Jubilees Leap Week Calendar

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Jubilees Leap Week Calendar

k.palmen@btinternet.com
Dear Walter and Calendar People

Walter has suggested a leap week calendar at
https://calendars.wikia.org/wiki/Jubilees_Leap_Week_Calendar

The distinctive feature of this calendar is its leap week rule.
It follows a 400-year cycle of 71 leap weeks, which is divided into 8 Jubilees of 50 years.
Each Jubilee has 9 leap week years, except the 8th Jubilee, which has 8 leap week years.
The intervals between the leap week years within each Jubilee are
6,5,6,5,6,6,5,6
except the 8th Jubilee, when the final 6 does not occur. The interval between the Jubilees varies it is 6, except between the 2nd & 3rd Jubilee and the 6th & 7th Jubilee, when it 5. If the interval between Jubilees is 5, then the 9 intervals add up to 50 and so the following Jubilee has exactly the same leap week years, else the leap week years occur one year later in the Jubilee. 

So the leap week years would be (with each row a Jubilee):
001  007 012  018 023  029  035 040  046  ;
052  058 063  069 074  080  086 091  097 ;
102  108 113  119 124  130  136 141  147  ;
153  159 164  170 175  181  187 192  198  ;
204  210 215  221 226  232  238 243  249  ;
255  261 266  272 277  283  289 294  300 ;
305  311 316  322 327  333  339 344  350  ;
356  362 367  373 378  384  390 395  ;

The leap week years are not spread as smoothly as possible as would be the case for the nearest Monday rule applied to the truncated 33-year cycle rule suggested by Walter, but may be considered to by structurally simpler.

To see this we look at the intervals of 5. They occur the following number of intervals apart (starting with first to second 5):
2,3,4,... . There are three or more different numbers rather than than the two that occur when the intervals are spread as smoothly as possible. Also this mean it does not have a structural complexity value, using the structural complexity I defined extended to some cycles such as Gregorian, where the leap years are not spread as smoothly as possible.

I may work out the jitter in a separate note. Irv may also add this to his jitter graphs.

Karl

Friday Beta April 2019

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Re: Jubilees Leap Week Calendar

k.palmen@btinternet.com
Dear Calendar People

Here I work out the jitter of Walter's Jubilees Leap Week Calendar.

I reckon the interval of the cycle with the biggest deficit of leap years is year 125 to 288 inclusive.

This 164-year period has 28 leap weeks compared with an average for 164 years of 164*(71/400) = 29.11 leap weeks and so the jitter is 1.11 weeks = 7.77 days, which is not much worse than the 6.9975 days that would result if the leap week years were spread as smoothly as possible.

However in the course of looking for the worst interval, I found out the calendar can be simplified by postponing the 5th and 8th leap weeks of each Jubilee by one year, then the leap weeks would normally follow a 17-year cycle of 3 leap weeks. The jitter would be reduced slightly, by shortening the worst interval from 125-288 to 131-288.

Karl

Tuesday Gamma April 2019
----Original message----
From : [hidden email]
Date : 12/04/2019 - 12:38 (BST)
To : [hidden email], [hidden email]
Subject : Jubilees Leap Week Calendar

Dear Walter and Calendar People

Walter has suggested a leap week calendar at
https://calendars.wikia.org/wiki/Jubilees_Leap_Week_Calendar

The distinctive feature of this calendar is its leap week rule.
It follows a 400-year cycle of 71 leap weeks, which is divided into 8 Jubilees of 50 years.
Each Jubilee has 9 leap week years, except the 8th Jubilee, which has 8 leap week years.
The intervals between the leap week years within each Jubilee are
6,5,6,5,6,6,5,6
except the 8th Jubilee, when the final 6 does not occur. The interval between the Jubilees varies it is 6, except between the 2nd & 3rd Jubilee and the 6th & 7th Jubilee, when it 5. If the interval between Jubilees is 5, then the 9 intervals add up to 50 and so the following Jubilee has exactly the same leap week years, else the leap week years occur one year later in the Jubilee. 

So the leap week years would be (with each row a Jubilee):
001  007 012  018 023  029  035 040  046  ;
052  058 063  069 074  080  086 091  097 ;
102  108 113  119 124  130  136 141  147  ;
153  159 164  170 175  181  187 192  198  ;
204  210 215  221 226  232  238 243  249  ;
255  261 266  272 277  283  289 294  300 ;
305  311 316  322 327  333  339 344  350  ;
356  362 367  373 378  384  390 395  ;

The leap week years are not spread as smoothly as possible as would be the case for the nearest Monday rule applied to the truncated 33-year cycle rule suggested by Walter, but may be considered to by structurally simpler.

To see this we look at the intervals of 5. They occur the following number of intervals apart (starting with first to second 5):
2,3,4,... . There are three or more different numbers rather than than the two that occur when the intervals are spread as smoothly as possible. Also this mean it does not have a structural complexity value, using the structural complexity I defined extended to some cycles such as Gregorian, where the leap years are not spread as smoothly as possible.

I may work out the jitter in a separate note. Irv may also add this to his jitter graphs.

Karl

Friday Beta April 2019