LAST EDITED ON Aug-28-03 AT 02:26 PM (EST)
 
All right. The whole business of proposing an accurate calendar in step with the sun is to find 2 integers L and P such that

L/P » t - 365 » 0.2421897 days

as close as possible. Then P is the period of the calendar in years and L is the number of leap years in the calendar period P. There are some reasonable requirements on the calendar period:

1. The period should be comparable to or greater than the average human lifespan. Then the exception from the simple rule of the Julian calendar "one leap year in 4 years" occurs at most once in anyone's lifetime.

2. The simple rule of the Julian calendar "years divisible by 4 are leap years" should be valid in any particular period. Then even if the exception from the rule "one leap year in 4 years" occurs someone's lifetime, things are the same after the exception.

3. The period should preferably be a simple round number. Then the calculations of remote dates and time periods between 2 remote dates are simple.

The Gregorian calendar uses L = 97 and P = 400, L/P = 0.2425. All 3 requirements are satisfied, although one could do better on the requirement #1 - the accuracy is a loss of 0.031 days/millenium = 7 hours 27 minutes/millenium.

The modern Persian calendar was proposed in 1925. At that time, the best experimental value of the solar year length was 365.242199 days. So the 2 integers L and P of the Persian calendar are selected as L = 683, P = 2820 years, L/P = 0.2421986. The accuracy (requirement #1) is excellent - loss of 12 min 49 sec/millenium. However, neither of the remaining 2 requirements are satisfied (128 and 132 years cycles, 29, 33, and 37 years subcycles).

It turns out that the best present day experimental value for the solar year length is a little shorter - about 365.2421897 days. Let's propose a new CTK Exchange calendar. On the first attempt, L = 15, P = 62 years, L/P = 0.2421935 - after 60 years of "one leap year in 4 years", there is a gap of 1 leap year in 6 years. The accuracy is excellent (loss of 5 min 28 sec/millenium, better than the Persian calendar), the period is simple and comparable to the average human lifespan. However, the rule "years divisible by 4 are the leap years" or "double even years are leap years" has to alternate with the rule "single even years are leap years" every 62 years, which would be inconvenient. The correct this defect, let's double the calendar period to P = 124 years and the number of leap years to L = 30. You simply skip a leap year every 124 years. What could be simpler than that?