Re: 5515-Year Luni-Solar Cycle

Dear Helios and Calendar People

Helios said about the 5515-year cycle:
The cycle of entirety
= 4173 yerms
= 5515 years
= 68211 months
= 154947 trecena (13-day periods)
= 2014311 days

But also
= 78 yerm eras
= 39 1749-month cycles
= 1248 drifts over 29-day cycle

The total number of days is 2,014,311 = 3 * (13^2) * 29 * 137.
So not only is the number (39) of 1749-month cycles is divisible by 13,
but the number of days (51649) in each 1749-month cycle.
Each 1749-month cycle
= 107 yerms
= 1749 months
= 3979 trecena
= 32 drifts over 29-day cycle
= 51649 days
= 2 yerm eras

Twenty 1749-month cycles contain a whole number of tzolkins:
= 2140 yerms
= 34980 months
= 3979 tzolkins (260-day periods)
= 640 drifts over 29-day cycle
= 40 yerm eras
= 15 1981-month cycles + 13 405-month cycles.

One curious thing is that a yerm era is approximately 100 tzolkins
(26,000 days) and this suggests the idea of starting a new yerm era at
the next opportunity after every 100 tzolkins. The resulting yerm eras
would all have either 52 yerms (25,101 days) or 55 yerms (26,548 days).

Karl

10(03(12

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 22 November 2008 02:29
To: CALNDR-L@...
Subject: 5515-Year Luni-Solar Cycle

5515-Year Luni-Solar Cycle

Here's the decomposition is smaller, more well-known cycles;
5515 years = 166*( 33 years ) + 37 years
5515 years = 7*( 334 years ) + 9*( 353 years )

The cycle of entirety
= 4173 yerms
= 5515 years
= 68211 months
= 154947 trecena
= 2014311 days

Mean year = 365 & 1336 / 5515 days = 365.2422484 days
Mean month = 29 & 928  / 1749 days = 29.5305889 days
13-month years = 2031

For a month count M and year count Y...

A luni-solar year has 13 months if
( 2031*Y + 2757 )MOD( 5515 ) < 2031

An ecclesiastical month has 30 days if
( 928*M + 874 )MOD( 1749 ) < 928

A month is a new year's month if
( 5515*M + 65453 )MOD( 68211 ) < 5515

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