So precise a measurement of the year, of course, would have been irrelevant to an early farmer, even if the astronomers could have measured it. A shift of five or ten days won't really matter too much, since annual variations in the weather will be greater than that. Once the calendar is out by a month or more, however, problems will arise if the farmer depends upon the calendar. It doesn't necessarily follow, however, that an agricultural society needs to keep its calendar tied, even loosely, to the seasons. Even if we assume that farmers really need someone to tell them when spring is coming, an alternate procedure would be for a specialist, for example a calendar priest, to announce when the proper planting time fell in the calendar.
Lunar cycles were the most common basis for early calendars. These calendars were often not based on any mathematical determination of the synodic month at all, but relied, particularly in their earliest formulations, upon direct observation to determine the new month. So when do you define the month as beginning? The two obvious starting points are the new or the full moon. Since the astronomical new moon occurs appears so close to the sun as to be invisible, this gives us three observational possibilities: the full moon, the first crescent of the ascending moon after the new moon, visible at sunset, or the last crescent of the descending moon, visible just before sunrise. There is a correlation between when the next day is considered to begin and which observational choice is made. For a society that begins the new day at dawn, the first day the waning moon is invisible just before sunrise is a good time to start the new month. If the next day begins at sunset, e.g., the Jewish Sabbath, the first observation of the new moon makes more sense. A full moon observation would seem to imply a midnight start. Such observations can be used in either a lunar or a lunisolar calendar. It will result in months that generally alternate between 29 and 30 days, but because the synodic month is not exactly 29.5 days, the alternation will not be completely regular.
Direct observation does have its drawbacks. Clouds might obscure observation, and in a large civilization, there is a problem with ensuring each location stays in sync with the rest. The historical development of lunar and lunisolar calendars is largely a matter of replacing direct observation by mathematical formulas and tables that allow the prediction of the month's start without the need for observation.
Lunisolar calendars have the additional problem of keeping the lunar months roughly aligned with the solar year. They generally do this by the insertion of a 13th, intercalary month at periodic intervals. Once again, in a calendar's earliest stages, this intercalation was generally accomplished through decree from a central source. In later times, regular rules were developed.
Obviously some of your decisions will be based on just how precise your measurements have been, but even more on the needs of your society (and your patron, who is footing the bill, after all). You will need to account for any preexisting traditions. If your people have been counting seven-day cycles for hundreds of years, resting on the seventh day, they will probably not accept a change to a ten-day cycle, which is what was attempted in revolutionary France. Religious aspects and cultural conservatism aside, neither inconsequential, this change would mean fewer days of rest for people. You also might want to consider your own needs. A complex calendar that is constantly changing with respect to the solar year, for instance, might seem like a bad choice. But if you can get this calendar accepted, you are guaranteed lifetime employment (i.e., tenure). After all, someone has to interpret this thing to tell people when to plant each year, when to celebrate the religious festivals, etc.
Once we've decided on what cycles, we have to decide how to count them. Do we cycle through a small number of names (e.g., our months)? Do we make a fixed numerical count of cycles from some predetermined epoch (e.g., our years)?
Since most calendars have been either solar (based on the tropical year), lunar (based on the synodic month), or lunisolar (a combination of the two), let's look at the problems we face making these cycles mesh.
Assume we take the day as the basic period (we don't have to, but it makes sense, since it's the light/dark rhythms that people base their activities upon). This means we need to fit the year and/or month cycles into some whole number scheme that approximates the observed values. As an approximation, we could round off the tropical year to 365.25 days and the synodic month to 29.5 days. These fractional days we can represent fairly easily, for the year by intercalating (inserting) one day every four years and for the months by making our lunar months alternate between 29 and 30 days.
With these approximations, we are only off the true period of the tropical year by about 1 day every 128.5 years, but with the lunar cycle it takes less than 3 years to slip a day (hence we?ll need to add some leap days here as well). Moreover, whether we use the true values or their approximations, there is no obvious way to get a whole number of lunar cycles into a whole number of solar cycles (in case we want a lunisolar calendar). The nearest rough approximation, and one that seems to have been a common early choice, is 365 days and 12 1/3 lunar cycles (also 365 days if we alternate 29 and 30 day months) per solar cycle.
A much better approximation, and one that we will see cropping up repeatedly, is the Metonic cycle, which observes that 19 tropical years are equal to 235 synodic months. Plugging in the actual lengths year and month to these numbers, we find 19 years = 6939.6018 days 235 months = 6939.68865 days which means this approximation has an error of only about 1 day every 219 years. This error value will change somewhat, of course, when we use the 19:235 ratio in a civil calendar, which contains its own approximations to the year length (see below, particularly the Julian calendar).
These considerations should also make it clear that just because a calendar doesn't match up to the solar or lunar cycles exactly doesn't necessarily imply that astronomers in that culture didn't have a much better idea of what the true values were. In fact, there's direct evidence to the contrary. A calendar must balance accuracy against simplicity, and once a calendar is well established in a society, changing it can be very difficult.
