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Old Earth Calendar
Dear Calendar People
The New Earth Calendar got me thinking about what the Old Earth calendar would be like.
Like the New Earth Calendar, the Old Earth calendar had months of 28 days, but instead of a leap week, it had a leap month also of 28 days. A common year had 13 months and a leap year had 14 months.
The 13 ordinary months were named:
Azo, Boyo, Cox, Dow, Evo, Fuo, Goto, Hoso, Iro, Joqo, Kop, Loo & Mono.
and the leap month as named Naf.
Leap years occurred alternately once every 22 and 23 years, so giving a mean year of 365.244444... days.
The Not So Old Earth Calendar was the same as the Old Earth Calendar, except that once every 13 leap years there was one leap year that was 23 years from both the neighbouring leap years. This created a 293-year cycle of 13 leap years whose leap months total up to one whole common year. Indeed each of the 13 leap months took a name from a different ordinary month of the year so they could easily be counted to 13. The successive leap months starting with the leap month of the leap year that was 23 years from both its neighbours were named thus:
Gotonaf, Azonaf, Hosonaf, Boyonaf, Ironaf, Coxnaf, Joqonaf, Downaf, Kopnaf, Evonaf, Loonaf, Fuonaf & Mononaf.
Then someone thought of placing each leap month straight after the month it was named from (e.g. Azonaf after Azo) rather than at the end of the year as done previously and lo and behold, every 294th month was a leap month!
Karl
08(02(09
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 Re: Old Earth Calendar
Dear Karl,
So the DOW is the same for evry day in the 4th month. How interesting.
Victor
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto: CALNDR-L@...]On Behalf Of Palmen, KEV (Karl)
> Sent: Friday, April 07, 2006 9:02 AM
> To: CALNDR-L@...
> Subject: Old Earth Calendar
>
>
> Dear Calendar People
>
> The New Earth Calendar got me thinking about what the Old
> Earth calendar would be like.
>
> Like the New Earth Calendar, the Old Earth calendar had
> months of 28 days, but instead of a leap week, it had a leap
> month also of 28 days. A common year had 13 months and a leap
> year had 14 months.
>
> The 13 ordinary months were named:
> Azo, Boyo, Cox, Dow, Evo, Fuo, Goto, Hoso, Iro, Joqo, Kop, Loo & Mono.
> and the leap month as named Naf.
>
> Leap years occurred alternately once every 22 and 23 years,
> so giving a mean year of 365.244444... days.
>
> The Not So Old Earth Calendar was the same as the Old Earth
> Calendar, except that once every 13 leap years there was one
> leap year that was 23 years from both the neighbouring leap
> years. This created a 293-year cycle of 13 leap years whose
> leap months total up to one whole common year. Indeed each
> of the 13 leap months took a name from a different ordinary
> month of the year so they could easily be counted to 13. The
> successive leap months starting with the leap month of the
> leap year that was 23 years from both its neighbours were named thus:
> Gotonaf, Azonaf, Hosonaf, Boyonaf, Ironaf, Coxnaf, Joqonaf,
> Downaf, Kopnaf, Evonaf, Loonaf, Fuonaf & Mononaf.
>
> Then someone thought of placing each leap month straight
> after the month it was named from (e.g. Azonaf after Azo)
> rather than at the end of the year as done previously and lo
> and behold, every 294th month was a leap month!
>
> Karl
>
> 08(02(09
>
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Re: Old Earth Calendar
On Apr 7, 2006, at 10:02, Palmen, KEV (Karl) wrote:
> The New Earth Calendar got me thinking about what the Old Earth
> calendar would be like.
<snip>
> Then someone thought of placing each leap month straight after the
> month it was named from (e.g. Azonaf after Azo) rather than at the
> end of the year as done previously and lo and behold, every 294th
> month was a leap month!
Bromberg says:
A very interesting idea, which led me to think of an idea that might be
of more interest to the present-day Bahai:
Take the Bahai 19 days x 19 months with 4 or 5 days left over, and make
it a leap month calendar where the leap month has 19 days, applying a
leap month positioning and naming scheme that is similar your Old New
Earth Calendar idea. Such a calendar may appeal to the Bahai because
it takes the orphaned "days of awe" (sorry folks, I know that those a
really Holy Days, not days "in limbo") and converts them into a fully
intact month, preserving the use of the 19 throughout the calendar
(except that leap years would have 20 months). They might also like to
see the number 19 factored into the leap cycle as many times as
possible.
