The Easter table of Beda Venerabilis begins (like that of Dionysius Exiguus) with the 19-year cycle from 532 CE:
A I II III IV V VI VII VIII
1 532 10 * 4 17 5. April 11. April 20
2 1/533 4/11 11 5 18 25. März 27. März 16
3 2/534 5/12 22 6 19 13. April 16. April 17
4 3/535 6/13 3 7 1 2. April 8. April 20
5 4/536 7/14 14 2 2 22. März 23. März 15
6 5/537 8/15 25 3 3 10. April 12. April 16
7 6/538 9/ 1 6 4 4 30. März 4. April 19
8 7/539 10/ 2 17 5 5 18. April 24. April 20
9 8/540 11/ 3 28 7 6 7. April 8. April 15
10 9/541 12/ 4 9 1 7 27. März 31. März 18
11 10/542 13/ 5 20 2 8 15. April 20. April 19
12 11/543 14/ 6 1 3 9 4. April 5. April 15
13 12/544 15/ 7 12 5 10 24. März 27. März 17
14 13/545 1/ 8 23 6 11 12. April 16. April 18
15 14/546 2/ 9 4 7 12 1. April 8. April 21
16 15/547 3/10 15 1 13 21. März 24. März 17
17 16/548 4/11 26 3 14 9. April 12. April 17
18 17/549 5/12 7 4 15 29. März 4. April 20
19 18/550 6/13 18 5 16 17. April 24. April 21
[NAB2]
| A: | Cycle year in the nineteen-year cycle (not available in Bede’s table) |
| I: | Anni Dominicae Incarnationis - Years since the birth of Christ [DTR chsp. 47; TRT pp. 126-129] |
| II: | Indictiones - Indiction [DTR chsp. 49; TRT p. 130] |
| III: | Epactae Lunares - Lunar epacts [DTR chsp. 52; TRT p. 135] |
| IV: | Epactae Solis sive Concurrentes dies - Solar epacts or concurrent days [DTR chsp. 53; TRT p. 136] |
| V: | Cyclus Lunaris - Lunar cycle [DTR chsp. 56; TRT p. 139] |
| VI: | Quarta Decima Luna Paschae - Luna XIV paschalis [DTR chsp. 59; TRT p. 142] |
| VII: | Dies Dominicus Paschae - Easter Sunday [DTR chsp. 61; TRT p. 145] |
| VIII: | Luna Ipsius Diei - The moon age of Easter Sunday [DTR chsp. 62; TRT p. 147] |
[NAB1; NAB2]
For the following calculation rules is defined: function mod1(a, b) { m = a mod b; return m ? m : b; }
Column
I: Anni Dominicae Incarnationis
= Years since the birth of Christ
The year (hereinafter: j ) is assumed to be given.
Column
II: Indictiones
= Indiction
Calculation:
ind = mod1( j+3, 15 )
[DTR chsp. 49; TRT p. 130]
Column
III: Epactae Lunares
= Lunar epacts
Calculation:
epalu = ((j mod 19 ) * 11 ) mod 30
[DTR chsp. 52; TRT p. 135]
Column
IV: Epactae Solis sive Concurrentes dies
= Solar epacts or concurrent days
Calculation:
epaso = mod1( floor( j * 5 / 4 ) + 4, 7 )
[DTR chsp. 53-54; TRT pp. 136-137]
Column
V: Cyclus Lunaris
= Lunar cycle
Calculation:
cyclu = mod1( j + 17, 19 )
Note: I use the modulus of j+17 instead of Bede’s j-2 so that the expression
for the years 0 and 1 is not negative.
[DTR chsp. 56-58; TRT pp. 139-142]
Column
VI: Quarta Decima Luna Paschae
= Luna XIV paschalis
Calculation: qdlup = epalu <= 15 ? 36 – epalu : 66 – epalu
qdlup takes the values 21 to 50,
21 to 31 is the date in March,
otherwise (lu14 – 31) is the date in April.
[DTR 59-60; TRT pp. 142-145]
Incidental remark: Up to this point, Beda had meticulously explained the calculation steps he used to arrive at his results. He no longer does so for the date of Easter Sunday [DTR ch. 61; TRT pp. 145-147] and the age of the Easter moon [DTR ch. 62; TRT p. 147]. I can therefore only assume that he adopts the calculation method of Dionysius Exiguus.
Intermediate step
Weekday of the Easter moon
Calculation: wtlup = mod1( 60 + qdlup + epaso, 7 )
wtlup assumes the values 1 to 7, 1 => Sun, 2 => Mon, ..., 7 => Sat
[DE3, Argument 10]
Column
VII: Dies Dominicus Paschae
= Easter Sunday
Calculation:
didop = qdlup + 8 - wtlup
didop assumes the values 22 to 57,
22 to 31 is the date in March, otherwise (didop – 31) is the date in April.
