Truncated Dee-Cecil Calendar

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Truncated Dee-Cecil Calendar

Walter J Ziobro
TRUNCATED DEE-CECIL CALENDAR

The Truncated Dee-Cecil Calendar is a variation of the calendar with the 33 year leap day cycle proposed by William Cecil.  In this version, the 33 year leap day cycle would continue for 12 cycles of 396 years, after which there would be one four-year olympiad, for a total of 400 years. The 33 year cycles would then recommence in the next year.  Then, one day would be dropped on average every 3,600 years.

There are 4 advantages of such a calendar:

1.  The 33 year leap day cycle would cause less jitter of the equinox and solstice dates.

2. The application of ISO 8601 rules to such a calendar would cause the 53rd week of the week numbering scheme to be more smoothly distributed over the 400 year period.  This could also make concurrence with leap-week calendars more symmetrical.

3.  The 400 year cycle would have 146,097 days, or 20,871 weeks, exactly the same as the current Gregorian Calendar, which would assist, either in conversion from one calendar to the other, or in date-to-date mapping, if both calendars run concurrently.

4. The 3600 year correction would give the calendar 1,314,872 days in as many years, for an average year of 365.242222 days, exactly the same average tropical year as Milankovich's Revised Julian Calendar. In this way, this calendar could be reconciled with the Revised Julian Calendar, as well. (However, there is an issue of which average year to use; see below).

Currently, both the Gregorian and the Truncated Dee-Cecil Calendar have the same calendar dates.  This is so because the 33 year cycle recommenced in 2001, and both calendars will have the same dates until 2036, which will be a leap year in the Gregorian Calendar, but not the Truncated Dee-Cecil Calendar.  Thus, it would be possible to convert from the Gregorian Calendar to the Truncated Dee-Cecil Calendar at any time from now until 2036 without adjusting any dates.  

However, if the calendar in not converted by then, both calendars could run concurrently.  To minimize any confusion, alternative month names can be used for the Truncated Dee-Cecil Calendar.  Since Dee and Cecil were both Englishmen, English names for the alternative months seem appropriate. So, the alternative month names for the corresponding Gregorian month names could be:

Gregorian to Truncated Dee-Cecil:

January = Newmonth (Nmt), 31 days
February = Shortmonth (Smt), 28/29 days
March = Firstmonth (1mt), 31 days
April = Secondmoth (2mt), 30 days
May = Thirdmonth (3mt), 31 days
June = Fourthmonth (4mt), 30 days
July = Fifthmonth (5mt), 31 days
August = Sixthmonth (6mt), 31 days
Septemebr = Seventhmonth (7mt), 30 days
October = Eighthmonth (8mt), 31 days
Novemebr = Ninthmonth (9mt), 30 days
December = Tenthmonth (Tmt), 31 days

As I mentioned above, dropping a day every 3600 years will produce a calendar that has a close approximation to the current value of the  length of the mean tropical year, as in the Revised Julian Calendar.  However, the Gregorian Calendar was intended at its inception to better track the mean northward vernal equinox year, to better calculate the date of Easter, which year varies from the mean tropical year over a 21,000 year cycle, as the perihelion point precesses relative to the equinoxes.  Dropping a day in the year 3600 will keep the calendar dates close to the current northward vernal equinox, but, after that, as the perihelion point will occur closer to the northward vernal equinox point, a more frequent adjustment will be necessary for several millenia.

This could be accomplished by dropping 2 days from some of the 3600 year cycles.  For instance, this could be done in the years 5600, 7200, 8800, and 10800 (intervals of 2000, 1600, 1600, and 2000 years).  But, there is plenty of time to decide this, and some future generation will be the one to decide, anyway.

-Walter Ziobro



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If Reformed Re: Truncated Dee-Cecil Calendar

Brij Bhushan metric VIJ
Walter, Karl cc sirs:
>However, if the calendar in not converted >by then, both calendars could run >concurrently.  To minimize any confusion, >alternative month names can be used for >the Truncated Dee-Cecil Calendar. 
If calendar gets Reformed to any 'candidate' to be a possible World Calendar, won't there be many changes compared with the proposal of my "JUST shifting the Day of July 31 to become February 29th (all years)  
image1.JPG
& and gain the title being the Easiest, Surest and Cheapest - EVER, proposed option for taming the passage of 'events & Time count' - with or without Leap Weeks; including Decimalisation of Time of the Hour in terms of 15* Arc-angle, also defining the Nautical Kilometre:
image2.JPG
NEVER in history man has done to attempt define/Reform calendars in ONE stroke, 
image3.JPG
addressing most issues, sir.
Regards,
Ex-Flt.Lt. Brij Bhushan VIJ, Author
Brij-Gregorian Modified Calendar
Sunday, 2017 July 23H09:64 (decimal)
Sent from my iPhone

On Jul 23, 2017, at 8:21 AM, Walter J Ziobro <[hidden email]> wrote:

TRUNCATED DEE-CECIL CALENDAR

The Truncated Dee-Cecil Calendar is a variation of the calendar with the 33 year leap day cycle proposed by William Cecil.  In this version, the 33 year leap day cycle would continue for 12 cycles of 396 years, after which there would be one four-year olympiad, for a total of 400 years. The 33 year cycles would then recommence in the next year.  Then, one day would be dropped on average every 3,600 years.

