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Re: Bahai leap month variant
by Irv Bromberg
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On Apr 10, 2006, at 07:34, Palmen, KEV (Karl) wrote:
> The page
> http://www.the-light.com/cal/kp_NdaySolarCyc2.html
> tells you which are the shortest cycles you can use. These are
>
>> From the 103-year and 9-year cycles, one gets a 112-year cycle:
>> From a number of 103-year cycles and one 112-year cycles one can
>> construct more accurate cycles.
>
> #103 Days Years LongYrs YrLength
> ----------------------------------
> 0 40907 112 25 365.24107
> 1 78527 215 48 365.24186
> 2 116147 318 71 365.24214
> 3 153767 421 94 365.24228
> 4 191387 524 117 365.24237
>
> The 524-year cycle is also a whole number (27341) of weeks.
>
> Irv has found this cycle and is aware that it is equivalent to the
> 524-year leap week cycle with 93 leap weeks. See cycle of mean year
> 365.242366 days in
> http://www.hermetic.ch/cal_stud/palmen/lweek1.htm#cycle
>
> Irv has also found the 9-year subcycle, but not the 103-year subcycle.
Bromberg says:
I actually did find all of the cycles that you outlined above, but
didn't report them because I felt that they weren't close enough to the
target mean equinoctial or solstitial year lengths, or because they
didn't have MOD 7 = 0 days in the cycle. I also found quite a few
cycles that are a few thousand years long (6709, 1993, 1469, 5567,
2311, 1160, 1899, and 2280 years, in order of descending mean year
length), but stuck them out. I was trying to limit the length of my
already long message on the topic, pending indication of interest in
this matter.
So I guess that the continued fraction search method isn't too bad
after all. Your method is more direct, systematic, and predictive, and
there could still easily be an advantageous cycle that I missed. And
Victor's and Karl's lists of cycles and cycles are very instructive.
-- Irv Bromberg, Toronto, Canada
<http://www.sym454.org/>
> The page
> http://www.the-light.com/cal/kp_NdaySolarCyc2.html
> tells you which are the shortest cycles you can use. These are
>
>> From the 103-year and 9-year cycles, one gets a 112-year cycle:
>> From a number of 103-year cycles and one 112-year cycles one can
>> construct more accurate cycles.
>
> #103 Days Years LongYrs YrLength
> ----------------------------------
> 0 40907 112 25 365.24107
> 1 78527 215 48 365.24186
> 2 116147 318 71 365.24214
> 3 153767 421 94 365.24228
> 4 191387 524 117 365.24237
>
> The 524-year cycle is also a whole number (27341) of weeks.
>
> Irv has found this cycle and is aware that it is equivalent to the
> 524-year leap week cycle with 93 leap weeks. See cycle of mean year
> 365.242366 days in
> http://www.hermetic.ch/cal_stud/palmen/lweek1.htm#cycle
>
> Irv has also found the 9-year subcycle, but not the 103-year subcycle.
Bromberg says:
I actually did find all of the cycles that you outlined above, but
didn't report them because I felt that they weren't close enough to the
target mean equinoctial or solstitial year lengths, or because they
didn't have MOD 7 = 0 days in the cycle. I also found quite a few
cycles that are a few thousand years long (6709, 1993, 1469, 5567,
2311, 1160, 1899, and 2280 years, in order of descending mean year
length), but stuck them out. I was trying to limit the length of my
already long message on the topic, pending indication of interest in
this matter.
So I guess that the continued fraction search method isn't too bad
after all. Your method is more direct, systematic, and predictive, and
there could still easily be an advantageous cycle that I missed. And
Victor's and Karl's lists of cycles and cycles are very instructive.
-- Irv Bromberg, Toronto, Canada
<http://www.sym454.org/>
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