I am curious about what rule-based lunar calendars are or have been in use. I know that such calendars can not predict the exact day of a new moon or an eclipse without becoming excessively complicated. This is because of eccentricity of the moon's orbit round the earth and the earth's orbit around the sun.
There are few rule-based lunar calendars around.
Assume a "reasonable" value for the synodic period of 29.53059 days
(precision 7 digits).
approximation of the lunar month
by an integer numbers of days and lunar months:
lms = lunar months
len = approximated lunar month length, len = days/lms
relative error = (len - synodic)/synodic
days lms len relative error
29 1 29.0000000000 -1.7967e-02
30 1 30.0000000000 +1.5896e-02
59 2 29.5000000000 -1.0359e-03 simple approximation
266 9 29.5555555556 +8.4541e-04 short whole-week yerm (human gestation period)
325 11 29.5454545455 +5.0336e-04 eleven month system
384 13 29.5384615385 +2.6656e-04 the classical lunar year
443 15 29.5333333333 +9.2898e-05 fifteen month yerm
502 17 29.5294117647 -3.9899e-05 seventeen month yerm
945 32 29.5312500000 +2.2350e-05 Simon Cassidy's basic Week of Weeks
1447 49 29.5306122449 +7.5328e-07 basic yerm calendar (17:17:15)
Information about other rule-based lunar calendars is appreciated.
First Moonnight Month 7 Yerm 2
Monday King of Hearts
The above emails have been subject to editing - refer to the CALNDR-L archive for full text
Observation-based lunar calendars are still in use today. A recent suggestion is the solunar YANUS calendar.
Karl Palmen's Calendars
Essays on mathematical themes
Copyright 1998, Mario Hilgemeier and Karl Palmen, (contact info).
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