1. Happy Easter!
2. Orthodox and Gregorian Easter
3. Aleppo Easter Proposal
4. Early Easters
5. Late Easters
6. The Exceptional Years 1981, 2000, 2019
7. Calendar Reform and Easter
8. The Lunisolar Dee Calendar
9. Easter on David's Lunar Calendar
10. Conclusion
Happy Easter!
That's right -- today is Easter Sunday. And I'll prove it to you. Let's start with a definition of Easter, courtesy the Oxford Dictionary:
https://en.oxforddictionaries.com/definition/easter
The most important and oldest festival of the Christian Church, celebrating the resurrection of Christ and held (in the Western Church) between 21 March and 25 April, on the first Sunday after the first full moon following the northern spring equinox.
And so let's check out the calendar. According to the calendar on the wall, the spring equinox was on March 20th, and the first full moon following that equinox was on March 21st. Thus Easter must be on the first Sunday following the March 21st full moon -- and that's today, March 24th. Therefore today is Easter. QED
Of course, you know that this proof must be flawed, because you put your Easter basket out and it's still empty, so the Easter Bunny hasn't come yet. So where is the flaw in my proof?
Well, you might check your own calendar and see that the full moon was on March 20th, while my calendar gives it as the 21st. The difference is caused by time zones. My calendar is based on Greenwich Mean Time, while yours, like many American calendars, is based on Eastern Time. On your calendar, the equinox and the full moon both occurred on March 20th.
But then again, nowhere in the above definition does it preclude the equinox and full moon falling on the same day. As long as the full moon follows the equinox -- even if it's just by a minute, even if it's just by a second -- then the following Sunday should be Easter.
And it's obvious that the full moon occurred after the equinox, since there exists a time zone (namely Greenwich) in which the equinox occurred on the 20th and the full moon on the 21st. But just to be sure, let's check the times of the equinox and full moon in a single time zone -- I'll choose my own time zone, Pacific Time:
Spring Equinox: March 20th at 2:58 PM
Full Moon: March 20th at 6:43 PM
Thus the full moon occurred 3 3/4 hours after the equinox. Since the full moon follows the equinox, that proves that the following Sunday, today is Easter.
So why isn't today Easter?
Orthodox and Gregorian Easter
In the Oxford definition of Easter, we notice the phrase "in the Western Church." This implies that in some churches that aren't Western, Easter might fall on a different day. And indeed this is true -- the Orthodox churches observe Easter on a different day.
So is today Orthodox Easter? No, it isn't. In fact, this year Orthodox Easter is even later than the Western Easter that you're used to. Western Easter is on April 21st, while Orthodox Easter is a week later, on April 28th. Indeed, Western Easter Sunday is Orthodox Palm Sunday.
But why is Orthodox Easter later than Western Easter? At first, it's apparent that it has something to do with the old style Julian vs. the new style Gregorian Calendar. In my last few posts, we celebrated the composer J.S. Bach with his Google Doodle. Ordinarily, Google Doodles appear on birthdays, so was it Bach's birthday?
It depends on the calendar. Bach grew up celebrating his birthday on March 21st, 1685. But he was born in Protestant Germany. A century earlier, Pope Gregory had announced the calendar named for him, the Gregorian Calendar, but at first only Catholic countries followed the new calendar. Most Protestant countries were slow to accept the change, and the Orthodox even slower.
Pope Gregory formed his calendar by dropping ten days from the Julian Calendar. Therefore Julian March 21st, Bach's birthday, was Gregorian March 31st. Notice that Google posted the doodle on Gregorian March 21st, which isn't his birthday. But once again, it's the day that Bach himself considered to be his birthday. By the time Bach died, Germany had accepted the Gregorian Calendar, and so his death day was Gregorian July 28th.
(The same thing happened with George Washington. He was born in the Protestant British colonies on Julian February 11th, and he died on Gregorian December 14th. But the holiday that eventually became known as Washington's Birthday was February 22nd, his Gregorian birthday.)
OK, so there are two calendars, the Julian and Gregorian. But in theory, the existence of two calendars shouldn't affect the day of Easter. After all, the equinox is the equinox and the full moon is the full moon. These are astronomical events that occur no matter what day the calendar says it is. So unless the two calendars disagree on whether today is Sunday (and they don't), then today should be Easter on either calendar.
But the fact that there are two different Easters at all -- April 21st and 28th -- implies that there must be more to the Easter date than just the equinox and full moon. Thus in order to answer the question:
Why isn't today Easter?
the following question might give us a hint:
Why are Gregorian Easter and Orthodox Easter on different dates?
Let's start with a history of the computus -- the calculation of the Easter date:
http://php.net/manual/en/function.easter-days.php
The date of Easter Day was defined by the Council of Nicaea in AD325 as the Sunday after the first full moon which falls on or after the Spring Equinox. The Equinox is assumed to always fall on 21st March, so the calculation reduces to determining the date of the full moon and the date of the following Sunday. The algorithm used here was introduced around the year 532 by Dionysius Exiguus. Under the Julian Calendar (for years before 1753) a simple 19-year cycle is used to track the phases of the Moon.
