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Computus (Latin for "computation") is the calculation used to determine the calendar date of Easter. Because the date is based on a calendar-dependent equinox rather than the astronomical one, there are differences between calculations done according to the Julian calendar and the modern Gregorian calendar. The name has been used for this procedure since the early Middle Ages, as it was considered the most important computation of the age. For most of its history Christians have calculated Easter independently of the Jewish calendar. In principle, Easter falls on the Sunday following the full moon that follows the northern spring equinox (the paschal full moon). However, the vernal equinox and the full moon are not determined by astronomical observation. The vernal equinox is fixed to fall on 21 March (previously it varied in different areas and in some areas Easter was allowed to fall before the equinox). The full moon is an ecclesiastical full moon determined by reference to a lunar calendar, which again varied in different areas. While Easter now falls at the earliest on the 15th of the lunar month and at the latest on the 21st, in some areas it used to fall at the earliest on the fourteenth (the day of the paschal full moon) and at the latest on the twentieth, or between the sixteenth and the 22nd. The last limit arises from the fact that the crucifixion was considered to have happened on the fourteenth (the eve of the Passover) and the resurrection therefore on the sixteenth. The "computus" is the procedure of determining the first Sunday after the first ecclesiastical full moon falling on or after 21 March, and the difficulty arose from doing this over the span of centuries without accurate means of measuring the precise tropical year. The synodic month had already been measured to a high degree of accuracy. The schematic model that eventually was accepted is the Metonic cycle which equates 19 (tropical) years to 235 synodic months. In 1583, the Catholic Church began using 21 March under the Gregorian calendar to calculate the date of Easter, while the Eastern Churches have continued to use 21 March under the Julian calendar. The Catholic and Protestant denominations thus use an ecclesiastical full moon that occurs four, five or 34 days earlier than the eastern one. ==History== (詳細はcontroversy as early as the meeting of Anicetus and Polycarp around 154. According to Eusebius' Church History, quoting Polycrates of Ephesus,〔(Eusebius' Church History 5.24 ).6〕 churches in the Roman Province of Asia "always observed the day when the people put away the leaven", namely Passover, the 14th of the lunar month of Nisan. The rest of the Christian world at that time, according to Eusebius, held to "the view which still prevails", of always fixing Easter on Sunday. Eusebius does not say how the Sunday was decided. Other documents from the 3rd and 4th centuries reveal that the customary practice was for Christians to consult their Jewish neighbors to determine when the week of Unleavened Bread would fall, and to set Easter on the Sunday that fell within that week.〔E. Schwartz,'' Christliche und jüdische Ostertafeln'', Berlin, 1905, p 104ff.〕〔Margaret Dunlop Gibson, ''The Didascalia Apostolorum in Syriac'', Cambridge University Press, London, 1903, p. 100.〕 By the end of the 3rd century some Christians had become dissatisfied with what they perceived as the disorderly state of the Jewish calendar. The chief complaint was that the Jewish practice sometimes set the 14th of Nisan before the spring equinox. This is implied by Dionysius, bishop of Alexandria in the mid-3rd century, who stated that "at no time other than the spring equinox is it legitimate to celebrate Easter" (Eusebius, ''Church History'' 7.20); and by Anatolius of Alexandria (quoted in Eusebius, ''Church History'' 7.32) who declared it a "great mistake" to set the paschal lunar month when the sun is in the twelfth sign of the zodiac (i.e., before the equinox). And it was explicitly stated by Peter, bishop of Alexandria that "the men of the present day now celebrate () before the () equinox...through negligence and error."〔Peter of Alexandria, quoted in the preface to the ''Chronicon Paschale'', Migne, ''PG'' 18, 512〕 Another objection to using the Jewish computation may have been that the Jewish calendar was not unified. Jews in one city might have a method for reckoning the Week of Unleavened Bread different from that used by the Jews of another city.〔Sacha Stern,'' Calendar and Community: A History of the Jewish Calendar Second Century BCE-Tenth Century CE'', Oxford University Press, 2001, pp. 72–79.〕 Because of these perceived defects in the traditional practice, Christian computists began experimenting with systems for determining Easter that would be free of these defects. But these experiments themselves led to controversy, since some Christians held that the customary practice of holding Easter during the Jewish festival of Unleavened Bread should be continued, even if the Jewish computations were in error from the Christian point of view.