## Month System[]

Each quarter has 3 months, with the following lengths: 30 days, 30 days, & 31 days, in that order.

There have been a number of calendar proposals with this month system. Its advantages are:

- With all months 30 or 31 days long, the months are as uniform as is possible with 12 months.
- For a given same year-start day, the 30,30,31 months' starting-days have the least possible maximum departure from the starting-days of the old Roman months.
- This ordering of month-lengths divides weekdays most evenly between the 3 months of a quarter.

## Leapyear System[]

### Year-Length[]

Ordinary (non-leap) years are 364 days long.

Leapyears have a "leap-week" added to their end, making leapyears 371 days long.

The 364-day length of the ordinary year is chosen because it's a multiple of 7. With an ordinary year's length that's a multiple of 7, and by using a leapweek instead of a leapday, every year begins on the same day. ...and each quarter's 3 months always begin on Monday, Wednesday, & Friday.

### Principle of Minimum-Displacement Leapyear Rule[]

Due to the integer number of days in a calendar year, every calendar experiences an ongoing change of the relation between date and season. (More specifically, the relation between date and solar ecliptic longitude). With all calendars, a leapyear periodically counters that variation. ...resulting in a periodic oscillation of the relation between date & season.

Minimum-Displacement centers that oscillation about a desired date/season relation, and minimizes the range of departure (displacement) from that desired center.

Minimum-Displacement accomplishes that by having a leapyear, adding a week to the end of a particular year, if the completion of that year would otherwise displace the calendar from its desired center by more than half of a week. Thus, the displacement from desired center never exceeds half of a week.

(With a leapweek calendar, half a week is the minimum possible value for the maximum displacement of the calendar's date/season relation from its desired center--hence the name "Minimum-Displacement".)

### Detailed Instruction for Minimum-Displacement Leapyear Rule[]

- Variable
- D (represents displacement)
- Constants
*Dzero*= -.6288 or 0 (initial value of D at calendar's epoch)*Y*= 365.24215 (That's the approximate number of days in a mean-tropical-year, optimized for the near future, for longer usefulness)

(More later about these choices of values for the 2 constants)

#### Leapyear Rule[]

At the end of every year, the value of D is changed by an amount equal to *Y* minus the number of days in that year.

If that, at the end of a particular year, would otherwise result in a *D* value greater than 3.5, then a leapweek is added to the end of that year. (… resulting in a *D* value between 0 and -3.5)

Thus, the magnitude of *D* is never greater than 3.5

*D* is always between -3.5 and +3.5

#### Explanation of the Choices of Values for the 2 Constants:[]

Two values are offered for the value of *Dzero*:

*Dzero* = 0 would center the date-season variation about the date-season relation existing on Gregorian January 1st, 2017, the day before this calendar's epoch..

*Dzero* = -0.6288 would center the date-season variation about the midpoint of the Gregorian Calendar's date-season variation between the Gregorian dates of January 1, 1950 and January 1, 2017.

The latter value, *Dzero* = - 0.6288 would center the calendar in the middle of the region where the Gregorian Calendar has been during the human lifetime preceding the calendar's epoch.

With the Minimum-Displacement leap-year-rule, calculation of durations, year-start days, day-of-the-week, calendar/season displacements, and leap-years aren't more difficult than calculations with the current Gregorian leapyear-rule. Yes, the determination of whether a year is a leap-year involves a calculation, but it isn't a difficult one, in comparison to calendrical calculations with our current Gregorian leapyear-rule.None of these calculations would be difficult for anyone.

Anyway, most people now don't do the calendrical calculations named above, though they could if they wanted to. It wouldn't even be necessary for everyone to determine whether a year is a leap-year, since that's a fact that would be repeatedly well-announced *during* any leapyear. (Leapweek would occur at the end of a leap-year).

## Epoch[]

This calendar's epoch (starting-date) is its January 1, 2017, which occurs on Gregorian January 2nd, 2017.

## Advantages of Minimum-Displacement in Comparison to Other Calendars[]

### Advantages in comparison to Hanke-Henry[]

Hanke-Henry uses the Nearest-Monday year-start rule, instead of having its own leapyear rule. Each year starts on the Monday that is closes to the Gregorian January 1st for that year. There's nothing wrong with Nearest-Monday. It's very briefly-stated, and doesn't require the definition of a really new leapyear rule. And its maximum displacement during a 400 year Gregorian cycle is barely more than Minimum-Displacement's overall displacement-range.

But it's defined in terms of the leapyear rule of another calendar (the Gregorian), as opposed to Minimum-Displacement's direct, ovious & natural minimization of displacement.

Because Hanke-Henry's Nearest-Monday year-start rule is based on the Gregorian Calendar, it inherits some properties of the Gregorian:

- The Gregorian leapyear rule was designed to minimize the variation of the (northern) Vernal Equinox with respect to the calendar's dates. But that emphasis on & favoring of the March Equinox is north-chauvinistic, because the March Equinox isn't everyone's Vernal Equinox. (In the Southern Hemisphere, it's their Autumnal Equinox). Hanke-Henry, by its use of Nearest-Monday, inherits that attribute. In contrast, Minimum-Displacement, by its use of the mean-tropical-year, minimizes variation in the date-season relation over the entire year.
- The Gregorian Calendar, in addition to the unavoidable periodic displacement, a unidirectional displacement
*drift*. ...with the result that there's no stationary center of oscillation. The center of oscillation experiences an ongoing unidirectional drift. Hanke-Henry, by its use of Nearest-Monday, inherits that drift. Minimum-Displacement has no drift. It has a stationary center of oscillation, chosen by the choice of Dzero value, as described above.

### Advantages in comparison to SymmetryXYX[]

- The Minimum-Displacement leapyear rule is the direct, natural obvious, and obviouisly-motivated way to minimize a calendar's displacement with respect to a desired center of oscillation.
- Symmetry454 's months of 28, 35, & 28 days are drastically unequal, whereas 30,20,31 Minimum-Displacement achieves the most uniform month-lengths possible with 12 months, except when a leap week occurs.
- In comparison to Symmetry010 's 30,31,30 quarters, 30,30,31 Minimum-Displacement (as described in the "Month-System" section above) minimizes the departure of the months' start-days from those of the current Roman months. ...and divides the quarter's weekdays as equally as possible between the quarter's 3 months.