tier list: Months in the Gregorian Calendar

In this article, the authors examine the value of months in the Gregorian Calendar. There are a few other calendars in widespread use on Earth, but for most readers outside China or Iran, this is almost certainly the calendar they are most accustomed to (or the only one they are aware of).

What do the authors mean by the "value" of a month? The reader will have noticed in their own life that months in the Gregorian Calendar are of unequal length. This disparity may appear a harmless quirk at first, but as the authors will demonstrate, it feeds into the power structure at the heart of Western society. Because much of of modern life is structured around fixed monthly payments (that is, payments which do not vary based on the length of the month) such as rent, loan repayments, subscription fees, and more, the reader will find that a month's "value" is a direct function of its length.

First the authors will examine what a month is and how they can be compared. Then the authors will classify existing months according to their value, specifically from the perspective of an individual whose right to shelter and security is contingent upon paying rent each month. Arguably, the perspective of a mortgage-paying homeowner is also relevant here. Finally, the authors will take a leap of imagination to explore a calendar which could be considered more equitable.

Defining a Month

A month is a unit of time roughly based on the length of a lunar phase cycle, or synodic month. The average length of this cycle is a little over 29.5 days, so months are typically about 30 days long in most calendars.

A year in the Gregorian Calendar is based on the solar year, or the time it takes the Earth to travel its orbit around the sun. This is complicated somewhat because solar year is about 365.25 days, but most calendars deal only in whole numbers of days. The Gregorian Calendar handles this discrepancy by varying the length of a year. A common year is 365 days (less than a solar year), and every fourth year is a "leap year" of 366 days.

Bringing these definitions together, we can determine that it is typical to have 12 months in a year: 365.25 / 29.5 = ~12.38

The reader will note that it is impossible to evenly divide a solar year into lunar months. In our calculation, we have a remainder of 0.38 months, or over 11 days. Owing to this, the Gregorian Calendar opts for months of unequal length - and therefore unequal value.

The Value of a Month

The value of any month can be determined by comparing it to the value of an average month in a given period which contains that month. Usually, that period is one calendar year, meaning from January 1 to December 31. But if the reader wishes to evaluate a specific month (e.g. "March 2020"), it may be more useful to define a different period - for example, the term of a 15-month lease. This is because the average length of a month in that period may be different from the average of a typical calendar year.

In this review, the authors will calculate the value of months relative to three time periods: an ordinary year of 365 days, a leap year of 366 days, and a generic year of 365.25 days. Each year is a period from January 1 to December 31. The first two calculations may be more relevant to a reader's specific circumstances, while the third is most abstract. The authors will further discuss the implications below.

Calculating an Average

The authors have used the term "average" loosely so far, but find it important to note than "average" is a broad term with many interpretations. There are three mathematical concepts often used to define "average": mean, median, and mode. Of these, the authors will use the mean exclusively in this article.

The mean is found by adding up the total number of days of all the months (365.25 in a generic year), and dividing by the number of months (12). The mean is useful because it defines the length of a month if all months were equal in length. In other words, this is the number of days purchased when a fixed monthly payment is made. This is the expected value of a month.

Other definitions of average are better at representing a “typical” month, because they can represent an actual month which the reader can experience. The mean value is not whole number of days, making it impossible for the reader to have experienced in the Gregorian Calendar, but the reader is invited to find these other methods are not useful in this article:

• The Median

  The median is the value which is in the middle of the set. In a set of "1", "2", and "10", the median value is "2". It should be readily apparent why this can be deceptive, because it can ignore values which are far from the median.
  
  In the set of all months in a single year, there are only three possible values: 31, 30, and the value of February (either 28 or 29). February is not the median, as it is the lowest value. It is possible that 31 could be the median, if there were many months of 31 days and few of 30 days. In fact, in the set of all months 28.25 30 30 30 30 30 * 31 31 31 31 31 31, the median is between 30 and 31 (denoted with an asterisk). This is then calculated as the mean of 30 and 31, which is 30.5 - a number that, while not completely wrong, ignores the varying length of the year.