And we've seen that 19-year cycle before -- it's the Metonic Cycle.
But this paragraph explains where the Easter date comes from. In the year 532, a Christian monk named Dionysius Exiguus created a table of 19 different full moon dates -- a table that repeats every nineteen years. So when it was time to determine Easter, no one looked at the sky to see whether the moon was full or not. Instead, they just looked at the chart to see when the full moon was -- a date known as the Paschal full moon. Then the following Sunday was Easter.
In other words, the Easter rule was rule-based, not observation-based. Originally, the Chinese Calendar was also rule-based, but now it's based on astronomical observations. And the Julian Calendar, is also rule-based.
As for the Gregorian Calendar, the above link explains:
Under the Gregorian Calendar (for years after 1753 - devised by Clavius and Lilius, and introduced by Pope Gregory XIII in October 1582, and into Britain and its then colonies in September 1752) two correction factors are added to make the cycle more accurate.
In other words, the Gregorian Calendar is also rule-based. Actually, there is one small part of the Gregorian Calendar that is observation-based -- the insertion of leap seconds. Everything else, including the calculation of Easter, is based on rules.
The link states that there are two correction factors. Easter is, after all, a holiday determined by both the sun and the moon. One of the correction factors is solar while the other is lunar.
The solar correction is well-known -- certain years have Leap Days in the Julian Calendar but not in the Gregorian Calendar, such as 1900 and 2100. The lunar correction is less familiar. It's related to the fact that the Metonic Cycle isn't perfectly accurate. I wrote about how to improve upon the Metonic Cycle back in my December 28th post on calendars.
But we see the lunar correction at work when we compare Gregorian and Orthodox Easter. The next full moon, according to my calendar, is April 19th, and Easter is the next Sunday, April 21st. But Orthodox Easter is based on the old Dionysius Exiguus tables, which are inaccurate since the erros in the Metonic Cycle are noticeable after 1500 years. By now, the tables are three or four days late, so instead of April 19th, the Orthodox Paschal Full Moon is on April 22nd or 23rd. Thus Orthodox Easter isn't until the following Sunday, April 28th.
It's the solar correction, however, that I wish to focus on now. As I quoted above, the equinox is always considered to fall on March 21st in the respective calendar -- Julian or Gregorian. And as I wrote earlier, in Bach's day the Julian "equinox" didn't occur until Gregorian March 31st. This means that the Paschal full moon, and thus Easter, could never fall earlier than that equinox. From that point on, if a Gregorian Easter fell in March, then the Orthodox Easter wouldn't fall until the next full moon, an entire month later.
In the Gregorian Calendar, the equinox is considered to fall on our March 21st. But as we see on our calendars, the actual equinox this year was on the 20th, not the 21st. The Gregorian Calendar is far more accurate than the Julian Calendar, but no rule-based calendar is perfect. Oh, you might be wondering about the fact that the full moon really was on the 21st in some time zones. Well, the Paschal full moon is calculated from tables -- and tables don't know anything about time zones.
And so this is why today isn't Easter. It would be Easter if we were using an observation-based calendar, but our actual calendar is rule-based. And based on the rules devised over 400 years ago, the full moon fell before the equinox, so Easter isn't until the after next full moon, a month from now.
Aleppo Easter Proposal
About 20 years ago, there was a proposal to define Easter based on astronomical events. This is mentioned at the bottom of the following link:
http://www.webexhibits.org/calendars/calendar-christian-easter.html
At at meeting in Aleppo, Syria (5-10 March 1997), organised by the World Council of Churches and the Middle East Council of Churches, representatives of several churches and Christian world communions suggested that the discrepancies between Easter calculations in the Western and the Eastern churches could be resolved by adopting astronomically accurate calculations of the vernal equinox and the full moon, instead of using the algorithm presented above. The meridian of Jerusalem should be used for the astronomical calculations.
And that's the only logical time zone where the calculation should take place -- after all, Easter commemorates the crucifixion of Jesus Christ, and that event took place in Jerusalem. Thus it makes sense to choose the Jerusalem time zone to determine when it is Sunday.
By the way, Jerusalem is two hours ahead of Greenwich. Daylight Saving Time is observed two days earlier than in Greenwich -- the Friday before the last Sunday in March. (I believe that the clocks move forward on Friday rather than Sunday so that they're set forward before the Jewish Sabbath starts the following sunset.)
Aleppo Easter was supposed to be implemented starting in 2001. It would replace both Gregorian and Orthodox Easter, thus allowing all Christians to celebrate Easter the same day. Notice that according to the link, 2019 would indeed be the first year when Aleppo Easter differs from Gregorian Easter:
If the new system were introduced, churches using the Gregorian calendar will hardly notice the change. Only once during the period 2001-2025 would these churches note a difference: In 2019 the Gregorian method gives an Easter date of 21 April, but the proposed new method gives 24 March.