There are 4 advantages of such a calendar:

1.  The 33 year leap day cycle would cause less jitter of the equinox and solstice dates.

2. The application of ISO 8601 rules to such a calendar would cause the 53rd week of the week numbering scheme to be more smoothly distributed over the 400 year period.  This could also make concurrence with leap-week calendars more symmetrical.

3.  The 400 year cycle would have 146,097 days, or 20,871 weeks, exactly the same as the current Gregorian Calendar, which would assist, either in conversion from one calendar to the other, or in date-to-date mapping, if both calendars run concurrently.

4. The 3600 year correction would give the calendar 1,314,872 days in as many years, for an average year of 365.242222 days, exactly the same average tropical year as Milankovich's Revised Julian Calendar. In this way, this calendar could be reconciled with the Revised Julian Calendar, as well. (However, there is an issue of which average year to use; see below).

Currently, both the Gregorian and the Truncated Dee-Cecil Calendar have the same calendar dates.  This is so because the 33 year cycle recommenced in 2001, and both calendars will have the same dates until 2036, which will be a leap year in the Gregorian Calendar, but not the Truncated Dee-Cecil Calendar.  Thus, it would be possible to convert from the Gregorian Calendar to the Truncated Dee-Cecil Calendar at any time from now until 2036 without adjusting any dates.  

However, if the calendar in not converted by then, both calendars could run concurrently.  To minimize any confusion, alternative month names can be used for the Truncated Dee-Cecil Calendar.  Since Dee and Cecil were both Englishmen, English names for the alternative months seem appropriate. So, the alternative month names for the corresponding Gregorian month names could be:

Gregorian to Truncated Dee-Cecil:

January = Newmonth (Nmt), 31 days
February = Shortmonth (Smt), 28/29 days
March = Firstmonth (1mt), 31 days
April = Secondmoth (2mt), 30 days
May = Thirdmonth (3mt), 31 days
June = Fourthmonth (4mt), 30 days
July = Fifthmonth (5mt), 31 days
August = Sixthmonth (6mt), 31 days
Septemebr = Seventhmonth (7mt), 30 days
October = Eighthmonth (8mt), 31 days
Novemebr = Ninthmonth (9mt), 30 days
December = Tenthmonth (Tmt), 31 days

As I mentioned above, dropping a day every 3600 years will produce a calendar that has a close approximation to the current value of the  length of the mean tropical year, as in the Revised Julian Calendar.  However, the Gregorian Calendar was intended at its inception to better track the mean northward vernal equinox year, to better calculate the date of Easter, which year varies from the mean tropical year over a 21,000 year cycle, as the perihelion point precesses relative to the equinoxes.  Dropping a day in the year 3600 will keep the calendar dates close to the current northward vernal equinox, but, after that, as the perihelion point will occur closer to the northward vernal equinox point, a more frequent adjustment will be necessary for several millenia.

This could be accomplished by dropping 2 days from some of the 3600 year cycles.  For instance, this could be done in the years 5600, 7200, 8800, and 10800 (intervals of 2000, 1600, 1600, and 2000 years).  But, there is plenty of time to decide this, and some future generation will be the one to decide, anyway.

-Walter Ziobro



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Re: Truncated Dee-Cecil Calendar

Victor Engel
In reply to this post by Walter J Ziobro
Dear Walter and Calendar People,

The biggest issue I see with such a scheme is that you lose the simplicity and accuracy of the Dee-Cecil calendar. Also, can you explain how interrupting the simple 33 year pattern causes less jitter? It seems like that would introduce jitter not already there, especially for the spring equinox, which is the one it is meant to track.

Victor

On Sun, Jul 23, 2017 at 10:21 AM, Walter J Ziobro <[hidden email]> wrote:
TRUNCATED DEE-CECIL CALENDAR

The Truncated Dee-Cecil Calendar is a variation of the calendar with the 33 year leap day cycle proposed by William Cecil.  In this version, the 33 year leap day cycle would continue for 12 cycles of 396 years, after which there would be one four-year olympiad, for a total of 400 years. The 33 year cycles would then recommence in the next year.  Then, one day would be dropped on average every 3,600 years.

There are 4 advantages of such a calendar:

1.  The 33 year leap day cycle would cause less jitter of the equinox and solstice dates.

2. The application of ISO 8601 rules to such a calendar would cause the 53rd week of the week numbering scheme to be more smoothly distributed over the 400 year period.  This could also make concurrence with leap-week calendars more symmetrical.

3.  The 400 year cycle would have 146,097 days, or 20,871 weeks, exactly the same as the current Gregorian Calendar, which would assist, either in conversion from one calendar to the other, or in date-to-date mapping, if both calendars run concurrently.

