103-year Cycle

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103-year Cycle

Karl Palmen - UKRI STFC
103-year Cycle

Dear Calendar People

I thought of mentioning the 103-year cycle of 25 leap days again, because the number of days (37620) it has a large number of divisors, so is ideal for a variety of calendars where the number of days in a month or week does not vary, but the number of months or weeks in a year does vary.

37620 = (2^2) * (3^2) * 5 * 11 * 19 leading to the following calendars (amongst others):

103 years normally of 73 five-day weeks, but with five long years of 74 weeks. The intervals between the long years could be 21,20,21,20,21.

103 years normally of 61 six-day weeks, but with 13 short years of 60 weeks. The short years would occur once every 8 years except one that occurs after 7 years.

103 years consisting of 43 short years of 40 nine-day weeks and 60 long years of 41 weeks.

103 years consisting of 54 long years of 37 ten-day weeks and 49 short years of 36 ten-day weeks. There could be five periods of 21 or 19 years in which the two types of year alternate. Only one such period would have 19 years and the other four would have 21 years.

103 years normally of 33 eleven-day week, but with 21 long years of 34 weeks. The long years would  normally occur once every five years.

103 years normally of 20 eighteen-day months, but with 30 long years of 21 months.

103 years normally of 19 nineteen-day months, but with 23 long years of 20 months

103 years normally of 18 twenty-day months, but with 27 long years of 19 months.

103 years normally of 12 thirty-day months, but with 18 long years of 13 months.

103 years normally of 11 thirty-three-day months, but with 7 long years of 12 months.

103 years normally of 10 thirty-six-day months, but with 15 long years of 11 months.

The main drawback is the rather long mean year of about 365.242718 days. It would be interesting to run several of these calendar concurrently,


Also if a lunisolar calendar were to have a basic year of 354 days to which is occasionally added a leap month of 30 days, then the addition of 20 leap days every 103 year would make the calendar very accurate, provided the leap months occur at an accurate rate.

Karl

10(05(10




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Re: 103-year Cycle

Sepp Rothwangl
Hi Karl

may I call this the Hare&Hedgehog Calendar?

Servus ;=))
Sepp


Am 04.02.2009 um 14:37 schrieb Palmen, KEV (Karl):

Dear Calendar People

I thought of mentioning the 103-year cycle of 25 leap days again, because the number of days (37620) it has a large number of divisors, so is ideal for a variety of calendars where the number of days in a month or week does not vary, but the number of months or weeks in a year does vary.

37620 = (2^2) * (3^2) * 5 * 11 * 19 leading to the following calendars (amongst others):

103 years normally of 73 five-day weeks, but with five long years of 74 weeks. The intervals between the long years could be 21,20,21,20,21.


103 years normally of 61 six-day weeks, but with 13 short years of 60 weeks. The short years would occur once every 8 years except one that occurs after 7 years.


103 years consisting of 43 short years of 40 nine-day weeks and 60 long years of 41 weeks.

103 years consisting of 54 long years of 37 ten-day weeks and 49 short years of 36 ten-day weeks. There could be five periods of 21 or 19 years in which the two types of year alternate. Only one such period would have 19 years and the other four would have 21 years.


103 years normally of 33 eleven-day week, but with 21 long years of 34 weeks. The long years would  normally occur once every five years.

103 years normally of 20 eighteen-day months, but with 30 long years of 21 months.

103 years normally of 19 nineteen-day months, but with 23 long years of 20 months

103 years normally of 18 twenty-day months, but with 27 long years of 19 months.

103 years normally of 12 thirty-day months, but with 18 long years of 13 months.


103 years normally of 11 thirty-three-day months, but with 7 long years of 12 months.

103 years normally of 10 thirty-six-day months, but with 15 long years of 11 months.

The main drawback is the rather long mean year of about 365.242718 days. It would be interesting to run several of these calendar concurrently,


Also if a lunisolar calendar were to have a basic year of 354 days to which is occasionally added a leap month of 30 days, then the addition of 20 leap days every 103 year would make the calendar very accurate, provided the leap months occur at an accurate rate.

