Re: 5515-Year Luni-Solar Cycle

Dear Helios, Victor and Calendar People

So the Octaeteris new year would drift through all the seasons
(spring->summer->fall->winter) three times in the course of one
5515-year cycle.

The Octaeteris has eight years (an even-number) so cannot be made into a
Helios cycle. This may be why Helios cannot find a leap-moon function
for it. However the three leap months can be spread perfectly evenly
through the 99 months of Octeateris exactly one every 33 months. To form
a Helios cycle of months, select the 17th, 50th and 83rd month as leap
months in the 99-month cycle.

The 5515-year cycle has 2014311 = 3 * (13^2) * 29 * 137 days and 5512 =
(2^3) * 13 * 53. So there is a common divisor of 13 for the 5512
Octeateris years. So the octaeteris cycle would repeat once every 424
octaeteris years = 53 octaeterides = three 1749-month cycles. This
arises from the fact that 1749 is divisible by 33=99/3 so makes up
1749/99 = 17 2/3 octaeterides = 141 1/3 years, which is one third of 424
Octeateris years.


I realise now that a lunar calendar using the 1749-month cycle could
have a 13-month solar calendar run alongside it so that three 1749-month
cycles of 5247 lunar months are exactly equal to 5515 solar months. The
5155 solar months (424 years and three months) would have 527 days in
addition to 28 days per month. In this period, there would be
5515-5247=268 solar months that do not contain the first day of a lunar
month. A 527/5515 calendar like Victor's 43/450 or 28/293 calendar would
do this. However there may be a way of using the lunar calendar to
determine which solar month gets an extra day.

One possibility is to have two long (29-day) solar months begin in each
17-month yerm and one long solar month begin in each short 15-month
yerm. There'd be ten exceptional 17-month yerms every three 1749-month
(107-yerm) cycles with just one long solar month beginning in it. This
leads to 2*321 - 10 + 105 = 527 long solar months as required. Also
between any two consecutive exceptions, there'd be exactly 103 solar
months every 6 yerms of 98 lunar months.
Another possibility is to have a long solar month after each solar month
that misses either the 1st or 15th day of a lunar month, with three
exceptions every 1749-month cycle. This leads to 268*2 - 3*3 = 527 long
months as required.



Karl

10(03(04


-----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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