• The Mode

  The mode is far simpler to calculate, as it is simply the value which occurs most often among the set. In the set of all months in a calendar year, this is actually 31, with 6 occurrences. By selecting the highest possible value as the average, expectations are skewed dramatically. It is no longer possible to have high-value months, only average and below-average.
  
  Further, the mode month is unrealistic. It is as far from the mean synodic month as can be. If every month were 31 days, a year would be 372 days long. This definition is completely out of line with the solar year.

Thus the authors determine the value of each month by comparing it to the value of the mean month in a given year (Fig. 1)

When comparing a set of months, the reader must consider whether the set contains one or more February. As a significant outlier, February has a more noticeable effect on the mean than other months. If comparing a set of months without a February, the reader may find more accurate results by calculating their own mean.

Incidentally, the mean value of a month in a leap year is identical to the median at 30 days and 12 hours exactly. But leap years are relatively uncommon. The mean common year month is about 30 days and 10 hours, while the mean month of a mean or generic year is 30 days, 10 hours, and 30 minutes.

The Tier List

The tier list is organized as follows, in descending order:

• S Tier, exceptional value
• A Tier, highly desirable
• B Tier, satisfying
• C Tier, tolerable
• D Tier, disappointing
• F Tier, unacceptable value

A Tier

These months offer the absolute best value available. In a leap year, an A Tier month such as October offers 12 hours more than the mean. In a common year, the advantage is nearly 14 hours. The reader is encouraged to value the half-day of liberated time in these months which represent more than half the year.

D Tier

One full third of the year is spent in months somewhat shorter than the mean month. 10 or 12 hours of time is lost in each of these months, compared to a hypothetical month in an evenly-distributed year. However, the individual loss is slightly less than what is gained in an A Tier month, and there are fewer months in this tier, so between these two tiers a rent-payer comes out slightly ahead. However, the reader will find this does not hold for the entire year.

F Tier

Regardless of the metric used, February is an objectively poor value. In the best case scenario, a leap year, February clocks in exactly 36 hours shorter than the mean month. With a fixed monthly rental payment, the wise reader will understand they begin paying for the month of March at lunchtime the day before the last day of February. The authors strongly discourage paying a full month's rent in February.

How can the year be made more fair?

There are many possible solutions to the issues outlined above. One is to simply prorate rental payments according to the actual number of days in a month. This would make the cost of renting in February noticeably less than in other months, which may go up or down. But another solution is to create an entirely new calendar.

The Gregorian Calendar is by no means the first calendar in the vast majority of the world. But although it has evolved from a long lineage of calendars, it also has clear flaws, obvious even to children who have not yet learned the inertia of tradition. Nor even is it the best calendar yet created - the authors are certainly not the first to attempt to create a successor to the Gregorian Calendar.

However, to replace a calendar used globally, and in highly intricate and interlinked systems such as this web page, would be a truly Herculean task. The authors invite the dear reader to consider carefully what other possible ways humanity could alleviate the burdens of the powerless.

What follows is a theoretical calendar the authors have crafted as a thought experiment. This calendar year is secular, but the authors advocate for an allowance of cultural holidays in addition to the secular holidays. This calendar favors predictability, stability, and transparency.

An Equal Terrestrial Calendar

This calendar retains the basic structure of traditional months: they are composed of a number of consecutive days which roughly corresponds to the length of a synodic month. Further, as in many calendars, months are subdivided into weeks. But in the Gregorian calendar, there is no relationship between calendar dates and days of the week - that is, nothing says a month must start on a Sunday or end on a Saturday. But in the equal terrestrial calendar, each month is composed of whole weeks - the first day of each month is also the first day of the week, and the last day of each month is always on the last day of the week.

However, the reader will recall that the number of days in a solar year is not an even multiple of 12. To solve this, the authors' calendar brings back a tradition from ancestors of the Gregorian Calendar: intercalary days. These days are not part of any month. In this calendar, they are also not part of any week, but are counted independently, and should be holidays. The arrangement of these days is discussed later.