-- Irv Bromberg, Toronto, Canada
< http://www.sym454.org/>
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Re: Old Earth Calendar
> (except that leap years would have 20 months). They might
> also like to
> see the number 19 factored into the leap cycle as many times as
> possible.
That might be hard to do since 19 is prime. <grin>
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Re: Old Earth Calendar
Dear Victor, Irv and Calendar People
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto: CALNDR-L@...]On Behalf Of Engel,Victor
Sent: 07 April 2006 17:29
To: CALNDR-L@...
Subject: Re: Old Earth Calendar
> (except that leap years would have 20 months). They might
> also like to
> see the number 19 factored into the leap cycle as many times as
> possible.
That might be hard to do since 19 is prime. <grin>
KARL SAYS: The page
http://www.the-light.com/cal/kp_NdaySolarCyc2.htmltells you which are the shortest cycles you can use. These are
N Days Years LongYrs YrLength
----------------------------------
19 3287 9 2 365.22222
19 37620 103 23 365.24272
19 34333 94 21 465.24468
----------------------------------
From the 103-year and 9-year cycles, one gets a 112-year cycle:
Days Years LongYrs YrLength
----------------------------------
3287 9 2 365.22222
37620 103 23 365.24272
40907 112 25 365.24107
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#cycleIrv has also found the 9-year subcycle, but not the 103-year subcycle.
Irv has also identified some longer cycles such as
the 627-year cycle made up of five 103-year cycles and one 112-year cycle and
the 739-year cycle made up of five 103-year cycles and two 112-year cycles.
Karl
08(02(11
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Re: Bahai leap month variant
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.
Bromberg says:
Interesting, although I am having trouble getting my brane to come to
grips with a calendar that has a 1-day week!
Karl wanted to see more cycles than Victor's original list, but chose
only those cycles that were the nearest SHORTER than Victor's with a
lesser and greater mean year.
How about seeing even more cycles by adding those cycles that are the
nearest LONGER than Victor's with a lesser and greater mean year?
For example, on such a list one would expect the 79-year cycle to show
up for N=7.
-- Irv Bromberg, Toronto, Canada
< http://www.sym454.org/>
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Re: Bahai leap month variant
(Has anyone mentioned the Pawukon calendar to him? two=day weeks through
10-day weeks, and a 1-day week that sometimes simply isn't?)
Pzed
Irv Bromberg wrote:
> Interesting, although I am having trouble getting my brane to come to
> grips with a calendar that has a 1-day week!
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Re: Bahai leap month variant
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/>
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Re: Bahai leap month variant
On Apr 10, 2006, at 07:34, Palmen, KEV (Karl) wrote:
> KARL SAYS: The page
> http://www.the-light.com/cal/kp_NdaySolarCyc2.html> tells you which are the shortest cycles you can use. These are
>
> N Days Years LongYrs YrLength
> ----------------------------------
> 19 3287 9 2 365.22222
> 19 37620 103 23 365.24272
> 19 34333 94 21 465.24468
> ----------------------------------
Bromberg says:
As you can see quoted above, and as shown on the page for the given
URL, the YrLength field for the 94-year cycle with N=19 has a typo, it
should be 365.24468.
Was the data not generated programmatically?
-- Irv Bromberg, Toronto, Canada
< http://www.sym454.org/>
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Re: Bahai leap month variant
Dear Calendar People
I just updated the Bahai Leap Month cycles spreadsheet, now it includes
worksheets "Fast Grouping" and a "Slow Grouping" which show the leap
year grouping patterns for the cycles shorter than 1000 years. It is
now increased to 108 KB. Once again, its URL is:
< http://individual.utoronto.ca/kalendis/Bahai_Leap_Month_cycles.xls>
The column label "DayEquiv" is a bit obscure. It is the numerator for
the fraction of a day in excess of 365 days that would apply if the
cycle was a leap day calendar. The denominator is the number of years
in the cycle. For example, for the 869-year cycle (picking a cycle at
random), its "DayEquiv"=210, which means its mean year length =
365+210/869 days, and a leap day calendar having 210 leap years in 869
years would have an exactly equal calendar mean year length.
