Dear Calendar List:
I see on the Calendar Wikia that there is posted a new calendar called the Celestial Calendar. This interesting calendar is a sidereal leap week calendar. It has thirteen 28 day months named for the 12 classical signs of the zodiac, plus
Ophiuchus, which is placed between Scorpio and Sagittarius. A leap week is added every 6 years, except that two leap weeks are added every 78th year.
While the average year length of 365.25641 days is quite good for a sidereal calendar, IMO adding 2 leap weeks in he 78th year is quite jittery. IMO, jitter could be reduced if an extra week were added only in the 39th year of the 78 year
cycle.
Walter Ziobro

Dear Walter and Calendar People
This is a very interesting point. I agree that offsetting the extra leap week by 3 years would reduce the jitter (Brij does this in his dividebysix leap week rules), but the reduction is small.
For no offset, the worst interval is the 1 year with two leap weeks. It has a surplus (over mean year) of 7*(21*(1/781/6)) = 12.7436... days. For any offset (not only 3 years), the worst interval is the 7 years beginning and ending with regular leap week years and containing the offset extra leap week. It has a surplus of 7*(37*(1/78+1/6)) = 12.2051... days. So if offset would reduce the jitter by about 0.5385 days, which is just under 13 hours.
Karl
Friday Gamma May 2020

Dear Walter and Calendar People
I did the calculation (of the reduction of jitter caused by offsetting) again using vulgar fractions to get the exact answer and got 1/13 week, which equals 13 hours less 1/13 hour. So if this time began at midnight, it would end just after five to one in a afternoon, when the two hands on the clock face are symmetrically placed.
This result also suggested that if the additional leap weeks were to occur once every n regular leap weeks (once every 6n years), offsetting would reduce the jitter by 1/n weeks. I then calculate:
If there is no offset, the part of the cycle with the biggest surplus (leap weeks minus average number of leap weeks in the same number of years) is 1 year with 2 leap weeks. If offset, this period is extended by 6 years to include the offset leap week year and the two regular leap week years either side of it. This adds 6 years and 1 leap week to the period. So the surplus is reduced by 1  6*(1/6 + 1/6n) = 1/n weeks.
I then consider the more general case in which t is the average number of regular leap weeks per additional leap week and reckon that if the spacing of the additional leap weeks is sensible, then offsetting extends the part of the cycle with the biggest surplus by six years and one leap week, so one gets the same saving of 1/t weeks.
Karl
Saturday Gamma February 2020

Dear Karl I notice that there is no comprehensive discussion of calendar jitter either in Wilipedia, or the Calendar Wikia. To your knowledge, does any such exist anywhere on the net? Walter Ziobro On Saturday, May 16, 2020 k.palmen <[hidden email]> wrote: Dear Walter and Calendar People
I did the calculation (of the reduction of jitter caused by offsetting) again using vulgar fractions to get the exact answer and got 1/13 week, which equals 13 hours less 1/13 hour. So if this time began at midnight, it would end just after five to one in a afternoon, when the two hands on the clock face are symmetrically placed.
This result also suggested that if the additional leap weeks were to occur once every n regular leap weeks (once every 6n years), offsetting would reduce the jitter by 1/n weeks. I then calculate:
If there is no offset, the part of the cycle with the biggest surplus (leap weeks minus average number of leap weeks in the same number of years) is 1 year with 2 leap weeks. If offset, this period is extended by 6 years to include the offset leap week year and the two regular leap week years either side of it. This adds 6 years and 1 leap week to the period. So the surplus is reduced by 1  6*(1/6 + 1/6n) = 1/n weeks.
I then consider the more general case in which t is the average number of regular leap weeks per additional leap week and reckon that if the spacing of the additional leap weeks is sensible, then offsetting extends the part of the cycle with the biggest surplus by six years and one leap week, so one gets the same saving of 1/t weeks.
Karl
Saturday Gamma February 2020

Dear Walter and Calendar People
Irv Bromberg deals with it on his verbose website.
Jitter is an overlooked aspect of calendar inaccuracy.
I wish there was a better website about it.
Karl
Monday Delta May 2020

In reply to this post by k.palmen@btinternet.com
Dear Karl Perhaps you can create a page in the Wikia. You seem to be the resident expert Is Irvs page copyrighted? Can a link be made to it from the Wikia? Walter Ziobro On Monday, May 18, 2020 k.palmen <[hidden email]> wrote: Dear Walter and Calendar People
Irv Bromberg deals with it on his verbose website.
Jitter is an overlooked aspect of calendar inaccuracy.
I wish there was a better website about it.
Karl
Monday Delta May 2020

Please excuse my ignorance. What precisely is meant by "jitter", aside from the standard dictionary definition of the word? the 3rd definition of the word in MerriamWebster's Third New International Dictionary (the 12.5 lbs unabridged edition) is as follows:
verb
verb
On Mon, May 18, 2020, 8:38 AM Walter J Ziobro <[hidden email]> wrote:

Dear Jamison, Walter and Calendar People
Jitter describes the jerky movement of the calendar year (or month) against its mean year (or month). I don't recall who first used the term 'jitter' for this, but it has been used on this Email list for many years.
The wikipedia page of the Gregorian calendar has a graph of the seasonal error of the Gregorian calendar, https://en.wikipedia.org/wiki/Gregorian_calendar#Calendar_seasonal_error nearly all of this seasonal error arises from the jitter rather than the inaccuracy of the mean year, which causes a drift.
I sometimes calculate the jitter of a calendar, which is the maximum range of its jitter movement. If the leap year cycle is sufficiently simple, I can find the part of the leap year cycle that has the most or least number of leap years compared to the mean number of leap years for the same number of years. For the Gregorian calendar, such a period is the 193 years from 1904 to 2096 inclusive, which has 49 leap years, compared to 193*(97/400) = 46.8025 leap years on average for 193 years. The difference is 2.1975 days. One can observe this difference by comparing the equinoxes and solstices of 1903 and 2096.
It seems I've already written part of a jitter article here.
Karl
Wednesday Delta May 2020
On Mon, May 18, 2020, 8:38 AM Walter J Ziobro <[hidden email]> wrote:

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