Gregorian leap cycle = 773*3^3 weeks

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Gregorian leap cycle = 773*3^3 weeks

Christoph Päper-2
Dear calednarists

As we all know, the Gregorian leap cycle of 400 years contains exactly 146'097 days or 20'871 weeks of the usual 7 days each. Those numbers divide well by 3, because 27 = 3*3*3 is a factor, but the only other prime factor is 773.

Few calendar designs exploit these numbers directly.

In [Kalentris], a _tricycle_ has 27 months of 27 days each, i.e. 729 days overall, and frequent leap _tierces_ of 3 days each, resulting in exactly 200 tricycles (or 600 "years" of 243 days each) per Gregorian leap cycle. [Trical] offers a similar Gregorian alignment, but a 729-day interval is called a _jear_ there and the 3-day leap item is called a _trip_. Both designs recognize that 729 days are roughly 2 solar years. Neither of these designs recognize the 7-day week.

I'm not quite sure how this could be used, and am looking for your ideas.

- 3 weeks = 21-day (short) "month"
  => 17 or 18 months per year, 243 times 357 and 157 times 378 days
- 9 weeks = 63-day (long) "bimonth"
  => 5 or 6 bimonths per year, 81 times 315 and 319 times 378 days
- 27 weeks = 189-day (long) "semiyear"
  => 378 days per year, 386.5 per cycle
- 773 weeks = 5411-day "subcycle"
  => 27 per leap cycle

[Kalentris]: https://calendars.wikia.com/wiki/Kalentris
[Trical]: https://calendars.wikia.com/wiki/Trical
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Re: Gregorian leap cycle = 773*3^3 weeks

Walter J Ziobro
Dear Cristophe:

In the Balinese calendar, there are 63 day cycles called ngunalatri used to determine the lengths of the lunar months.  There happen to be exactly 2,319 such 63-day cycles in 400 Gregorian years. 773*3=2,319


-Walter Ziobro


-----Original Message-----
From: Christoph Päper <[hidden email]>
To: CALNDR-L <[hidden email]>
Sent: Thu, Nov 29, 2018 10:41 am
Subject: Gregorian leap cycle = 773*3^3 weeks

Dear calednarists

As we all know, the Gregorian leap cycle of 400 years contains exactly 146'097 days or 20'871 weeks of the usual 7 days each. Those numbers divide well by 3, because 27 = 3*3*3 is a factor, but the only other prime factor is 773.

Few calendar designs exploit these numbers directly.

In [Kalentris], a _tricycle_ has 27 months of 27 days each, i.e. 729 days overall, and frequent leap _tierces_ of 3 days each, resulting in exactly 200 tricycles (or 600 "years" of 243 days each) per Gregorian leap cycle. [Trical] offers a similar Gregorian alignment, but a 729-day interval is called a _jear_ there and the 3-day leap item is called a _trip_. Both designs recognize that 729 days are roughly 2 solar years. Neither of these designs recognize the 7-day week.

I'm not quite sure how this could be used, and am looking for your ideas.

- 3 weeks = 21-day (short) "month"
  => 17 or 18 months per year, 243 times 357 and 157 times 378 days
- 9 weeks = 63-day (long) "bimonth"
  => 5 or 6 bimonths per year, 81 times 315 and 319 times 378 days
- 27 weeks = 189-day (long) "semiyear"
  => 378 days per year, 386.5 per cycle
- 773 weeks = 5411-day "subcycle"
  => 27 per leap cycle