Celestial Calendar

classic Classic list List threaded Threaded
8 messages Options
Reply | Threaded
Open this post in threaded view
|

Celestial Calendar

Walter J Ziobro
This email originated from outside ECU.

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 
Reply | Threaded
Open this post in threaded view
|

Re: Celestial Calendar

k.palmen@btinternet.com
This email originated from outside ECU.

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 divide-by-six 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*(2-1*(1/78-1/6)) = 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*(3-7*(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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]
Sent: Thursday, 14 May, 2020 At 13:59
Subject: Celestial Calendar

This email originated from outside ECU.

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
Reply | Threaded
Open this post in threaded view
|

Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

k.palmen@btinternet.com
This email originated from outside ECU.

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




------ Original Message ------
From: "[hidden email]" <[hidden email]>
To: "Walter J Ziobro" <[hidden email]>; [hidden email]
Sent: Friday, 15 May, 2020 At 14:06
Subject: Re: Celestial Calendar

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 divide-by-six 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*(2-1*(1/78-1/6)) = 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*(3-7*(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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]
Sent: Thursday, 14 May, 2020 At 13:59
Subject: Celestial Calendar

This email originated from outside ECU.

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
Reply | Threaded
Open this post in threaded view
|

Re: Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

Walter J Ziobro
This email originated from outside ECU.

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




------ Original Message ------
From: "[hidden email]" <[hidden email]>
To: "Walter J Ziobro" <[hidden email]>; [hidden email]
Sent: Friday, 15 May, 2020 At 14:06
Subject: Re: Celestial Calendar

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 divide-by-six 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*(2-1*(1/78-1/6)) = 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*(3-7*(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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]
Sent: Thursday, 14 May, 2020 At 13:59
Subject: Celestial Calendar

This email originated from outside ECU.

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
Reply | Threaded
Open this post in threaded view
|

Re: Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

k.palmen@btinternet.com
This email originated from outside ECU.

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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]; [hidden email]
Sent: Sunday, 17 May, 2020 At 03:44
Subject: RE: Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

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




------ Original Message ------
From: "[hidden email]" <[hidden email]>
To: "Walter J Ziobro" <[hidden email]>; [hidden email]
Sent: Friday, 15 May, 2020 At 14:06
Subject: Re: Celestial Calendar

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 divide-by-six 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*(2-1*(1/78-1/6)) = 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*(3-7*(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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]
Sent: Thursday, 14 May, 2020 At 13:59
Subject: Celestial Calendar

This email originated from outside ECU.

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
Reply | Threaded
Open this post in threaded view
|

Re: Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

Walter J Ziobro
In reply to this post by k.palmen@btinternet.com
This email originated from outside ECU.

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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]; [hidden email]
Sent: Sunday, 17 May, 2020 At 03:44
Subject: RE: Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

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




------ Original Message ------
From: "[hidden email]" <[hidden email]>
To: "Walter J Ziobro" <[hidden email]>; [hidden email]
Sent: Friday, 15 May, 2020 At 14:06
Subject: Re: Celestial Calendar

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 divide-by-six 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*(2-1*(1/78-1/6)) = 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*(3-7*(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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]
Sent: Thursday, 14 May, 2020 At 13:59
Subject: Celestial Calendar

This email originated from outside ECU.

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
Reply | Threaded
Open this post in threaded view
|

Re: Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

Jamison Painter
This email originated from outside ECU.

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 Merriam-Webster's Third New International Dictionary (the 12.5 lbs unabridged edition) is as follows: 
  • "irregular random movement (as of a pointer or an image on a television screen)
    also : vibratory motion"
  • How does that word apply in the calendrical sense?
  • Jamison E. Painter, MA
verb
verb

On Mon, May 18, 2020, 8:38 AM Walter J Ziobro <[hidden email]> wrote:
This email originated from outside ECU.

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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]; [hidden email]
Sent: Sunday, 17 May, 2020 At 03:44
Subject: RE: Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

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




------ Original Message ------
From: "[hidden email]" <[hidden email]>
To: "Walter J Ziobro" <[hidden email]>; [hidden email]
Sent: Friday, 15 May, 2020 At 14:06
Subject: Re: Celestial Calendar

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 divide-by-six 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*(2-1*(1/78-1/6)) = 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*(3-7*(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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]
Sent: Thursday, 14 May, 2020 At 13:59
Subject: Celestial Calendar

This email originated from outside ECU.

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
Reply | Threaded
Open this post in threaded view
|

Jitter Re: Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

k.palmen@btinternet.com
This email originated from outside ECU.

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 E-mail 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




------ Original Message ------
From: "Jamison Painter" <[hidden email]>
To: [hidden email]
Sent: Monday, 18 May, 2020 At 16:51
Subject: Re: Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

This email originated from outside ECU.

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 Merriam-Webster's Third New International Dictionary (the 12.5 lbs unabridged edition) is as follows:
  • "irregular random movement (as of a pointer or an image on a television screen)
    also : vibratory motion"
  • How does that word apply in the calendrical sense?
  • Jamison E. Painter, MA
verb
verb

On Mon, May 18, 2020, 8:38 AM Walter J Ziobro <[hidden email]> wrote:
This email originated from outside ECU.

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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]; [hidden email]
Sent: Sunday, 17 May, 2020 At 03:44
Subject: RE: Offsetting additional leap week years in Divide By Six Re: Celestial Calendar

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




------ Original Message ------
From: "[hidden email]" <[hidden email]>
To: "Walter J Ziobro" <[hidden email]>; [hidden email]
Sent: Friday, 15 May, 2020 At 14:06
Subject: Re: Celestial Calendar

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 divide-by-six 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*(2-1*(1/78-1/6)) = 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*(3-7*(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




------ Original Message ------
From: "Walter J Ziobro" <[hidden email]>
To: [hidden email]
Sent: Thursday, 14 May, 2020 At 13:59
Subject: Celestial Calendar

This email originated from outside ECU.

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