4. The 3600 year correction would give the calendar 1,314,872 days in as many years, for an average year of 365.242222 days, exactly the same average tropical year as Milankovich's Revised Julian Calendar. In this way, this calendar could be reconciled with the Revised Julian Calendar, as well. (However, there is an issue of which average year to use; see below).

Currently, both the Gregorian and the Truncated Dee-Cecil Calendar have the same calendar dates.  This is so because the 33 year cycle recommenced in 2001, and both calendars will have the same dates until 2036, which will be a leap year in the Gregorian Calendar, but not the Truncated Dee-Cecil Calendar.  Thus, it would be possible to convert from the Gregorian Calendar to the Truncated Dee-Cecil Calendar at any time from now until 2036 without adjusting any dates.  

However, if the calendar in not converted by then, both calendars could run concurrently.  To minimize any confusion, alternative month names can be used for the Truncated Dee-Cecil Calendar.  Since Dee and Cecil were both Englishmen, English names for the alternative months seem appropriate. So, the alternative month names for the corresponding Gregorian month names could be:

Gregorian to Truncated Dee-Cecil:

January = Newmonth (Nmt), 31 days
February = Shortmonth (Smt), 28/29 days
March = Firstmonth (1mt), 31 days
April = Secondmoth (2mt), 30 days
May = Thirdmonth (3mt), 31 days
June = Fourthmonth (4mt), 30 days
July = Fifthmonth (5mt), 31 days
August = Sixthmonth (6mt), 31 days
Septemebr = Seventhmonth (7mt), 30 days
October = Eighthmonth (8mt), 31 days
Novemebr = Ninthmonth (9mt), 30 days
December = Tenthmonth (Tmt), 31 days

As I mentioned above, dropping a day every 3600 years will produce a calendar that has a close approximation to the current value of the  length of the mean tropical year, as in the Revised Julian Calendar.  However, the Gregorian Calendar was intended at its inception to better track the mean northward vernal equinox year, to better calculate the date of Easter, which year varies from the mean tropical year over a 21,000 year cycle, as the perihelion point precesses relative to the equinoxes.  Dropping a day in the year 3600 will keep the calendar dates close to the current northward vernal equinox, but, after that, as the perihelion point will occur closer to the northward vernal equinox point, a more frequent adjustment will be necessary for several millenia.

This could be accomplished by dropping 2 days from some of the 3600 year cycles.  For instance, this could be done in the years 5600, 7200, 8800, and 10800 (intervals of 2000, 1600, 1600, and 2000 years).  But, there is plenty of time to decide this, and some future generation will be the one to decide, anyway.

-Walter Ziobro




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Re: If Reformed Re: Truncated Dee-Cecil Calendar

Walter J Ziobro
In reply to this post by Brij Bhushan metric VIJ
Dear Brij:

I thank you for your interest in my proposal.

However, as I see it, changing the lengths of the months, and the frequency of the leap dates are two separate issues.  It seems to me to be very difficult to change the relative lengths of the months within a year because people are accustomed to birthdays, anniversaries, and holidays occurring on certain calendar dates, and will show resistance to any such changes that they they perceive are too radical.  Recall that Pope Gregory made no changes to the lengths of the months in his reform; he only dropped some days, and changed the leap year rule, and only modestly.  This was probably so because many members of his own church had become accustomed to feasts and saints' days occurring on particular dates and would be disoriented by changing any of those too much. In fact, even Julius Caesar in his reform of the calendar tried to retain the lengths of the old lunar months as nearly as possible, and even kept the nones and ides even though they had no correspondence to actual astronomical events in his calendar. I believe that these cultural reasons are more powerful that the economic reasons that are often given for resisting such changes.

It is for this reason that it is my usual approach to create new month names if I construct a calendar that doesn't follow the month lengths of the Gregorian Calendar.  The alternative months are intended to be run in concurrence with the traditional Gregorian months, so that people can use either. This is not as unusual or impractical as it may sound.  Many business have alternative calendars for payroll purposes because many employees are paid weekly or biweekly, although their in-house calendars may not be as specific as mine.    And, as you can see, my proposal for the Truncated Dee-Cecil Calendar doesn't vary any of the month lengths.  I have, in fact, already created alternative month names for several variants of the Gregorian Calendar and leap year calendars based upon the Gregorian Calendar.  I can do the same for Truncated Dee-Cecil Calendar, if need be, but I want to focus on the change to the leap year rule in this proposal.

