30-year cycle drift cycle RE: 3663 lunisolar year cycle

Dear Helios and Calendar People

Helios has reckoned the drift cycle for a year of exactly 136/11
lunations, which arises from an 11-year cycle.

This has got me thinking of the drift cycle for a year of exactly 371/30
lunations, which arises from a 30-year cycle.

I then realised that a lunisolar cycle whose length is equal to one of
these drift cycles would have 371 saltus lunae corrections. I list such
cycles below:

Years Leap Months Year/Month
Years/Truncations
7679 2828 12.368277 365.667
(exactly 365 2/3)
7709     2839 12.368271 350.409
7739        2850              12.368265 336.478
7769        2861 12.368258 323.708

Note that the number of days in the cycle does not affect the number of
saltus lunae, so is not shown or even calculated.

I've shown the number of years per truncation of the 19-year cycle to 11
years to enable comparison with the 334-year and 353-year cycles. For a
given mean month, the 7739-year cycle has a slightly longer mean year
than the 334-year cycle and the 7709-year cycle has a slightly shorter
mean year than the 353-year cycle.

So if we use the 7709-year cycle as the drift cycle we have
= 1 drift cycle
= 7709 solar years
= 7710 years of the 30-year cycle (of 371/30 lunations).

This fits in with there being 7710*371/30 = 95347 = 12*7709 + 2839 lunar
months in the cycle.

A 30 year cycle can be generated by dividing each lunar month into 30
tithis and each year into 371 tithis.
Each tithi can be set equal to a day except for six tithis every common
year or five tithis every leap year, which have no duration (I expect
Charles Moyer has been cleaning up after his most recent uruz bull
sacrifice).
This 30-year cycle is corrected by occasionally adding a tithi to a
year, which gives rise to a saltus lunae.
Then the number of 'leap' years (with five tithis of zero duration)
needs to be reduced by the number of these saltus lunae corrections to
become equal to the number of abundant years as in column C in my
lunisolar spreadsheets
http://www.the-light.com/cal/kp_Lunisolar_xls.html .

Karl

10(11(01

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 20 July 2009 10:49
To: CALNDR-L@...
Subject: Re: 3663 lunisolar year cycle

One more thing on this. By the parameters of the 3663y luni-solar cycle,
which is 111 33y cycles, the mean year of the 11-year luni-solar cycle
evidently drifts through the seasons every 2664 years.

Therefore

= 1 drift cycle
= 2664 solar years
= 2665 luni-solar years ( 11y-cycle )

I have now made a web-page for the IM calender
http://www.helios.netne.net/ivymike.htm 
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