The 61-day perennial calendar

There have been many different proposals for reform of the calendar to simplify the relationship between dates and weekday names - notably the World Calendar proposed in 1930 - but I don't think I've seen this one before.  It has a number of unusual features which mean it'd be unlikely to be adopted in practice, but I think it's an interesting idea.

A calendar year is either 365 or 366 days long.  Our current calendar assumes 365 days as the default and inserts an extra day in leap years, but what happens if we assume 366 days as the default instead?  One advantage of 366 is that it is exactly divisible by 6, which allows the year to be divided into six identical periods of 61 days each.  (We'll see how to deal with the missing day in common years later on.)

61 days can be further divided into one month of 30 days and one month of 31 days.  Let's assume this pattern throughout the year, so that the odd months (Jan, Mar, May, Jul, Sep, Nov) are all 30 days long and the even months (Feb, Apr, Jun, Aug, Oct, Dec) are all 31 days long.  This is obviously a slight change from the current pattern, although the months August to December are unchanged.  But it's more regular than the current pattern, and there are only two possible lengths instead of four as at present.

It would also be convenient to divide this 61-day period into an exact number of weeks.  Clearly this is impossible if the weeks are all the same length, since 61 is prime.  But why not introduce variable week lengths as well as variable month lengths?  If we allow six-day weeks as well as the conventional seven-day weeks, then we can have two six-day weeks and seven seven-day weeks in each 61-day period, making a total of nine weeks (or 54 weeks in a year).  Therefore I propose omitting two Mondays in each period of nine weeks, shortening the working week to four days.

Two short weeks out of nine is a rather awkward pattern, though.  It would be rather neater if the four-day working week came round on a regular basis - let's say once every three weeks.  So I propose further that one Monday in each nine-week period should be declared a holiday.  To keep it simple, let's start each nine-week period on a Monday, and always make the first day a holiday.  This gives rise to the following pattern, with non-working days in boldface:

		Mon	Tue	Wed	Thu	Fri	Sat	Sun
		1	2	3	4	5	6	7
Odd months		8	9	10	11	12	13	14
(Jan, Mar, May,		15	16	17	18	19	20	21
Jul, Sep, Nov)			22	23	24	25	26	27
		28	29	30
					1	2	3	4
Even months		5	6	7	8	9	10	11
(Feb, Apr, Jun,			12	13	14	15	16	17
Aug, Oct, Dec)		18	19	20	21	22	23	24
		25	26	27	28	29	30	31

This calendar may look strange at first, but it has some interesting properties:

• The pattern of working weeks is completely regular - one four-day week followed by two five-day weeks, all year round.  
• There are six regularly spaced three-day weekends throughout the year, with no need for any additional holidays beyond the one on the first of odd months (but see below).  In particular New Year's Day and May Day automatically become holidays in this calendar.
• The number of working days per year is 252 - more or less the same as at present when bank holidays are taken into account.
• There are always exactly 21 working days per month.
• There is a transparent relationship between the date and the weekday name.  For example, any date ending in a 2 must fall on a Tuesday or a Friday; in a 3, Wednesday or Saturday; and so on.  Apart from the holiday Mondays on the 1st of alternate months, dates ending in 1 fall on a Thursday or a Sunday.

This is a secular rather than a religious calendar, and no attempt has been made to accommodate the seven-day cycle of Christianity and other major faiths; nor does it take account of traditional holidays like Christmas and Easter.  But it would be possible to declare additional holiday Mondays if needed, creating extra four-day working weeks outside the regular cycle.  In particular, since December 25th always falls on a Monday in this calendar, it would be relatively straightforward to keep Christmas on its existing date - in fact easier than in the current calendar, where the weekday changes from one year to the next!

All the above presumes a year of 366 days, of course.  How should we deal with the three years out of four (plus years like 2100 in the Gregorian calendar) which are only 365 days long?

To avoid losing any of the dates in the year (which would cause problems with birthdays among other things), I propose combining two dates into one - perhaps the 28th and 29th of December, the last two workdays of the year.  For legal purposes, the date would change at midday, so 11.59am on Thursday 28th would be followed by 12 noon on Friday 29th.  There may be better alternatives though.

Obviously the above arrangements will take some getting used to - in particular the organizers of events that regularly take place on a Monday will have to deal with the fact that there are now only 42 Mondays per year, of which six are holidays.  On the other hand, there are now 54 weekends a year rather than 52 - surely an improvement?