An Idea for a New Calendar

Antony Galton

Anyone designing a calendar has to face the awkward fact that none of the astronomical cycles which it is customary to base calendars on form whole-number multiples of any other. There are about 365¼ days in a year, about 29½ days in a month, and therefore between 12¼ and 12½ months in a year.

The only sensible solution to the "days in a year" problem, and the one which we currently use, is to have a four-year cycle in which the first three years have 365 days each and the fourth (the "leap year") has 366 days. Errors from this method accumulate fairly slowly and can be corrected, very nearly, by making three leap years in every 400 years normal (with 365 days).

As regards months, the mismatch between the lunar and solar cycles makes it pretty much impossible to have a workable calendar taking both into account. The months of our present calendar, although obviously owing their origin to the lunar month, are too long for this purpose. It seems to me that if we want to have a division of the year into some small number of periods, we can still call them months, but there is no point in trying to tie them into the lunar cycle.

Devising a calendar must involve some admixture of both astronomy and arithmetic. Astronomy provides the two basic (sun-based) cycles: days and years. These give us the number 365¼, which arithmetic has to do its best with. Astronomy also gives us four natural dividing points in the year: the two solstices and the two equinoxes. These are actually moments of time, which are not keyed in to the cycle of days. The moment of the Northern Summer Solstice, for example, will occur at different times of the day in different years. The best we can say is that in each year it will fall on a particular day, but this sequence of days does not form an absolutely regular cycle from one year to the next. Nonetheless, it would be nice to take these four key moments into account in our calendar, for example as holidays (currently Easter and Christmas are related to, though they do not actually fall on the Northern Spring Equinox and the Northern Winter Solstice respectively). I would like to call these four days "Sun Days". To avoid confusion with "Sundays", let’s call them "Big Sundays".

Almost the only useful property of that number 365 is its proximity to 360, which is an extremely "round" number, having a relatively large number of small factors. If we have 12 months of 30 days each, that leaves 5 extra days to accommodate. We already know what four of these could be: the Big Sundays! What about the fifth extra day?

I suggest that it would be elegant to have the Big Sundays arranged symmetrically in the year. Between two consecutive Big Sundays, there are, on average, just over 90 days. For a symmetrical arrangement we want a year of the form:

 
45 days + BS1 + 90 days + BS2 + 90 days + BS3 + 90 days + BS4 + 45 days
This adds up to 364 days; to preserve the symmetry, the missing day must go exactly in the middle, i.e., half-way between BS2 and BS3. We now have a year of the form:
45d + BS1 + 90d + BS2 + 45d + MYD + 45d + BS3 + 90d + BS4 + 45d

"MYD" stands for "Mid Year Day", which is the obvious name for it.

Looking at this pattern, it is pretty clear that our calendar should consist of 8 months of 45 days each, with five extra days coming after the 1st, 3rd, 4th, 5th, and 7th months. These five days will be called Major Holidays. How do we remember which months have an extra day after them? We learn the pattern 121121, which gives the number of months between consecutive Major Holidays.

Now, what about weeks? Our seven-day week (corresponding roughly to a quarter of a lunar cycle) doesn’t fit in with this calendar at all; come to that, it doesn’t fit in with our present calendar at all either. It is ripe for redevelopment! But how?

The key to the solution is to notice that the number of days in a new month, 45, is like the number of days in the year, 365, in that both numbers leave a remainder of 5 when divided by 8. We can divide the month up in a way that is exactly analogous to the way we divided up the year. It will have 8 weeks of 5 days each, with 5 days left over which we shall call Minor Holidays. The distribution of Minor Holidays within the month will be the same as the distribution of Major Holidays within the year. Thus the month has the structure:

5 + 1 + 5 + 5 + 1 + 5 + 1 + 5 + 1 + 5 + 5 + 1 + 5.
 

This will be easy to remember, since it has the same pattern 121121 that we noticed earlier. The Minor Holiday in the middle can be called Mid Month Day, and doubtless suitable names could be devised for the others. Every month will have the same structure; we have to learn "121121", but we can forget about "Thirty days hath September" and all that, and there’ll be no more frantically consulting diaries to check whether the 17th is on a Thursday or a Friday.

The smallest division above a day is thus the 5 day week, of which the year contains 64 altogether, making 320 days. The remaining 45 days are holidays (exactly one month’s worth, interestingly enough), which fall outside the weeks. The 5 Major Holidays fall outside the months, too. The working week can be based on the five-day structure. Of course, we get fewer holidays than in our current system with a two-day weekend, but this could be compensated for in various ways. Perhaps we will have a shorter working day, or perhaps it will be customary to take one afternoon a week off.

If all this looks a little colourless, perhaps it is because we have jettisoned the beautiful names we give our days and months: Monday, Tuesday, etc, and January, February, etc. But there is plenty of scope for invention here, too. We need 8 names for the months of the year, 8 names for the weeks in each month, and 5 names for the days in each week. We can also have names for the 5 Major Holidays in each year and the 5 Minor Holidays in each month. That’s 31 names altogether.

We must not forget leap years. Every fourth year must have an extra day, and the question is where we should put it. When leap years were first invented, the solution was obvious: put it at the end of the year. Since in those days the year began in March (so September really was the seventh month), this meant that the extra day was added at the end of February. We can do the same. Every fourth year will have an extra Major Holiday immediately after the last month. It can be called Four Years’ End, or if you prefer, LeapHoliday.

How does this scheme correspond to our present way of doing things. We agreed that the year must start half-way between two Big Sundays. It is rather arbitrary which two we choose, but the most natural choice from the point of view of dwellers in the northern hemisphere is probably the Winter Solstice and the Spring Equinox. That places New Year’s Day on February 5th. Everything else is then determined:

Month 1 February 5th to March 21st
Spring Equinox Day March 22nd
Month 2 March 23rd to May 6th
Month 3 May 7th to June 20th
Summer Solstice Day June 21st
Month 4 June 22nd to August 5th
Mid Year Day August 6th
Month 5 August 7th to September 20th
Autumn Equinox Day September 21st
Month 6 September 22nd to November 5th
Month 7 November 6th to December 20th
Winter Solstice Day December 21st
Month 8 December 22nd to February 4th

All that remains now is to think of those 31 names! Any suggestions?

Here's another suggestion for a new calendar, which represents a less radical departure from the existing state of affairs, but is quite neat.