Leap week calendar

A leap week calendar is a calendar system with a whole number of weeks every year, and with every year starting on the same weekday. Most leap week calendars are proposed reforms to the civil calendar, in order to achieve a perennial calendar. Some, however, such as the ISO week date calendar, are simply conveniences for specific purposes.

The ISO calendar in question is a variation of the Gregorian calendar that is used (mainly) in government and business for fiscal years, as well as in timekeeping. In this system a year (ISO year) has 52 or 53 full weeks (364 or 371 days).

Leap week calendars vary on whether the concept of month is preserved and whether the month (if preserved) has a whole number of weeks. The Pax Calendar and Hanke-Henry Permanent Calendar (formerly the Common-Civil-Calendar-and-Time) preserve or modify the Gregorian month structure. The ISO week date and the Weekdate Dating System are examples of leap week calendars that eliminate the month.^[1]

Most leap week calendars take advantage of the 400-year cycle of the Gregorian calendar, which has exactly 20,871 weeks. With 329 common years of 52 weeks plus 71 leap years of 53 weeks, leap week calendars would synchronize with the Gregorian every 400 years (329 × 52 + 71 × 53 = 20,871).

Advantages

• The calendar starts on the same day of the week every year.
• There are no fragments of weeks at the beginning or end of the year.
• Unlike the Gregorian Calendar, variations of years are limited to the possible addition of a leap week.
• For leap week calendars without months, each date of the year can be completely specified with three data (week, weekday, year) instead of four (weekday, month, ordinal day, year).
• Unlike certain proposed calendar reforms such as the World Calendar and International Fixed Calendar, there are no exceptions to the 7 day cycle of the week. This avoids opposition from religious groups who object to the interruption of the weekday sequence.

Disadvantages

• A year with an intercalary/leap week is at least 7 days longer than a year without an intercalary week. Consequently, the equinoxes and solstices must vary over 7 days, i.e. ±3 of the average date, or even more, such as 19 days in the Pax Calendar.
• Persons born during the added intercalary week lose their birthday in common years, like those born on 29 February. Approximately 1 in 294 days would belong to an intercalary week, compared to approximately 1 in 1506 days that occur on 29 February.
• Leap year rules are usually more complicated than the Gregorian rule. The arises from the fact there is no simple approximation like one in 4 years. See Pax Calendar and Hanke-Henry Permanent Calendar#disadvantages and Symmetry454#Leap_rule.
• Quarterly accounting statistics will not be consistent over multiple years because the yearly quarter containing the intercalary week will sometimes include 14 weeks instead of the usual 13.

Year structures

Note that the new years of the calendars shown need not be synchronised.

The years according to ISO week date applied to months, i.e. a month has as many weeks as it has Thursdays, are shown depending on the weekday of 1 January, shaded weeks belong to the month they are labeled with in regular years and to the other adjoining one in leap years.

References

External links

• Hermetic Leap Week Calendar - a leap week calendar with four quarters of three months each, suitable for business purposes
• Leap Week Calendars
• Weekdate Dating System