Symmetry Statement and Divide-by-Six RE: using Primary cycles of 11,15,19&33-years RE:

Dear Brij, Irv, Tom and Calendar People

Brij said (quoting me in bold type):

>If a leap cycle is arranged such that the list of leap years is symmetrical, so that year n of each cycle has the same leap status as >the symmetrical year occurring n years before the first year of the next cycle, then the start of the first year of every cycle will >always be at the average for that cycle.
I have been attempting to build table of my Div. six(6) approach to place Leap Weeks and Keplers' Leap Weeks in my 7*128=896-year cycle using 159 Leap Weeks or 834-years/148 Leap Weeks

Brij refers to his idea of having a leap week on each year whose number is divisible by 6 plus some additional years referred to as Kepler’s Leap Week years. No such cycle can have the symmetry to which I refer to in the statement I made and Brij quoted and so the statement does not apply to any such cycle (i.e. the first year of such a cycle need not have an average start).

However the 834-year cycle may have one or two years that do have an average start, but they are not easy to find.

The 896-year cycle, has no year with an average start no matter how the 159 leap weeks are arranged, because each year has a start that is an odd multiple of 1/256 days from average. The same applies to the 400-year cycle with 71 leap weeks, because each year has a start that is an odd multiple of 1/800 days from average.

Karl

10(07(28

Irv, Tom Peters, Karl & CC:
>If a leap cycle is arranged such that the list of leap years is symmetrical, so that year n of each cycle has the same leap status as >the symmetrical year occurring n years before the first year of the next cycle, then the start of the first year of every cycle will >always be at the average for that cycle.
I have been attempting to build table of my Div. six(6) approach to place Leap Weeks and Keplers' Leap Weeks in my 7*128=896-year cycle using 159 Leap Weeks or 834-years/148 Leap Weeks & see combination for other cycles like 9405-years. From what I place at:
http://www.brijvij.com/bb_harappaTithi-Cycles.pdf
it may be seen that ANY cycle could be built using 11,19 & 33-years. I have tried to re-check my results and there could have been some typographic mistakes. I shall be grateful for pointing these. Karl's previous mail suggested to use larger PRIMARY cycles which, to my mind, can be made from my smaller cycle approach - especially the 19-year Lunar-Tithi cycle (in 6932.5 Tithi).
During this International Astronomy Year (2009) my inputs for A possible World Calendar  http://www.brijvij.com/bb_IndianContri..pdf and 
http://www.brijvij.com/bb_metro-contrbn.2007.pdf can become the cause for initaiating corrective actions for Reform of the Gregorian calendar.
 In my 896-year cycle, I place the start Era at [(Y2000 - 80) +/- 128] i.e. Y1920 [as also Year 0000 CE] and first Keplers LWk year at Year 2007 i.e. 87th year, followed by 9 more KLWs at intervals of 90-years; and likewise Era start for 834-year cycle remain at Y1920 but the First Keplers' Leap Week would be at Y2001 i.e. 81st year followed by 8 more KLWks at intervals of 84-years and repeating every 834-years.
 I am aware that Karl has a point suggesting (3*896)=2688-years to give Mean Year =365.2421875 days, while this distribution that I place has (149+10) 159 LWks, since 896-years have EACTLY 159 LWks to account. Karl's suggestion of (3*834)=2502-years is like saying (2*417)-years =834-years/(139+9)149 LWks.
Most cycles can be constructed from a combination of base cycles: 19-year Lunar (5*47=235 lunation) cycles, 33-year (12053-days) Solar cycle & 15-year cycle of indiction. What is the 'significance/importance' of this 15-year cycle of indiction, I am unaware? 11-year cycle does make some sense (being 3*11 of 33-solar cycle) that I have used in examining some break-ups for larger cycles!
Regards,
Brij Bhushan Vij
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