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 |
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
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