The current consensus calendar is called the Gregorian calendar.

Types of calendars, and facts about calendar design

Primary classification of calendars:

Other named calendar attributes:

Some facts/difficulties:


Months are divisions of the calendar roughly as long as a natural period related to the orbit of the moon. A sidereal month, which is the moon's orbital period in a non-rotating frame of reference, is about 27.3 days. However, a cycle of moon phases (synodic month) is about 29.53 days [4].


Most calendars appear to segment time into periods of 5 to 13 days called weeks, although a few cultures had weeks as short as 3 or as long as 20.

Often one or two days per week is special, and often ordinary work is interrupted on that day (a sabbath, or vacation, or market day, or unlucky day).

Some ideal design goals

These are not possible to simultaneously achieve; and some are redundant:

My prioritization of the ideal design goals

I think the primary goals should be:

Non-goals/lower priorities:

Design implications

Some proposals

Blank-day proposals include:




There are also leap week calendar proposals, such as Hanke-Henry, Pax, Symmetry454, the 4-4-5 calendar, but these do worse than blank-day proposals on the criterion of keeping the number of days per quarter as close to equal as possible.

Winnowing these down

Given the priorities above, I think either the World Calendar or International Fixed or World Season are best, because the other blank-day proposals have different names that causes a marketing problem for the proposals (it may make them sound fanciful). All of these are perennial blank-day calendars. I'll list these again with more details:

Note that all of these proposals have the same quarterly structure (4 91-day quarters, plus an extra day at the end of the year, plus leap-days at the end of the second quarter), but with different month structures. World Season is the simplest, having nothing else besides this common quarterly structure. World Calendar has 12 months, which align with quarters, but which have different lengths and which do not align with weeks (except at quarterly boundaries). International Fixed has 13 months, each with the same length, and each aligned with weeks, but is not aligned with quarters.

As noted above, i would modify each of these proposals slightly to consider the extra days part of the preceding months/quarters rather than standing outside of them.

Some (novel?) proposals

Now i'll present some other proposals that i haven't heard before.

The prime factorization of 365 is 5*73.

Proposal 1: Instead of having 4 quarters/seasons, have 5 fifths/seasons of 73 days each. Stop there; since 73 is prime, this has the disadvantage that the fifths can't be further evenly divided into weeks or months.

Proposal 2: Instead of having 4 quarters/seasons, have 5 fifths/seasons of 73 days each. Declare the last day of each season to be extra/special. Now we have 72 other days. The prime factorization of 72 is 2*2*2*3*3. Divide the 'non-extra' part of each season into 12 weeks of 6 days each (with 24 days = 4 weeks forming a month, so 3 months per season).

Proposal 3: Like Proposal 2, except instead divide the regular 72-day portion of each season into 9 weeks of 8 days each (with 3 months of 24 days = 3 weeks each per season).

Proposal 4: Have 3 extra days at the end of the year. Divide the rest of the year into 10 weeks, organized as 5 fifths of 14 days = 2 weeks each. This proposal has the advantage of 7-day weeks over #1-3, but I don't like this as much as proposals 1 thru 3 because the 3 extra days, when added to the last fifth, makes the fifths more uneven than necessary.

Note that 'fifths' is hard to pronounce, so call them 'cinqs' (pronounced "sinks") instead.


The current consensus calendar (Gregorian) was introduced in 1582, replacing the older Julian calendar. The Julian calendar was introduced in 46 BC, replacing the earlier Roman calendar(s).

Apparently the World Calendar, a blank-day calendar, made some headway but was not adopted due to blank-day religious objections [9] World Calendar.

Tangentially related: The Antikythera mechanism, thought to be the first analog computer, was a system of gears for a detailed computation of various calendrical and related astronomical quantities.


I think i like any of the following better than the current Gregorian calendar: World Calendar, International Fixed Calendar, World Season Calendar, novel(?) proposals #1-#3.

I haven't decided yet which of these three proposals i like best. World Season Calendar and novel(?) proposal 1 are appealing for their simplicity. International Fixed Calendar and novel(?) proposals 2 and 3 are appealing for having months which fall on weekly boundaries and for having the same number of days in each month. World Calendar and novel(?) proposals 2 and 3 are appealing for having months with quarterly alignment. World Season Calendar, International Fixed Calendar, and World Calendar are appealing for having 7-day weeks.

Proposal 2 is additionally appealing because if 2 days per 6-day week were weekends, then the workweek would be only 4 days instead of 5, about 16% shorter, and also because each cinq has about 12 weeks (the last cinq has an extra day), and 12 is a nice divisible number.

Of course, i suppose that ideally one would have an algorithm that would start with 365 (the rounded mean tropical year) and spit out a calendar system.