Note on the Maya Calendar
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Introductory Glyph
9 Baktun
16 Katun
Zero Tun
2 Winal
Zero K'in
3 Ahaw (Tzolk'in)
13 Yaxk'in (Haab)

See  a collection of calendar glyphs from  
Nancy McNelly's Rabbit in the Moon  

The Maya calendar includes (1) The long count, which measures time elapsed since the creation of the world, and (2) The calendar round,  which combines dates in a 260 day cycle, called the tzolk'in,  and a 365 day year, the haab.
 
Long Count  glyphs represent periods of time. 
k'in = day
winal = 20 day month
tun =  360 day long count year (18 winal)
katun = 7200 days (20 tun)
baktun = 144000 days (20 katun)
The periods are listed from largest to smallest in the inscriptions. Each period glyph is preceded by a number,  usually written in "dot and bar" form: Bar = 5, and  dot = 1. Zero is indicated by a "shell" glyph.  The first numbered glyph here reads 9 baktun. It counts 9 x 144000 = 1296000 days since creation.  The long count is the sum of  the multiples of each of the five periods. 
The example can written (in the short-hand used by Mayanists) from baktun to k'in as 9.16.0.2.0.  This is a total count of   (9 x 144,000) + (16 x 7200) + (0 x 360) + (2 x 20) +  (0 x 1) = 1411240 days.


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Quirigua Stela C
Records creation date
The beginning of the long count was within a day or two of 13 August, 3114 BC.  Converting a long count to a Gregorian calendar date is straightforward, but requires a lot of arithmetic.  9.16.0.2.0 correlates to 18 June 751 AD. Calendar conversion programs are quite useful because they do the tedious arithmetic required to find an exact correlation. 
Impress your friends & family --- Rough conversions can be done without much calculation. The completion of baktun 9, the long count 9.0.0.0.0, occurred in 435 AD.  Most long count dates are within about 20 katuns from this date. The katun is a bit less than 20 years, and the tun is about a year.  Using these approximations to "up date" or "back date" from 435 AD will produce conversions accurate to within a few years. Our example is about 16 katuns, a bit less than 320 years, after 9.0.0.0.0. 
Almost all Mayanists agree that the base date of the long count is in 3114 BC, but there are three versions of the accepted GMT correlation, placing creation on either August 11, 12, or 13.  The "August 13" version is used in these web pages, but merely for consistency. The "August 11" correlation is preferred by nearly as many scholars as the "August 13" version.

Almost all long counts record dates in the Classical period of Maya civilization (200 -900 AD),  baktun counts 8 to 10.  The dates carved on free-standing monuments called stelae usually record events in the lives of rulers: Birth, coronation, marriage, rituals performances, death, and occasionally historical events such as wars and dedication of buildings. Long counts also appear in the Dresden Codex, a Maya glyph book. Although it was written in the post-Classical period (c. 1200 AD), the dates of astronomical tables in the codex are Classical. 

A few monuments memorialize events of the mythic age. In these texts, creation is written 13.0.0.0.0 rather than 0.0.0.0.0, suggesting that the present age followed an earlier world that endured 13 baktuns. A monument at Coba records even earlier epochs, counting back for some 13 x 2021 years (see more about this  number at the Tzuk-Te website).  If the present age also lasts 13 baktun,  the current cycle of the long count will be completed when the count again reaches 13.0.0.0.0, in 2012. 
 

The "period end" glyph (left) is used with period glyphs to mark the end of a complete period. Period end rituals (particularly katun ends) are frequently recorded in the inscriptions.  On Quirigua Stela C, it is used in place of zero  to mark completion of  katun, tun and  k'in  periods.


 
 
Quirigua Stela C

 

LONG COUNT CALCULATOR
Convert long count to European calendar date


Enter Long Count...... Baktun   Katun   Tun   Winal   Kin ..

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Year
Month 
Day
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Convert European Calendar date to Long Count
This date converter is written in Java Script, and uses the 13 Aug 3114 BC version of the GMT correlation.  It is valid for dates AD and BC, but  dates before AD are reported as negative numbers, using the astronomer's convention  3114 BC = - 3113 (This is required because there is no "0"  BC/AD).  All dates are reported  in the Gregorian Calendar. 

Download a full-featured converter, The Burden of Time  free-ware Maya calendar program,  at this web-site.



