Re: Alternating Periodic Sequences

Dear Helios

Neither of these suggestions is as accurate as

Case 3) 5th of a year 47 / 19 months
Mean interval between leap 5ths 1 / [ 1 - ( 365/ Y ) ] in days
Metonic year = Y = 365 & 149/600 days
Mean interval between leap 5ths 1470 & 119/149 days

But even this does not provide a very accurate year.


The 334-year cycle has 243*17 lunar months hence 243*(11/8) = 334 + 1/8
11-L's years. Hence we can get an accurate mean year by making every
334th year have nine of these '8ths' instead of the usual 8. Using the
same mean '8th' as Helios, we get a mean year of (2673/2672)*( 365 & 29
/ 275 days ), which is approximately 365.2420958 days.

But the mean yerm of 8ths is only about 165 days or 3.6 '8ths' and so is
too short for the yerm concept to be of much use. Also the correction of
one '8th' every 334 years would produce a jitter in excess of one month.


Instead, we could abandon the alternating sequence and divide each 8th
into 17 parts and have 136 parts in 317 years and 137 parts in 17 years
each 334-year cycle. Each part corresponds to 1/11 lunar month. We still
need a rule for the number of days in each part. One such rule may have
been suggested to the list.

For case three once can divide the 47th into 5 parts and have 235 parts
in most years and correct by removing a part about once every 300 to 400
years. Each part corresponds to 1/19 of a lunar month. We still need a
rule for the number of days in each part. I believe at least one such
rule has been suggested to the list.

Karl

10(08(11

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 02 May 2009 05:40
To: CALNDR-L@...
Subject: Re: Alternating Periodic Sequences

I see two cases of alternating periodic sequences that seem compelling
to
calculate

Case 1) 9th of year = 11 / 8 months
mean yerm of 9ths = 1 / [ 2 - ( 729 / Y ) ]
octaeteris year = Y = 365 & 187 / 424 days
mean yerm of 9ths = 194 & 45 / 266 days = 212 / 399 Y
--------------------------------------------
Case 2) 8th of year = 17 / 11 months
mean yerm of 8ths = 1 / [ 2 - ( 728 / Y ) ]
11-L'S year = Y = 365 & 29 / 275 days
mean yerm of 8ths = 165 & 21 / 152 days
--------------------------------------------
and these cases, used for a calendar, reckon for the 11 and 17 month
interval

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