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This is a rule-based solar calendar. A modification of the current Gregorian calendar, it is meant to be perpetual, i.e. every year starts on the same day of the week.

Calendar structure[]

A calendar year is made up of 52 weeks divided into 12 months. The month lengths are the same as in the Gregorian calendar, except for December, which only has 30 days in this calendar, making the common calendar year 364 days (52 weeks) long. Note: February always has 28 days in this calendar.

Correction mechanism[]

In order to make every single calendar year begin with the same day of the week and to stay approximately in sync with the solar year in the long term, leap weeks are regularly intercalated into the calendar year. These 7 extra days belong to the month of December, making it 37 days long in leap years.

How exactly are leap weeks added?[]

For that question we first have to work out the length of the tropical year in weeks - a tropical year is currently around 365.2421987 days long, which converts to 52.177457 seven-day weeks. For this reason, we have to insert 8 leap weeks in 45 years to stay approximately in sync (the approximation of the tropical year under this rule is 52.177777... weeks, which is quite close).

Which years contain a leap week? To answer this question, first work out 45 / 8, which is 5.625. Multiply this number by 1, 2, 3, 4, 5, 6, 7, 8 and take the integer part of the products, and we get this sequence:

5, 11, 16, 22, 28, 33, 39, 45

The 45 here must be changed to 0, forming a new sequence:

0, 5, 11, 16, 22, 28, 33, 39

If the year count modulus 45 is one of these numbers, that year is a leap year (contains a leap week). Otherwise, that year is a common year consisting of 52 weeks.

Year counts and reference point[]

The year counts in this calendar are the same as those in the Gregorian calendar (i.e. starting from Christ's birth and designated AD or CE).

The reference point of the calendar is Monday, January 1, 2018. This date was also January 1, 2018 in the 52-week calendar.

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