And yes -- we already determined at the start of this post that today is Aleppo Easter. So obviously, this means that the Aleppo Easter proposal was never adopted, since no one celebrates Easter today.
And before you ask, yes, it is spring break in my old district, but no, it's not because our district secretly decided to observe Aleppo Easter. In our district, spring break has nothing to do with Easter at all. If today had been Easter, then there would have been no school two days ago, since it would have been Good Friday. (Good Friday and Easter Monday are always holidays in my old district.)
Notice that an April 21st Easter is preferable to March 24th for people living in cold northern climates where there is still snow on the ground as late as early-to-mid April. On the other hand, perhaps those in Australia and New Zealand wish that today were Easter after all.
But what about teachers and students in schools? Those attending schools with Easter break might be longing for the holiday to come (during the "Big March"). Then again, they'd return to school after Easter and find that there are no more holidays for two months, until Memorial Day.
In my old school district, late Easters may be desirable because this week is spring break no matter when Easter is. Thus we get both spring break and a four-day Easter weekend, whereas if today were Easter, we'd get only spring break.
On the other hand, schools in Boston observe spring break the week of Patriots' Day -- the third Monday in April. They also close on Good Friday. But if this is the Friday after Patriots' Day (as it is in 2019), then there is no extra holiday. Thus Boston students and teachers might wish that today were Easter, so that they'd get separate holidays for both Good Friday and spring break, instead of just spring break.
On the other hand, Bostonian adults who don't work at schools might prefer the late Easter in order to avoid cold New England weather. Thus what students and teachers want is often at odds with what non-school adults prefer. I notice that in Boston, today the high is near 60 degrees with temps closer to freezing with snow chances both before and after -- if only today were Easter. (Go figure!)
There's one more interesting thing mentioned at the above link:
Note that the new method makes an Easter date of 21 March possible. This date was not possible under the Julian or Gregorian algorithms. (Under the new method, Easter will fall on 21 March in the year 2877. You’re all invited to my house on that date!)
Under either Gregorian or Julian Easter, the range of possible Easter dates is March 22nd-April 25th in the respective calendar. (Julian March 22nd-April 25th currently corresponds to April 4th-May 8th on the Gregorian Calendar.) The link tells us that Aleppo Easter will fall on March 21st, 2877 -- and who knows, maybe the Aleppo Easter proposal will finally be adopted by the 29th century.
But wait a minute -- Aleppo Easter is determined by observation, not a rule or formula. So how can we know when the full moon will be over 800 years from now?
Actually, astronomical full moons can be calculated -- it's just that the calculations are much more sophisticated than those used by Exiguus or Lilius/Pope Gregory. (Indeed, we've seen that solar and lunar eclipses can be calculated up to a millennium in advance.) In this case, 2877 will be just like 2019, with an equinox followed by a full moon on March 20th. The difference is that March 20th, 2877 is a Saturday, allowing Easter to fall on Sunday, March 21st, 2877.
This is a math blog. It's possible that some of you readers are new -- you stumbled upon this post by searching for Google when you realized that today was supposed to be Easter, but isn't. Well, your question has been answered. The rest of this post includes some complex math calculations related to Easter, full moons, and equinoxes. Unless you're a math teacher or mathematically inclined, I recommend that you stop reading this post and check out other Google results. For example, I found the following Farmer's Almanac link:
https://www.farmersalmanac.com/when-easter-10797
Early Easters
Obviously, March 21st, 2877 would be an especially early Easter. The earliest Easter can fall on the Gregorian Calendar is March 22nd. This date is particularly rare. According to the following link:
http://tlarsen2.tripod.com/thomaslarsen/easterdates.html
the last time Easter fell on March 22nd was 1818, and the next time won't be until 2285. Why is the earliest possible Easter so rare?
Last year, Easter fell on April 1st -- which isn't nearly as rare. Knowing that Easter date, let's go backwards and determine the date of the Paschal Full Moon. There are seven possibilities:
Sunday, March 25th
Monday, March 26th
Tuesday, March 27th
Wednesday, March 28th
Thursday, March 29th
Friday, March 30th
Saturday, March 31st
As it turns out, the last date above was the Paschal Full Moon for 2018. Now let's work backwards to determine the Paschal Full Moon for a March 22nd Easter:
Sunday, March 15th
Monday, March 16th
Tuesday, March 17th
Wednesday, March 18th
Thursday, March 19th
Friday, March 20th
Saturday, March 21st
But we know that since the equinox was defined as March 21st, the Paschal Full Moon can't occur on March 20th or earlier. So the list of possible Paschal Full Moons becomes:
Saturday, March 21st
There's only one possible Paschal Full Moon for a March 22nd Easter, while there are in fact seven possibilities for an April 1st Easter. This is why April 1st Easters are about seven times as common as March 22nd Easters. In order to have a March 22nd Easter, not only must the Paschal Full Moon be March 21st, but that date must be a Saturday so that the 22nd can be Easter Sunday.
