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User:Karl Palmen writes:
The section on the age of the moon is not aparently NPOV. So I have moved it here.
It asserts that the age of the moon equals the day of the lunation. Also the concluding paragraph contradicts the Catholic encyclopeadia article referenced and the end of the article.
The epact is often defined as the age of the Moon at the begin of the (solar) year. Now when a new lunar month begins on 1 January, the epact is 0. However we count the days of the lunar calendar as ordinal numbers, i.e. in this case the 1st day of January is also the 1st day of the lunar year and the 1st day of the lunar month. We can accordingly assign an age of 1 day to the Moon, if we follow the ancient convention that the lunar month starts when the New Moon is first visible. This is actually some time after the astronomical conjunction of Sun and Moon (also called Dark Moon), when the "astronomical age of the Moon" is 0. Indeed the lunar calendar used for Calculating the date of Easter in the Gregorian calendar has its months starting systematically a day after the astronomical New Moon. In this reckoning the astronomical opposition of Sun and Moon indeed usually falls on the 14th day of the lunar month, which is consistent with the tradition of having the Paschal Full moon on the 14th day of the spring month.
The epact can then be defined as the age of the Moon on the day before the begin of the (solar) year. This is not the same as the age of the Moon on the last day of the previous year, because the epact may be corrected by 1 at the start of the new year.
Karl August 15 10h UT
Oh well, how about this text then:
"The epact is often defined as the age of the Moon at the begin of the (solar) year. Now when the epact is 0, 1 January is also the 1st day (i.e. the day of first visibility of the lunar crescent) of the 1st lunar month. However age used to be expressed as an ordinal number, starting with 1 (a newborn baby was said to be "in its 1st year"). A supposed age of 0 of the Moon is translated to the 1st ordinal number, which is an apparent discrepancy.
Also there has been a historical change in the definition of "age". A baby that was said to be "in its first year", is now called "0 years old". Events used to be timed with a hierarchy of periods labeled with ordinals numbers (e.g starting point is 1st day of 1st month of 1st year). We now interpret time as a continuous variable starting from 0 at some specific moment, and count fully completed days and years for age. But calendar dates are labels that are still expressed the old way, as ordinal numbers. This is the underlying reason for the milennium controversy (start at 1 January 2000 or 2001?).
Also it has become custom to define New Moon at the moment of astronomical conjunction, which is at the same moment everywhere on Earth, and take that as the zero point for counting the (continuous) age of the Moon. In contrast the crescent Moon becomes first visible one or two days later, and the moment of first visibility depends on the place on Earth.
The epacts of the ecclesiastic calendar are usually still consistent with the age of the Moon in the modern sense, if interpreted in the following way:
"
-- 194.109.250.130 21:00, 15 Aug 2003 (UTC)
Tom has given here two alternative interpretations of the concept of age of moon, which are both different from the one normally used in the description of the Calculation of Easter.
Karl 18 Aug 2003 09h UT
So it seems that the concept of age of moon is far from clear-cut. Therefore, in discussions about such things as epacts or Easter Calculations, it is better to use something else, such as day of moon (defined to begin with new moon) or number of days after new moon. -- Karl 19 Aug, 13h UT.
In the Preface in the Book of Common Prayer of the Church of England, in a section decreed by the Calendar Act, there is a page listing the Moveable Feasts for about 40-50 years. Its third column contains Epacts. The Act and Book do not seem to have any definition of the Epact. Just what formal definition does the Church use?
Note that such a table is in Statutes at Large 1765, but not in the database which represents the Act as amended to date.
I suggest that the Article should contain a short section explicitly answering this point.
82.163.24.100 ( talk) 10:01, 3 May 2008 (UTC)
The current article text under "Lilian (Gregorian) epacts"
I suggest that the relevant sources here are those that refer to the actual work that culminated in the Gregorian reform of 1582, especially the papers given in the 1983 commemorative conference. These sources (primarily the papers by O Pedersen, J D North, G Moyer and A Ziggelaar) appear to show that the lunar equation in the Lilian system of epacts was a systematic empirical adjustment, intended to reflect the fact that the Moon's mean rate of motion had turned out to be just a little faster than the expectation embodied in the traditional form of 19-year cycle. In the second half of the sixteenth century, full moons were occurring much sooner than the dates indicated on the traditional tabular basis (which by then had been in use for over a thousand years). According to the text of "Inter gravissimas" the paschal full moons needed to be "put back in place" from a deviation of something more than 4 days ("et XIV paschalem suo in loco, a quo quatuor et eo amplius dies hoc tempore distat, reponendam".) Lilius' periodical adjustment was intended as a correction to bring the tabular epact value closer to the real age of the Moon, and prevent any repeat of the long-term divergence which had been seen with the traditional tables.