Karl

10(05(10





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The Alternating 8th Month

Helios
In reply to this post by Karl Palmen - UKRI STFC
What have hitherto been called solar months have been twelfths of a solar year. I don't know if a "solar yerm" and a "natural solar yerm" have been defined but it can't be other than;

N = 1 / ( [ 61 / W ] - 2 ),  W = Y / 12

N = 1 / ( [ 732 / Y ] - 2 )

a period of about 241 days. Anyway, I found the pattern of the alternating 8th solar month

30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( -- )

and the intervention after 103 months.
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Solar yerms RE: The Alternating 8th Month

Karl Palmen - UKRI STFC

Dear Helios, Victor and Calendar People

 

I believe I have some time ago worked out the yerm-like periods for solar months of 1/12 of a tropical year. These solar yerms would have odd-numbered months of 30 days and even-number months of 31 days.

 

A solar calendar cycle would have two solar yerms per common year. Therefore four Julian years have 6 solar yerms. They'd could alternate between seven and nine months. The seven-month solar yerm has 213 days and the nine-month solar yerm has 274 days.

 

While a Julian calendar mean year can be produced with alternating solar yerms of seven and nine months, a more accurate solar calendar would require a more seven-month yerms than nine-month yerms. The 33-year cycle would have 50 solar yerms, which can be made of 27 seven-month solar yerms and 23 nine-month solar yerms. Therefore a solar calendar cycle of C years with L leap years, would have an excess E of seven-month solar yerms over nine-month yerms given by

 

E = 4*(C - 4*L)

 

The number of seven-month solar yerms is (C-L) + 2*(C - 4*L) = 3*C - 9*L

and the number of nine-month solar yerms is (C-L) - 2*(C - 4*L) = 7*L - C

 

This gives rise to the following solar-yerm mixes:

 

Years Leap  7-month 9-month   Mean Solar Yerm        Mean Year

  4     1      3       3       243.5 days exactly    365.25 days exactly

 33     8     27      23       241.06 days exactly   365.242424 days

 62    15     51      43       240.904 days          365.241935 days

 95    23     78      66       240.958 days          365.242105 days

128    31    105      89       240.984 days          365.2421875 days exactly

161    39    132     112       241 days exactly      365.242236 days

293    71    240     204       241.027 days          365.242321 days

400    97    327     279       241.084 days          365.2425 days exactly

103    25     84      72       241.154 days          365.242718 days

 

I note that the 103-year cycle breaks into twelve equal parts of 103 months grouped into 7 seven-month solar yerms and 6 nine-month solar yerms. These 13 solar yerms can be rearranged into one yerm of seven months followed by 12 yerms alternating between fifteen months and one month to produce the months that Helios has listed.

 

I have also found some lunisolar cycles, where the number of yerms in the equivalent lunar calendar is equal to the number of common years in the equivalent leap day solar calendar. Therefore the number of solar yerms is exactly twice the number of lunar yerms. I’ve listed some of these cycle at http://www.the-light.com/cal/LunisolarEF.html

of http://www.the-light.com/cal/kp_Lunisolar_xls.html .

 

Karl

 

10(06(14

 

PS: I don’t understand Helios’s equations, because he has not defined the variables N, Y and W.

 

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios
Sent: 10 March 2009 05:29
To: [hidden email]
Subject: The Altermating 8th Month

 

What have hitherto been called solar months have been twelfths of a solar

year. I don't know if a "solar yerm" and a "natural solar yerm" has been

defined but it can't be other than;

 

N = 1 / ( [ 61 / W ] - 2 ),  W = Y / 12

 

N = 1 / ( [ 732 / Y ] - 2 )

 

a period of about 241 days. Anyway, I found the pattern of the altermating

8th solar month

 

30 31 30 31 30 31 30 ( 30 )

30 31 30 31 30 31 30 ( 31 )

30 31 30 31 30 31 30 ( 30 )

30 31 30 31 30 31 30 ( 31 )

30 31 30 31 30 31 30 ( 30 )

30 31 30 31 30 31 30 ( 31 )

30 31 30 31 30 31 30 ( 30 )

30 31 30 31 30 31 30 ( 31 )

30 31 30 31 30 31 30 ( 30 )

30 31 30 31 30 31 30 ( 31 )

30 31 30 31 30 31 30 ( 30 )

30 31 30 31 30 31 30 ( 31 )

30 31 30 31 30 31 30 ( -- )

 

and the intervention after 103 months.

