Leap Year Day

February 29th: the most disruptive weekday of all time.

The leap year, or leap day, is the most disruptive aspect of the Gregorian Calendar. Not the leap year day itself, which keeps the calendar year aligned with the seasons, but making a leap year day a weekday throws what would otherwise be a reasonable calendar system out of whack.

If leap day were not a weekday, then it would be easier to follow the Gregorian Calendar. If we only look at the 365 days of the year, then the weekdays would progress regularly. Jan 1st 2012 fell on a Monday. Without a leap day, Jan 1st 2013 would be Tuesday, 2014 a Wednesday, 2015 a Thursday, 2015 a Friday, 2016 a Saturday, 2017 Sunday and so on. An even schedule of progressive weekdays. This would be the same situation for birthdays, holidays and observations based on dates (Groundhog’s Day, Halloween, Christmas and so on). However, because February 29th is a weekday, every four years (with omissions 3 days out of every 400 years) this progression is thrown off.

Also, observing the leap day two months into the year is more disruptive than if it were added at the end of the year (March used to be the first month of the Roman Calendar. The switch to January 1st didn’t include a change in the leap year observation. As a result, instead of the cycle of months and weekdays repeating itself every 7 years, they repeat themselves every 400 years, with lesser cycles every 28, but these are thrown off every century.

There are a number of strategies to deal with aligning one’s calendar to the year.

Lunar and lunisolar calendars (Chinese, Hebrew, Hindu, Muslim) avoid this by inserting embolismic lunar months periodically, so they are excluded from this comparison. They follow the moon and don’t have the same problems as do purely solar calendars.

The Egyptian Calendar had 12 months of 30 days, and an extra five days left over. They didn’t insert a leap year day (at least not initially, they were later brought into alignment with the Roman Calendar). This isn’t necessarily a big deal. The Mesoamerican calendar does the same dance. The Winter Solstice would fall one day later every four years. At that rate, it would take 1460 years for the calendar to drift with respect to the seasons to come around to its starting point again.

The way we measure the year varies a great deal. We generally accept the mean tropical year of  365.2421897 or 365 days, 5 hours, 48 minutes, 45.19 seconds (as of Jan 1st 2000). The leap year is meant to account for that fraction of 0.2421897 or 5 hours, 48 minutes, 45.19 seconds. There are a number of schemes to account for it, some of which are more accurate than others.

Here’s a comparison of some of different leap year schedules:

Mean Tropical Year

0.242 189 7

Calendar

Leap Year Schedule

Fraction

Difference

Julian

1 day per 4 years

0.25 + 0.007 810 3

Gregorian

1 day per 4 years

- 3 days every 400 years

0.242 5 + 0.000 310 3

Persian Calendar

8 days every 33 years

0.242 198 52 *see below

theAbysmal

1 day per 4 years

- 1 day every 128 years

0.242 18 75 -  0.000 002 2

*the Persian Calendar system is much more complex than indicated above, as it uses astronomical observations to determine its leap year schedule. As a result, it is the most accurate of the periods measured above, as it doesn’t measure itself against the mean tropical year, and takes variance into account.

The advantage to theAbysmal Calendar is the simplicity compared to the Persian. Also, the Leap Year day can be added or removed to ensure seasonal accuracy without disrupting the year of 52-weeks. This is one of the biggest advantages to observing the leap year day at the end of the year, and excluding it from the cycle of weekdays. One can add or remove leap seconds, minutes, hours or days, while keeping the rest of the year perpetual.

What do you think?

296 Days to Dec 21st 2012

2 Responses to Leap Year Day

  1. Sebastian says:

    Why is February 29, not February 30 a leap year day?

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