A leap cycle of 293 years contains exactly 71 leap days, 52 leap weeks or 13 leap months (of 4 weeks each) and thus overall 107016 days, 15288 weeks and 3822 four-week months or 3516 twelfth-of-a-year months. Its mean year length is ca. 365.242321 days or 365 days, 5 hours, 48 minutes and ca. 56.5 seconds.
A peculiar detail of the number of leap weeks and leap months is that they add up to another year, i.e. the cycle is equal in length to one of 294 years of 364 days each.
The number of years, 293, is prime. There are no “simple” Olympiad-based leap rules for this cycle. Possibly the simplest rule if the year count is reset each era (i.e. leap cycle run) is this: There is a leap day in every year divisible by 4, except in centennial years 100 and 200. Similarly, there is a leap week in every year divisible by 11 and 5 years before or 6 years after these (or vice versa) within the same era, except in one particular year to be specified (e.g. the one between 143 and 154).
Probably the most prominent use cases for this leap cycle are the Symmetry454 and Symmetry010 Calendars created by Irv Bromberg, who proposes a leap rule that spreads leap items equally across its length thereby minimizing astronomic “jitter”.
Leap day rules[]
- 71⁄293 ≈ 0.24232082
- = 1⁄4 − 9⁄1172
- = 1⁄4 − 2⁄293 − 1⁄1172
- = 1⁄4 − 3⁄293 + 3⁄1172
Leap week rules[]
- 52⁄293 ≈ 0.1774744
- = 1⁄5 − 33⁄1465
- = 1⁄5 − 7⁄293 + 2⁄1465
- = 1⁄5 − 6⁄293 − 3⁄1465
- = 1⁄6 + 19⁄1758
- = 1⁄6 + 3⁄293 + 1⁄1758
- = 1⁄6 + 4⁄293 − 5⁄1758
- = 1⁄6 + 4⁄293 − 1⁄586 − 1⁄879
All items (13)