--

View this message in context: http://www.nabble.com/103-year-Cycle-tp21830699p22428348.html

Sent from the Calndr-L mailing list archive at Nabble.com.

 




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Re: The Altermating 8th Month

Victor Engel
In reply to this post by Helios
Dear Helios,

You state that the period is about 241 days, and then you show several
periods none of which have 241 days. I see 243, 244, and 213 days,
which average to just over 241 days. The mean year is about 365.2427
days.

Victor

On 3/10/09, Helios <[hidden email]> wrote:

> What have hitherto been called solar months have been twelfths of a solar
>  year. I don't know if a "solar yerm" and a "natural solar yerm" has been
>  defined but it can't be other than;
>
>  N = 1 / ( [ 61 / W ] - 2 ),  W = Y / 12
>
>  N = 1 / ( [ 732 / Y ] - 2 )
>
>  a period of about 241 days. Anyway, I found the pattern of the altermating
>  8th solar month
>
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( -- )
>
>  and the intervention after 103 months.
>
> --
>  View this message in context: http://www.nabble.com/103-year-Cycle-tp21830699p22428348.html
>  Sent from the Calndr-L mailing list archive at Nabble.com.
>
>

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Re: The Alternating 8th Month

Karl Palmen - UKRI STFC
Dear Victor and Helios

An mean solar yerm of exactly 241 days can be obtained with

(1) 13 solar yerms of 103 months = 3135 days (mean solar yerm 241.1538
days)
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30

(2) 11 solar yerms of 87 months = 2648 days (mean solar yerm 240.7272
days)
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30

(3) 13 solar yerms of 103 months = 3135 days
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30

(4) 11 solar yerms of 87 months = 2648 days
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30

(5) 13 solar yerms of 103 months = 3135 days
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30

This yerm of yerms of solar yerms forms one quarter of a 161-year cycle
of 39 leap days, which is familiar to Victor.

(3135+2648+3135+2648+3135)/(13+11+13+11+13) = 241 and so the mean solar
yerm is exactly 241 days.

Karl

10(06(14

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]] On Behalf Of Victor Engel
Sent: 10 March 2009 15:31
To: [hidden email]
Subject: Re: The Altermating 8th Month

Dear Helios,

You state that the period is about 241 days, and then you show several
periods none of which have 241 days. I see 243, 244, and 213 days,
which average to just over 241 days. The mean year is about 365.2427
days.

Victor

On 3/10/09, Helios <[hidden email]> wrote:
> What have hitherto been called solar months have been twelfths of a
solar
>  year. I don't know if a "solar yerm" and a "natural solar yerm" has
been
>  defined but it can't be other than;
>
>  N = 1 / ( [ 61 / W ] - 2 ),  W = Y / 12
>
>  N = 1 / ( [ 732 / Y ] - 2 )
>
>  a period of about 241 days. Anyway, I found the pattern of the
altermating

>  8th solar month
>
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( 30 )
>  30 31 30 31 30 31 30 ( 31 )
>  30 31 30 31 30 31 30 ( -- )
>
>  and the intervention after 103 months.
>
> --
>  View this message in context:
http://www.nabble.com/103-year-Cycle-tp21830699p22428348.html
>  Sent from the Calndr-L mailing list archive at Nabble.com.
>
>

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Yerm of Solar Yerms RE: The Alternating 8th Month

Karl Palmen - UKRI STFC
In reply to this post by Helios
Dear Calendar People

The 103-month period that Helios has discovered can have its months
arranged as a yerm of 13 solar yerms alternating between seven and nine
months

103 = 7+9+7+9+7+9+7+9+7+9+7+9+7. It has 3135 days.

This alone creates a 103-year cycle of 25 leap days.

A more accurate cycle would require this being mixed with a shorter yerm
of 11 solar yerms equal to 87 months

87 = 7+9+7+9+7+9+7+9+7+9+7. It has 2648 days.