When Exiguus first constructed his table of Paschal Full Moons, there were 19 possible full moon dates, one for each year of the Metonic Cycle. Only one of those dates was March 21st -- and only about 1/7 of those years was that date a Saturday. Thus the probability of a March 22nd Easter works out to be 1/19 * 1/7 = 1/133 -- that is, Easter on March 22nd occurs once every 133 years.
But the two years with Easter on March 22nd -- 1818 and 2285 -- are more than 400 years apart. Of course, these are Gregorian Easters that have nothing to do with the Exiguus tables.
How many possible Paschal Full Moon dates are there, anyway? It would seem that the first full moon of spring could fall at any time during the first month after March 21st -- that is, there are 30 possible full moon dates. But due to the Metonic Cycle, full moon dates repeat every 19 years. In other words, there are only 19 possible full moon dates, not 30. On the Exiguus tables, there are 19 full moon dates, not 30.
We know that the Gregorian tables have solar and lunar corrections. As it turns out, these corrections are applied only at years that are multiples of 100. (We already know that solar corrections occur in such years, and to make it simple, lunar corrections are applied in such years too.)
This means that within a given century, the 19 possible full moon dates are fixed, but different centuries can have different Paschal Full Moons. Within a given century, let's call a possible full moon date "golden" if it's one of the possible full moon dates in that century. I choose the name "golden" because it refers to the Golden Numbers used in the Easter calculation. The Golden Number of a year is one more than its remainder when divided by 19. So in a given century a "golden date" is the Paschal Full Moon corresponding to all the years in that century with the same Golden Number.
Let's also agree to call a possible moon date "silver" if it is not golden. If in a given century a certain date is silver, then it will not be the Paschal Full Moon date for any year in that century.
Notice that there can never be two silver dates in a row. If April 4th is silver, then both April 3rd and 5th must be golden. Likewise, there can never be three golden dates in a row. If April 2nd and 3rd are both golden, then both April 1st and 4th must be silver.
Now you can start to see what I'm getting at. The only possible Paschal Full Moon date for a March 22nd Easter is March 21st. But in centuries when March 21st is silver, the full moon can't fall on March 21st at all that centuries. Thus in such centuries, March 22nd can't be Easter. We'll have to wait until the next century -- or even several centuries -- until March 21st is golden again before March 22nd can be Easter.
Let's look at a table of Paschal Full Moons for the current 21st century:
Golden Number Paschal Full Moon
1 April 14th
2 April 3rd
3 March 23rd
4 April 11th
5 March 31st
6 April 19th
7 April 8th
8 March 28th
9 April 16th
10 April 5th
11 March 25th
12 April 13th
13 April 2nd
14 March 22nd
15 April 10th
16 March 30th
17 April 18th
18 April 7th
19 March 27th
The dates in this chart are the golden dates for the current century. The missing dates are all silver:
Silver Dates: March 21st, 24th, 26th, 29th, April 1st, 4th, 6th, 9th, 12th, 15th, 17th
And we observe that indeed, March 21st is silver this century, so March 22nd can't be Easter. It's also silver during the 20th and 22nd centuries, and so March 22nd isn't Easter in those centuries either. On the other hand, March 21st is golden during the 18th, 19th, and 23rd centuries. And indeed, all three centuries have a March 22nd Easter according to the above link (1761, 1818, 2285).
The earliest Easter in the 21st century is March 23rd. The possible Paschal Full Moons for a March 23rd Easter are:
Friday, March 21st
Saturday, March 22nd
Since there can't be two silver dates in a row, these can't both be silver. And in the current century, March 22nd is golden. Easter was early 11 years ago -- March 23rd, 2008.
Let's look for March 24th Easters, since today is March 24th and ought to be Easter. The possible Paschal Full Moons for a March 24th Easter are:
Thursday, March 21st
Friday, March 22nd
Saturday, March 23rd
Even though both March 22nd and 23rd are golden this century, it just so happens that neither is the Paschal Full Moon in a year when March 24th is on a Sunday. The last time today was Easter was back in 1940. The table at the above link doesn't even go far enough to the next March 24th Easter. It just so happens that Easter will fall on both March 22nd and 23rd before it falls on the 24th again.
As we go later in March, there are more possible full moon dates for each date of Easter. The possible Paschal Full Moons for a March 25th Easter are:
Wednesday, March 21st
Thursday, March 22nd
Friday, March 23rd
Saturday, March 24th
Of these, both March 22nd and 23rd are golden this century. Easter will fall on March 25th twice this century -- in 2035 and 2046.
By the way, there's one more thing to say about early Easters. It is impossible to Easter to fall in March in two years in a row. To see why, suppose Easter is on March 31st one year. This means that the latest possible Paschal Full Moon that year would be March 30th. But then there would be a full moon the following year on March 19th (11 days earlier, since 12 lunar months are 11 days shy of a solar year). But this is too early to be the Paschal Full Moon. Instead, the Paschal Full Moon would be a month later, leading to a late Easter in April.