 
9.16.0.2.0
Long count glyphs: Inscriptions almost always begin with a long count called the "initial series" date.  This date is introduced by a distinctive "initial series introductory glyph" (ISIG), followed by the period glyphs and numbers. Period glyphs are usually "head" types, as at the left. Glyphs are usually written in two columns,  and read from left to right in each row, but in some inscriptions, the date is written in a single row. 

The "head" style glyphs are rather variable in detail. More abstract "symbol" type period glyphs are also encountered. But since the periods are always listed in order from baktun to k'in, they can be read even if they are not individually recognizable. 

Here  is another example of a long count, using the symbol forms of the period glyphs. It counts 1394815 days, and correlates to 29 June 706 AD: 

In the Dresden Codex, the only Maya glyph book that includes long counts, the introductory and period glyphs are omitted. The number glyphs are in a single column, and the order in which they are written is enough to determine their meaning. The codex style date at the right reads 9.16.0.2.0. Note the distinctive codex form of the zero glyph. 

The long count is actually a modified base 20 number system: All periods except the tun are 20 times the previous period. The Maya used place holding arithmetic and the concept of zero before they were invented in the Old World.

 

See examples of period glyphs  in both  symbol and head styles from  Nancy McNelly's Rabbit in the Moon.  Examples of numbers  (also from Rabbit in the Moon) in both the usual "dot and bar" style, and  less common, harder to decipher "head" types:  (0-6) (7-13) (13-19).  See an example of elaborate, but rare, "full figure" number and period glyphs from a  Palenque inscription   at Mesoweb).
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Origin of the long count: During the  Classical period (200-900 AD), only the Maya kept the long count, but it appears to have been invented by late pre-Classical  peoples on the western border of the Maya area.  The oldest known example is Chiapa de Corzo Stela 2, dated to 32 BC.  Maya civilization emerged during the pre-Classical, perhaps as early as 400 BC,   but the earliest long count that is unequivocally Maya is early Classical, found on Tikal stelae 29.  It is inscribed with the long count 8.12.14.8.15 =  292 AD. 

The base date was almost certainly set in late summer  for astronomical reasons.  In Maya Cosmos, Linda Schele noted that in mid-August, the Milky Way rises high in the sky.  This likely represents the "World Tree" or "Raised Up Sky" (Wakah chan) in Classical Creation accounts. See The Maya Creation Myth and the Milky Way  at this web site.  Vincent Malmström suggests that August 13 was chosen as the base date because the sun is at the zenith on this date at Izapa, an important pre-Classical site in Chiapis, where he argues the Maya calendar originated.  See Malmström's theory of calendrical origins on-line.

Whether there is also astronomical significance in the choice of 3114 BC as the base date is more debatable.  Victoria Bricker has pointed out that if the base date is 11 Aug 3114 BC,  the current "great cycle" of the long count will end on the winter solstice ( LC 13.0.0.0.0 =  21 Dec 2012).  She suggests that the base date was chosen so the LC  would end on the solstice.  John Major Jenkins has elaborated this theory.  Due to precession of the equinoxes, in the early 21st century  the position of the sun at the solstice moves into the centre of the Milky Way.  He suggests that this ties completion of the long count cycle to the creation symbolism associated with the beginning of the count.  However, whether the Maya were aware of precession  is still regarded by many archaeoastronomers as an open question.  See Jenkins,  The How and Why of the Mayan End Date in 2012 AD on-line.