〔Epiphanius, Adversus Haereses 3.1.10, quotes a version of the ''Apostolic Constitutions'' used by the sect of the Audiani, which advises Christians not to do their own calculation, but to use the Jewish computation even if the Jewish computation is in error.〕 At the First Council of Nicaea in 325, it was agreed that the Christians should observe a common date, independent from the Jewish method.〔See ("the letter from emperor Constantine to the absent bishops" ).〕 Because of the divergence of tables mentioned above it was usual to negotiate a common date when discrepancies arose. It took several centuries before a common method was accepted throughout Christendom. The process of working out the details generated still further controversies. The method from Alexandria became authoritative. In its developed form it was based on the epacts of a reckoned moon according to the 19-year cycle (a.k.a. the Metonic Cycle). Such a cycle was first proposed by Bishop Anatolius of Laodicea (in present-day Syria), c. 277.〔The lunar cycle of Anatolius, according to the tables in ''De ratione paschali'', included only two bissextile (leap) years every 19 years, so could not be used by anyone using the Julian calendar, which had four or five leap years per lunar cycle. See C.H. Turner, "(The Paschal Canon of Anatolius of Laodicea )", ''The English Historical Review'' 10 (1895) 699–710, or Daniel McCarthy, "(The Lunar and Paschal Tables of ''De ratione paschali'' Attributed to Anatolius of Laodicea )", ''Archive for History of Exact Sciences'' 49 (1995–96) 285–320.〕 Alexandrian Easter tables were composed by Bishop Theophilus about 390 and within the bishopric of Cyril about 444. In Constantinople, several computists were active over the centuries after Anatolius (and after the Nicaean Council), but their Easter dates coincided with those of the Alexandrians. Having deviated from the Alexandrians during the 6th century, churches beyond the eastern frontier of the former Byzantine Empire, including the Assyrian Church of the East,〔() "The Many Easters & Eostres for the Many: A Choice of Hallelujahs", Retrieved 2013-07-20〕 now celebrate Easter on different dates from Eastern Orthodox churches four times every 532 years.〔() "Computus", Retrieved 2013-07-20〕 The Alexandrian computus was converted from the Alexandrian calendar into the Julian calendar in Rome by Dionysius Exiguus, though only for 95 years. Dionysius introduced the Christian Era (counting years from the Incarnation of Christ) when he published new Easter tables in 525.〔See ("''Liber de Paschate''" )〕〔For confirmation of Dionysius's role see Blackburn & Holford-Strevens p. 794.〕 Dionysius's tables replaced earlier methods used by the Church of Rome. The earliest known Roman tables were devised in 222 by Hippolytus of Rome based on 8-year cycles. Then 84-year tables were introduced in Rome by Augustalis near the end of the 3rd century.〔Although this is the dating of Augustalis by Bruno Krusch, see arguments for a 5th-century date in Alden A. Mosshammer, ''The Easter Computus and the Origins of the Christian Era'' (Oxford University Press), pp. 217 and 227–228.〕 A completely distinct 84 - year cycle, the ''Insular latercus'', was used in the British Isles. These old tables were used in Northumbria until 664, and by isolated monasteries as late as 931. A modified 84-year cycle was adopted in Rome during the first half of the 4th century. Victorius of Aquitaine tried to adapt the Alexandrian method to Roman rules in 457 in the form of a 532-year table, but he introduced serious errors.〔Blackburn & Holford-Strevens p. 793.〕 These Victorian tables were used in Gaul (now France) and Spain until they were displaced by Dionysian tables at the end of the 8th century. In the British Isles Dionysius' and Victorius's tables conflicted with the indigenous tables. These employed an 84-year cycle because this meant the dates of Easter would repeat every 84 years, but there was an error which caused the full moons to fall progressively too early. Add to that the fact that Easter could fall at earliest on the fourteenth day of the lunar month and it was often the case that Eanfleda, who followed the Roman system, was fasting on Palm Sunday at the same time as her husband Oswy, king of Northumbria, was feasting on Easter Sunday. The Irish Synod of Mag Léne in 631 decided in favor of either the Dionysian or Victorian Easter and the northern English Synod of Whitby in 664 adopted the Dionysian tables. Bede records that "there happened an eclipse of the sun on the third of May, about ten o'clock in the morning." The time is correct but the date is two days late. This was done to conceal the inaccuracy that had accumulated in the new cycle since it was originally constructed. The Dionysian reckoning was fully described by Bede in 725.〔Faith Wallis, ''Bede: The Reckoning of Time'', (Liverpool: Liverpool Univ. Pr., 1999), pp. lix–lxiii.〕 It may have been adopted by Charlemagne for the Frankish Church as early as 782 from Alcuin, a follower of Bede. The Dionysian/Bedan computus remained in use in Western Europe until the Gregorian calendar reform, and remains in use in most Eastern Churches, including most Eastern Orthodox Churches and Oriental Orthodox Churches.