Leap Week Calendar Leap Rules RE: CALNDR-L Digest - 12 Feb 2012 to 13 Feb 2012 (#2012-62)

Dear Walter and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:CALNDR-L@...] On Behalf Of Amos Shapir
Sent: 12 February 2012 15:49
To: CALNDR-L@...
Subject: Fwd: CALNDR-L Digest - 10 Feb 2012 to 11 Feb 2012 (#2012-60)

The number of days in the 33 year cycle (a.k.a. the Khayam-Dee cycle)
is 12053, which is not divisible by 7; so there is no advantage to
this scheme.  If a leap-week calendar is in use, there is no point in
tying its leap rule to any leap-day calendar.  In order to keep the
400-year cycle, whose number of days (146097) is divisible by 7, it's
sufficient to just distribute the 71 leap weeks as evenly as possible,
with a scheme similar to:

656-656-65656-656-656-65656-656-656-65656-656-65656-656-656-65656-656-656-65656-656-65656



WALTER REPLIES TO BOTH AMOS & KARL:  

Thank you both for your imput.

When I apply the ISO 8601 week numbering rule to my modified 33 year leap rule, I get the following sequence (beginning with the 99th year of the prior quadricentury):

65656-656-656-65656-656-65656-656-656-65656-656-656-65656-656-656-65656-656-65656-656-656

KARL SAYS: (1,4,6,9,12,15,17)

I’m not quite sure what Walter means by  beginning with the 99th year of the prior quadricentury . It may be either 1699 or 1700. Making use of

http://the-light.com/cal/converter/  which  has a Dee-Cecil 33-year cycle calendar converter, I see that 1699  ended on a Thursday in both the Gregorian and Dee-Cecil calendars so could have leap week in Walter’s suggestion. I assume this.

The 19 leap week years that correspond to the start of the cycle and the hyphens are then

1699; 1727, 1744, 1761; 1789, 1806; 1834, 1851, 1868; 1896, 1913, 1930; 1958, 1975, 1992; 2020, 2037; 2065, 2082, where the comma is a ‘656’ and the semicolon is a ‘65656’.  Year 2099 occurs after the last comma.

This sequence can be matched with any of the sequences that Amos or Karl produce, altho at different starting points.  It seems to me that we have a distinction without a different, the distinction being that I applied the week numbering rules to the 33 year leap day rule, limited to 396 years, plus one extraneous quadrennial.

KARL SAYS:

Walter has not stated where the extraneous quadrennial would go.

Walter’s 65656-656-656-65656-656-65656-656-656-65656-656---656-65656-656-656-65656-656-65656-656-656 cycle does have a symmetry and it is about the hyphen I have lengthened. The corresponding leap week year is 1913.  This corresponds to 1800 or 2200 in my symmetrical suggestion.  My symmetrical suggestion has a long period of 4-yearly leap years 1984 ... 2016, which would contain the extraneous quadrennial. This corresponds to 2097 .. 2129 or 1697 ... 1729 in Walter’s suggestion. Also his placing of the last leap year of the 33-year cycle at year 33 rather than year 32 leads to the extraneous quadrennial occurring at the start of the long period of 4-yearly leap years, so it would be 1697 to 1701. I prefer the 32^nd year of the 33-year cycle being a leap years so that all leap years within a 33-year cycle are 4 years apart.

BTW, if I am not mistaken,  if the 33 year leap day rule is applied continuously without interruption for 3200 years, it will only be shorter than one day from the current Gregorian leap day rule, at which point there may be some adjustment required to the Gregorian rule anyway.  So, even a leap week calendar using a 400 year cycle will be accurate to the day for 8 such cycles, more or less.

KARL REPLIES:  Walter was mistaken as pointed out by  Simon Cassidy.  It is 13,200 years, which is 33 400-year cycles with  33*97 = 3201 leap days or 400 33-year cycles with 400*8 = 3200 leap days. The 3200 year arises from the comparison of the Gregorian 400-year cycle with the 128-year cycle of 31 leap days, which has a mean year of exactly 365.2421875 days. When made into a leap week calendar we get a 896-year cycle with 159 leap weeks.

Karl

12(08(23

-Walter Ziobro
  


KARL SAYS:
The arrangement of 656s and 65656s is exactly the same as for the 12-month and 13-month years of a 19-year Metonic cycle. Furthermore, Amos has arranged them (3,6,9,11,14,17,19) almost as for the Hebrew Calendar. The Hebrew calendar arrangement (3,6,8,11,14,17,19) would be

656-656-65656-656-656-65656-656-65656-656-656-65656-656-656-65656-656-656-65656-656-65656

A symmetrical arrangement based on (2,5,7,10,13,15,18) is

656-65656-656-656-65656-656-65656-656-656-65656-656-656-65656-656-65656-656-656-65656-656

And if the first interval is 200th to 206th year of the 400-year cycle, then the symmetry of the Gregorian calendar is kept and with Sunday starting weeks the mean new year can be exactly the same.

Note this symmetry is not the same as the Helios symmetry that Irv and I often refer to.