In fact, not even an April 1st Easter can be followed by a March Easter in the Gregorian Calendar (even though this is exactly what happens with Aleppo Easter from 2018 to 2019). If Easter is on April Fool's Day, then the Paschal Full Moon is no late than March 31st. And once again, 11 days earlier is March 20th, which is too early for the Paschal Full Moon the following year.
Instead, the earliest Easter can be the year before a March Easter is April 2nd. This happens when the Paschal Full Moon is on April 1st. The following Paschal Full Moon is 11 days earlier on March 21st, with Easter the following Sunday -- most likely March 25th, possibly the 24th. This combination most recently occurred in 1893-1894 and will occur again in 2265-2266.
In centuries where March 21st is silver, April 3rd is the earliest Easter that can be followed by a March Easter. This most recently occurred in 1988-1989 and will occur again in 2140-2141.
Late Easters
When is the latest possible Easter? Consider the first Easter after I was born -- 1981. The Golden Number for this year is 6 -- and there was no solar or lunar adjustment in 2000, so the chart I listed earlier applies to both the 20th and 21st centuries.
So the Paschal Full Moon for 1981 was on April 19th. Since this was a Sunday, Easter would be a full week later -- April 26th. But let me tell you something -- April 26th, 1981 was not Easter on the Gregorian Calendar. Indeed, April 26th isn't even listed as a possible Easter date! So what gives?
On the original Exiguus charts, it just so happened that April 19th was silver. The latest possible golden date was April 18th, and so the latest possible Easter was a week later, April 25th. On the Orthodox Calendar, April 25th was the mirror image of March 22nd, since the list of Paschal Full Moon Dates for an April 25th Easter would be:
Sunday, April 18th
And both March 22nd and April 25th Easters would be equally rare.
But the Gregorian Calendar has solar and lunar adjustments. This opened up the possibility that April 19th, while silver in some centuries, might be golden in others. And in centuries when April 19th is golden, Easter could fall on April 26th. It turns out that the 20th century is such a century and that 1981 is such a year.
When the Gregorian Calendar was first devised, there was a slight tweak in the calculation of the Easter date, introduced for the sole purpose of preventing Easter from falling on April 26th. Here's the tweak -- if the calculation gives April 19th as the Paschal Full Moon, then just change April 19th to April 18th. So the Paschal Full Moon for Easter was April 18th, with Easter the next day, the 19th.
So if April 19th is golden, we change it to April 18th. In some centuries when April 19th is golden, it just so happens that April 18th is golden as well. It was decided that having two Golden Numbers share the same Paschal Full Moon in a century was undesirable. Thus in centuries when April 18th and 19th are both golden, not only do we change April 19th to the 18th, but we also change April 18th to the 17th.
Note that the second adjustment only occurs in centuries when both April 18th and 19th are golden. If April 18th is golden but the 19th is silver, then we don't adjust the golden April 18th. And since there can never be three golden dates in a row, the 17th, 18th, and 19th can't all be golden. Thus there's never a reason to adjust golden April 17th.
Let's extend our golden/silver analogy. Instead of referring to golden April 19th, we adjust it to April 18th and call it "fool's gold" or "pyrite." (If April 19th is silver, then April 18th remains golden rather than pyrite.) If both April 18th and 19th are golden, then we adjust these to the pyrite 17th and 18th.
So our current Paschal Full Moon table for the 20th and 21st centuries becomes:
Golden Number Paschal Full Moon
1 April 14th
2 April 3rd
3 March 23rd
4 April 11th
5 March 31st
6 April 18th (pyrite)
7 April 8th
8 March 28th
9 April 16th
10 April 5th
11 March 25th
12 April 13th
13 April 2nd
14 March 22nd
15 April 10th
16 March 30th
17 April 17th (pyrite)
18 April 7th
19 March 27th
Silver Dates: March 21st, 24th, 26th, 29th, April 1st, 4th, 6th, 9th, 12th, 15th
The pyrite dates break the symmetry between early and late Easters. March 22nd Easter is impossible in centuries when March 21st is silver, but April 25th is possible in all centuries because April 18th is always either golden or pyrite. Easter will next fall on April 25th in the year 2038.
Meanwhile, there is one year this century -- 2049 -- when Easter would have fallen on April 25th had it not been for the pyrite rule. Instead, the Paschal Full Moon for 2049 is pyrite April 17th and so Easter is on April 18th instead of the 25th.
In fact, the most common Easter date is April 19th. This is because not only are there seven possible Paschal Full Moons for an April 19th Easter:
Sunday, April 12th
Monday, April 13th
Tuesday, April 14th
Wednesday, April 15th
Thursday, April 16th
Friday, April 17th
Saturday, April 18th
but some Easters are changed from the 26th to the 19th by the pyrite rule. Easters changed from the 26th to the 19th are rare, but they are enough to break a tie and make April 19th the most common date for Easter. The second most common date for Easter is the 18th. It's second to the 19th since only some Easters are changed by the pyrite rule from the 25th to the 18th.