The 33-year cycle has three 103-month yerms of yerms and one 87-month
yerm of solar yerms (33*12 = 103+103+103+87). The 29-year cycle has four
87-month yerms of solar yerms (29*12 = 4*87).

This leads to the following mixture of these yerms of solar yerms:

33-year cycle: 3 long 1 short
62-year cycle: 3 long 5 short
95-year cycle: 6 long 6 short (1:1 mix, alternating)
128-year cycle: 9 long 7 short
161-year cycle: 12 long 8 short (3:2 mix, mean solar yerm 241 days)
293-year cycle: 24 long 12 short (2:1 mix)
400-year cycle: 39 long 9 short (13:3 mix)
103-year cycle: 12 long 0 short (pure long)

Karl

10(06(14

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]] On Behalf Of Helios
Sent: 10 March 2009 05:29
To: [hidden email]
Subject: The Altermating 8th Month

What have hitherto been called solar months have been twelfths of a
solar
year. I don't know if a "solar yerm" and a "natural solar yerm" has been
defined but it can't be other than;

N = 1 / ( [ 61 / W ] - 2 ),  W = Y / 12

N = 1 / ( [ 732 / Y ] - 2 )

a period of about 241 days. Anyway, I found the pattern of the
altermating
8th solar month

30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( -- )

and the intervention after 103 months.
--
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103-month Helios Cycle RE: The Alternating 8th Month

Karl Palmen - UKRI STFC
In reply to this post by Helios
Dear Helios and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]] On Behalf Of Helios
Sent: 10 March 2009 05:29
To: [hidden email]
Subject: The Altermating 8th Month

What have hitherto been called solar months have been twelfths of a
solar
year. I don't know if a "solar yerm" and a "natural solar yerm" has been
defined but it can't be other than;

N = 1 / ( [ 61 / W ] - 2 ),  W = Y / 12

N = 1 / ( [ 732 / Y ] - 2 )

a period of about 241 days. Anyway, I found the pattern of the
altermating
8th solar month

30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( 30 )
30 31 30 31 30 31 30 ( 31 )
30 31 30 31 30 31 30 ( -- )

and the intervention after 103 months.

KARL SAYS: Rearranging the months as shown next makes it into a Helios
cycle:

30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30
30 31 30 31 30 31 30 31 30
30 31 30 31 30 31 30

This is a Helios cycle because it is a yerm of yerms. Therefore month M
has 31 days if and only if

(45*M + 51) mod (103) < 45

The same applies to the Yerm of yerm of yerms, that produces a quarter
of a 161-year cycle and has a mean yerm of exactly 241 days. Therefore
month M has 31 days if and only if

(211*M + 241) mod (483) < 211


Karl

10(06(14
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Re: The Alternating 8th Month

Karl Palmen - UKRI STFC
In reply to this post by Helios
Dear Helios and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]] On Behalf Of Helios
Sent: 10 March 2009 05:29
To: [hidden email]
Subject: The Altermating 8th Month

What have hitherto been called solar months have been twelfths of a
solar
year. I don't know if a "solar yerm" and a "natural solar yerm" has been
defined

KARL SAYS: I sent a note to this list in 2007 shown next:
------------------------------------------------------------------------
------------------------------------------
Dear Helios and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Helios
Sent: 25 January 2007 14:04
To: [hidden email]
Subject: Re: Division of Year by Alternating Terms


I think it's worth mentioning that the 21-22 day alternating sequencing
admits to it's own "yerm-like" definitions. We have  a "natural solar
yerm".
It's the time it takes for the mean term to fall half a day AHEAD of the
21.5 day cycle. It is 1/(43 - 2t) mean terms or t/(43 -2t) days, where t
is
the mean term in days. The result is 32.993769 terms or 708.86604 days.
Some
"solar yerms" look like

31 terms = 666 days
33 terms = 709 days
35 terms = 752 days

It seems that the useful solar period  of years are composed of "solar
yerms". ie,

1461 = 709 + 752
146097 = 205 ( 709 ) + 752
12053 = 17 ( 709 )
34698 = 48 ( 709 ) + 666
46751 = 65 ( 709 ) + 666
227546 = 320 ( 709 ) + 666

I think the name "solar yerm" should be replaced with a new and less
confusing name.

