Re: Mean Year of 353-year lunisolar cycle

Dear Helios and Calendar People

The 6707-year cycle is a multiple of 19-years and is listed in
http://www.the-light.com/cal/Lunisolar19.html of
http://www.the-light.com/cal/kp_Lunisolar_xls.html . It is equivalent to
353 19-year cycles with one lunar month returned.

Thanks for noticing that the 82954 months are a multiple of 703 months.
For this to be a multiple of the 703-month lunar cycle its number of
yerms (5074) must be the same multiple of the number of yerms (43) in
the 703-month cycle.

We have 82954 = 703*118 and 5074 = 43*118. So this 19-multiple of the
353-year cycle is indeed a multiple of the 703-month lunar cycle. It is
another good example of a lunisolar cycle that is a multiple of a short
lunar calendar cycle (besides 5515-year and 725-year cycles).

See http://www.hermetic.ch/cal_stud/lunarcal/lunacycl.htm for the
703-month cycle.

The spreadsheet gives a mean year of 365.24228 days and a mean month of
29.5305832 days.
The mean year and month are a little shorter than in Irv's 13-multiple
of the 353-year cycle. Intermediary multiples exist of 15 and 17
353-year cycles of which the 17-multiple has a whole number of weeks and
also has 6001 years.

The 19-multiple is special in that it is a multiple of a lunar calendar
cycle less than 1000-months long, each consisting of a single year era
(of 43 yerms).

Irv has pointed out that the number of months in this 6707-year cycle is
a multiple of 37. This 37 is a multiple of the 703-month cycle 703=37*19
and so if you (as suggested by Helios) defined a short year, so that 3
short years equal 37 months, the 703-month cycle would have 57 short
years in it. The whole 6707-year cycle so has 118*57=6726 short years,
so the short year would drift 19 times through the 6707-year cycle,
which is indeed once every 353-year cycle as Helios thinks.

The number of months in the 6707-year cycle is also divisible by 59 and
so a 2-month cycle of 59 days would drift a whole number of months with
respect to the 6707-year cycle and this number of months is the number
of yerms divided by 59, which is 86. So the 2-month cycle drifts a whole
month once every 964 25/43 lunar months or 965 50/86 2-month cycle
months.

Karl

10(08(17

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 09 May 2009 10:41
To: CALNDR-L@...
Subject: Mean Year of 353-year lunisolar cycle

I've found one more lunisolar cycle made up of the same repetition of
one
lunar calendar cycle listed in
Karl P,'s "Lunar Calendar Cycles less than 1885 Months"

This is the case of the 43 yerm era with 703 months with
mean month = 29 & 373 / 703 days
that factors into
-----------------------------------

6707 years = ( 2*59 )*2*2*2*3*5*173 = 82954 months

-----------------------------------
This is 19 repeats of the 353-year cycle of 4366 months. This scheme
allows
us to write

mean year of 353-year cycle = 365 & 1625 / 6707 days

mean year of 3-year cycle = 364 & 4 / 19 days

I think the 3-year cycle's new year drifts through the seasons 19 times
in
6707 years, that is once every 353 years

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