Easters between March 28th and April 17th are about equally common, since each of these dates has a full set of seven possible Paschal Full Moons. (They aren't exactly equal since as it turns out, some dates are more likely to fall on Sunday in the Gregorian Calendar than other dates.)
Easters before March 28th or after April 19th are rare, since these extreme Easters have fewer possible Paschal Full Moons. They become decreasingly rare as we approach the extreme dates on either side, March 22nd and April 25th. The rarest Easter of all is March 22nd and not April 25th, since once again, March 21st might be silver, whereas April 18th is always either golden or pyrite.
In the current century, Easter on April 24th occurs twice -- 2011 and 2095. Easter on April 23rd occurs in both 2000 and 2079. Easter on April 22nd occurs in both 2057 and 2068. And this year is the first of four years in this century with an April 21st Easter (2030, 2041, 2052). There are five possible Paschal Full Moons for an April 21st Easter:
Sunday, April 14th
Monday, April 15th
Tuesday, April 16th
Wednesday, April 17th
Thursday, April 18th
The Exceptional Years 1981, 2000, 2019
The three years 1981, 2000, and 2019 are clearly exceptional years when it comes to calculating the date of Easter. We see that 1981 was a year when Easter would have fallen on April 26th had it not been for the pyrite rule. One Metonic Cycle later was 2000, when Easter was also especially late (falling on April 23rd). And one more Metonic Cycle later is this year, when the Gregorian and Aleppo rules produce different dates for Easter.
The reason for all of this is the fact that in all three years, a full moon occurs especially close to the spring equinox. In my discussion of the David Lunar Calendar (December 28th post), I wrote that in the years preceding these three Easters (1980, 1999, 2018), a full moon also occurred around the winter solstice.
Now is a good time to distinguish between "solar months" and "lunar months." A lunar month is simply a lunation -- the time from one moon to the next. On the Chinese Calendar the lunations run from new moon to new moon, whereas for Easter our focus is on full moons.
Now as defined on the Chinese Calendar, a solar month is the time it takes the earth to complete exactly 1/12 of its orbit around the sun. Twelve solar months is exactly one year, whereas twelve lunar months are about 11 days shy of a year. Therefore on average, a lunar month is shorter than a solar month.
But the earth's orbit is elliptical, and so Kepler's Laws tell us that the solar months are shorter when the earth is closer to the sun (perihelion in January) and longer when the earth is farther from the sun (aphelion in July). This explains why the Chinese Calendar rarely has Leap Months after the first or last month of the year. In the winter, the lunar and solar months are about the same length, whereas in summer, the solar months are noticeable longer than the lunar months.
Because of this, the phase of the moon is almost the same at both the winter solstice and the next spring equinox. If there's a full moon at the winter solstice, then the moon at the following spring equinox will also be nearly full. On the other hand, the phase at the following summer solstice will be a waning gibbous moon, at the fall equinox will be a waning half moon (last quarter), and at the winter solstice a year later will be a waning crescent.
All of this tells us that the exceptional winter solstice full moons that I mentioned for the David Lunar Calendar (1980, 1999, 2018) correspond to spring equinox full moons three months later.
We've seen that Aleppo Easter this year is March 24th. But when would Aleppo Easter have fallen in the other two years, 1981 and 2000? Is it possible that Aleppo Easter would have fallen in March in both of those years?
The Webexhibits link from earlier doesn't mention the years 1981 and 2000. After all, Aleppo Easter wasn't even proposed until 1997 and not scheduled to be implemented until 2001. No one is going to build a time machine and go back to 1981 to tell everyone that they were celebrating Easter on the wrong day! This is why links describing the Aleppo Calendar only mention the future. It's only for the interests of creating the David Lunar Calendar where 1980-1981 becomes the Year 0 that we're suddenly interested in full moons from that year.
But here's a link to a webpage created in 1997. The author lists all Aleppo Easters starting from that year and extending to 2205. Thus it includes Aleppo Easter 2000:
http://www.moonwise.co.uk/neweaster.php
According to this link, Gregorian Easter 1998 was on April 12th but Aleppo Easter, had it existed, would have fallen on the 19th instead. It states that while the Paschal Full Moon that year was on April 11th, the full moon in Jerusalem was 45 minutes after midnight on Sunday the 12th, thus forcing Easter to be a week later. But Gregorian and Aleppo Easter do agree in 2000 -- the March full moon that year was definitely before the equinox.
This suggests that the same probably happened in 1981 as well -- the full moon was before the equinox, and so Easter was correctly celebrated in April. What the chart doesn't tell us is whether the full moon fell on Saturday the 18th or Sunday the 19th. If the latter, then Aleppo Easter would have fallen on April 26th -- a date forbidden on the Gregorian Calendar by the pyrite rule.