KARL SAYS: Agreed.

A solar yerm could be taken as a period of seven or nine solar months
that alternate between 30 and 31 days beginning and ending with a 30-day
month.

A Julian 4-year cycle can be constructed from six solar yerms
alternating between seven and nine months making up 48 solar months.

30  31  30  31  30  31  30; 30  31  30  31  30
31  30  31  30; 30  31  30  31  30  31  30; 30
31  30  31  30  31  30  31  30; 30  31  30  31
30  31  30; 30  31  30  31  30  31  30  31  30;

A more accurate cycle can be made by increasing the proportion of
7-month solar yerms. So forming superyerms that alternate between solar
yerms of seven and nine months beginning and sending with a seven-month
solar yerm.

A seven-month solar yerm has 213 days, while a nine-month solar yerm has
274 days. So:

3*213 + 3*274 = 1461  4 years
6*213 + 2*274 = 1826  5 years

The 1826 days are equivalent to five years with one leap day. Any solar
calendar cycle can be made by mixing this with a larger number of 4-year
cycles. So we get

27*213 + 23*274 = 12053: 33 years
105*213 + 89*274 = 46751:  128 years
327*213 + 279*274 = 146097: 400 years

The difference between the number of seven-month solar yerms and
nine-month solar yerms is the number of superyerms needed. Each
superyerm can have either 11 or 13 solar yerms.

The 33-year cycle has four superyerms (of 99 months average length)
three of 13 solar yerms and one of 11 solar yerms.
The 128-year cycle has 16 superyerms (of 8 years average length)  
9 of 13 solar yerms and 7 of 11 solar yerms.
The 400-year cycle has 48 superyerms (of 100 months average length)
39 of 13 solar yerms and 9 of 11 solar yerms.

A 13-solar-yerm superyerm has 103 months of 3135 days and
a 11-solar-yerm superyerm has 87 months of 2648 days.

Finally
78*213 + 66*274 = 34698: 95 years

This 95-year cycle has 12 superyerms (of 95 months average length)
which alternate between 11 and 13 solar yerms.

Karl

08(12(07

------------------------------------------------------------------------
--------------------------------------------------

Karl

10(06(14 till noon

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Solar Month Count

Helios
Yes, along these lines, I used the formula ( with Y = mean year )

mean term-yerm = 1 / [ ( 731 / Y ) - 2 ]

and set this to exactly 24 months. After what mean year could be suitable, I found a 5963 year cycle, but solar months are superior to terms in the realm of this 5963 year cycle. The real cycle is just under half a millenium.
---------------------------------------------
= 376 yerms
= 753 solar yerms
= 5963 solar months
= 6146 months
= 181495 days
---------------------------------------------
Composition:
123 15-month lunar yerms
253 17-month lunar yerms
346 nine-month solar yerms
407 seven-month solar yerms
---------------------------------------------

A Solar Month Count could start just as if an imaginary celestial body, the ghost moon, were reaching conjunction along with the 0th moon of the Brown Lunation Count.

Solar Month Count Zero = JD 2423407.44655 = Brown Lunation Zero

with the months, now solar and lunar
Solar Month Count K  & days ( 1 - 31 )
Brown Lunation  L  & days ( 1 - 30 )
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Re: Solar Month Count

Karl Palmen - UKRI STFC
Dear Helios and Calendar People

The formula for the mean solar yerm is very similar to that for a mean
term yerm:

mean term-yerm = 1 / [ ( 732 / Y ) - 2 ]

It's the same but with 732 instead of 731.


A term is a period of 21 or 22 days arranged into term yerms so that an
odd-number term has 21 days and an even-number term has 22 days. There
are also exactly 17 terms to a year. If all term yerms were to have 33
terms, then a 33-year cycle of 8 leap years would result from 17 term
yerms. All these term yerms would have 709 days.

24 lunar months have about 708.734 days, so it is tempting to put in a
few shorter 31-term term yerms to make the mean term-yerm equal to 24
months, but I don't see any benefit in this.