A rival theory of the origin of the long count was proposed by John Teeple in 1930, and recently revived by Malmström.  This theory assumes that the inventors of the Long count would have chosen a base date that was both a full number of katuns and a full number of haabs, approximate solar years, in the past.  The LC base date  was on the haab date 8 Kumk'u.  Thus the long count would have been introduced on  a zero katun count that fell on 8 Kumk'u.  Because katuns end on a particular haab date only once every 73 katuns, the only likely candidate is LC  7.6.0.0.0  = 14 September 236 BC.  Earlier 8 Kumk'u katun ends occurred  before the rise of Mesoamerican civilization, and later examples are long after the LC appeared in inscriptions.  If this explanation of the base date is correct, 3114 BC has no astronomical meaning.  See Malmström,  The Astronomical Insignificance of 13.0.0.0.0. on-line
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Long count names:  The last initial series was recorded at Tonina, on  10.4.0.0.0 (20 Jan 909 AD).  Since it was no longer in use when the Spanish arrived, we are uncertain about some LC terminology.  Only the period names katun, winal, and kin are known with assurance. Tun is a Yucatec word for "year,"   but both LC and calendar round "years" seem to have sometimes been called haab. Baktun is only a plausible Yucatec name.  Linda Schele noted that  the phonetic value of the symbol form of the baktun glyph is pi.  The ISIG glyph has recently been read tzik haab’, "the count of years." 
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ISIG
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The tzolk'in  is a cycle of 260 days. Each day in the cycle is identified by both a day number and a day name glyph. The tzolk'in date in this example is a day 3 Ahaw.  Thirteen day numbers and 20 day names were used. The sequence of day names is Imix, Ik, Ak'bal, K'an, Chikchan, Kimi, Manik', Lamat, Muluk', Ok, Chuwan, Eb, Ben, Ix, Men, Kib, Kaban, Etz'nab, Kawak, Ahaw.  The day before 3 Ahaw is 2 Kawak. On the day after 3 Ahaw, the sequence of 20 day names begins again, with 4 Imix.  The day numbers continue to increase to 13, then revert to 1.  Thus counting ten days from 3 Ahaw,  the day 13 Ok is reached. It is followed by 1 Chuwan.
 
 Because 13 x 20 = 260, each day in the tzolk'in cycle has a unique name-number combination. The day 3 Ahaw repeats only after 260 days. This system may seem rather complicated, but it is really little different than combining week day names with the day of the month in our system. Thus, for example "Tuesday the 31st" might be followed by "Wednesday the lst." 
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See examples of day glyphs in codex and inscription styles at McNelly's Rabbit in the Moon web site.   The animated tzolk'in glyphs above and the colourized month glyphs below are from drawings of glyphs at Ivan Van Laningham's Tzuk-Te web site, and are  licensed under GGPL.
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Calendar Divination: The tzolk'in is a sacred almanac, used to time rituals and make auguries.  Knowledge of it was lost in the Yucatan after the Spanish conquest, but the cycle of 260 days is still kept by Quiche "day keepers" in highland Guatemala.  In fact, even the Yucatec name of the cycle was lost.  "Tzolk'in" is merely a transliteration into Yucatec of the Quiche name, ch'olk'ij.  Quiche day keepers still make auguries using the ch'olk'ij. For more about calendar divination, including a list of auguries for days of the tzolk'in, see Maya Augury and Prophecy in the Books of Chilam Balam at this web-site.
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The haab is a 365 day year. Since the Maya often aligned buildings to sunrise on the solstices, it is clear that they were aware that the solar year is not exactly 365 days long. The haab was likely set to 365 days to make it more easily commensurate with other calendrical cycles. The haab was divided into 18 named months (winals), each 20 days long, with a 5 day period at year end, the Wayeb, during which New Year rituals were performed. A haab date combines the day of the month with the month name. In this example, the date is 13 Yaxk'in. 

The Yucatec names of the months are: Pop, Wo, Sip, Sotz', Sek, Xul, Yaxk'in, Mol, Ch'en, Yax, Sak, Seh, K'ank'in, Muan, Pax, K'ayeb, Kumk'u. The name glyphs, ending with the Wayeb glyph, are illustrated in order at the right. 

The post-Classical Maya numbered the days of the month from 1 to 20, but in Classical inscriptions, the last day of the month was written as the day on which the new month was "seated" (chum).  Thus the last day of Yaxk'in was usually written as chum Mol, rather than as 20 Yaxk'in. This amounts to taking chum Mol as the first day of Mol, and numbering the days of the month from 0 (chum) to 19. 
 


See examples of month glyphs in codex and inscription styles at McNelly's Rabbit in the Moon web site
The calendar round  combines the tzolk'in and haab dates. The lowest common multiple of  the 260 days in the tzolk'in and 365 days in the haab is 18980. This is 52 haab, just short of 52 years in our calendar. Thus a combined tzolk'in and haab date repeats only after this lapse of time.
The calendar round was the longest calendrical period recorded by the Aztecs and other Mesoamerican peoples outside the Maya zone. Only the Maya and their pre-Classical predecessors kept the long count that fixes a date unequivocally in time. 