A temporary 'patch' had been applied in the 1568 edition of the Breviary, namely, to move the Golden Numbers up four places and to warn that they would need to be reviewed again and moved every 300 years or so. But the text of "Inter gravissimas" complains that previously-proposed solutions were not long-term ("neque perennes erant"), and it praises Lilio's effort for providing in principle a perpetual arrangement to restore "all the things in the calendar that had got into disarray" so that there would be no future "mutation" ("omnia quæ in calendario collapsa sunt, constanti ratione et sæculis omnibus duratura, sic restitui posse ostendit ut calendarium ipsum nulli umquam mutationi in posterum expositum esse videatur.").
In all of this there seems to be no reference to Metonic relations or tithis. It seems appropriate to take out the material about these factors, unless good sources are given for their relevance to the 16th-century work. Terry0051 ( talk) 01:01, 4 December 2009 (UTC)
Tom Peters ( talk) 10:22, 20 February 2010 (UTC)
I see the quality of the article has eroded since 2007. First, someone "cleaned" the prose of my translation of the original verbose Latin quote for style, and then removed the original text altogether. Then it was claimed that this text from the Gregorian calendar Canon was the first to define epacts as the excess of the solar over the lunar year: but it was only an explanation, not a formal original definition, of a concept that had been widely known among computists for over a millennium before the reform. Then Terry picked up the definition of "age at 1 January" from the paper by Perdersen in the commemorative conference: he defines it as age at 1 January, and shows that epacts were introduced in the computus with the latercula of 354: Terry here incorrectly assumes that the "1 January" is then the older, original definition. However from the very name it is obvious that the "excess" definition is the original one of the concept of epacts, and Pedersen only uses the equivalent "1 January" definition for computist convenience. Moreover, as you could have seen on this discussion page in the thread from 2003, the "1 January" definition is problematic, and therefore is best avoided. Also see the first sentence in the lemma on epacts in the Catholic encyclopedia, which succinctly supports my view: http://www.newadvent.org/cathen/05480b.htm . So I am inclined to revert this article back to its 2007 version! Tom Peters ( talk) 19:28, 20 February 2010 (UTC)
If I may reopen an old debate, I just came across this passage in Bede, On the Reckoning of Time, cap. 50 (p. 131, Wallis Translation):
It seems quite clear that for Bede, and for those who followed him, the epact was related to the age of the Moon. I'll have to do a bit of thinking about Pedersen's referring the epact to 1 January, but I wouldn't dismiss him out of hand. He was a leading student of medieval astronomy. -- SteveMcCluskey ( talk) 23:00, 23 January 2017 (UTC)
The word 'computistical is used a number of times in this article. Does anyone out there know what this word means? Duncan.france ( talk) 00:58, 19 October 2018 (UTC) > The article already has a cross-reference to 'computus'. The explanation is there. [Terry0051, April 30, 2020]
The original definition of the epact (ἐπακται ἡμεραι, "added days") seems to have been the difference between the lunar date (either observational, or in any pre-calculated lunisolar or purely lunar calendar) and the solar date (in any arithmetical solar calendar; nowadays it would also be possible to implement epacts with any minor observational solar calendar, such as e.g. the Persian calendar). With this definition, it is very understandable why this "quantity" is different from the actual lunar date, and also why the modern Gregorian epact equals the lunar date on the day before the beginning of the Gregorian solar year. Originally in Alexandria, when pope Demetrios I wrote about epacts and used them for paschal calculations, his epacts were most certainly defined as the difference between a "schematic" lunar calendar (very similar or identical to the one used in modern Ethiopia, as described by Neugebauer 1979) and the Alexandrian solar calendar as instituted by Augustus. When these epacts (and their associated pre-calculated lunar calendar) were implemented by Dionysius Exiguus into the roman Julian solar calendar, the Alexandrian "sedes epactarum" (on 1 Thoth = 29/30 August) was not redefined to 1 January (or any other Julian date, as e.g. 1 March), probably because Dionysius Exiguus himself did not understand the basis for the calculations he made, and it was left to later computists, as Beda Venerabilis, to find out empirically that the value of the Alexandrian epact is equal to "the age of the moon on 22 March" in the Julian calendar. But the modern Gregorian epacts have their "sedes epactarum" on 1 January in the Gregorian solar calendar; therefore, they are equal during most years to the "schematic" lunar date of 31 December in the year before. However, these "schematic" lunar dates can be compared to real, observational lunar dates, from e.g. (the true, observational version of) the Islamic calendar (preferably from the Middle East - e.g. Cairo, Medina or Mecca) or the observational Qaraite calendar (from Israel). It can then be observed that, in most cases, there is a slight difference between the observational lunar dates and the Gregorian ones. True values of the original meaning of epact (daily, monthly, or yearly) can be calculated from the observational lunar dates and the Gregorian solar dates, as given by this simple algorithm:
• Calculate the difference between the true, observational lunar date L and the Gregorian solar date S, i.e. E1 = L-S
• If E1 should happen to be a negative number, add the number of days in the current Gregorian month to the difference, i.e. E2 = L-S+28/29/30/31
• If E2 should happen to be equal to 30, subtract 30 from it, giving the epact the value of "0" (or, in traditional computistic style, "*"), i.e. E3 = L-S+28/29/30/31-30
• The last calculated value of "E" (in most cases E1 or E2, seldom E3) is the "true" epact of the date considered, and also of all days in the whole lunar month in which it is situated
Today, the Gregorian solar date is "17" (17 June 2021 C.E.) and the observational lunar date is "6" (in e.g. "Chodesh revii" or "Dhu al-Qadah"). Thus, E1 = 6-17 = -11, which is negative. Therefore we will add the number of days in June, "30", to get E2 = 6-17+30 = -11+30 = 19, which is therefore the true epact for today. It is also the monthly value of the epact for the current lunar month, which started with the observation of the Crescent New Moon on the evening of 11 June 2021 C.E. However, the true yearly epact of 2021 C.E. is equal to the true daily epact of 1 January 2021 C.E. which was E1 = 16-1 = 15, but the "schematic" Gregorian epact of 2021 C.E. is "16", a difference by one day.
