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 729day interval is called a _jear_ there and the 3day leap item is called a _trip_. Both designs recognize that 729 days are roughly 2 solar years. Neither of these designs recognize the 7day week. I'm not quite sure how this could be used, and am looking for your ideas.  3 weeks = 21day (short) "month" => 17 or 18 months per year, 243 times 357 and 157 times 378 days  9 weeks = 63day (long) "bimonth" => 5 or 6 bimonths per year, 81 times 315 and 319 times 378 days  27 weeks = 189day (long) "semiyear" => 378 days per year, 386.5 per cycle  773 weeks = 5411day "subcycle" => 27 per leap cycle [Kalentris]: https://calendars.wikia.com/wiki/Kalentris [Trical]: https://calendars.wikia.com/wiki/Trical 
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 63day cycles in 400 Gregorian years. 773*3=2,319
Walter Ziobro
Original Message
From: Christoph Päper <[hidden email]> To: CALNDRL <[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 729day interval is called a _jear_ there and the 3day leap item is called a _trip_. Both designs recognize that 729 days are roughly 2 solar years. Neither of these designs recognize the 7day week.
I'm not quite sure how this could be used, and am looking for your ideas.
 3 weeks = 21day (short) "month"
=> 17 or 18 months per year, 243 times 357 and 157 times 378 days
 9 weeks = 63day (long) "bimonth"
=> 5 or 6 bimonths per year, 81 times 315 and 319 times 378 days
 27 weeks = 189day (long) "semiyear"
=> 378 days per year, 386.5 per cycle
 773 weeks = 5411day "subcycle"
=> 27 per leap cycle
[Kalentris]: https://calendars.wikia.com/wiki/Kalentris
[Trical]: https://calendars.wikia.com/wiki/Trical

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