As for your proposal to add one day to February, and subtract one day from July, my alternative month names can accommodate this proposal quite well.  Several of the month names that I have proposed here:

  http://calendars.wikia.com/wiki/Alternate_month_Gregorian_calendars

can be adopted to your proposal by using several of the alternative months that would start on the same days as each of the months that would be changed by you.  This would produce a calendar like this:

January (31 days)
February (29 days/30 in LY)
Primember (31 days)
Secundilis (30 days)
Tertember (31 days)
Quartilis (30 days)
Quintember (30 days)
August (31 days)
September (30 days)
October (31 days)
November (30 days)
December (31 days)


-Walter Ziobro


 

-----Original Message-----
From: Brij Bhushan metric VIJ <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Sun, Jul 23, 2017 12:38 pm
Subject: If Reformed Re: Truncated Dee-Cecil Calendar

Walter, Karl cc sirs:
>However, if the calendar in not converted >by then, both calendars could run >concurrently.  To minimize any confusion, >alternative month names can be used for >the Truncated Dee-Cecil Calendar. 
If calendar gets Reformed to any 'candidate' to be a possible World Calendar, won't there be many changes compared with the proposal of my "JUST shifting the Day of July 31 to become February 29th (all years)  
image1.JPG
& and gain the title being the Easiest, Surest and Cheapest - EVER, proposed option for taming the passage of 'events & Time count' - with or without Leap Weeks; including Decimalisation of Time of the Hour in terms of 15* Arc-angle, also defining the Nautical Kilometre:
image2.JPG
NEVER in history man has done to attempt define/Reform calendars in ONE stroke, 
image3.JPG
addressing most issues, sir.
Regards,
Ex-Flt.Lt. Brij Bhushan VIJ, Author
Brij-Gregorian Modified Calendar
Sunday, 2017 July 23H09:64 (decimal)
Sent from my iPhone

On Jul 23, 2017, at 8:21 AM, Walter J Ziobro <[hidden email]> wrote:

TRUNCATED DEE-CECIL CALENDAR

The Truncated Dee-Cecil Calendar is a variation of the calendar with the 33 year leap day cycle proposed by William Cecil.  In this version, the 33 year leap day cycle would continue for 12 cycles of 396 years, after which there would be one four-year olympiad, for a total of 400 years. The 33 year cycles would then recommence in the next year.  Then, one day would be dropped on average every 3,600 years.

There are 4 advantages of such a calendar:

1.  The 33 year leap day cycle would cause less jitter of the equinox and solstice dates.

2. The application of ISO 8601 rules to such a calendar would cause the 53rd week of the week numbering scheme to be more smoothly distributed over the 400 year period.  This could also make concurrence with leap-week calendars more symmetrical.

3.  The 400 year cycle would have 146,097 days, or 20,871 weeks, exactly the same as the current Gregorian Calendar, which would assist, either in conversion from one calendar to the other, or in date-to-date mapping, if both calendars run concurrently.

4. The 3600 year correction would give the calendar 1,314,872 days in as many years, for an average year of 365.242222 days, exactly the same average tropical year as Milankovich's Revised Julian Calendar. In this way, this calendar could be reconciled with the Revised Julian Calendar, as well. (However, there is an issue of which average year to use; see below).

Currently, both the Gregorian and the Truncated Dee-Cecil Calendar have the same calendar dates.  This is so because the 33 year cycle recommenced in 2001, and both calendars will have the same dates until 2036, which will be a leap year in the Gregorian Calendar, but not the Truncated Dee-Cecil Calendar.  Thus, it would be possible to convert from the Gregorian Calendar to the Truncated Dee-Cecil Calendar at any time from now until 2036 without adjusting any dates.  

However, if the calendar in not converted by then, both calendars could run concurrently.  To minimize any confusion, alternative month names can be used for the Truncated Dee-Cecil Calendar.  Since Dee and Cecil were both Englishmen, English names for the alternative months seem appropriate. So, the alternative month names for the corresponding Gregorian month names could be:

Gregorian to Truncated Dee-Cecil:

January = Newmonth (Nmt), 31 days
February = Shortmonth (Smt), 28/29 days
March = Firstmonth (1mt), 31 days
April = Secondmoth (2mt), 30 days
May = Thirdmonth (3mt), 31 days
June = Fourthmonth (4mt), 30 days
July = Fifthmonth (5mt), 31 days
August = Sixthmonth (6mt), 31 days
Septemebr = Seventhmonth (7mt), 30 days
October = Eighthmonth (8mt), 31 days
Novemebr = Ninthmonth (9mt), 30 days
December = Tenthmonth (Tmt), 31 days

As I mentioned above, dropping a day every 3600 years will produce a calendar that has a close approximation to the current value of the  length of the mean tropical year, as in the Revised Julian Calendar.  However, the Gregorian Calendar was intended at its inception to better track the mean northward vernal equinox year, to better calculate the date of Easter, which year varies from the mean tropical year over a 21,000 year cycle, as the perihelion point precesses relative to the equinoxes.  Dropping a day in the year 3600 will keep the calendar dates close to the current northward vernal equinox, but, after that, as the perihelion point will occur closer to the northward vernal equinox point, a more frequent adjustment will be necessary for several millenia.

