, long after this date; see e.g. Miller and Taube (1993, p.50).
  8. ^ Voss (2006, p.138)
  9. ^ See separate brief Wikipedia article Lords of the Night
  10. ^ a b Kettunen and Helmke (2011)，Different Tzolk'in date of name, pp.58–59
  11. ^ Classic-era reconstructions are as per Kettunen and Helmke (2005), pp.45–46..
  12. ^ Kettunen and Helmke (2005), pp.47–48
  13. ^ These names come from de Landa's description of the calendar, and they are commonly used by Mayanists, but the Classic Maya did not use these actual names for the day signs. The original names are unknown. See Coe, Michael D.; Mark L Van Stone (2005). Reading the Maya Glyphs. London: Thames & Hudson. p. 43. ISBN 978-0-500-28553-4.
  14. ^ a b c d Coe, Michael D.; Mark L Van Stone (2005). Reading the Maya Glyphs. London: Thames & Hudson. p. 43. ISBN 978-0-500-28553-4.
  15. ^ Zero Pop actually fell on the same day as the solstice on 12/27/−575, 12/27/−574, 12/27/−573, and 12/26/−572 (astronomical year numbering, Universal Time), if you don't account for the fact that the Maya region is in roughly time zone UT−6. See IMCCE seasons. Archived August 23, 2012, at the Wayback Machine
  16. ^ Boot (2002), pp.111–114.
  17. ^ For further details, see Thompson 1966: 123–124
  18. ^ Thompson 1966: 124
  19. ^ For a thorough treatment of the Year Bearers, see Tedlock 1992: 89–90; 99–104 and Thompson 1966
  20. ^ See Coe 1965
  21. ^ Tedlock 1992: 92
  22. ^ Miles, Susanna W, "An Analysis of the Modern Middle American Calendars: A Study in Conservation." In Acculturation in the Americas. Edited by Sol Tax, pp. 273–84. Chicago: University of Chicago Press, 1952.
  23. ^ As quoted in USA Today (MacDonald 2007).
  24. ^ Thompson, J. Eric S. Maya Hieroglyphic Writing, 1950 Page 236
  25. ^ Teeple 1931:53
  26. ^ Thompson Maya Hieroglyphic Writing 1950:240
  27. ^ Linden 1996:343–356.
  28. ^ Schele, Grube, Fahsen 1992
  29. ^ Teeple 1931:67
  30. ^ Grofe, Michael John 2007 The Serpent Series: Precession in the Maya Dresden Codex page 55 p.206
  31. ^ Maya Hieroglyphic Writing 1961 pp. 212–217
  32. ^ Decipherment of Maya Script , David Kelley 1973 pp.56—57
  33. ^ Star Gods of the Maya Susan Milbrath 1999, University of Texas Press
  34. ^ "Lloyd B. Anderson The Mayan 819-day Count and the "Y" Glyph: A Probable association with Jupiter". Traditional High Cultures Home Page. Archived from the original on 2015-05-06. Retrieved March 30, 2015.
  35. ^ Coe, William R. 'TIKAL a handbook of the ancient Maya Ruins' The University Museum of the University of Pennsylvalia, Philadelphia, Pa. 1967 p. 114
  36. ^ Roys 1967: 132, 184–185

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Teeple, John E. (November 1931). "Maya Astronomy". Contributions to American Archaeology. Vol. Volume I (Pub. 403 ed.). Washington D.C.: Carnegie Institution of Washington. pp. 29–116. {{cite book}}: |volume= has extra text (help); External link in |chapterurl= (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)
Popol Vuh: The Definitive Edition of the Mayan Book of the Dawn of Life and the Glories of Gods and Kings. with commentary based on the ancient knowledge of the modern Quiché Maya. New York: Simon & Schuster. 1985. ISBN 0-671-45241-X. OCLC 11467786. {{cite book}}: Unknown parameter |editors= ignored (|editor= suggested) (help)CS1 maint: others (link)
Thomas, Cyrus (1897). "Day Symbols of the Maya Year". In J. W. Powell (ed.). Sixteenth Annual Report of the Bureau of American Ethnology to the Secretary of the Smithsonian Institution, 1894–1895 (EBook online reproduction). Washington DC: Bureau of American Ethnology, Smithsonian Institution; U.S. Government Printing Office. pp. 199–266. OCLC 14963920 – via Project Gutenberg. {{cite book}}: External link in |chapterurl= (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)[dead link]
Thompson, J. Eric S. (1960). Maya Hieroglyphic Writing: An Introduction. Civilization of the American Indian Series, No. 56 (3rd ed.). Norman: University of Oklahoma Press. ISBN 0-8061-0447-3. OCLC 275252.
Landa's Relación de las cosas de Yucatán: a translation. Papers of the Peabody Museum of American Archaeology and Ethnology, Harvard University vol. 18. Charles P. Bowditch and Ralph L. Roys (additional trans.) (translation of Diego de Landa's Relación de las cosas de Yucatán [original c. 1566], with notes, commentary, and appendices incorporating translated excerpts of works by Gaspar Antonio Chi, Tomás López Medel, Francisco Cervantes de Salazar, and Antonio de Herrera y Tordesillas. English ed.). Cambridge, MA: Peabody Museum of Archaeology and Ethnology. 1941. OCLC 625693. {{cite book}}: Unknown parameter |editors= ignored (|editor= suggested) (help)CS1 maint: others (link)
Voss, Alexander (2006). "Astronomy and Mathematics". In Nikolai Grube (ed.). Maya: Divine Kings of the Rain Forest. Eva Eggebrecht and Matthias Seidel (assistant eds.). Cologne, Germany: Könemann. pp. 130–143. ISBN 978-3-8331-1957-6. OCLC 71165439.
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