Looking at the chart at the Moonwise link some more, we see that an April 26th Aleppo Easter is definitely possible. Near the bottom, we see Aleppo Easter on April 26th, 2201. Indeed, the link gives the following line:
The range of dates for the years around now is ... 22 March to 26 April (for a few centuries ahead*) for the astronomical [Aleppo -- dw] definition.
If this chart had extended all the way up to 2877, then March 21st would have appeared. Therefore it appears that the full range of dates for Aleppo Easter is March 21st-April 26th.
Calendar Reform and Easter
Since Aleppo Easter is based on astronomy, no rule-based Calendar Reform will make Easter always fall on the astronomically correct date. But some rules can come close. I've mentioned the Archetypes Calendar, a rule-based calendar that nonetheless seems to match astronomical Chinese New Year:
https://www.hermetic.ch/cal_stud/arch_cal/arch_cal.htm
Still, it's interesting to look at the various proposed calendars to see what Easter looks like on various rule-based calendar.
Of course, this doesn't refer to calendars which seek to fix Easter to a particular date (that is, ignore the moon completely). For example, on the World Calendar, it's sometimes suggested that Easter be fixed to April 8th. (Notice that this is exactly the midpoint of the Gregorian March 22nd-April 25th range as well as the Aleppo March 21st-April 26th range.)
For today's post, our focus is on lunisolar calendars. Not all of these calendars define an Easter, but an Easter is implied if the spring equinox and full moons can be determined from the calendar.
For example, we look at the Meyer-Palmen Solilunar Calendar (named for its two creators):
https://www.hermetic.ch/cal_stud/nlsc/nlsc.htm
On this calendar, the first month, Aristarchus, is supposed to start on the new moon closest to the spring equinox. Thus the full moon of Aristarchus should be the full moon after the equinox. If Aristarchus 1st is a new moon, then the full moon would be around Aristarchus 15th. So we can define the Paschal Full Moon to be Aristarchus 15th, and so Easter is implied to be the following Sunday in the Aristarchus 16th-22nd range. (This calendar doesn't define days of the week, so we can assume that Sundays are the same as on the Gregorian Calendar.)
It may be a complicated, but interesting, exercise to determine "Easter" on this calendar using the definition given above. How often during, say, the current 60-year cycle does "MPSLC Easter" agree with Gregorian or Aleppo Easter?
Suppose we wanted to create a new calendar that agrees with Aleppo Easter as closely as a rule-based calendar possibly can. Well, why don't we start with the following link:
https://calendars.fandom.com/wiki/Easter_Calendar
So apparently, on this calendar, Easter is defined to be New Year's Day. It states that years on this calendar are either 50, 51, 54, or 55 weeks. But other than that, nowhere is it mentioned how to divide the year into months or days. (There is a link on this website, but it's dead.)
So let's try to fill in the calendar ourselves. Let's see -- since 50 and 55 are both multiples of five, we'll divide those years into 10 or 11 months of five weeks each. And since 51 and 54 are both multiples of three, we'll divide those years into 17 or 18 months of three weeks each.
This approach works, but the resulting calendar is terrible. How would you celebrate birthdays on this calendar if there are sometimes 10-11 long months and sometimes 17-18 short months? The same is true for holidays -- in fact, the only holiday that's easy to celebrate is Easter itself!
The number of days in this calendar is always divisible by seven, since it always contains a whole number of weeks. So why don't we try dividing it into seven months instead. Then within a given year, all the months have the same length -- either 50, 51, 54, or 55 days each.
While still awkward, this approach is at least more reasonable than the previous one. The seven months at least correspond roughly to seasons (the first month is always spring, the third month is always around summertime, and the last month is always Lent). Those with birthdays in the first month (from Easter to Pentecost) will celebrate them on the same day of the week every year, while those with birthdays in other months will celebrate on different days of the week (with a maximum of four possible days).
The most logical Easter Calendar is one that is lunisolar, since after all, Easter itself is technically a lunisolar holiday. Since Easter occurs around the full moon, each of the 12-13 months should start around a full moon.
But since the first month always starts on Sunday, every month should begin on Sunday -- indeed, the Sunday after the corresponding full moon (just like Easter itself). The resulting calendar would have 12-13 months of 4-5 weeks each.
Since Easter is so complicated to determine, it may be interesting to create our Easter Calendar based on the simplest Easter rule (the Orthodox one) first. A Gregorian Easter Calendar would be a bigger challenge, where we try to fit in the solar/lunar corrections and the pyrite rules. Only afterward would we attempt to create an Easter Calendar that reproduces the Aleppo definition.
By the way, this Easter Calendar may be the first to require checking the following QNTM box:
(x) the lunar month cannot be evenly divided into seven-day weeks
since it's the only proposed lunisolar calendar that attempts to divide lunar months into weeks.
The Lunisolar Dee Calendar
Another way to create a lunisolar calendar is just to consider the solar and lunar parts separately.