This could be accomplished by dropping 2 days from some of the 3600 year cycles.  For instance, this could be done in the years 5600, 7200, 8800, and 10800 (intervals of 2000, 1600, 1600, and 2000 years).  But, there is plenty of time to decide this, and some future generation will be the one to decide, anyway.

-Walter Ziobro



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Re: Truncated Dee-Cecil Calendar

Walter J Ziobro
In reply to this post by Victor Engel
Dear Victor Engel:

I thank you for your comments.

Putting aside the proposal for the long-term adjustments, which we won't have to worry about for 1600 years, the use of the 33 year leap day rule would eliminate the 8 year leap day gap that happens in the Gregorian Calendar around century years not divisible by 400.  Using the 33 year rule over 400 years would not result in any leap day occurring any later than 5 years after the prior one, even across the 400 year change.  So the jitter in the calendar would be reduced almost to the level found in the uninterrupted 33 year cycle.

So, why not run the 33 year cycle uninterrupted, you ask?  The convenient number of total days in 400 years of the Gregorian Calendar has a number of whole weeks that can produce a repeatable cycle of symmetric leap weeks if such leap weeks are defined in accordance with ISO 8601 applied to the 33 year leap day cycle   It also makes mapping between the traditional Gregorian Calendar and the proposed calendar easy over a shorter period (400 years), if both run concurrently.  The uninterrupted 33 year leap day rule doesn't reconcile with the Gregorian Calendar, and eventually falls out of syn by one day after 13,200 years

Now, returning to the question of the long term adjustment, it may be true that the Dee-Cecil calendar with the uninterrupted 33 year leap day rule may not need to make a long term adjustment as soon as my proposal, but, eventually, even the uninteruped Dee-Cecil calendar will prove to be too long for any tropical year and have to make a long term adjustment.  If this isn't done by dropping a day, then the cycle may have to be modified to a 29 year cycle for a few cycles to accomplish the adjustment.  Perhaps over the very long run that is less jittery, but certainly much more complicated.  The benefit of my long term adjustment by dropping a day every 3600 years, on average, is that it brings the proposed calendar into sync with the Revised Julian Calendar.  But, once again, we should not worry too much about the long term adjustment because the decision will be made in the distant future by a generation with more historical data than we have currently.

-Walter Ziobro




-----Original Message-----
From: Victor Engel <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Sun, Jul 23, 2017 12:45 pm
Subject: Re: Truncated Dee-Cecil Calendar

Dear Walter and Calendar People,

The biggest issue I see with such a scheme is that you lose the simplicity and accuracy of the Dee-Cecil calendar. Also, can you explain how interrupting the simple 33 year pattern causes less jitter? It seems like that would introduce jitter not already there, especially for the spring equinox, which is the one it is meant to track.

Victor

On Sun, Jul 23, 2017 at 10:21 AM, Walter J Ziobro <[hidden email]> wrote:
TRUNCATED DEE-CECIL CALENDAR

The Truncated Dee-Cecil Calendar is a variation of the calendar with the 33 year leap day cycle proposed by William Cecil.  In this version, the 33 year leap day cycle would continue for 12 cycles of 396 years, after which there would be one four-year olympiad, for a total of 400 years. The 33 year cycles would then recommence in the next year.  Then, one day would be dropped on average every 3,600 years.

There are 4 advantages of such a calendar:

1.  The 33 year leap day cycle would cause less jitter of the equinox and solstice dates.

2. The application of ISO 8601 rules to such a calendar would cause the 53rd week of the week numbering scheme to be more smoothly distributed over the 400 year period.  This could also make concurrence with leap-week calendars more symmetrical.

3.  The 400 year cycle would have 146,097 days, or 20,871 weeks, exactly the same as the current Gregorian Calendar, which would assist, either in conversion from one calendar to the other, or in date-to-date mapping, if both calendars run concurrently.

4. The 3600 year correction would give the calendar 1,314,872 days in as many years, for an average year of 365.242222 days, exactly the same average tropical year as Milankovich's Revised Julian Calendar. In this way, this calendar could be reconciled with the Revised Julian Calendar, as well. (However, there is an issue of which average year to use; see below).

Currently, both the Gregorian and the Truncated Dee-Cecil Calendar have the same calendar dates.  This is so because the 33 year cycle recommenced in 2001, and both calendars will have the same dates until 2036, which will be a leap year in the Gregorian Calendar, but not the Truncated Dee-Cecil Calendar.  Thus, it would be possible to convert from the Gregorian Calendar to the Truncated Dee-Cecil Calendar at any time from now until 2036 without adjusting any dates.  

