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The Minimum Displacement Calendar (MDC) by Michael Ossipoff is any of a number of modified Gregorian calendars with a custom leap rule. The Symmetry454 calendar, for instance, is in effect a MDC with D(1) = 0 and Y = 52 × (294/293) weeks, where D(1) and Y are paremeters that are fed into the leap rule.

Leap Rule[]

A leapday or leapweek is added to the end of a displacement year (and is part of that DY) if the completion of that DY would otherwise result in D being greater than 3.5 in a fixed calendar version, or 0.5 in a nonfixed calendar version.
Calendar Common DY length Leap DY length LIP
Non-Fixed (leap-day) calendar 365 days 366 days 28 February
Fixed (leap-week) calendar 364 days 371 days 31 December
Leap-year Insertion Point (LIP)
the day at the end of which a leap day or week is inserted in the calendar when the year is a leapyear.
Displacement Year (DY)
a calendar year that starts with the date that, in a common year, immediately follows the LIP.
Reference Tropical Year (RTY)
a tropical year (TY), either the mean tropical year (MTY) or a TY beginning and ending at an ecliptic longitude herein designated as the ecliptic reference point (ERP).
The estimated and assumed (but not necessarily actual) length of the RTY is used as an assumed fixed value of the RTY’s length, in the formulas below as Y.
Displacement (D)
In DY 2016, D has a value of D₀ (numerically-specified below).

At the end of each DY, D changes by an amount equal to Y minus the length (in days) of that DY.

DDY+1 = DDY+ Y – length(DY)


The calendar can be fixed or not fixed. If it’s fixed, it has a leap-week, otherwise it has a leap-day.

The calendar can use the traditional and currently-used Roman months, or it can use quarters of 3 months with 30:30:31 days.


Y is the RTY’s assumed length.

  1. MTY: Y = 365.24219 days
  2. Average Equinox Year (AEY): The RTY-length is the mean of the lengths of the lengths of the two equinox years
    Y = 365.24219 days
  3. June solstice year: Y = 365.24165 days


The value with respect to which D is defined is either of:

  1. 1582 is the 0-displacement year (with the Gregorian Calendar extended back to January 1, 1582). D is defined with respect to 1582.
  2. 0 displacement is the midpoint of the extreme positive and negative displacement excursions of the displacement of the Gregorian calendar from January 1, 1950 to March 1, 2016 (inclusive).

D₀ values for 2016[]

With the new calendar’s January 1, 2016 coinciding with Gregorian Friday, 1 January 2016:

Variant values of D₀ for 2016
RTY 1582 1950–2016
MTY +0.11046 +0.25008
June solstice ERP –0.1239 +0.2328

The above D₀ values assume that the new calendar’s 1 January 2016 start-day is Gregorian 1 January 2016. But of course the new calendar could be started on a nearby different date, in order to start on a different day of the week:

  • If the new calendar’s 1 January 2016 start-day is later than Friday, Gregorian 1 January 2016, subtract 1 from the above D₀ values for every day by which it is later.
  • If the new calendar’s 1 January 2016 start-day is earlier than Friday, Gregorian 1 January 2016, add 1 to the above D₀ values for every day by which it is earlier.

Preferred starting dates[]

Ossipoff recommends that the Roman-months versions start with their 1 January 2016 on Saturday, Gregorian 2 January 2016, because then its dates will be the same as those of the Gregorian Calendar for all of 2016 after 29 February.

Ossipoff recommends that the fixed versions with 30:30:31 quarters start with their 1 January 2016 on Monday, Gregorian 4 January 2016, because with a month system different from the current Roman months, there’s no point trying to make the calendar's match during 2016. Monday is the current favorite day of the week for a proposed new calendar's January 1 to start, especially for fixed calendars.

With the Monday start-day, and a fixed calendar with 30:30:31 quarters, there’d be no Friday the 13ths.