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The Year and Its Parts: The Calendar

Revised: 26 March A.D. 2001, 
Annunciation of the Blessed Virgin Mary

    There is no holy day as universally observed by Christians as Easter, yet there has never been a complete consensus as to how its date should be set. We know from the Scriptures that the Last Supper took place on a Thursday on or close to the Passover, Jesus was crucified on a Friday, and that He rose from the dead on Easter Sunday. This caused Christians to observe Sunday as the Sabbath in commemoration of the Resurrection. Nonetheless, in some places Easter was observed on the same day as Passover (the 14th of the Jewish month of Nisan) without regard to the day of the week.(1) The Council of Nicæa (A.D. 325) determined that the feast should always be observed on the first Sunday after the full moon after the vernal equinox. Yet, there remained a substantial faction that insisted that the observance must follow the Jewish Passover.

    But even if everyone were to agree on the exact method for determining the Easter date, there remain some practical problems. Prior to the Gregorian reform of the calendar, the vernal equinox was drifting toward the beginning of the year.(2) Such a drift would require that the date of the equinox be determined through astronomical observation -- not particularly difficult to do, but more difficult to predict in advance. The full moon would also have to be predicted, which is not terribly difficult. In the fourth century world of Nicæa communications were abysmally poor by modern standards, so such observations would probably be duplicated by each metropolitan archbishop, increasing the possibility of differences. Worse yet, phenomena like the day of the week, the equinoxes and the phases of the moon are dependent on the observers longitude. If it is Sunday in Hawaii, it is Monday on the other side of the International Date Line in Australia -- the moon may be truly full only when it is not visible at my longitude.

    To avoid the problems associated with astronomical measurement and the ambiguities caused by differences in longitude, the Church decided centuries ago to base the Easter date on predictive tables, no matter where in the world it might be celebrated. It recognizes that there will be some rare errors, but that the convenience and uniformity make these worth accepting.

    The first step in using the Gregorian tables is to determine the "Sunday Letter" or "Dominical Letter" (DL) for the year in question. The DL indicates the day of the week on which the year begins. (Once known, the DL also denotes the days that fall on Sundays in the "Kalendarium" section of the Missale Romanum.) The DLs count "backwards" through the week:

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

    While it is not hard to look at this December's calendar to figure what next year's Dominical Letter will be, the table below will be helpful to find the Letter for any year of interest since the Gregorian reform.

    Having obtained the Dominical Letter (DL) it remains necessary to determine the "epact," which is simply the age of the moon in days on January 1st. The epact may be known by making reference to the 19 year cycle of the moon, discovered in 432 B.C. by the Greek astronomer Meton. The current point on the "Metonic" cycle is identified with the "golden number" (the ancient Greeks marked it on a pillar in gold paint). In the Missale Romanum, the golden number is called by the Latin term "aureus numererus." The golden number must be an integer between 1 and 19 inclusive, and is very easily computed:

            Golden Number = (year + 1) MOD 19.

    For those not familiar with modular division, this is the same as "add 1 to the year, divide by 19, and keep just the "remainder," which is the golden number. If it is not intuitively obvious, the reader is assured that (year +1) MOD 19 is exactly equal to (year) MOD 19 +1, as the formula is often given in secular references.

    By way of example, the golden number for the year 2007 will be 2007+1 MOD 19. Or 2008/19 = 105 remainder 13, where the remainder, 13, is the golden number for 2007.   If there is no remainder, the golden number is 19.

    Before the Gregorian reform, the golden number would have sufficed to find the Easter date (in conjunction with the Sunday letter). But the essence of the reform was the attempt to bring the solar and lunar calendars into conformity with astronomical observation. Sometimes the lunar and solar corrections cancel each other, but every few centuries they do not, requiring that (for the few hundred years under consideration) a new table of epacts be related to the golden numbers.

    Once the epact and Dominical Letter have been identified, it is easy to look up the date of Easter on the table of moveable feasts.

    The following chart may be used to determine the DL for the years between 1600 and 2800 inclusive.


