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The Standard Calendar
January   February   March   April
Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun
01 02 03 04 05 06 07 01 02 03 04 31 01 02 01 02 03 04 05 06
08 09 10 11 12 13 14 05 06 07 08 09 10 11 03 04 05 06 07 08 09 07 08 09 10 11 12 13
15 16 17 18 19 20 21 12 13 14 15 16 17 18 10 11 12 13 14 15 16 14 15 16 17 18 19 20
22 23 24 25 26 27 28 19 20 21 22 23 24 25 17 18 19 20 21 22 23 21 22 23 24 25 26 27
29 30 31 26 27 28 29 30 24 25 26 27 28 29 30 28 29 30
May June July August
Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun
01 02 03 04 30 01 01 02 03 04 05 06 01 02 03 04
05 06 07 08 09 10 11 02 03 04 05 06 07 08 07 08 09 10 11 12 13 05 06 07 08 09 10 11
12 13 14 15 16 17 18 09 10 11 12 13 14 15 14 15 16 17 18 19 20 12 13 14 15 16 17 18
19 20 21 22 23 24 25 16 17 18 19 20 21 22 21 22 23 24 25 26 27 19 20 21 22 23 24 25
26 27 28 29 30 31 23 24 25 26 27 28 29 28 29 30 26 27 28 29 30 31
September October November December
Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun
30 01 01 02 03 04 05 06 01 02 03 30 31 01
02 03 04 05 06 07 08 07 08 09 10 11 12 13 04 05 06 07 08 09 10 02 03 04 05 06 07 08
09 10 11 12 13 14 15 14 15 16 17 18 19 20 11 12 13 14 15 16 17 09 10 11 12 13 14 15
16 17 18 19 20 21 22 21 22 23 24 25 26 27 18 19 20 21 22 23 24 16 17 18 19 20 21 22
23 24 25 26 27 28 29 28 29 30 31 26 27 28 29 30 23 24 25 26 27 28 29

The Standard Calendar is a proposal for reforming the Gregorian calendar. It is broadly similar to the Gregorian Calendar, but with the following differences:

  1. The leap day is at the end of the year.
  2. February has 30 days in all years.
  3. July has 30 days.
  4. December has 30 days in common years and 31 days in leap years.
  5. The timing of leap years are computed with an algorithm that spaces the leap years more evenly.
  6. The date of Easter is calculated with a simpler algorithm that abolishes the epacts and golden numbers. (Alternatively, Easter can be fixed such that Good Friday is always the first Friday in April.)

Month lengthsEdit

The Standard Calendar is intended to regularize the lengths of the months while making as few changes as possible to the lengths of the months in the Gregorian calendar. The major change to month lengths in the Standard Calendar is the month of February. That month is lengthened to 30 days in all years. To allow February to be lengthened, a day is taken from July and December.

Another change is the placement of the intercalary day. In the Gregorian calendar, that day is February 29. This causes all dates from March to December to have a different Julian Day number depending on whether the year is a common year or a leap year.[1] Furthermore, calculations of the number of days between two dates often treat January and February as the 13th and 14th month of the previous year, so that February 29 occurs at the end of the year.[2]

These difficulties would no longer occur if the intercalary day was at the end of the year. Thus, the intercalary day is moved to December 31.

Month lengths
Month Common years Leap years
January 31 31
February 30 30
March 31 31
April 30 30
May 31 31
June 30 30
July 30 30
August 31 31
September 30 30
October 31 31
November 30 30
December 30 31
italic month lengths are different to the Gregorian calendar.
bold month length is the month that is lengthened to accommodate the leap day.

The month lengths that result are not as evenly spaced as they can be. For example, the span from October to March has 183 or 184 days and the span from April to September has only 182. The four quarters of the year also have 91 or 92 days. However, when dividing five or six days among 12 months some irregularity in distribution is inevitable, especially when dividing the year into quarters. In the Standard Calendar, these slight irregularities are the result of preserving the lengths of nine Gregorian months. The result is months of 30 or 31 days and quarters of 91 and 92 days.

The Standard Calendar does have some regularity in distribution. This regularity is most evident in leap years because leap years have an even number of days. In a leap year:

  • The two halves of the year have 183 days each.
  • Any two consecutive months in the same half of the year have 61 days.
  • Any two months that are six months apart have 61 days.
  • Any two months where the month numbers add up to 13 have the same number of days.

Leap yearsEdit

Gregorian-error-2000-4000
Standardcal-error-2000-4000

The Gregorian leap-year rule intercalates an extra day every 4 years or every 8 years. This scheme is deficient in that the time of an equinox or solstice will drift by more than 53 hours in a 400-year intercalation cycle. This causes some complications for various groups that rely on accurate seasonal tracking.

The Standard Calendar solves this problem by intercalating the leap years in more evenly-spaced intervals. The timing of leap years is calculated using simple arithmetic such that the mean March equinox is fixed to the Standard Calendar date of March 18 (UT). The formula is a little more complex than the Gregorian formula for leap years, but unlike the Gregorian formula has no exceptions.

A year is a leap year in the Standard Calendar if (Year × 159 + 522) mod 656 is less than 159. Leap years generally occur every four years, but at the end of a cycle of 29 or 33 years a pair of leap years occurs five years apart instead of four. Leap years are arranged such that the March equinox occurs on March 18.

The year length of 365159/656 days (365.242378048) is close to the mean length of the March equinox year between the years 2000 and 5000.

Date of EasterEdit

Calculating the date of Easter can be done in one of two ways, depending on whether Easter remains as a movable holiday, or has its date fixed to a single week.