In the same way other "true epacts" can be defined e.g. by comparision of (the true observational version of) the Islamic calendar and the Persian official solar calendar, in which all years begin at Nowruz, situated as close as possible to the "true astronomical vernal equinox" as calculated for some meridian in Iran (possibly the capital, Teheran). In the same way, in Egypt, other "true epacts" could be calculated from the difference between the (observational) Islamic lunar dates and the Coptic (Alexandrian) solar dates, but these, if calculated for "1 Tut", would differ much more from the traditional Alexandrian calculated epact values; as is well known, the original Alexandrian lunar calendar, still used by the christian Copts of Egypt, and also used in both Ethiopia and Eritrea, has accumulated very grave errors during the centuries of its use, because of too high values both for the average tropical solar year (365.25 days, compared to the "true" average value at about 365.2422 days), and the average synodic lunar month (about 29.53085 days, compared to the "true" average value of about 29.53059 days). /Erik Ljungstrand (Sweden)
At present, the section Solar and lunar years begins:
A solar calendar year has 365 days (366 days in leap years). A lunar calendar year has 12 lunar months which alternate between 30 and 29 days for a total of 354 days (in leap years, one of the lunar months has a day added; since a lunar year lasts a little over 354+1⁄3 days, a leap year arises every third year rather than every fourth.)
Is the reference to a single leap day every three years correct? It certainly would not bring the lunar year back into synchronisation with the solar year. Later in the section, there is a much more convincing statement:
After two years the difference is 22 days, and after 3 years, 33. Whenever the epact reaches or exceeds 30, an extra (embolismic or intercalary) month is inserted into the lunar calendar, and the epact is reduced by 30.
and at the Intercalation article, the section on lunisolar calendars says
The solar year does not have a whole number of lunar months (it is about 365/29.5 = 12.37 lunations), so a lunisolar calendar must have a variable number of months in a year. Regular years have 12 months, but embolismic years insert a 13th "intercalary" or "leap" or "embolismic" month every second or third year (see blue moon). Whether to insert an intercalary month in a given year may be determined using regular cycles such as the 19-year Metonic cycle ( Hebrew calendar and in the determination of Easter) or using calculations of lunar phases ( Hindu lunisolar and Chinese calendars). The Buddhist calendar adds both an intercalary day and month on a usually regular cycle.
In a nutshell, I really can't make sense of the statement that a single leap day is added every three years. What am I missing? -- John Maynard Friedman ( talk) 16:41, 4 October 2021 (UTC)
In this article and at Gregorian calendar, the decision to change the base to 1 January is either uncited or inadequately cited. The info needed is almost certainly somewhere in the Canons that accompanied Inter gravissimas, specifically this one:
So all we need is a medievalist who can find out exactly where.
If it helps to show that the work is likely to be fruitful, the preceding Canon has the gem
The year of the ten-year cycle, which is the golden number 6, ends at the same time in the year of the Lord 1582 in the month of December. And in the month of January begins another year of the Lord, that is, 1583. And in the same month of January also, another year of the golden number is ushered in, namely 7.
— Kalendarium Gregorianum perpetuum, Canon I [1]
(which, after I corrected the mistranscription of ⟨ſ⟩ as ⟨f⟩ and a few other obvious typos, Google translate made an astonishingly good job of converting into credible English). But to transcribe and google-translate the whole chapter would take more time that I am willing to give. 𝕁𝕄𝔽 ( talk) 10:20, 23 April 2023 (UTC)
References
Annus Cycli decennouennalis, qui dr Aureus numerus est 6. terminaturque simulcu ipso anno Domini 1582 in mése Decembri. In mense autem Ianuario initium sumit alius annus Domini , nempe 1583. & in eodem mense Ianuario aslumitur etiam alius annuis Aurei numeri, nimirum 7.