The beginning of the long count occurred on the calendar round date 4 Ahaw 8 Kumk'u. The calendar round date of any long count can be calculated by adding cycles of 260 and 365 days from 4 Ahaw  and 8 Kumk'u to reach the long count position. Once again, the arithmetic is simple in principle, but a calendar calculator program will make the task much easier. 

In dates on monuments, the calendar round usually follows immediately after the long count (as in the example above). However, in some inscriptions, the tzolk'in date and haab date are separated by 5-8 glyphs called the "lunar series". The LS is the date in yet another cycle, a lunar calendar. 

Right: The day 3 Xochitl in the Aztec tonalpohauli, equivalent to 3 Ahaw in the Maya tzolk'in
 

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Origin of the Calendar RoundThe tzolk'in (called the tonalpohauli in central Mexico) is the oldest part of the Mesoamerican calendar.  The haab (the Mexican xiuhpohualli) is probably nearly as old. Both may have originated in the first high civilization of Mesoamerica, the early pre-Classical Olmec (c. 1200 BC).  However, the oldest known calendrical signs were recorded on  inscriptions at Monte Alban (Oaxaca), dated from 500 to 250 BC.  Find more about pre-Classical calendar glyphs at Ancient Scripts.com,  and see the  description of the The Aztec calendar round at Mexico Connect.

Why the 260 day cycle assumed such importance is unknown.  Suggestions include the length of agricultural seasons and the human gestation period.  The most convincing are astronomical.  Early in the 20th C., Zelia Nuthall noted that a missionary report, the Manuscript of Serna, asserts that the tonalpohauli approximates the time Venus is visible to the naked eye as morning star.   The 365 day "year" is clearly a solar calendar.  Anthony Aveni suggests  that the Calendar Round  "synthesizes the primary solar and Venus intervals."

Another popular theory in the early years of Mesoamerican studies equated the 260 day cycle to the time between summer and spring zenith passages of the sun at the latitude of Copan.  This theory lost support when it was discovered that the calendar round antedates the foundation of Copan by nearly a millennium.  It has recently been revived by Vincent Malmström, however.  He notes that 260 days is also the time between zenith passages at Izapa, which flourished from the "Olmec" era to the time when Maya civilization emerged.  More about Malmström's theory of calendrical origins on-line.

An interesting  recently published theory notes that multiples of the tzolk'in closely approximate  several astronomical cycles that interested the Maya,  including the solar year, lunar month, and periods of Venus nd Mars.  Robert D. Penden, "The Maya Calendar --- Why 260 Days?",  an on-line article,  argues that 260 days is an optimal choice of a ritual period fitting astronomical cycles. 

As Anthony Aveni has suggested, given the Mesoamerican love of commensuration and the sacred significance attributed to the meshing of cycles of time, more than one explanation of the length of the tzolk'in may have been known to the scribes. 


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More about the calendar: The long count and calendar round were the basic elements of the Maya calendar, used to date  inscriptions and time rituals. But the outline above is not a complete account of Maya calendrics. 

Some "advanced" topics in Maya calendrics include: 


27th day of the Lunar Cycle
1. Distance numbers --- Inscriptions often record a series of events. The Initial Series date that begins the inscription is usually the only complete long count. Events are dated by "distance numbers", which count forward or back from the Initial Series date. (See  Gregory Reddick's Distance Numbers at his Xoc Software site and an example here

2. Lunar cycle -- The "Lunar Series" glyphs sometimes appended to long counts recorded the days elapsed since new moon, and kept track of lunar months of alternating 29 and 30 day length.  (See Lunar Astronomy in the Inscriptions at this web site and Robert Kihm's Lunar Glyphs at Astra's Stargate web page)

3. U kahlay katunob --- "The count of katuns" or "short count" replaced the long count for recording historical events in the post-Classical era. It is 13 katuns long. Tzolk'in dates of katun endings are always a day Ahaw, one of 1 Ahaw to 13 Ahaw. Each of these tzolk'in dates names a katun in the u kahlay katunob.  (See  U kahlay katunob: The short count and katun prophecy at this web site)

4. 819 day count --- Some inscriptions count back from the Initial Series date to one of the "stations" of the 819 day count. These dates are multiples of 819 days apart, and each is associated with a colour and a direction.  (See Gregory Reddick's 819 Day Cycle, and an example of an 819 day count inscription from a Palenque inscription at the Mesoweb site).

