Solar yerms RE: The Alternating 8th Month

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:CALNDR-L@...] On Behalf Of Helios
Sent: 10 March 2009 05:29
To: CALNDR-L@...
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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