〔(【引用サイトリンク】title=The Orthodox Church Calendar )〕 Churches beyond the eastern frontier of the former Byzantine Empire use an Easter that differs four times every 532 years from this Easter, including the Assyrian Church of the East. The Gregorian Easter has been used since 1583 by the Catholic Church and was adopted by most Protestant churches between 1753 and 1845. German Protestant states used an astronomical Easter based on the ''Rudolphine Tables'' of Johannes Kepler between 1700 and 1774, while Sweden used it from 1739 to 1844. This astronomical Easter was one week before the Gregorian Easter in 1724, 1744, 1778, 1798, etc.〔Samuel Butcher, ''The Ecclesiastical Calendar: its theory and construction'' (Dublin, 1877) p.153. Available at ()〕〔Roscoe Lamont, "(The reform of the Julian calendar )", ''Popular astronomy'' 28 (1920) 18–31.〕 ==Theory== The Easter cycle groups days into lunar months, which are either 29 or 30 days long. There is an exception. The month ending in March normally has thirty days, but if 29 February of leap year falls within it, it contains 31. As these groups are based on the lunar cycle, over the long term, the average month in the lunar calendar is a very good approximation of the synodic month, which is 29.53058872 days long. There are 12 synodic months in a lunar year, totaling either 354 or 355 days. The lunar year is about 11 days shorter than the solar year, which is either 365 or 366 days long. These days by which the solar year exceeds the lunar year are called epacts ().〔.〕 It is necessary to add them to the day of the solar year to obtain the correct day in the lunar year. Whenever the epact reaches or exceeds 30, an extra intercalary month (or embolismic month) of 30 days has to be inserted into the lunar calendar: then 30 has to be subtracted from the epact. The Rev C Wheatly〔Rev C Wheatly, ''A Rational Illustration of the Book of Common Prayer of the Church of England'', Oxford 1794, p. 42.〕 provides the detail: "Thus beginning the year with March (for that was the ancient custom) they allowed thirty days for the moon () in March, and twenty - nine for that () in April; and thirty again for May, and twenty - nine for June &c. according to the old verses: :''Impar luna pari, par fiet in impare mense; :''In quo completur mensi lunatio detur.'' "For the first, third, fifth, seventh, ninth, and eleventh months, which are called ''impares menses'', or unequal months, have their moons according to computation of thirty days each, which are therefore called ''pares lunae'', or equal moons: but the second, fourth, sixth, eighth, tenth, and twelfth months, which are called ''pares menses'', or equal months, have their moons but twenty nine days each, which are called ''impares lunae'', or unequal moons." The nineteen-year Metonic cycle assumes that 19 tropical years are as long as 235 synodic months. So after 19 years the lunations should fall the same way in the solar years, and the epacts should repeat. However, 19 × 11 = 209 ≡ 29 (mod 30), not 0 (mod 30); that is, 209 divided by 30 leaves a remainder of 29 instead of being a multiple of 30. So after 19 years, the epact must be corrected by +1 day in order for the cycle to repeat. This is the so-called ''saltus lunae'' or moon's leap, and it is handled by having three consecutive months of 29 days in the summer of the last year in the cycle. The extra 209 days are made up of seven embolismic months of thirty days, for a total of (19 × 12) + 7 = 235 lunations, less the one day removed from the second of the three successive 29 - day months in the last year of the cycle. The sequence number of the year in the 19-year cycle is called the "Golden Number", and is given by the formula :''GN'' = ''Y'' mod 19 + 1 That is, the remainder of the year number ''Y'' in the Christian era when divided by 19, plus one.〔"the (Number ) of a year AD is found by adding one, dividing by 19, and taking the remainder (treating 0 as 19)." Blackburn & Holford-Strevens p. 810.〕 Using the method just described, a period of 19 calendar years is also divided into 19 lunar years of 12 or 13 lunar months each. In each calendar year (beginning on 1 January) one of the lunar months must be the first one within the calendar year to have its 14th day (its formal full moon) on or after 21 March. This lunar month is the paschal or Easter-month, and Easter is the Sunday ''after'' its 14th day (or, saying the same thing, the Sunday ''within its third week''.) The paschal lunar month always begins on a date in the 29-day period from 8 March to 5 April inclusive. Its 14th day, therefore, always falls on a date between 21 March to 18 April inclusive, and the following Sunday then necessarily falls on a date in the range 22 March to 25 April inclusive. In the solar calendar Easter is called a moveable feast since its date varies within a 35-day range. But in the lunar calendar, Easter is always the third Sunday in the paschal lunar month, and is no more "moveable" than any holiday that is fixed to a particular day of the week and week within a month. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Computus」の詳細全文を読む スポンサード リンク
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