*The Minimum-Displacement Leapyear Rule:* This is a leap-week leapyear-rule. The common (non-leap) year is 364 days long. A leapyear is 364 + 7 = 371 days long. The leapweek is added at the end of the year, becoming part of that year Epoch: Gregorian January 2, 2017 ....is this calendar's start, being this calendar's January 1, 2017..
*Variable: * D D stands for "displacement". Though this definition isn't needed for the specification of this leapyear-rule, displacement is a change or difference in the relation between date and ecliptic longitude. Actually the progress of a mean-year, or an approximation to one, usually stands in for ecliptic longitude in a leapyear-rule. D, here, is the difference between the current year's displacement from the year's desired relation between date & ecliptic longitude (where ecliptic longitude is represented by the progress of the mean-year). *Constants:* 1. Dzero is the starting value of D, the value of D at the calendar's epoch. (The epoch is the time at which the calendar is defined to start). 2. Y is the length of the leapyear-rule's mean-year (I sometimes call it the "reference-year" too). For the value of Dzero, I offer -.6288 or 0. Of those two, I recommend -.6288 (...for reasons I'll get to later in this post.) A Dzero of -.6288 means that the year is, at its epoch, displaced by -.6288 days from its desired relation of date & season. For the value of Y, I recommend 365.24217, the approximate number of mean solar days in a mean tropical year (MTY). Dzero & Y are the two adjustment-parameters that I spoke of in a previous post. *Year-End Change in D:* At the end of a calendar year (whether common or leap), the value of D changes by an amount equal to Y minus the length of that year in days. If that change would otherwise result in a D value greater than +3.5, then 7 days are added to the end of that year, before implementing the paragraph before this one. ...making that year a leapyear. [end of Minimum-Displacement leapyear-rule] In this way, the value of D is kept within the limits of -3.5 days to + 3.5 days. D is a good measure of the calendar's displacement from its desired date/season relation defined by Dzero. The -.6288 value of Dzero is consistent with a desired relation of calendar-date and ecliptic-longitude (...where ecliptic-longitude is represented by the progress of the 365.24217 day mean-year) that is the midpoint of the extremes of the values that that relation had between January 1, 1950 and January 1, 2017. ...in order that the calendar's center of displacement-oscillation be the average of its variation-extremes since January 1, 1950. ...so that the calendar's date-season relation will stay close to where it has been during the experience of currently-living humans. Though I like the ISO WeekDate calendar, and it's said that it has a good chance of eventually displacing Roman-Gregorian, via gradually-increasing usage, my proposal is a calendar using the 30,30,31 quarters, and the Minimum-Displacement leapyear-rule, with Dzero = -.6288, and with Y = 365.24217. I should add that calculation, with the Minimum-Displacement rule, of durations, day-of-the-week, & displacements are no more difficult than the same calculations with the Gregorian leapyear-rule. And determination of whether a particular far-distant year is a leapyear is no more difficult than those calculations. ...and of course the determination of whether the *next* year is a leapyear is just a matter of directly applying the leapyear-rule, as defined above. . ..and of course, any time when the current year is a leapyear, that fact will be amply announced long before the end of that year. Michael Ossipoff approx. 26N, 80W
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