# Comput

Comput , of Latin computus for computation, indicates the calculation of the movable dates of feasts in the Christian religion. It is also the name which has given to the fictitious moon (the the moon of comput or the moon Pascale ), used for these calculations. Key dates used or known within the civil framework are thus concerned (bank holidays for example). Particular religious periods start or finish on these dates (the bonds at the foot of the page return towards the whole of the religious calendar).

## Definition of the comput

If these festivals are not defined compared to a fixed date, they are nevertheless dependant between them compared to the festival of Easter. The base of the comput will consist thus, initially and above all, with to define this date of Easter (Sunday this year). These festivals are then dependant as follows  :
(one considers weeks beginning Monday according to the legal standard ISO 8601).
• Easter, which always takes place Sunday which puts an end to the Lent (D-day, to see the Calcul of the date of Easter);

• the Easter Monday (generally non-working) which falls the following day from Easter Sunday (J+1)   ;

• Thursday of the Ascension (generally non-working) which falls ten days before Pentecost, which corresponds to Thursday of the 6th week succeeding Easter (J+39)   ;
• Sunday of the Pentecost which falls exactly 7 weeks after Easter (J+49)   ;
• the Whit Monday (generally non-working) which falls obviously the following day from Pentecost (J+50)   ;
• the Trinity, which is located Sunday following Pentecost (J+56)   ;
• the Corpus Christi, which takes place Thursday following the Trinity (J+60)   ;
• But also, by consequence, of periods or events intended for the more practitioners ranging between these key dates. Like, for example, three Days of Rogations (Monday to Wednesday which precedes the Ascension Day), the Septuagésime or Passion. (See the complete calendar in the internal bonds at the foot of the page.)

Taking into account the existence different Calendar S (at least at the time), this comput depends obviously on the calendar considered. In particular there exists a comput Julien and a Gregorian comput . The second interests us still today.

## History

The comput appeared with Bède Worthy the, at the 7th century and the 8th century. In the neighborhoods of the Year thousand, there was new work on the comput, with in particular the Birtferth monk.

## Precept and the moon of comput

One sometimes also speaks about “  the moon Pascale .   ”

All these festivals, whose Easter, unfortunately depends on the lunar cycles and that is a problem to calculate their dates. Even if the Calendar Julien -   used at the time   - or the Gregorian Calendrier is based on natural cycles, the the Moon does not have a perfectly regular cycle. It cannot thus remain perfectly synchronous with different the Calendrier S which as for them is based on an average cycle.

Moreover, the practices and dates appointed for Easter differ according to the communities (Jewish Passover in particular).

To ensure this comput , it was thus necessary as a preliminary to be advisable of a method of calculating of the lunar cycles which can be appropriate for all without disavowing the real movements of our star. It is what the Église did by choosing a perpetual lunar calendar having 19 years a repetitive cycle. This fictitious moon was named the moon of Comput and from the real moon (It is not very far away is necessary to include/understand a “  here; cycle fictitious but retained as bases calcul  ”.)

Even if this perpetual lunar calendar is in agreement with the average movement of the the Moon, a variation of 1 or 2 days is possible with the astronomical new moon. That in consequence of the inequalities of the real movement and the discontinuity of the values of the lunation of the comput (29 or 30 days whole). According to whether the fourteenth day of the Moon is the 20 or on March 21st, the calculated date of Easter can be pushed back or advanced of a lunation relative at the date which would be obtained by the use of the astronomical éphémérides.

The rate/rhythm of the “  the new moons   ” retained is born from empirical knowledge of the time on the realized movements of the Moon and the Sun. The moon of comput thus carries out 235 lunations before falling down on the same dates of the year. This choice is thus strongly based on the cycle of Méton (known as cycle metonic ).

## Perpetual lunar calendar

The lunar calendar perpetual Julien goes back to the 6th century. It fixes, in a 19 years cycle, the dates of the new moons juliennes. They are distributed rather regularly to deviate very little the astronomical new moons.

Such a cycle of 19  average years juliennes 235  contains almost exactly; average lunations. The synodical revolution average of the Moon is worth 29  12  days; H 44  min and 2,8  S. Thus 235  lunations last 6  939,6882  days, whereas 19 years juliennes last 6  939,75  days (either a delay of 1  H 29  min 2  S by 19 years cycle juliennes, the variation being translated into a delay of 1 day at the end of a little more than 16 complete cycles, is 304 years juliennes).

The Gregorian lunar everlasting calendar results from the precedent, but of the blow has less of regularity. The Gregorian comput is thus more complex in the absolute.

However, the Gregorian year (by the fact of the quadri-secular adjustment nonbissextile) has one 365,2425 days intermediate duration. A cycle (nonmetonic) 19 Gregorian years would thus last 6  939,6075 days (either an advance of 1  H 56  min 10  S by 19 Gregorian years cycle, the variation being translated into an advance of 1 day at the end of a little more than 12 cycles, is 228 Gregorian years, which would have to be compensated for more souvent  ; for this reason, the Julienne year remains still preferred in the determination of Easter lunations, and before calculating the moons, one must convert the Gregorian dates of the civil calendars into dates juliennes).

Let us note that one allots to each year a golden section which represents its position in the cycle of 19  years. A lunar calendar builds correctly for a 19 years cycle will remain valid for the cycles suivants  ; real lunar phenomena advancing in fact of almost 1  H 30  min with each cycle. The calendar will indicate them with a delay which will reach one day every approximately 307,3 years (if one does not take account of the slow lengthening of lunations because of the progressive distance of the moon due to the weakening of the effects of tide, but also of the slow lengthening of the real terrestrial days because also of these same effects).

Let us note that it is currently impossible to predict exactly when this correction of the lunar cycle is necessary, the moon having irregularities of rotation depending on the solar acyclic activity, the effects of tides to the so irregular variations they induced by the terrestrial coat or the oceanic currents depending on the evolution of the terrestrial climate, the irregularities of terrestrial rotation following these tides, and of its revolution around the Sun disturbed by massive planets of the solar system or the crossing of clouds of dust.

## See too

### Internal bonds

• the article devoted to with the Calculation of the date of Easter (complete calculation of the date);
• the catholic liturgical Calendar which gathers all the festivals and the complete calendar.

### External bonds

• Calendar with religious holidays Calendar, Diary, Festivals, saints, school vacations (with some errors), cycles lunar.

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