The Five-Day Week

In this calendar a week is five days long. This allows a simpler and more predictable calendar, and allows a significantly more favorable ratio of free time. The authors cannot recommend fewer than two days of this week being devoted to rest ("weekends"), likely the first and last day of each week. This arrangement is a holdover from the Gregorian work week, but becomes far more tolerable under the new regime.

The Six-Week Month

Each month of the equal terrestrial calendar is exactly six weeks, and thus exactly 30 days. Incidentally, this is less than the mean value of a month of any Gregorian year. But it is predictable, evenly valued, and easier to experience than 12 hours of a hypothetical day. There are also several other interesting effects of this month structure.

One effect is that each month is as close as possible to an exact lunar cycle (without using partial days). This means that for any two consecutive months, the phases of the moon will fall on nearly the same day. Of course, significant drift will add up over the course of a year: from one new year to the next, the lunar cycle will lag by over one-third. Lunar drift is unavoidable in a solar calendar because, as the reader has seen, a solar year does not match up to any whole number of synodic months.

However, this structure especially shines in predictability: Calendar dates always line up with the same days of the week (Fig. 2). The weeks themselves are also numbered - or named, according to cultural values.

The Intercalary Days

Twelve months, each being six weeks, makes 360 days. This leaves the astute reader lacking 5 days of a full year (6 in a leap year!). While the ancient Western calendars were chaotic even compared to the Gregorian calendar, adjusted ad-hoc by political motives and wildly inconvenient for modern computing, they do offer a tool of tremendous value: intercalary days, which belong to no month.

The intercalary days should be treated as holidays, where working would be abnormal, as on Rest days. Of course, there may always be some labor which can be neither automated nor ceased for an entire day (although the authors discourage such operations whenever possible). Shamefully, past civilizations often relied upon enslaved people to support their days of leisure and rest. Almost as shamefully, modern civilizations rely upon low wages and unstable housing to compel constant service for their privileged classes. The reader is invited to consider that any labor which is absolutely critical to the functions of an economy must be respected as such. Those who work such jobs must be allowed more total free time to compensate for the demands placed on their schedules.

While the reader may be tempted to collect all intercalary holidays in a single pseudo-week at the beginning or the end of the year, the authors believe this all-or-nothing approach has a less stable effect on the emotions and health of humans.

Instead these holidays are spaced throughout the year. Too evenly spaced and they are reduced to a single day every other month at best. Rather, these holidays are most wisely arranged in two groups: 3 days before the beginning of January, and 2 days between June and July. Every fourth year, this mid-year break becomes 3 days as well. The authors believe it is important to begin the year on a universal holiday; understanding that people are encouraged to stay up to an unhealthy time and drink alcohol while observing the changing of the year, the authors advise rest.

The authors have also slightly adjusted the timing of the beginning of the year. Appreciating the symbolism of the year ending at the beginning of winter (in the northern hemisphere), the final day of the year is on the median day of the winter solstice, the shortest day of the year. This usually occurs on December 21 in the Gregorian calendar. This relatively small change would also help to ease any hypothetical transition in society.

The obvious question is raised: Who pays for housing on a day that belongs to no month, a day that almost no one will work? To the authors, the answers is just as obvious: it is the ones who build wealth without working anyway. Should the global economic system maintain the right of individuals to directly profit from the labor of others by owning and renting out housing, it would be unthinkable to ask concessions of those in the more vulnerable position. In the case of public housing, the authors see no reason not to extend the same argument: the party of greater means and wealth should bear the burden, extending housing contracts without extra cost to the renters.

With this authors conclude their experiment: A new year dawns with a new calendar. On the first day after the winter solstice, a three-day celebration brings comfort and free time to all before beginning six weeks of January. Days grow lighter and longer for six regular months, until the summer solstice is celebrated on a weekend and for two or three more days of rest. Over the next six months, the days grow shorter and darker until the year ends with the final weekend of December and a new cycle. Months are characterized by their weather, their astronomical events, their individual holidays - not their arbitrary length. And no one pays rent for 36 hours of their life unlived.