
Re: Ariadne's thread
Posted:
Nov 20, 2011 6:51 AM


Milo Gardner informed me about a 405lunation period in the Maya calendar. Further periods were 13 and 20 days, combined in the Tzolkin of 260 days. How long are 405 lunations? 15 and 17 lunations counted in the 30 29 30 29 30 29 30 ... mode are 443 and 502 days respectively. 17 15 17 15 17 lunations yield 502 945 1447 1890 2392 days for 17 32 49 64 81 lunations respectively. One lunation is 29 days 12 hours 44 minutes 2.9 seconds (modern average from 1989 AD). 81 lunations are 2391.977... or practically 2392 days, mistake less than half a minute per lunation, or five hours in a lifetime. 5 periods of 81 lunations are 405 lunations, 11959.8885... or practically 11960 days, 920 periods of 13 days or 596 periods of 20 days or 46 Tzolkin, periods of 260 days.
The Tzolkin and the rounded year of 365 days were combined in the Calendar Round of 94900 days. An actual year is a little longer than 365 days, 365.24219879 days, called a tropical year. Is there a reasonable way to combine the Tzolkin with the tropical year? Let us find out. 10 Tzolkin are a little more than 7 tropical years, while 7 Tzolkin are slightly less than 5 years:
10/7 (plus 7/5) 17/12 24/17 31/22 38/27 45/32 52/37 59/42
59 Tzolkin are 15340 days. 42 tropical years are 15340.172... days or practically 15340 days.
73 Tzolkin = 18980 days = 52 rounded years 59 Tzolkin = 15340 days or 42 tropical years 46 Tzolkin = 11960 days or 405 lunations
I don't know whether a period of 59 Tzolkin or 42 tropical years played a role in the Maya calendar, but the numbers make sense.
The idea of the Maya calendar may have been a solid structure provided by the 260day count, while the astronomical cycles were 'hung' into the calendar whose weight was carried by gods ('burdened with bundles of time').
The synodic Venus year lasts 583.92 days, the synodic Mars year 779.936 days. The Maya counted 584 days for the Venus year, and may have counted 780 days for the Mars year. Two Calendar Rounds are 18980 days or 325 rounded Venus years, while 3 Tzolkin are one rounded Mars year.
Next time: a strange period of 819 days