-- Irv Bromberg, Toronto, Canada
< http://www.sym454.org/>
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Re: Bahai leap month variant
Dear Irv, Victor and Calendar People
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto: CALNDR-L@...]On Behalf Of Irv Bromberg
Sent: 10 April 2006 18:49
To: CALNDR-L@...
Subject: Re: Bahai leap month variant
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.
KARL SAYS: I showed the shorter cycles as a means of showing how I got the more accurate cycles.
IRV CONTINUED:
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.
KARL SAYS: I decided it was sufficient to limit myself to cycles that have three rows in the fast grouping.
4 5 4 5 4 ...
9 9 9 ... 9 13 9 ...
112 103 103 ...
IRV CONTINUED
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.
Karl
08(02(12 till noon
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Re: Bahai leap month variant
Dear Irv and Calendar People
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto: CALNDR-L@...]On Behalf Of Irv Bromberg
Sent: 11 April 2006 05:28
To: CALNDR-L@...
Subject: Re: Bahai leap month variant
Dear Calendar People
I just updated the Bahai Leap Month cycles spreadsheet, now it includes
worksheets "Fast Grouping" and a "Slow Grouping" which show the leap
year grouping patterns for the cycles shorter than 1000 years. It is
now increased to 108 KB. Once again, its URL is:
< http://individual.utoronto.ca/kalendis/Bahai_Leap_Month_cycles.xls>
The column label "DayEquiv" is a bit obscure. It is the numerator for
the fraction of a day in excess of 365 days that would apply if the
cycle was a leap day calendar. The denominator is the number of years
in the cycle. For example, for the 869-year cycle (picking a cycle at
random), its "DayEquiv"=210, which means its mean year length =
365+210/869 days, and a leap day calendar having 210 leap years in 869
years would have an exactly equal calendar mean year length.
KARL SAYS:
So "DayEquiv" is equivalent to the "Leap Years" in my lunisolar spreadsheets.
http://www.the-light.com/cal/kp_Lunisolar_xls.htmlFor example, the 334-year cycle with 123 long years and 65 abundant years has the equivalent of 81 leap years, so has a mean year of 365 81/334 = 365.24251497 days.
Irv could add the 85-year cycle with 19 leap years to his spreadsheet because it is interesting.
Karl
08(02(12 till noon
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Re: Bahai leap month variant
Dear Irv and Calendar People
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto: CALNDR-L@...]On Behalf Of Irv Bromberg
Sent: 10 April 2006 17:42
To: CALNDR-L@...
Subject: Re: Bahai leap month variant
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.
Bromberg says:
Interesting, although I am having trouble getting my brane to come to
grips with a calendar that has a 1-day week!
KARL SAYS: That is simply equivalent to simply having a whole number of days each year rather than a whole number of weeks (of multiple days).
IRV CONTINUES:
Karl wanted to see more cycles than Victor's original list, but chose
only those cycles that were the nearest SHORTER than Victor's with a
lesser and greater mean year.
How about seeing even more cycles by adding those cycles that are the
nearest LONGER than Victor's with a lesser and greater mean year?
KARL SAYS: There is no such thing as the nearest longer cycle!
If there were such thing, one could find a nearer cycle that is also longer, which contradicts the 'nearest' in the if clause.
The two shorter cycles can generate ALL the cycles whose mean years lie in between there's by adding them together. This includes ALL the cycles whose mean year is within the range of 365.2416 days and 365.2428 days. I have the two bounding cycles outside the range so that they generate all cycles within the range.
IRV CONTINUES
For example, on such a list one would expect the 79-year cycle to show
up for N=7.
KARL SAYS:
For N=7 of the list is
----------------------------------
7 6209 17 3 365.23529
7 22645 62 11 365.24194
7 16436 45 8 364.24444
----------------------------------
The 79-year cycle with 14 leap weeks is simply the sum of the 17 and 62 year cycles. Then we could have the 141-year cycle with 25 leap weeks got by adding the 79-year cycle to the 62-year cycle and so on.