We think back to the Dee Calendar. This is mainly proposed as a solar calendar -- there are eight Leap Days every 33 years. This calendar is supposed to fix the spring equinox to a particular date (March 21st, or March 20th in the Dee-Cecil variant) in one particular time zone -- God's Longitude.
But God's Longitude isn't the meridian of Jerusalem (even though that meridian would appear to be a godly location for Christians). Instead, it's on the East Coast of North America. A different Leap Day rule would have to be adopted (still 8/33 years, but different years from Dee/Dee-Cecil would have the Leap Day) if we wish Jerusalem to be the meridian on which it's based.
That takes care of the solar part. As for the lunar part, there actually was a lunar correction as part of Dee's original proposal. I once found this at the Hermetic link above -- but while the Dee Calendar is still listed there, the calendar correction isn't.
Here's the correction -- we combine the solar and lunar corrections into a single correction where the Paschal Full Moon dates (golden and silver) advance by one day every 231 years (whenever Monday, February 29th is followed five years later by Sunday, February 29th).
It's possible to make this fit the Aleppo Easter given above, if this correction occurs at some point between 2000 and 2019. Then the Paschal Full Moon date would be April 19th, 2000, but then advance and wrap around back to March 21st, 2019, thus making today Easter.
That still doesn't match Aleppo Easter for 1998 -- and we can't just advance the full moons one day in 1998 since we'd have to move them back for 2000. But we don't know which years will have Leap Days in this calendar. It's possible that 1998 might have a Leap Day. Then the Paschal Full Moon can still fall on April 11th, but the Leap Day would change this from Saturday to Sunday, thereby forcing Easter to be a week later on April 18th (Gregorian April 19th).
Once again, no rule-based calendar can capture Aleppo Easter perfectly. It's possible that we'll have to advance the full moons again -- but not exactly 231 years later -- in order to match Aleppo Easter.
Easter on David's Lunar Calendar
I haven't completely decided what my goals for David's Lunar Calendar are, and whether Easter should even appear in my calendar.
On one hand, I want David's Lunar Calendar to describe David -- in other words, me. The main lunisolar holiday that I, David, celebrate is Easter -- Gregorian Easter, not Aleppo Easter. Thus David's Lunar Calendar would be similar to the Easter Calendar (Gregorian) described above, where a particular day on the calendar might correspond to Gregorian Easter. If we wish to improve on the Gregorian rule, then it shouldn't happen until long after I leave this world, since the Easters would no longer correspond to dates actually celebrated by me, David.
If this is my goal, then for one thing, New Year's Day on this calendar should be late in the years 0 (1980-1981), 19 (1999-2000), 38 (2018-2019), and so on. The idea was for the first day of the calendar to be my birthday -- December 7th, 1980. This would require the other years to start in the month leading up to my birthday.
Thus most years would start in November, and Easter would fall in the fifth month (Greenlong). It's impossible to make "Easter" always fall on a Sunday, of course, since my days of my 12-day week have nothing to do with the seven-day week. Once again, the idea is just to define the Paschal Full Moon to be, say Greenlong 15th (which would fall on either Violetday or Violetend) -- one would have to retreat to Gregorian days to find the following Sunday.
On the other hand, I might want David's Lunar Calendar to improve on the Gregorian Calendar, so that Greenlong 15th is always the Aleppo Paschal Full Moon. So if Year 19 (1999-2000) starts on December 7th, Year 38 (2018-2019) would start a full month earlier, around November 7th, in order to make Greenlong 15th fall near last week's full moon. This means that a deviation from the Metonic Cycle must occur between Year 19 and Year 38. The rules I stated on January 6th (the date I first posted David's Lunar Calendar) don't do this.
Actually, making a correction between Year 19 and 38 is awkward (especially when the first correction specified on January 6th was for a 57-year correction). It makes more sense to deviate from the Metonic Cycle at either the beginning or end of a larger cycle.
One thing I first noticed about the Meyer-Palmen Solilunar Calendar (or a generalization thereof, which Karl Palmen calls a "YLM calendar") is that the deviation from the Metonic Cycle occurs right at the start. In fact, this is why Year 0 of his calendar starts on the latest possible date, April 8th. The calendar immediately adjusts so that Year 19 starts about a month earlier.
So in order to capture Aleppo Easter, we can declare Year 0 to be 1999-2000 and start the calendar on my birthday, December 7th. Then Year 19 will start around November 7th, and both the late Aleppo Easter in 2000 and the early Aleppo Easter in 2019 fall during the second full week of Greenlong.
(This also allows me to remove my birth year from the calendar, and instead makes Year 0 line up with Gregorian Year 2000, which is convenient.)
Conclusion
Well, I hope that you learned a lot about Easter in this post, my first of two spring break posts. It allows me to return to one of my favorite topics -- calendars -- just ahead of the main lunisolar holiday that I celebrate, Easter, and gives me a chance to use the calendar that I just invented.
I wish everyone a Happy (Aleppo) Easter today!
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