Shifting Month Calendar RE: French Republican Leap Year Compromise? RE: ...

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Shifting Month Calendar RE: French Republican Leap Year Compromise? RE: ...

Karl Palmen

Dear Walter and Calendar People

 

Walter said

I am thinking that the 900 year rule would work nicely with the French Republican calendar, and require very little adjustment of the calendar to the current length of the average tropical year for a long period.  The long month lengths  (of 31 days) could be shifted to the subsequent months on the calendar every 1.800 years, to keep the equinox and solstices close to the commencement of each quarter. This periodic shifting would keep the lengths of the seasonal tropical years close to the actual lengths of each.

 

KARL REPLIES:  This concerns a solar calendar whose months have 30 or 31 days whose 31-day month cluster around the aphelion to ensure that ecliptic longitudes of the months are nearly spaced evenly at 30 degrees. The run of 31-day months is occasionally shifted so that it remains around the aphelion.

If you want a calendar with shifting long months of 31 days, it’s mean year, as determined by the leap year rule, must not be the mean tropical year, but the tropical year starting at its new year, assuming the shift takes effect from a new year.

 

If the shift takes effect from some other time of year, the tropical year starting at that time of year must be used. Also the shift may add or remove a day to/from the year within which it begins to takes effect. This suggests initially 33-year cycle and shift taking effect at March equinox time of year and later perhaps a cycle suited to the June solstice and the shift changes taking effect at the June solstice time of year. Note that the shifts add jitter.

 

 

I look at this again in more detail. Suppose the shift takes effect at the start of the calendar year. Then the mean year for the calendar year is exactly the mean year determined by the leap year rule. That is not always so for years starting at other months and this is how other months stay with their respective ecliptic longitudes.  

 

If the calendar year ends with a 31-day month before a shift so begins with a 31-day month after the shift, the shift will extend one run of 31-day months. This will cause any year ending with a 30-day month before the shift so starting with a 30-day month after the shift, to have an extra day, when the shift occurs within it. So the mean year for such years will be 1/1,800 days more than the mean year determined by the leap year rule, if shifts occur once every 1,800 years.

 

Similarly, if the calendar year ends with a 30-day month before a shift so begins with a 30-day month after the shift, the shift will extend one run of 30-day months. This This will cause any year ending with a 31-day month before the shift so starting with a 31-day month after the shift, to have one day less, when the shift occurs within it. So the mean year for such years will be 1/1,800 days less than the mean year determined by the leap year rule, if shifts occur once every 1,800 years.

 

So at any one time two mean years will be in operation. These two mean years change only when a calendar year begins with the first month of a run of 31-day or 30-day months. At other times, each shift changes the mean year for two of the months to the other of the two mean years.

 

So let’s look at a simple example. Suppose the leap year rule give mean year of 365.242 days and shifts occur once every 2000 years. Then we’ll have mean years

365.2425 days (l)

365.242 days (m) &

365.2415 days (s)

 

Then as the shifting goes one years beginning with the months shown have the mean lengths shown

 

31(m) 31(m) 31(m) 31(m) 31(m) 30(l) 30(l) 30(l) 30(l) 30(l) 30(l) 31(m)

31(m) 31(m) 31(m) 31(m) 31(m) 31(m) 30(l) 30(l) 30(l) 30(l) 30(l) 30(l)

30(m) 31(s) 31(s) 31(s) 31(s) 31(s) 31(s) 30(m) 30(m) 30(m) 30(m) 30(m)

30(m) 30(m) 31(s) 31(s) 31(s) 31(s) 31(s) 31(s) 30(m) 30(m) 30(m) 30(m)

30(m) 30(m) 30(m) 30(m) 30(m) 31(s) 31(s) 31(s) 31(s) 31(s) 31(s) 30(m)

30(m) 30(m) 30(m) 30(m) 30(m) 30(m) 31(s) 31(s) 31(s) 31(s) 31(s) 31(s)

31(m) 30(l) 30(l) 30(l) 30(l) 30(l) 30(l) 31(m) 31(m) 31(m) 31(m) 31(m)

31(m) 31(m) 30(l) 30(l) 30(l) 30(l) 30(l) 30(l) 31(m) 31(m) 31(m) 31(m)

 

In an actual calendar, the leap year rule would be changed several times in a precession cycle, then the (l), (m) & (s) would indicate relative mean year lengths. Also the interval between shifts would not be exactly 2000 years, but a little less, so the differences between the mean year lengths would be a little larger.

 

The months are shown by their lengths in a leap year. In a common year, the last month would have one day less.

 

Karl

 

15(14(22

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Walter J Ziobro
Sent: 26 July 2016 06:07
To: [hidden email]
Subject: Re: French Republican Leap Year Compromise? RE: Georgian Calendar New Year Solstice. 124-year cycle?

 

Dear Karl and Calendar List:

I have been thinking some more about applying a 33 year leap day rule to the French Republican Calendar.  One could either apply the invariable leap day rule of the Dee and Dee-Cecil calendars, and get an average year length of 365.242424..days.

However, I have thought of two variations of the 33 year leap day rule:

1, The 400 year truncated 33-year leap day rule (I have mentioned this idea before). and

2  The 900 year truncated 33- year leap day rule.

The 400 year rule would have twelve periods of 33 years, plus one 4 year olympiad.  It would have exactly as many days in 400 years as the current Gregorian calendar (146.097 days), and have the same average year length of 365.2425 days.

The 900 year rule would have 27 periods of 33 years, plus 9 years with 2 leap days.  It would have 328,718 days, exactly as many as 900 years of the Revised Julian calendar', and like the Revised Julian calendar, have an average length of 365.2422222...
 

4 cycles of the 900 year rule period would have 1,314,872 days. exactly 1 day less than 3600 years of the 400 year rule, or of the Gregorian calendar

I am thinking that the 900 year rule would work nicely with the French Republican calendar, and require very little adjustment of the calendar to the current length of the average tropical year for a long period.  The long month lengths  (of 31 days) could be shifted to the subsequent months on the calendar every 1.800 years, to keep the equinox and solstices close to the commencement of each quarter. This periodic shifting would keep the lengths of the seasonal tropical years close to the actual lengths of each.

-Walter Ziobro