Note that 17*8-45*3=1. This ensures that ALL the cycles whose mean year lies in between can be made up by adding whole numbers of those cycles. Hence every one the cycles in between must be longer than either of the two bounding cycles.
You'll see that this is true for all the N
N=2: 29*23 - 37*18 = 1
N=3: 87*3 - 65*4 = 1
N=4: 39*23 - 74*9 = 1
N=5: 21*2 - 41*1 = 1
etc.
If this quantity were more than 1, there'd be a cycle in between that is shorter than one or both of the bounding cycles.
Karl
08(02(13
PS: I varied the range of mean years to get
http://www.the-light.com/cal/kp_NdaySolarCyc.htmland
http://www.the-light.com/cal/kp_NdaySolarCyc1.html
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Re: Bahai leap month variant
Dear Irv and Calendar People
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto: CALNDR-L@...]On Behalf Of Irv Bromberg
Sent: 10 April 2006 20:45
To: CALNDR-L@...
Subject: Re: Bahai leap month variant
On Apr 10, 2006, at 07:34, Palmen, KEV (Karl) wrote:
> KARL SAYS: The page
> http://www.the-light.com/cal/kp_NdaySolarCyc2.html> tells you which are the shortest cycles you can use. These are
>
> N Days Years LongYrs YrLength
> ----------------------------------
> 19 3287 9 2 365.22222
> 19 37620 103 23 365.24272
> 19 34333 94 21 465.24468
> ----------------------------------
Bromberg says:
As you can see quoted above, and as shown on the page for the given
URL, the YrLength field for the 94-year cycle with N=19 has a typo, it
should be 365.24468.
Was the data not generated programmatically?
KARL SAYS: I just used my head and a calculator for the mean year (which I then typed in). This is the main reason why I stopped at N=30.
Karl
08(02(13
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Re: Bahai leap month variant
On Apr 11, 2006, at 07:53, Palmen, KEV (Karl) wrote:
> IRV CONTINUES:
> How about seeing even more cycles by adding those cycles that are the
> nearest LONGER than Victor's with a lesser and greater mean year?
>
> KARL SAYS: There is no such thing as the nearest longer cycle!
> If there were such thing, one could find a nearer cycle that is also
> longer, which contradicts the 'nearest' in the if clause.
>
> The two shorter cycles can generate ALL the cycles whose mean years
> lie in between there's by adding them together. This includes ALL the
> cycles whose mean year is within the range of 365.2416 days and
> 365.2428 days. I have the two bounding cycles outside the range so
> that they generate all cycles within the range.
<snip>
Irv replies: Thanks for the explanation!
> PS: I varied the range of mean years to get
> http://www.the-light.com/cal/kp_NdaySolarCyc.html> and
> http://www.the-light.com/cal/kp_NdaySolarCyc1.htmlHmm, unlucky 19, I guess:
For N=19, both of the above web pages contain the line:
19 116147 318 71 376.24214
That mean year column should say 365.24214
-- Irv Bromberg, Toronto, Canada
< http://www.sym454.org/>
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Re: Bahai leap month variant
Dear Irv, Victor and Calendar People
I found two interesting cycles
851 years 190 leap months
and
936 years 209 leap months
The former can be generated by having every leap month 86 months after the previous leap month, except every 10th leap month, which is a month later.
The latter can be generated by having every leap month 86 month after the previous leap month, except every 11th leap month, which is a month later.
The mean years are approximately 365.2421 and 365.2425 days respectively.
All cycles whose mean year is between these values can be made by adding these cycles, but if the number of years in the resulting cycle is divisible by 19, then the cycle is overlong and can be divided by 19.
Karl
08(02(13
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto: CALNDR-L@...]On Behalf Of Irv Bromberg
Sent: 11 April 2006 05:28
To: CALNDR-L@...
