Overview of Rule-Based Lunar Calendars

Dear Calendar People

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.

Mario produced a list of approximations for the lunar month good enough to give rise to the basic yerm calendar:

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.

Karl Palmen

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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