Normally Equal Year Parts RE: Alternating Periodic Sequences

Dear Helios, Victor and Calendar People

Similar to this, one could have a calendar where each year contains a
fixed number of parts and each part with a small number of exceptions
have the same number of days and the exceptions either all have one day
more or all have one day less than the normal part.

One can then work out the mean interval between the exception parts for
a mean year of Y

1 / [ 1 - (365/Y) ] applies to
1/5 years normally of 73 days exceptions of 74 days and
1/73 years normally of 5 days exceptions of 6 days.

1/ [ 1 - (364/Y) ] applies to
1/4 years normally of 91 days exceptions of 92 days,
1/7 years normally of 52 days exceptions of 53 days,
1/13 years normally of 28 days exceptions of 29 days (e.g. Victor's
293/28 calendar)
1/14 years normally of 26 days exceptions of 27 days and numerous
others.

1/ [ (366/Y) - 1 ] applies to
1/3 years normally of 122 days exceptions of 121 days,
1/6 years normally of 61 days exceptions of 60 days,
1/61 years normally of 6 days exceptions of 5 days,
1/122 years normally of 3 days exceptions of 2 days.

These three intervals are approximately, 1508, 294 and 482 days
respectively.

Karl

10(06(22

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 12 March 2009 10:34
To: CALNDR-L@...
Subject: Alternating Periodic Sequences

I can make a batch of these "mean yerm" formulas. I think they work
because
730 = 2*365. There's a sort of range between 727 and 733 which are prime
numbers. So, there are certain subdivisions of the year and a "mean
yerm" to
each...

mean yerm of 8ths = 1 / [  2 - ( 728 / Y ) ]

mean yerm of 3rds = 1 / [  2 - ( 729 / Y ) ]

mean yerm of 10ths = 1 / [  2 - ( 730 / Y ) ]

mean yerm of 17ths = 1 / [ ( 731 / Y ) - 2 ]

mean yerm of 12ths = 1 / [ ( 732 / Y ) - 2 ]

Some years lead to integer mean yerms. These 5 "elegant" years are

365 & 71 / 293
365 & 119 / 491
365 & 365 / 1507
365 & 8 / 33
365 & 39 / 161

and all cycles are odd numbered. These cycles are then described by
their
alternating periodic sequence,

8ths = 46, 45, ...
3rds = 122, 121, ...
10ths = 37, 36, ...
17ths = 21, 22, ...
12ths = 30, 31, ...

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