Movable EasterEdit

Easter in the Standard Calendar is calculated by determining a date for the ecclesiastical Easter full moon, then finding the following Sunday by adding between 0 and 7 days and then converting the result to a date. The calculations are simpler than the current method of calculating Easter because the Standard Calendar uses a 353-year lunar cycle instead of the 19-year Metonic cycle with adjustments that the current method of calculating Easter employs.

Calculating the date of Easter in the Standard Calendar requires eight steps:

  1. Lunar Term = (Year × 223 + 183) mod 353
  2. Full Moon = floor (Lunar Term × 108 / 1291)
  3. Leap Day Count = floor ((Year × 159 + 363) / 656)
  4. Extra Days = 7 − ((Leap Day Count + Year + 2 + Full Moon) mod 7)
  5. Easter Date = Full Moon + Extra Days + 19
  6. Easter Date = Easter Date − 7 × floor (Easter Date / 55)
  7. Month = floor (Easter Date / 32) + 3
  8. Day = Easter Date + 93 - Month × 31

The resulting date is not a Gregorian date, but a Standard Calendar date which is two days earlier in the month in common years and one day earlier in the month in leap years. These differences are due to the month of February having 30 days in all years.

Movable Easter in the Standard Calendar can have Easter Sunday fall on any date in the five-week span from March 20 to April 23.

Example
Find the date of Easter in the Standard Calendar for the year 2009.
  1. Lunar Term = (2009 × 223 + 183) mod 353 = 233
  2. Full Moon = floor (233 × 108 / 1291) = 19
  3. Leap Day Count = floor ((2009 × 159 + 363) / 656) = 487
  4. Extra Days = 7 − ((487 + 2009 + 2 + 19) mod 7) = 3
  5. Easter Date = 19 + 3 + 19 = 41
  6. Easter Date = 41 − 7 × floor (41 / 55) = 41
  7. Month = floor (41 / 32) + 3 = 4
  8. Day = 41 + 93 − 4 × 31 = 10

Easter in 2009 in the Standard Calendar falls on April 10. This is equivalent to April 12 in the Gregorian Calendar, the same date of Easter in 2009 as the Gregorian Calendar.

Fixed EasterEdit

One difficulty with Easter being a movable feast in the Gregorian calendar is that it adds an extra permutation to the Gregorian Calendar. The Gregorian calendar can have Common or Leap years starting on any day of the week with Easter in any of five different weeks. This gives a total of 2 × 7 × 5 = 70 different permutations.

The Standard Calendar would also have 70 different permutations if Easter remained a movable feast.

Some calendar designs reduce the number of permutations of the calendar by making the calendar perpetual. The Standard Calendar is not a perpetual calendar, but can instead reduce the number of permutations by fixing Easter to a single week instead of allowing Easter to fall in any of five different weeks. Fixing Easter in this way also ensures that events that are tied to Easter have dates that move around less from year to year.

The best time to fix Easter is equivalent to the third week of movable Easter, being the midpoint of the five-week period during which movable Easter can occur. This would have Good Friday always falling in the first week of April. Two of the most likely dates for the Crucifixion of Jesus are April 3, 33 AD and April 7, 30 AD. Both dates have the Crucifixion in the first week of April. For these reasons, this week is adopted as the Fixed Easter for the Standard Calendar.

Calculation of the date of Fixed Easter is similar to the calculation of Movable Easter, except the Full Moon is always assumed to fall on April 2 for purposes of calculation. This allows five steps to be eliminated from the calculation, leaving three steps:

  1. Leap Day Count = floor ((Year × 159 + 363) / 656)
  2. Extra Days = 7 − ((Leap Day Count + Year + 2) mod 7)
  3. Day = Extra Days + 2

The month does not need to be calculated because it is always April.

One can also rearrange the steps to a more complex formula on a single line:

  • Day = 9 − ((floor ((Year × 159 + 363) / 656) + Year + 2) mod 7)
Example
Find the date of fixed Easter for 2009.
  1. Leap Day Count = floor ((2009 × 159 + 363) / 656) = 487
  2. Extra Days = 7 − ((487 + 2009 + 2) mod 7) = 1
  3. Day = 1 + 2 = 3

Or, using the single-line formula:

  • Day = 9 − ((floor ((2009 × 159 + 363) / 656) + 2009 + 2) mod 7)
  • = 9 - ((floor (319794 / 656) + 2009 + 2) mod 7)
  • = 9 − ((487 + 2009 + 2) mod 7)
  • = 9 - 2498 mod 7
  • = 9 − 6
  • = 3

The date of Fixed Easter for 2009 is April 3, in the Standard Calendar. This is one week earlier than the Movable Easter for 2009 as calculated above.

Changeover from Gregorian calendarEdit

The Standard Calendar has three sets of rules that are different to the Gregorian Calendar: the lengths of the months, the timing of intercalation and the date of Easter. Each rule can be implemented separately, but for best results these rules should all be implemented concurrently.

The introduction of the Standard Calendar is best done at the beginning of a period where the intercalation rules for both calendars agree as to which years are leap years. This gives people plenty of time to adjust. The periods of time where this is true for a decade or more are shown in the following table:

Year Range Number of Years
2041 to 2075 35
2169 to 2199 31
2300 to 2335 36

The table shows that periods of about 30 years of matching intercalation are separated by periods of about a century where the rules do not match in the timing of the leap years.

ReferencesEdit

  1. Jean Meeus, Astronomical Algorithms (second edition), page 65.
  2. Jean Meeus, Astronomical Algorithms (second edition), page 61.

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