Re: Gregorian calendar jitter and lunar calendar in Wikipedia computus

Dear Tom and Calendar People

Actually proving that an arbitrary uniform correction system (of 43
corrections per 100 centuries) has worse lunar jitter than the Gregorian
computus is not simple and might not be possible.

Perhaps we could find out what Lichtenburg's proposal was.

I've already identified one weak point of a uniform correction system,
which is a leap century year with a correction. This enables a period of
235 lunar months and 19 lunisolar years to have 6941 days which is one
more than maximum of 6940 that can occur in the Gregorian computus.
Mockingbird has pointed out that a uniform correction system need not
have any of its corrections on a leap century year.

I've since identified another weak point of a uniform correction system.
It is two consecutive common century years with no correction. This
leads to six consecutive periods of 235 lunar month and of 19 lunisolar
years having one day less than the minimum that can occur in the
Gregorian computus.

However it is possible to create a uniform correction system free of
both these weaknesses. If there is just one correction between two leap
century years, place it half way in between.

One such system could be defined by starting with the Gregorian and
postponing by one century each lunar equation correction that occurs on
a leap century year. This would differ from Gregorian for 8% of
centuries. However the sequence of corrections would be so complicated
as to have no advantage in simplicity over Gregorian.

Another could be to have corrections on years

0100 0300
0600
0900 1100 1300 1500 1700 1900
2200
2500 2700 2900 3100
3400
3700 3900 4100 4300 4500 4700
5000
5300 5500 5700 5900 6100 6300
6600
6900 7100 7300 7500
7800
8100 8300 8500 8700 8900 9100
9400
9700 9900
and so in every 10,000 years.

To get the same mean moon phase as Gregorian, postpone the cycle by 1600
years.

Karl

10(06(23

-----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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