However, if the calendar in not converted by then, both calendars could run concurrently.  To minimize any confusion, alternative month names can be used for the Truncated Dee-Cecil Calendar.  Since Dee and Cecil were both Englishmen, English names for the alternative months seem appropriate. So, the alternative month names for the corresponding Gregorian month names could be:

Gregorian to Truncated Dee-Cecil:

January = Newmonth (Nmt), 31 days
February = Shortmonth (Smt), 28/29 days
March = Firstmonth (1mt), 31 days
April = Secondmoth (2mt), 30 days
May = Thirdmonth (3mt), 31 days
June = Fourthmonth (4mt), 30 days
July = Fifthmonth (5mt), 31 days
August = Sixthmonth (6mt), 31 days
Septemebr = Seventhmonth (7mt), 30 days
October = Eighthmonth (8mt), 31 days
Novemebr = Ninthmonth (9mt), 30 days
December = Tenthmonth (Tmt), 31 days

As I mentioned above, dropping a day every 3600 years will produce a calendar that has a close approximation to the current value of the  length of the mean tropical year, as in the Revised Julian Calendar.  However, the Gregorian Calendar was intended at its inception to better track the mean northward vernal equinox year, to better calculate the date of Easter, which year varies from the mean tropical year over a 21,000 year cycle, as the perihelion point precesses relative to the equinoxes.  Dropping a day in the year 3600 will keep the calendar dates close to the current northward vernal equinox, but, after that, as the perihelion point will occur closer to the northward vernal equinox point, a more frequent adjustment will be necessary for several millenia.

This could be accomplished by dropping 2 days from some of the 3600 year cycles.  For instance, this could be done in the years 5600, 7200, 8800, and 10800 (intervals of 2000, 1600, 1600, and 2000 years).  But, there is plenty of time to decide this, and some future generation will be the one to decide, anyway.

-Walter Ziobro




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Brij-Gregorian Modifued Re: Truncated Dee-Cecil Calendar

Brij Bhushan metric VIJ
Victor, Walter, cc sirs:
  I am aware that I have NO right to comment on the 'historiography' and aims in sight for the Reform of Gregorian calendar. I am NO religious 'pundit' but a man on street who thinks for the betterment of astronomy for any Reform of the calendar. Unfortunately my qualification is restricted to my 'examination of any material that came my way'; not having gone to find flaws but to make desired corrections needed in the interest of Tax Payer, the new learners at school/college/the banker for his ease & savings, if the Reform ever took shape. Thus, I set my target for Mean Year at Astronomers Average Mean Year Value i.e. 365.242189669781 days (not with permutations/combinations) but going the simplest way: Mean Year=(365+31/128)= 365.2421875 days (with or without Leap Days/Leap Weeks), under discussions/ examination since 1971 June 06....
image1.JPG
>....which we won't have to worry about for 1600 years, the use of the 33 year leap day rule would eliminate the 8 year leap day gap that happens in the Gregorian Calendar around century years not divisible by >400.

Leap Day modification desired is only at 128th Year by omitting a day like the 'centurion leap rule'; and get desired Mean Year. Where is the need for any recurring correction, the difference being only 0.1874692 second! 

Correction/alignments to current Gregorian /Julian Mean Years; and historical records of past or future events - can be done, as discussed, adding/ deleting ONE day every 3200-years!


>The uninterrupted 33 year leap day rule doesn't reconcile with the Gregorian Calendar, and eventually falls out of syn >by one day after 13,200 years.

Practically NO change is desired in case of my 'modification' of shifting the Day of July 31 to the advantage of February 29-people born to celebrate & enjoy their birthdate "every year". Leap Day if used gets placed between June 30 & July 01, making two half years equal; or alternately place the added 53rd week of year' ONCE every six(6) years per Leap Week Rule, discussed with listserv. There is NO need to drop or add any Day for adjustments, as I see, for 460876-years!


>The benefit of my long term adjustment by dropping a day every 3600 years, on average, is that it brings the proposed calendar into sync with the >Revised Julian Calendar. 

World is familiar with the use & or implementation of dates in currently used Gregorian calendar: where is the need to empty the Tax-Payers' 💰, which can be used for productive projects. Syncing of any calendar is already being done for Gregorian calendar; with National/regional calendars - some 400 odd currrntly used in the world. I often wonder, what are we after - stall the need to Reform the calendar 'available' at NO or minimal cost; or continue for search of "a hitler like religious head to implement his 'veto-calendar'. Pity the tiny-tots at schools and the lady at home managing her monthly/weekly budget, sirs!

Regards,

Ex-Flt.Lt. Brij Bhushan VIJ, 

Author

Brij-Gregorian Modified Calendar, 

Monday, 2017 July 24H00:33 (decimal)


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On Jul 23, 2017, at 9:13 PM, Walter J Ziobro <[hidden email]> wrote:

The benefit of my long term adjustment by dropping a day every 3600 years, on average, is that it brings the proposed calendar into sync with the Revised Julian Calendar. 
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Re: Truncated Dee-Cecil Calendar

Irv Bromberg
In reply to this post by Walter J Ziobro
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Walter J Ziobro [[hidden email]]
Sent: Sunday, July 23, 2017 11:21

The Truncated Dee-Cecil Calendar is a variation of the calendar with the 33 year leap day cycle proposed by William Cecil.  In this version, the 33 year leap day cycle would continue for 12 cycles of 396 years, after which there would be one four-year olympiad, for a total of 400 years. The 33 year cycles would then recommence in the next year.  Then, one day would be dropped on average every 3,600 years.

