## Overview of Rule-Based Lunar Calendars

Dear Calendar People,

While most lunar calendars are observation-based (especially the Islamic Calendar), 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.
Examples:

And invented recently:

Mario Hilgemeier 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 (The Invisible Landscape)
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.

The above emails have been subject to editing — refer to the CALNDR-L archive for full text