Last two digits of Year

First two digits of Year

          17xx 18xx 19xx 20xx
          21xx 22xx 23xx 24xx
          25xx 26xx 27xx 28xx
          Dominical Letters:
00   C E G BA
01 29 57 85   B D F G
02 30 58 86   A C E F
03 31 59 87   G B D E
04 32 60 88   FE AG CB DC
05 33 61 89   D F A B
06 34 62 90   C E G A
07 35 63 91   B D F G
08 36 64 92   AG CB ED FE
09 37 65 93   F A C D
10 38 66 94   E G B C
11 39 67 95   D F A B
12 40 68 96   CB ED GF AG
13 41 69 97   A C E F
14 42 70 98   G B D E
15 43 71 99   F A C D
16 44 72     ED GF BA CB
17 45 73     C E G A
18 46 74     B D F G
19 47 75     A C E F
20 48 76     GF BA DC ED
21 49 77     E G B C
22 50 78     D F A B
23 51 79     C E G A
24 52 80     BA DC FE GF
25 53 81     G B D E
26 54 82     F A C D
27 55 83     E G B C
28 56 84     DC FE AG BA
          17xx 18xx 19xx 20xx
          21xx 22xx 23xx 24xx
          25xx 26xx 27xx 28xx


    The "epact," the reader will remember, is the nineteen year lunar cycle.  Two peculiarities are found in the epact tables. Sometimes we see an epact denoted by the asterisk (*). This is simply a zero -- which was not in use until relatively modern times in the western world -- indicating that the new moon falls on the first day of the year -- it is zero days old. Apart from the "*," all of the epacts have been designated with roman numerals -- printed in red, where red and black printing is available. 

    A second peculiarity will be found in the table below for A.D. 1900-2199. Since the lunar month is not an integral number of days long, the "Kalendarium" section of the Missal makes up for the discrepancy by "doubling up" epacts xxiv and xxv during the shorter months of the year. But sometimes this adjustment needs to be counter adjusted. The epact "25" in black Arabic numerals represents an epact greater than xxv and less than xxvi -- "25-1/2," for lack of a way to represent fractions in Roman numerals. The "black 25" epact occurs whenever its corresponding golden number is from 12 to 19 (inclusive). Golden numbers 1 through 11 (inclusive) correspond to the epact "red xxv." Understanding the numerical value of "25" will help the reader to detect the printing errors that are sometimes found in the paschal tables of modern missals.

    Before the Gregorian reform -- from year 1 through October 1582-- the epacts and golden numbers consistently followed the chart below (although the term "epact" was unnecessary and not used before the reform):

                   A.D. 1 through October A.D. 1582
Golden Number:   1    2      3     4     5     6    7      8        9
Epact            xj   xxij   iij   xiv   xxv   vi   xvij   xxviij   ix

Golden No:  10   11   12    13      14   15   16     17   18      19
Epact:      xx   j    xij   xxiij   iv   xv   xxvj   vij  xviij   xxix

    The Gregorian reform altered the Metonic cycle, leaving us with the epact table below for the days in 1582 after the October correction, until 1699 (inclusive):

                      A.D. 1582-1699 (inclusive)
Golden Number:  6     7     8       9     10   11     12   13     14
Epact:         xxvj   vij   xviij   xxix   x    xxj   ij   xiij   xxiv

Golden No:    15    16    17      18     19   1   2    3       4    5
Epact:        v    xvj   xxvij   viij   xix   j   xij  xxiij   iv   xv

    A.D. 1700 not being a leap year (a solar correction) brought a new table into play:

                      A.D. 1700-1899 (inclusive)
Golden Number:  10   11   12  13    14     15   16   17    18   19
Epact:          ix   xx   j   xij   xxiij  iv   xv   xxvj  vij  xviij

Golden Number:  1   2    3      4     5     6     7    8      9
Epact:          *   xj   xxij   iij   xiv   xxv   vj   xvij   xxviij

               Epact Table: A.D. 1900-2199 (inclusive)
Golden Number:     1      2   3     4    5      6      7   8     9
Epact:             xxix   x   xxj   ij   xiij   xxiv   v   xvj   xxvij

Golden Number:    10     11   12  13   14    15   16    17   18   19
Epact:            viij   xix  *   xj   xxij  iij  xiv   25   vj   xvij

         Adapted from Missale Romanum, "The Year and its Parts"

