From: John Bishop <jbishop@blkbrd.zko.dec.com>
Subject: (urth) Re: lunar calendars [Digest urth.v028.n014]
Date: Thu, 12 Aug 1999 16:08:53 

Mantis says:

> Lunar calendars have thirteen months (13 x 28 = 364).  Period.

Not that I ever read.  The islamic calendar still offically
depends on a witness to the new Moon, the Judaic calendar used
to (before it could rely on calculation), and the Classic 
world's lunar calendars did also (in particular, the calendars
used to calculate possible eclipse times), though in later
times astronomers calculated a sequence of short and long
months that would be predictable (by reference) but never
more than half a day off the real new Moon.

A fixed lunar calendar would pretty quickly cease to be aligned
with the moon, which kind of loses the point, and produces the
kind of "months" we have, which are unrelated to the Moon.

Thus a year would be either 12 or 13 months, depending on whether
it had an extra month or not (Judaic "second Adar"), and the 
months would have either 28 or 29 days.  Trusted witnesses would
look at the sky, searching for a new Moon to start a new month,
and a trusted (priestly) authority would determine when to insert
an extra month depending on astronomical observations (such as
the Pontifex Maximus in Rome).

During the late Classic time, there was a 19-year cycle of long
and short months, long and short years which kept the Moon phase
predicted by the calendar within half a day of the real Moon
phase, and the seasons within half a month of the real season,
so direct observation (and the consequent need for messengers to
spread the news, etc.) wasn't required.

It wasn't perfect (there was a long-term drift), and there was a
57-year cycle which solved most of the drift, but it never became
widely accepted.  The 19-year calendar was useful because the
eclipse cycle is also 19 years (due to the precession of the
moon's orbit, which moves the location of the ascending and 
descending nodes of the moon's orbit along the ecliptic).  You
could put "eclipse" seasons into the 19-year cycle: they marked
the points at which the Earth, Moon and Sun were aligned in such
a way that an eclipse was very likely.

See Abell's astronomy text and various encyclopedias.  I once long
ago programed up a calendar maker which used modern data to construct
the 19 and 57 year calendars, but I don't know if the Classic ones
would have had the same distribution of longs and shorts.

        -John Bishop

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