Re: Gregorian calendar jitter and lunar calendar in Wikipedia computus

Dear Tom and Calendar People

Putting aside the issue of short-term accuracy, I notice that the 43
corrections in 100 centuries normally follow a 7-century cycle of 3
corrections and once every 14 of these seven-century cycles and a two
century period with once correction is inserted.

Now I look at which of these cycles have exactly the same mean moon
phase as the Gregorian cycle. The Gregorian cycle is symmetrical about
years 1600, 6600, 11600 etc. There are two of the above-mentioned
43-correction cycles that have the same symmetry one of which can be
given exactly the same mean moon phase as the Gregorian.

One of these have corrections at
1400 1600 1800  
2100 2300 2600
2800 3000 3200
3500 3700 3900
and so on every 700 years until
6300 6500 6700 6900
7200 7400 7600
7900 8100 8300
and so on every 700 years to 11400.

The other has corrections at
1300 1500 1700 1900
2200 2400 2600
2900 3100 3300
And so one every 700 years to 11300.

The years (1800, 2100, 2300 and 2600) that Mockingbird picked for his
example belong to the first of these two cycles.
However it has a correction in the symmetry year 1600 in which the
Gregorian has no correction. So it's the other cycle that has the same
mean moon phase as the Gregorian.

This other 43-correction cycle agrees with Gregorian from its start
(1583 or year 900 proleptic) until year 2300. Then 2300-2399 is a day
ahead and 2400-2499 is a day behind then there is no more disagreement
till year 3300. I expect disagreements to become more frequent in later
years.

I notice that the Gregorian and 43-correction cycle almost repeat once
every 28 centuries. The only differences after 28 centuries is one
Gregorian lunar correction per cycle of 8 in 25 centuries is a century
late and four corrections in the 43-correction cycle are a century early
. This suggests 28 centuries could be a good period to do comparisons
over rather than just 800 years or the whole 10,000 years.

Karl

10(06(22




-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Tom Peters
Sent: 08 March 2009 14:02
To: CALNDR-L@...
Subject: Gregorian calendar jitter and lunar calendar in Wikipedia
computus

Joe Kress and others:
I noticed that in the Wikipedia article on the computus (http://
en.wikipedia.org/wiki/Computus), at some time the explanation has  
been removed how the use of a separate solar and lunar  
"equation" (=correction) prevents introducing the jitter in the  
Gregorian solar calendar into its lunar calendar.  Is that  
intentional?  I make a point of it because some years ago Heiner  
Lichtenberg published some papers on the Lilius lunar calendar, in  
which he promotes the idea that the calendar could be simplified/
improved by distributing the net 43 corrections evenly; which is not  
a bright idea as explained in the deleted paragraph.

--
Tom Peters

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