There are 4 advantages of such a calendar:

1.  The 33 year leap day cycle would cause less jitter of the equinox and solstice dates.

[Bromberg] The jitter, relative to the calendar mean year, of the truncated Dee-Cecil calendar 400-year cycle (ignoring the stupid idea of dropping another day every 3600 years or so) is 399/400 days, which is slightly greater than the 32/33 day jitter of the Dee calendar. Note that the leap rule becomes multi-step:
  • compute the year# in the 400-year cycle Yin400 = MOD(Year, 400)
  • within each 400-year cycle compute the year# in the 33-year cycle Yin33 = MOD(Yin400,33)
  • leap if MOD(8 * Yin33, 33) < 8

The southward equinox and both solstices are irrelevant.

Don't confuse short-term arithmetic jitter with long-term astronomical drift.


3.  The 400 year cycle would have 146,097 days, or 20,871 weeks, exactly the same as the current Gregorian Calendar, which would assist, either in conversion from one calendar to the other, or in date-to-date mapping, if both calendars run concurrently.

[Bromberg] Having a whole number of weeks per cycle is advantageous for having a parallel ISO-like leap week calendar, but this attribute ought to be irrelevant for inter-converting calendar dates, which for any calendar conversions can be conveniently and universally carried out using the ordinal day number relative to an agreed-upon epoch as the common denominator, such as the rata die of Dershowitz and Reingold in "Calendrical Calculations".

4. The 3600 year correction would give the calendar 1,314,872 days in as many years, for an average year of 365.242222 days, exactly the same average tropical year as Milankovich's Revised Julian Calendar. In this way, this calendar could be reconciled with the Revised Julian Calendar, as well.

[Bromberg] The mean tropical year is irrelevant to calendars, because it is in the wrong time units (atomic time) not the mean solar time that calendars need. In the present era the discrepancy is arguably negligible (I don't agree), but it is growing approximately quadratically into the future. If one were to compute the average of the instantaneous lengths of the solar year in mean solar days at the solar longitudes of aphelion and of perihelion (difficult to determine because of the astronomical jitter of those events caused by Earth and Moon careening around the Earth-Moon barycenter), then that might be a valid target, but why pick any target that can't be observationally verified or accurately calculated?
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Re: Truncated Dee-Cecil Calendar

Karl Palmen
Dear Walter, Irv and Calendar People

It is not clear whether 399 or 400 is a leap year.

For computational purposes the leap year rule can be simplified to year Y is a leap if and only if

(97*Y + K) mod 400 < 97

where K = 97 if 399 is a leap year or 96 if 400 is a leap year.

This can then be converted to a day of new year rule, if an epoch is provided.

I've expressed a preference for K=235, which has the same symmetry as the Gregorian calendar and Irv has expressed a preference for K=200, which makes the 400-year cycle starting from year 1 almost symmetrical. It also makes a year's accumulator have the same last digit as the year.

Karl

16(12(03
________________________________
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Irv Bromberg [[hidden email]]
Sent: 25 July 2017 01:03
To: [hidden email]
Subject: Re: Truncated Dee-Cecil Calendar

From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Walter J Ziobro [[hidden email]]
Sent: Sunday, July 23, 2017 11:21

The Truncated Dee-Cecil Calendar is a variation of the calendar with the 33 year leap day cycle proposed by William Cecil.  In this version, the 33 year leap day cycle would continue for 12 cycles of 396 years, after which there would be one four-year olympiad, for a total of 400 years. The 33 year cycles would then recommence in the next year.  Then, one day would be dropped on average every 3,600 years.

There are 4 advantages of such a calendar:

1.  The 33 year leap day cycle would cause less jitter of the equinox and solstice dates.

[Bromberg] The jitter, relative to the calendar mean year, of the truncated Dee-Cecil calendar 400-year cycle (ignoring the stupid idea of dropping another day every 3600 years or so) is 399/400 days, which is slightly greater than the 32/33 day jitter of the Dee calendar. Note that the leap rule becomes multi-step:

  *   compute the year# in the 400-year cycle Yin400 = MOD(Year, 400)
  *   within each 400-year cycle compute the year# in the 33-year cycle Yin33 = MOD(Yin400,33)
  *   leap if MOD(8 * Yin33, 33) < 8

The southward equinox and both solstices are irrelevant.

Don't confuse short-term arithmetic jitter with long-term astronomical drift.


3.  The 400 year cycle would have 146,097 days, or 20,871 weeks, exactly the same as the current Gregorian Calendar, which would assist, either in conversion from one calendar to the other, or in date-to-date mapping, if both calendars run concurrently.

[Bromberg] Having a whole number of weeks per cycle is advantageous for having a parallel ISO-like leap week calendar, but this attribute ought to be irrelevant for inter-converting calendar dates, which for any calendar conversions can be conveniently and universally carried out using the ordinal day number relative to an agreed-upon epoch as the common denominator, such as the rata die of Dershowitz and Reingold in "Calendrical Calculations".