Sunday    Cycle of       Septua-   Easter    Sundays    First
Letter    the Epact      gesima    Sunday     after     Advent
 (DL)                                       Pentecost   Sunday
   D      xxiii          18 Jan    22 Mar      28      29 Nov
   D      xvi-xxii       25 Jan    29 Mar      27      29 Nov
   D      ix-xv           1 Feb     5 Apr      26      29 Nov
   D      ii-viii         8 Feb    12 Apr      25      29 Nov
   D  *,i,xxiv-xxix,25   15 Feb    19 Apr      24      29 Nov
   E      xxii-xxiii     19 Jan    23 Mar      28      30 Nov
   E      xv-xxi         26 Jan    30 Mar      27      30 Nov
   E      viii-xiv        2 Feb     6 Apr      26      30 Nov
   E      i-vii           9 Feb    13 Apr      25      30 Nov
   E    xxiv-xxix,*,25   16 Feb    20 Apr      24      30 Nov
   F      xxi-xxiii      20 Jan    24 Mar      28       1 Dec
   F      xiv-xx         27 Jan    31 Mar      27       1 Dec
   F      vii-xiii        3 Feb     7 Apr      26       1 Dec
   F      *,i-vi         10 Feb    14 Apr      25       1 Dec
   F      xxiv-xxix,25   17 Feb    21 Apr      24       1 Dec
   G      xx-xxiii       21 Jan    25 Mar      28       2 Dec
   G      xiii-xix       28 Jan     1 Apr      27       2 Dec
   G      vi-xii          4 Feb     8 Apr      26       2 Dec
   G      xxix,*,i-v     11 Feb    15 Apr      25       2 Dec
   G      xiv-xviii,25   18 Feb    22 Apr      24       2 Dec
Sunday    Cycle of       Septua-   Easter    Sundays    First
Letter    the Epact      gesima    Sunday     after     Advent
 (DL)                                        Pentecost  Sunday
   A      xix-xxiii      22 Jan    26 Mar      28       3 Dec
   A      xii-xviii      29 Jan     2 Apr      27       3 Dec
   A      v-xi            5 Feb     9 Apr      26       3 Dec
   A xxviii,xxix,*,i-iv  12 Feb    16 Apr      25       3 Dec
   A      xxiv-xxvii,25  19 Feb    23 Apr      24       3 Dec
   B      xviii-xxiii    23 Jan    27 Mar      27      27 Nov
   B      xi-xvii        30 Jan     3 Apr      26      27 Nov
   B      iv-x            6 Feb    10 Apr      25      27 Nov
   B xxvii-xxix,*,i-iii  13 Feb    17 Apr      24      27 Nov
   B      xxiv-xxvi,25   20 Feb    24 Apr      23      27 Nov
   C      xvii-xxiii     24 Jan    28 Mar      27      28 Nov
   C      x-xvi          31 Jan     4 Apr      26      28 Nov
   C      iii-ix          7 Feb    11 Apr      25      28 Nov
   C 25,xxvi-xxix,*,i,ii 14 Feb    18 Apr      24      28 Nov
   C      xxiv,xxv       21 Feb    25 Apr      23      28 Nov
Sunday    Cycle of       Septua-   Easter    Sundays   First
Letter    the Epact      gesima    Sunday     after    Advent
 (DL)                                        Pentecost Sunday

    In leap years the saints' days that fall on February 24-28 are observed on February 25-29. In the cases where Septuagesima falls in January or early February, it and the following Sunday observances must be adjusted to fall on Sunday, even though they fall before the correction is made.

    The "Kalendarium" section of the Missale Romanum is a listing of each of the days of the months of the year as observed in the Proper of Saints -- beginning with the feast of the Circumcision of Our Lord on January 1st, and ending with the feast of Pope Saint Sylvester on December 31st. The "Kalendarium" is somewhat like the secular calendar in that it makes no mention of Easter and the moveable feasts. It must be integrated with the moveable feasts in order to produce the ecclesiastical calendar for any given year. Nonetheless, the way it is printed in the Missal -- with a consecutive epact and Sunday (Dominical) letter printed in front of each day's date -- it can be used to determine the phase of the moon, and the days of the year that fall on Sundays.

    In the "Kalendarium" section, the new moon falls on the days corresponding to the year's epact. If, for example, the epact for the year is "xxiv," all of the days in the "Kalendarium" having this number prefixed will be the days of the new moon. And, also by way of example, if the Sunday Letter (DL) is "e," the days with an "e" prefixed will all be Sundays. Do not forget that the DL changes after the leap year correction is made in years with two DLs.


    Much of the information contained herein has been adapted from the section, "The Year and Its Parts" in the Missale Romanum.  The Catholic Encyclopedia, s.v. "epact," has tables through the year 5000 A.D.

    An excellent reference for the history and science of calendar creation is Faith Wells, Bede: The Reckoning of Time (Liverpool: Liverpool University Press, 1999), available through the University of Pennsylvania Press in these United States.  Dr. Wells' introduction and notes on translation are worth the price of the book, and the Venerable Bede gives an impressive example of scientific analysis conducted in the middle ages.

(1) The 14th day gave its name to the debate: the "Quartodecemian" controversy.

(2) See The Our Lady of the Rosary Parish Bulletin, March 1999, for an explanation of the Gregorian calender reform.


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