Re: The Alternating 8th Month

Dear Helios and Calendar People

-----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

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:CALNDR-L@...]On Behalf Of Helios
Sent: 25 January 2007 14:04
To: CALNDR-L@...
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

--
Scanned by iCritical.