4. The 3600 year correction would give the calendar 1,314,872 days in as many years, for an average year of 365.242222 days, exactly the same average tropical year as Milankovich's Revised Julian Calendar. In this way, this calendar could be reconciled with the Revised Julian Calendar, as well.

[Bromberg] The mean tropical year is irrelevant to calendars, because it is in the wrong time units (atomic time) not the mean solar time that calendars need. In the present era the discrepancy is arguably negligible (I don't agree), but it is growing approximately quadratically into the future. If one were to compute the average of the instantaneous lengths of the solar year in mean solar days at the solar longitudes of aphelion and of perihelion (difficult to determine because of the astronomical jitter of those events caused by Earth and Moon careening around the Earth-Moon barycenter), then that might be a valid target, but why pick any target that can't be observationally verified or accurately calculated?
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Re: Truncated Dee-Cecil Calendar

Karl Palmen
Dear Walter Irv and Calendar People

Oops! K=235 & K=200 were for leap week calendars. My preference is K=48 for a leap day calendar. This is just 48 different from 96 and 49 different from 97, so only that number of leap years differ (by one year).

Karl

________________________________
From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 26 July 2017 12:36
To: East Carolina University Calendar discussion List
Subject: RE: Truncated Dee-Cecil Calendar

Dear Walter, Irv and Calendar People

It is not clear whether 399 or 400 is a leap year.

For computational purposes the leap year rule can be simplified to year Y is a leap if and only if

(97*Y + K) mod 400 < 97

where K = 97 if 399 is a leap year or 96 if 400 is a leap year.

This can then be converted to a day of new year rule, if an epoch is provided.

I've expressed a preference for K=235, which has the same symmetry as the Gregorian calendar and Irv has expressed a preference for K=200, which makes the 400-year cycle starting from year 1 almost symmetrical. It also makes a year's accumulator have the same last digit as the year.

Karl

16(12(03
________________________________
From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Irv Bromberg [[hidden email]]
Sent: 25 July 2017 01:03
To: [hidden email]
Subject: Re: Truncated Dee-Cecil Calendar

From: East Carolina University Calendar discussion List [[hidden email]] on behalf of Walter J Ziobro [[hidden email]]
Sent: Sunday, July 23, 2017 11:21

The Truncated Dee-Cecil Calendar is a variation of the calendar with the 33 year leap day cycle proposed by William Cecil.  In this version, the 33 year leap day cycle would continue for 12 cycles of 396 years, after which there would be one four-year olympiad, for a total of 400 years. The 33 year cycles would then recommence in the next year.  Then, one day would be dropped on average every 3,600 years.

There are 4 advantages of such a calendar:

1.  The 33 year leap day cycle would cause less jitter of the equinox and solstice dates.

[Bromberg] The jitter, relative to the calendar mean year, of the truncated Dee-Cecil calendar 400-year cycle (ignoring the stupid idea of dropping another day every 3600 years or so) is 399/400 days, which is slightly greater than the 32/33 day jitter of the Dee calendar. Note that the leap rule becomes multi-step:

  *   compute the year# in the 400-year cycle Yin400 = MOD(Year, 400)
  *   within each 400-year cycle compute the year# in the 33-year cycle Yin33 = MOD(Yin400,33)
  *   leap if MOD(8 * Yin33, 33) < 8

The southward equinox and both solstices are irrelevant.

Don't confuse short-term arithmetic jitter with long-term astronomical drift.


3.  The 400 year cycle would have 146,097 days, or 20,871 weeks, exactly the same as the current Gregorian Calendar, which would assist, either in conversion from one calendar to the other, or in date-to-date mapping, if both calendars run concurrently.

[Bromberg] Having a whole number of weeks per cycle is advantageous for having a parallel ISO-like leap week calendar, but this attribute ought to be irrelevant for inter-converting calendar dates, which for any calendar conversions can be conveniently and universally carried out using the ordinal day number relative to an agreed-upon epoch as the common denominator, such as the rata die of Dershowitz and Reingold in "Calendrical Calculations".

4. The 3600 year correction would give the calendar 1,314,872 days in as many years, for an average year of 365.242222 days, exactly the same average tropical year as Milankovich's Revised Julian Calendar. In this way, this calendar could be reconciled with the Revised Julian Calendar, as well.

[Bromberg] The mean tropical year is irrelevant to calendars, because it is in the wrong time units (atomic time) not the mean solar time that calendars need. In the present era the discrepancy is arguably negligible (I don't agree), but it is growing approximately quadratically into the future. If one were to compute the average of the instantaneous lengths of the solar year in mean solar days at the solar longitudes of aphelion and of perihelion (difficult to determine because of the astronomical jitter of those events caused by Earth and Moon careening around the Earth-Moon barycenter), then that might be a valid target, but why pick any target that can't be observationally verified or accurately calculated?
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