5. Tzolk'in almanacs --- The codices consist mostly of tzolk'in almanacs, used for divination and to time rituals.  Each almanac counts through a series of tzolk'in dates with ritual or augural significance.  See an example from the Dresden Codex here, and further discussion at the Madrid Codex Project website.  See also Tzolk'in Augury at this web site. 

6.  Other astronomical cycles ---  The Maya keep track of astronomical cycles in addition to the lunar month, including the periods of Venus and Mars, and eclipse cycles.  These cycles are recorded in tables in the Dresden Codex glyph book.

7. Maya Mathematics --- Although the Maya number system was functionally a modified base-20 system,  the Maya scribes may have conceived of it in a more complicated fashion, as a  composite of three distinct counts.  See Michael Closs, "the nature of the Maya chronological count."  But  however it may have been conceived and developed,  as  W. French Anderson, "Arithmetic in Maya numerals" shows,  quite sophisticated calculations are possible using the Maya number system. 
 


Dresden Codex Almanac
The Maya were deeply concerned to locate all events . . . within a cosmological framework designed to insure the regeneration of life. . . . Time past and time future were fixed in a discernible pattern that could be read and predicted. In addition to this nearly five-thousand year cycle [of the calendar] were a series of other cycles, which the Maya marked, celebrated, and sometimes feared  in detail. (David Carrasco, Religions of Mesoamerica )
 

Links

Several good introductions to the Maya calendar and number system are available on-line. The best short introduction is Nancy McNelly's Calendar Notes  from her excellent Rabbit in the Moon site, which is reproduced here.  For a more detailed account, see Ivan Van Laningham's The Mayan Calendar  at his Tzuk-Te web site.

Some additional technical information can be found in Peter Meyer's The Maya Calendar and Gregory Reddick's notes on calendrical topics at his Xoc Software Site. The number system used in the calendar and astronomical tables is discussed in an article on Mayan Mathematics at the History of Mathematics web site.  There is a good selected bibliography of the Maya calendar at Peter Meyer's web site.

The best on-line Maya calendar calculator is Ivan Van Laningham's Calendar Tools.  My Burden of Time Maya calendar freeware program, a full-featured Maya Calendar converter and calculator can be downloaded at this web site.  Peter Meyer  and Gregory Reddick both have fine shareware calendar programs available.  Another available freeware calendar program is Mayadate.  These programs all run under Microsoft Windows.  Macintosh OS users should try Chac 1.1.1.  There does not seem to be a graphic, full featured Linux Maya Calendar Program, but CDAY (available in Linux and Windows formats) calculates dates in several calendar systems, including the Maya.

See also the Aztec on-line calendar program at the Aztec Calendar page.

If you insist on trying to convert Maya dates by hand,  see Samuel Y. Edgerton,  How to Convert the Ancient Maya Calendar into Western-style Gregorian dates  (rtf format) for some hints.


The Real Maya Prophecies: Astronomy in the Inscriptions and Codices

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Books About the Maya Calendar..

The best up-to-date introduction to the Maya Calendar is in Anthony Aveni's  Skywatchers (University of Texas Press, 2001), which is also the best introduction to Mesoamerican astronomy. The book assumes no knowledge of either astronomy or Mesoamerican history, taking the reader from a discussion of observation methods to a thorough description of Maya astronomy in the inscriptions and codices.  This is a new edition of Skywatchers of Ancient Mexico, one of the books that established the modern science of archaeoastronomy.

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S.G. Morley's classic, An Introduction to the Study of the Maya Hieroglyphs (Dover reprint, 1975) is, despite its title, actually about the Maya calendar --- when it was written in 1915, calendrical glyphs were nearly all that could be read of the Maya script. This is still a very good, very carefully explained introduction to the calendar, with lots of nice line drawings. The price is also right.  Well worth having.

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Barbara Tedlock's Time and the Highland Maya (University of New Mexico, rev. 1992) is an amazing account of the calendar lore of Quiche shamans in Highland Guatemala, who still use the sacred round of 260 days to time festivals and make auguries.  Tedlock apprenticed herself to a Quiche "day keeper" to learn the secrets of calendar augury. 

The Real Maya Prophecies: Astronomy in the Inscriptions and Codices


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Michael John Finley   Saskatoon, Saskatchewan,  Canada  May 2002 (Revised April 2003/Jan-Feb 2004)