Karl

10(06(15

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]] On Behalf Of Helios
Sent: 11 March 2009 12:31
To: [hidden email]
Subject: Solar Month Count

Yes, along these lines, I used the formula ( with Y = mean year )

mean term-yerm = 1 / [ ( 731 / Y ) - 2 ]

and set this to exactly 24 months.

--
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Rectified Symmetry010 calendar (making it 365 days by adding December 31.) Re: Solar Month Count

Ryan Provost-2
But there are 12 solar months in a solar year! The solar year is about
365.242199 days, divide that by 12, that equals 30.4368499. That's the
average number of days in a solar month.

However, speaking of solar calendars, let's review the symmetry010. They
have 30 + 31 + 30 = 91 days in a quarter, that equals 364 days in a non-leap
year. I will add an extra day at the end of the December, making the last
day of the year, December 31 (That won't affect Christmas, in which it
retains on December 25). That will make it 365 days For leap years, it will
be either at January 31 or March 31. Under the proposed calendar system,
running on the Gregorian leap year system, today is 2009.03.10-We (compared
to the Gregorian date of 2009.03.11-We)

--------------------------------------------------
From: "Palmen, KEV (Karl)" <[hidden email]>
Sent: Wednesday, March 11, 2009 11:10 AM
To: <[hidden email]>
Subject: Re: Solar Month Count

> Dear Helios and Calendar People
>
> The formula for the mean solar yerm is very similar to that for a mean
> term yerm:
>
> mean term-yerm = 1 / [ ( 732 / Y ) - 2 ]
>
> It's the same but with 732 instead of 731.
>
>
> A term is a period of 21 or 22 days arranged into term yerms so that an
> odd-number term has 21 days and an even-number term has 22 days. There
> are also exactly 17 terms to a year. If all term yerms were to have 33
> terms, then a 33-year cycle of 8 leap years would result from 17 term
> yerms. All these term yerms would have 709 days.
>
> 24 lunar months have about 708.734 days, so it is tempting to put in a
> few shorter 31-term term yerms to make the mean term-yerm equal to 24
> months, but I don't see any benefit in this.
>
> Karl
>
> 10(06(15
>
> -----Original Message-----
> From: East Carolina University Calendar discussion List
> [mailto:[hidden email]] On Behalf Of Helios
> Sent: 11 March 2009 12:31
> To: [hidden email]
> Subject: Solar Month Count
>
> Yes, along these lines, I used the formula ( with Y = mean year )
>
> mean term-yerm = 1 / [ ( 731 / Y ) - 2 ]
>
> and set this to exactly 24 months.
>
> --
> Scanned by iCritical.
>
>

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Re: Rectified Symmetry010 calendar (making it 365 days by adding December 31.) Re: Solar Month Count

Irv Bromberg
On 2009.03.11, at 12:40 , ELITE 3000 wrote:
However, speaking of solar calendars, let's review the symmetry010. They have 30 + 31 + 30 = 91 days in a quarter, that equals 364 days in a non-leap year. I will add an extra day at the end of the December, making the last day of the year, December 31 (That won't affect Christmas, in which it retains on December 25). That will make it 365 days For leap years, it will be either at January 31 or March 31. Under the proposed calendar system, running on the Gregorian leap year system, today is 2009.03.10-We (compared to the Gregorian date of 2009.03.11-We)

Irv replies:

By converting a leap week calendar into a leap day calendar you wipe out the most important attribute of the calendar, it will no longer be a perpetual calendar, always starting each year on the same weekday, unless the added day is a "null" day outside of the traditional 7-day weekly cycle, which will be subject to insurmountable religious objections.

One can propose all manner of calendar reforms to improve upon the Gregorian calendar, but the only one that really really matters is to end up with a perpetual calendar that preserves the traditional 7-day weekly cycle.

Other enhancements such as symmetrical structure of quarters, a symmetrical smoothly spread sequence of leap years with a shorter mean year, every day of every month always on the same weekday, etc. are nice enhancements to carry out "while we're at it" in the scheme of calendar reform, because introducing such enhancements will not make the reform any more difficult to implement than a reform limited to just the primary objective of making the calendar perpetual.


-- Irv Bromberg, Toronto, Canada