103-month Helios Cycle 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 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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