Subject: Re: Bahai leap month variant
Dear Calendar People
I just updated the Bahai Leap Month cycles spreadsheet, now it includes
worksheets "Fast Grouping" and a "Slow Grouping" which show the leap
year grouping patterns for the cycles shorter than 1000 years. It is
now increased to 108 KB. Once again, its URL is:
< http://individual.utoronto.ca/kalendis/Bahai_Leap_Month_cycles.xls>
The column label "DayEquiv" is a bit obscure. It is the numerator for
the fraction of a day in excess of 365 days that would apply if the
cycle was a leap day calendar. The denominator is the number of years
in the cycle. For example, for the 869-year cycle (picking a cycle at
random), its "DayEquiv"=210, which means its mean year length =
365+210/869 days, and a leap day calendar having 210 leap years in 869
years would have an exactly equal calendar mean year length.
-- Irv Bromberg, Toronto, Canada
< http://www.sym454.org/>
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Re: Bahai leap month variant
On Apr 11, 2006, at 04:06, Palmen, KEV (Karl) wrote:
> Irv could add the 85-year cycle with 19 leap years to his spreadsheet
> because it is interesting.
Irv says:
At last! A cycle that has a 19 in it!
I added it, but too bad that the mean year length is so long, it's even
a bit longer than the Traditional Hebrew Calendar.
On Apr 11, 2006, at 10:28, Palmen, KEV (Karl) wrote:
> I found two interesting cycles
> 851 years 190 leap months
> and
> 936 years 209 leap months
936 was already in my list. The fast way to check it on the "Cycles"
page is to either use the autofilter menu to pull down the "Years"
column (C), which lists them in numeric order, or else to use the Excel
Sort... command to sort the list by the number of years per cycle.
I added 851 to the spreadsheet, with fast and slow grouping. Now 116
KB.
< http://individual.utoronto.ca/kalendis/Bahai_Leap_Month_cycles.xls>
Anybody who already got the file earlier today might need to refresh
their web browser or clear its cache to get the updated version.
The 851-year cycle is interesting because the total number of months in
the cycle is divisible by 19, and the cycle contains a whole number of
weeks. However, it is intermediate in mean year length between the
northward equinoctial year and the north solstitial year.
-- Irv Bromberg, Toronto, Canada
< http://www.sym454.org/>
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Re: Bahai leap month variant
Dear Irv and Calendar People
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto: CALNDR-L@...]On Behalf Of Irv Bromberg
Sent: 11 April 2006 16:21
To: CALNDR-L@...
Subject: Re: Bahai leap month variant
On Apr 11, 2006, at 04:06, Palmen, KEV (Karl) wrote:
> Irv could add the 85-year cycle with 19 leap years to his spreadsheet
> because it is interesting.
Irv says:
At last! A cycle that has a 19 in it!
I added it, but too bad that the mean year length is so long, it's even
a bit longer than the Traditional Hebrew Calendar.
On Apr 11, 2006, at 10:28, Palmen, KEV (Karl) wrote:
> I found two interesting cycles
> 851 years 190 leap months
> and
> 936 years 209 leap months
The 851-year cycle is interesting because the total number of months in
the cycle is divisible by 19, and the cycle contains a whole number of
weeks. However, it is intermediate in mean year length between the
northward equinoctial year and the north solstitial year.
KARL SAYS:
All three of these cycles (85, 936 & 851) have a total number of months divisible by 19, because the total number of leap months is divisible by 19.
The 85-year cycle is the difference between the 936-year and 851-year cycles.
It is interesting that the 851-year cycle also has a whole number of weeks.
Karl
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Re: Bahai leap month variant
Dear Irv, Victor and Calendar People
I've made my own spreadsheet
http://www.the-light.com/cal/LBahaiMth1.xlswhich is similar to the lunisolar spreadsheets at
http://www.the-light.com/cal/kp_Lunisolar_xls.htmlYou can try out a cycle by copying a row and then change the number of years (Years) and number of leap months (Long) to your values and all the other values then appear in the row.
I think all the columns except the last three are self-explanatory. The last three are:
Alts: Number of alternating sequences of 4 and 5 year intervals between leap years. This is equal to the number of items in the 3rd row of the fast grouping, if it exists.
