13-month Solar Calendar for 5515-Year Luni-Solar Cycle

Dear Helios, Victor and Calendar People

The 5512 octaeteris years in 5515 years lead me to realise that a
13-month solar calendar ran alongside a lunar calendar with the
1749-month cycle could produce a 5515-year cycle.

Both the lunar and solar calendars can run in a Helios cycle.

The lunar calendar can run as alternate 52-yerm and 55-yerm cycles ( see
http://www.hermetic.ch/cal_stud/palmen/yerm1.htm and
http://www.hermetic.ch/cal_stud/lunarcal/lunacycl.htm )
The Helios cycle would begin with yerm 29 of each 55-yerm cycle and have
yerm 27 of each 52-yerm cycle in the middle. It is a Helios cycle for
both months and yerms.

The 13-month solar calendar can also be made into a Helios cycle.
Solar month M of a 5515-month cycle has an extra day (to 28 days) if and
only if
(527*M + 2757) mod (5515) < 527
I believe that the resulting years also form a Helios cycle, so year Y
has 366 days (rather than 365 days) if and only if
(1336*M + 2757) mod (5515) < 1336.

Each 5515-month cycle has exactly the same number of days as three
1749-month cycles and forms 1/13 of a 5515-year cycle.

Karl

10(03(05

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 01 December 2008 00:17
To: CALNDR-L@...
Subject: Re: Lunisolar Cycles made up of Short Lunar Cycles RE:
5515-Year Luni-Solar Cycle

5515-Year Luni-Solar Cycle

Here's one more observation of the 5k515 ( or V_DXV ) lunisolar and
solar
cycle

The cycle can now include the
octaeteris year = 365 & 187 / 424 days

The cycle of entirety
= 4173 yerms
= 5512 octaeteris years
= 5515 years
= 68211 months
= 154947 trecena
= 2014311 days

This proportionality constant K = 5512 / 5515 could just serve to define
this lunisolar year,
Y = K*( octaeteris year )

I don't know yet if the octaeteris leap-moon function
( 3*Y +  3 + ?? )MOD( 8 ) < 3
2, 5, 7, 10, 13, 15, 18, 21, ??, ??
can be tweaked and functionally related to K to yield the same output as
( 2031*Y +  2757 )MOD( 5515 ) < 2031

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