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The Gregorian Lunar Calendar is indirectly specified by the Easter Computus. There are at least two possible variants: the Tabular Gregorian Lunar Calendar adheres stricly to the Computus exceptions and thus sometimes has months of 28 or 31 days, whereas the Regular Gregorian Lunar Calendar restricts the month length to either 29 or 30 days, usually alternating.

Nomenclature[]

  • A year whose corresponding Gregorian Solar Calendar year has 29 February is usually also a leap year in the Gregorian Lunar Calendar, i.e. the second month gets an extra leap day.
  • Years with a leap month, i.e. 13 months in total instead of the usual 12, are called embolismic years.
  • The 13th or leap month is called embolismic month.
  • A long month of 30 days is called a full month.
  • A short month of 29 days is called a hollow month.
  • A year with the Golden number 19 is called a hollow year, i.e. the last one of a Metonic cycle.
  • The Dominical letter (DL) is the DOW designator for the Sundays of the year, running from A to G, where 1 January in the corresponding solar year is always A and 1 March is always D – even in leap years.
  • The Gregorian epact is a quasi-numeric label (‘1’…‘29’ and ‘25*’) based upon the numeric Julian epact (1–29) with solar and lunar corrections. The Julian epact has a 1:1 mapping to the Golden Number of the year, the Gregorian epact does not.
  • A solar correction is subtracted in every centennial year that is a leap year in the Julian Calendar but not in the Gregorian Solar Calendar, i.e. 3 years within a 400-year cycle.
  • A lunar correction is added eight times within a 2500-year cycle, in centennial years 2, 5, 8, 11, 14, 18!, 21 and 24.

Months[]

Gregorian Lunar Months or Lunations or Moons
### Hebrew Gaulish Madore Germanic EB Days Exceptional length
L01 Tevet Shevat Simivisonnios Terminus Wintermonth 30 29 when previous year was hollow but not embolismic
L02 Shevat Adar I Equos Lipidus Mudmonth 29 30 when the Julian year is leap, but for centennial years only when the sum of corrections is negative
L03 Adar Adar II Elembivios Venuch Springmonth 30
L04 Nisan Edrinios Amber Eastermonth 29
L05 Iyar Cantlos Pook Joymonth 30
L06 Sivan Samonios Jupe Ploughmonth 29
L07 Tammuz Dumannios Tibery Haymonth 30
L08 Av Rivros Claudy Harvestmonth 29
L09 Elul Anagantio Septil Windmonth 30
L10 Tishrei Ogronios Octil Vintagemonth 29
L11 Cheshvan Cutios Novil Autumnmonth 30
L12 Kislev Giamonios Decil Holymonth 29
L13 Tevet Antaran… Mercuary Leapmonth 30 29 in hollow years

The ecclesiatical Paschal full moon is usually on L04-14, only for year epacts 24 and 25* it is in L05-14 – Easter is the following Sunday.

Easter[]

Easter dates by epact and Dominical letter in Gregorian solar dates
Epact Paschal moon A B C D E F G
24 04-18 04-23 04-24 04-25 04-19 04-20 04-21 04-22
25
25* 04-17 04-18
26
27 04-16 04-17
28 04-15 04-16
29 04-14 04-15
0 04-13 04-14
1 04-12 04-13
2 04-11 04-12
3 04-10 04-11
4 04-09 04-10
5 04-08 04-09
6 04-07 04-08
7 04-06 04-07
8 04-05 04-06
9 04-04 04-05
10 04-03 04-04
11 04-02 04-03
12 04-01 04-02
13 03-31 04-01
14 03-30 03-31
15 03-29 03-30
16 03-28 03-29
17 03-27 03-28
18 03-26 03-27
19 03-25 03-26
20 03-24 03-25
21 03-23 03-24
22 03-22 03-23
23 03-21 03-22

Tabular[]

Epact table for all dates of the year
DOM 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
January 0 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
February 29 28 27 26 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
March 0 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
April 29 28 27 26 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 29
May 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 29 28
June 27 26 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 29 28 27
July 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 29 28 27 26
August 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 29 28 27 26 25 24
September 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 29 28 27 26 24 23
October 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 29 28 27 26 25 24 23 22
November 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 29 28 27 26 24 23 22 21
December 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 29 28 27 26 25 24 23 22 21 20

Each day whose label in the table equals the epact of the year marks the start of a lunar month. If the year has an epact of “25” or “25*”, the day label “25” applies where it exists, but since it is skipped every other time between “26” and “24” (marked by a thick border), the replacement then is “24” for “25” and “26” for “25*”.

Regular[]

Suggested leap-month rule: Years with an epact in

  • [0, …, 11] are never embolismic,
  • [12, …, 15] are embolismic if the following year is not,
  • [16, …, 24, 25*] are always embolismic,
  • [25, …, 29] are never embolismic.

External links[]

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