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The Negative Leap Year Solar Calendar differs from other solar calendars in that instead of adding one day to the calendar every 4 years, this calendar subtracts 1 day from the calendar 3 out of every 4 years.

A year looks like this
Month Length Quarter Length
January 30 days 91 days
February 31 days
March 30 days
April 31 (30) days 92 (91) days
May 30 days
June 31 days
July 30 days 91 (90) days
August 31 (30) days
September 30 days
October 31 days 92 (91) days
November 30 days
December 31 (30) days

Negative leap day happens every 16 months on the last day of the month, and is a day that is skipped on the calendar. That leads to negative leap day occuring on the following days on the following years:

YEAR Day YEAR Day
1 none 5 none
2 April 31 6 April 31
3 August 31 7 August 31
4 December 31 8 December 31

and so forth.

The main advantage of this calendar is that 16 month periods are always going to have the same number of days unlike most other calendars that have leap days or intercalary days that change the number of days. In that 16 month period the months always alternate between 30 and 31 days until the last day of the last month which is skipped totalling to 30+31+30+31+30+31+30+31+30+31+30+31+30+31+30+30 = 487. In this system like the current system the standard year is 365 days and leap year is 366 days, only in this system leap years don't contain leap days, instead each standard year has a negative leap day.

Another small advantage is that unlike leap day that occurs only once every 4 years, the day skipped by negative leap day is not skipped 3 out of 4 years. For people born on these non-leap days it means being able to celebrate their birthday on that day more often than not.

One major drawback to this calendar is that it does not account for the fact that the tropical year is actually less than 365.25 days. To account for that an additional negative leap day would have to be inserted once in a while. Maybe the best way to do that would be to repeat another year with a negative leap day on December 31 on years that would otherwise not have a negative leap day. If it's calculated the same way that non-leap years that are divisible by 4 are calculated on the Gregorian calendar then this would only occur every 100 years at most. The main advantage of the calendar of having 16 month periods of constant length would be interrupted but that's a small price considering that that only happens once every 100-200 years.

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