Column
VIII: Luna ipsius diei
= Moon age of this Easter Sunday
Calculation:
if ( didop <= 31 ) { luipd = 8 + epalu + didop } else { luipd = 9 + epalu + didop – 31 }
luipd = mod1( luipd, 30 )
[DE3, Argument 9]
(Here Microsoft Excel 2007, German licence)
|
Field |
Contents |
Meaning |
|
A1 |
'ADNIC |
Year number |
|
B1 |
'Indic |
Indiction |
|
C1 |
'IS |
Intermediate step |
|
D1 |
'Epact lun |
Lunar epacts |
|
E1 |
'Epact sol |
Solar epacts, that is concurrent days |
|
F1 |
'Cycl Lu |
Lunar cycle |
|
G1 |
'Luna XIV |
Luna XIV paschalis |
|
H1 |
'Wd Lu XIV |
Weekday of Luna XIV |
|
I1 |
'Dom Pasc |
Easter Sunday |
|
J1 |
'Lu Dom Pasc |
Moon age ES 1st step |
|
K1 |
'Lu Dom Pasc |
Moon age of Easter Sunday |
|
A2 |
532 |
532 |
|
B2 |
=WENN(REST(A2+3;15);REST(A2+3;15);15) |
|
|
C2 |
=REST(A2;19)*11 |
|
|
D2 |
=REST(C2;30) |
|
|
E2 |
=WENN(REST(GANZZAHL(A2*5/4+4);7);REST(GANZZAHL(A2*5/4+4);7);7) |
|
|
F2 |
=WENN(REST(A2+17;19);REST(A2+17;19);19) |
|
|
G2 |
=WENN(D2<=15;36-D2;66-D2) |
|
|
H2 |
=WENN(REST(60+G2+E2;7); REST(60+G2+E2;7); 7) |
|
|
I2 |
=G2+8-H2 |
|
|
J2 |
=WENN(I2<=31;8+D2+I2;9+D2+I2-31) |
|
|
K2 |
=WENN(REST(J2;30); REST(J2;30);30) |
|
|
A3 |
=A2+1 |
|
|
B3:K3 |
Copy from B2:K2 |
|
|
A4:K96 |
Copy from A3:K3 |
|
function DaynumberToDayAndMonth( daynumber ) {
// assert( daynumber > 0 && daynumber < 62 );
if ( daynumber <= 31 ) {
this.dd = daynumber;
this.mm = 3;
} else {
this.dd = daynumber - 31;
this.mm = 4;
}
return this;
}
function mod1( a, b ) {
var m = a % b ;
return m ? m : b ;
}
function BedaVenerEasterTableLine( annus ) {
// assert( annus > 0 && annus <= 4999 );
this.adi = annus;
this.indic = mod1( annus + 3, 15 );
this.epalu = (( annus % 19 ) * 11 ) % 30;
this.epaso = mod1( floor( annus * 5 / 4 ) + 4, 7 );
this.cyclu = mod1( annus + 17, 19 );
this.qdlup = this.epalu <= 15 ? 36 - this.epalu : 66 - this.epalu;
this.wtlup = mod1( 60 + this.qdlup + this.epaso, 7 );
this.didop = this.qdlup + 8 - this.wtlup;
var lu = this.didop <= 31 ? 8 + this.epalu + this.didop : 9 + this.epalu + this.didop - 31;
this.luipd = mod1( lu, 30 );
return this;
}
function BedaVenerEasterTable( annus, times, outputformatter ) {
// assert( annus > 0 && annus <= 4996 );
// assert( times >= 4 && times <= 532 );
// assert( annus + times <= 5000 );
for ( let j = annus; j < annus + times; j++ ) {
var line = BedaVenerEasterTableLine( j );
generateExiguusEasterTableOutput( line );
}
}
If you click on the button below, a new calculation of the data appears for comparison with
the first 19-year section of the Easter table of Beda Venerabilis shown above,
generated according to the algorithm just developed with the JavaScript functions shown,
whereby in this newly calculated table the first column ("A") -
the number of the year in the 19-year lunar cycle, which is not part of Bede’s original table
and is insignificant for the calculation - is omitted.
An Easter calculator with this algorithm, where you can choose the start year,
the number of years and the output format, can be found at
The Easter table of Beda Venerabilis
as a table calculator.
DE3 = Dionysius Exiguus (525): Argumenta Paschalia Aegyptiorum; <https://web.archive.org/web/20221014111543/http://www.nabkal.de/osterstreit/anhang/dionysius_3.html> see also DELP, DEOE
DELP = Dionysius Exiguus (2003): Liber de Paschate; <http://henk-reints.nl/cal/audette/denys.html>
DEOE = Dionysius Exiguus (2003): On Easter, or, the Paschal Cycle; <https://www.tertullian.org/fathers/dionysius_exiguus_easter_01.htm>
DTR = Beda Venerabilis: De Temporum Ratione; <https://web.archive.org/web/20221208193930/http://www.nabkal.de/beda.html>
NAB1 = Die Ostertabelle des Beda Venerabilis; <https://web.archive.org/web/20220526230407/http://www.nabkal.de/ostrechbeda.html>
NAB2 = Die Ostertafel des Beda Venerabilis (nach der Tabelle des Dionysius Exiguus); <https://web.archive.org/web/20220928225838/http://www.nabkal.de/osterstreit/anhang/zyklbeda.html>
TRT = Faith Wallis (1999): Bede: The Reckoning of Time; Translated Texts for Historians, Volume 29; Liverpool University Press
The author is a mathematician and worked as a software developer.
Karl-Heinz Lewin, Haar: karl-heinz.lewin@t-online.de
Copyright © Karl-Heinz Lewin, 2024