LongAlts: In an accurate cycle, most Alts have 103 years and some have 112 years. This is the number of Alts that would have 112 years, if all other Alts had 103 years.
Generally, it is the number of 9-year periods needed to be added to Alts of 103 years to get the cycle.
L87m: If every leap month were to occur either 86 or 87 months after the previous leap month, this is the number of leap months that would occur 87 months after the previous leap month.
Karl
08(02(13
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto: CALNDR-L@...]On Behalf Of Irv Bromberg
Sent: 11 April 2006 01:17
To: CALNDR-L@...
Subject: Re: Bahai leap month variant
Dear Calendar People:
I've posted an Excel spreadsheet that gives the 19-day leap month
cycles that I've found as possible candidates for the Bahai Leap Month
variant calendar. The 79 KB spreadsheet is posted at:
< http://individual.utoronto.ca/kalendis/Bahai_Leap_Month_cycles.xls>
Some of the cycles are a few thousand years, those that are of modest
interest are 19 times well-known leap day cycles.
For example, the cycles that I gave yesterday as equivalent to
Gregorian and to Revised Julian and to Dee were actually just close
approximations, the exact values are obtained by taking 19 times their
respective years per cycle (or 1/2 those years in the case of the
overlong Revised Julian).
I tried to broaden my search for shorter and longer cycles in relation
to the northward equinoctial year length and the north solstitial year
length, with the idea of mixing subcycles to obtain intermediate
values. The shortest cycles that are longer than Victor's originals
are not particularly short!
The list is sorted by descending mean year length, but being a
spreadsheet you can re-sort it any way that you please.
-- Irv Bromberg, Toronto, Canada
< http://www.sym454.org/>
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Re: Bahai leap month variant
On Apr 11, 2006, at 11:49, Palmen, KEV (Karl) wrote:
> On Apr 11, 2006, at 10:28, Palmen, KEV (Karl) wrote:
>> I found two interesting cycles
>> 851 years 190 leap months
>> and
>> 936 years 209 leap months
>
> Bromberg said:
> The 851-year cycle is interesting because the total number of months in
> the cycle is divisible by 19, and the cycle contains a whole number of
> weeks. However, it is intermediate in mean year length between the
> northward equinoctial year and the north solstitial year.
Bromberg now adds:
Having considered the 851-year cycle further, that intermediate mean
year length may actually allow it to "hold on" to the equinox for much
longer, yet still maintain reasonably good alignment with the equinox,
especially if we adjust its start point so that at the Bahai epoch it
was too late, and comes close to proper alignment by the present era.
Minor mean year differences have a less apparent effect with a leap
month calendar, with regard to equinox or solstice alignment.
> KARL SAYS:
> All three of these cycles (85, 936 & 851) have a total number of
> months divisible by 19, because the total number of leap months is
> divisible by 19.
> The 85-year cycle is the difference between the 936-year and 851-year
> cycles.
> It is interesting that the 851-year cycle also has a whole number of
> weeks.
Bromberg says:
Good points. I've added a Leaps/19 column and moved the Months/19
column beside it.
< http://individual.utoronto.ca/kalendis/Bahai_Leap_Month_cycles.xls>
I also updated the lunisolar fast and slow grouping spreadsheets,
adding several cycles from your lunisolar spreadsheets plus a bunch of
intermediate cycles as well as the short sub-cycles that everything
else is mixed from. There are now 41 lunisolar cycles listed. From
your lunisolar lists I omitted any cycles >1000 years, and any where my
cycle mean year was dramatically different from your list.
< http://individual.utoronto.ca/kalendis/hebrew/
Leap_Month_Cycles_Forward.xls> 56 KB
< http://individual.utoronto.ca/kalendis/hebrew/
Leap_Month_Cycles_Reverse.xls> 56 KB
< http://individual.utoronto.ca/kalendis/leap/
Combined_Slow_Grouping.xls> 429 KB
(Don't try to print any of these spreadsheets -- they are much too
wide! Check the print preview before wasting paper.)
(Don't forget: refresh browser or clear cache if downloading any
spreadsheet for the second time same day.)
-- Irv Bromberg, Toronto, Canada
< http://www.sym454.org/>
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