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In an old book of Prescott (died in 1859), The conquest of Mexico, the author described Aztec calendar with a year of 365 days. To compensate for the difference, every 52 years an additional 12.5 days were added (so that every other 52-years period started at noon, and the rest at midnight). This gives the average length of the year 365.24038 day which is only 2 minutes short, and is more precise than any European calendar before the Gregorian one. He refers to the research by Gama, Descripcion historica y chronologica de las Dos Piedras, (Mexico 1832).

However I was unable to find a confirmation of this information in modern books, for example, in Thurston, Early astronomy, Springer, 1994. Modern sources such as Wikipedia, Thurston and others say that Aztec calendar is the same as Maya calendar, and none of them addresses the intercalary days and length of the year. Thurston cites some modern works which try to estimate the average length of the year in Maya calendar and concludes that the claims on high accuracy are unfounded. But nobody mentions the ingenious intercalation described by Prescott and Gama. Does this mean that Gama's research was somehow disproved or is it simply forgotten?

EDIT. Following the suggestion in the comments I looked in the book by M. Coe, The Maya. It indeed contains a sentence:

We know that none of the Maya intercalated days on leap years or the like, as we do, and it has been shown that more sophisticated corrections thought to have been made by them are a figment of the imagination.

No explanation, no references. He even does not mention Gama, the founding father of Maya studies. The question remains how the Maya did agriculture with a calendar not tied to seasons.

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  • $\begingroup$ This "talk" page on the wiki site appears to suggest that the use of intercalary days by the Aztecs has be "disproven" by Z.A. Simon and Micheal Coe. en.wikipedia.org/wiki/Talk%3AAztec_calendar#The_Aztec_calendar $\endgroup$
    – nwr
    Commented Mar 15, 2017 at 0:48
  • $\begingroup$ @Nick: Unfortunately the author of the text cites some paper without giving proper reference to it, and adds that "some experts disagree" with it. $\endgroup$
    – Alexandre Eremenko
    Commented Mar 15, 2017 at 17:37
  • $\begingroup$ There is a vague account of Coe's reasoning given, although, as pointed out, it is not universally accepted. I looked for Simon's text from 1984 but could not find anything. If nothing else, it does indicate considerable debate amongst specialists. $\endgroup$
    – nwr
    Commented Mar 15, 2017 at 17:49
  • $\begingroup$ @Nick: Can you give a reference on Coe? $\endgroup$
    – Alexandre Eremenko
    Commented Mar 15, 2017 at 18:11
  • $\begingroup$ Unfortunately the two or three paragraphs describing Coe's views do not include any references. The wiki page on Coe does list his "major works" and we can infer that it must be a work prior to 1984. I would guess the 1966 text "The Maya" looks like the most likely. en.wikipedia.org/wiki/Michael_D._Coe $\endgroup$
    – nwr
    Commented Mar 15, 2017 at 18:24

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The standard literature on the Mayan calendar is:

J. Eric S. Thompson, Maya Hieroglyphic Writing, Washington : Carnegie Institution, 1950.

Lis Brack-Bernsen, 'Die Basler Mayatafeln', Verhandlungen der Naturforschenden Gesellschaft in Basel, Vol.86 (1977), 1-76.

Floyd G. Lounsbury, 'Maya numeration, computation, and calendrical astronomy', Dictionary of Scientific Biography, Volume XV, Supplement I, 1978.

All of these agree that the year had 18 “months” of 20 days each and one “month” of 5 days, making a year of 365 days. There is no evidence for intercalation.

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FWIW: ~ Gama, 1790, P.25 indicates

...pero la corrección no se hacia hasta el fin del Ciclo, en que se intercalaban juntos los 13 días, que gastaban en fiestas, en honor de los dioses seculares, de los quales era uno el mismo Xiuhteuctli TletL...

P.110

...pues sabiendo ellos bien, que al fin del Ciclo había retrocedido el principio de su año civil 13 dias; y para igualarlo con el solar, los intercalaban; les era fácil saber, en qualquier año, los dias que debían computar en su cuenta, para verificar en ellos el preciso tiempo de los Equinoccios y Solsticios, y del tránsito del Sol por el vértice de la Ciudad.."

and a few other references to intercalations (in addition to the intro which gives a primary purpose of the book as including

Explícase el sistema de los Calendarios de los Indios, el método que tenian de dividir el tiempo, y la corrección que hacian de él para igualar el año civil, de que usaban, con el año solar trópico....

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"The Dresden Codex Lunar Series presents a span of 11,457 days, equaling 11,292 degrees solar orbit. This amount has a sidereal correspondence with 857 days of lunar orbit motion.Also, 11,457 lunar orbits equates to 857 solar orbits and 10,600 lunar synodic periods (moons). And, 857 full moon periods represents a precise integer number of earth rotations:

857.0 full moons = 930.013 lunar nodal = 25,377.003 earth rotations 857.0 solar orbits = 11,457.016 lunar orbits = 10,600.016 full moons

Apparently, the focus of the lunar series is lunar nodal (the eclipses) and ratios far more accurate than either the Saros or Metonic eclipse periods represent or the eclipse intervals presented in the lunar series."

https://jqjacobs.net/archaeology/maya_astronomy.html

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