The calendar we know as the Egyptian calendar has no link to the moon at all, although it kept the old hieroglyph. In the Egyptian calendar, there were 12 months of 30 days each. The months each had three "weeks" of 10 days each. Between the end of the 12th month and the beginning of the first month of the next year were five epagomenal (extra) days, resulting in a fixed year of 365 days every year. This calendar, almost a quarter of a day shorter than the tropical year, constantly shifted with respect to the seasons.
For agricultural purposes, the seasons were determined not by the solar equinox or solstice, but by the heliacal rising of the star Sirius (Sothis in Egyptian), which roughly coincided with the flooding of the Nile. Every 1461 Egyptian years (1460 Julian years) the heliacal rising of Sirius came back around to its original position, a time known as the Sothic period. Early interpreters of the Egyptian calendar thought that the Egyptians actually maintained a separate calendar to track Sirius, but in the absence of any evidence, this position has been vigorously disputed by later scholars.
Originally, the months were simply numbered as a month of a season, rather than named. There were three seasons, each of four months. These names suggest that the seasons were originally intended to coincide with the Nile's flooding (and probably did when the calendar was still lunar), but once the calendar took on the form we know they rolled through the seasonal year with the months. From the New Kingdom on, the months are often named.
Years were reckoned by pharaonic reign. For example, one actual Egyptian date appears as "Year 9 under the Majesty of the King of Upper and Lower Egypt Djeserkare. The Feast of the Opening of the Year III Shemu 9. The Going forth of Sothis."
Since Djeserkare is a name for Amenhotep I, we can interpret this as "in year 9 of Amenhotep I, the heliacal rising of Sirius fell in the 3rd month of Shemu, day 9."
This particular date is one of only a handful surviving that record the Sothis rising in terms of the civil year. It's from the so-called Ebers Calendar, and in theory provides a good correlation of the civil calendar to Julina days. Unfortunately, a precise determination of when this fell is impossible. We don't know where the observation was made or what the exact conditions of observation were (which would determine how many degrees above the horizon a star would need to be before being visible to the naked eye. A range of dates, however requires that it be some time in the 2nd half of the 16th century BCE.
In 238 BCE, during the reign of Ptolomy III, the Canopus decree ordered that every four years there should be 6, rather than 5 epagomenal days, in other words, a leap year. Egyptians were very resistant to this change, however, and the attempted reform seems to have failed. An effective implementation of this so-called Alexandrian calendar did not come until Augustus introduced it (25 BCE).
The Egyptian calendar had an importance well beyond its purely Egyptian use. Astronomers used the old Egyptian (not the Alexandrian) calendar throughout antiquity and the Middle Ages because its absolute regularity in the number of days in both the months and the year made calculations much easier. Such regularity was highly desirable, as antiquity had neither arabic numerals nor even the concept of zero to make complex mathematics tractable.
The Babylonian calendar was lunisolar, which means that periodic leap months were required to keep the lunar and solar years in synchronization. The months began at the first visibility of the new crescent at sunset. In later Babylonian times, the new moon was determined not by direct observation but by a complex mathematical rule, which in fact yielded a very close result.
The intercalary month was inserted either after Ululu or Addaru, and it was simply called Second Ululu, or Second Addaru. There is some evidence that by the reign of Nabonassar (747 BCE) Babylonian astronomers had discovered the Metonic 19-year cycle, but until the 4th century BCE, there is no evidence that a 19-year cycle was used to assign fixed intercalary years within the cycle. In its fully developed form, years 3, 6, 8, 11, 14, and 19 had a second Addaru, and year 17 had a second Ululu.
For earlier Babylonian history, years are reckoned by the regnal year of the ruler. After Seleucus I conquered Babylon, scribes began to record dates in the Selucid Era (SE), a continuous count of years that did not stop with the death of Seluceus. Year 1 SE corresponds to 312/11 BCE, a correspondence that can be confirmed by records of astronomical observations dated in this era.
After the Parthians conquered Mesopotamia, the western part of the Selucid empire switched the beginning of its year from spring (Nisanu) to fall (Tashritu), under Greek influence. The Parthians kept Nisanu as the beginning of the year.
The seven-day cycle makes its earliest appearance in Babylonian documents of the 7th century BCE. It is not quite yet the week as we know it, however. In origin, it seems to have been one fourth of the approximate time in a month the moon was visible. In short, it does not include the days around the new moon, and is not therefore a continuous cycle. To picture what this "week" was like, imagine one of our months with four regular weeks, and then a few epagomenal days at the end of the month, which do not belong to any week.
Despite this obvious Babylonian influence, Jews did not adopt the regular 19-year cycle for inserting intercalary months, nor did they use Babylonian mathematical calculation of new moon. The decision to insert an extra month was made by the Sanhedrin in Jerusalem on rather vague criteria such as the appearance of new plants. Because they measured neither the equinox nor helical risings, the old Hebrew calendar cannot be reconstructed by mathematical formula.
Another difference between the Hebrew and the Babylonian calendar is the treatment of the 7-day cycle. Recall that the Babylonians had a 7-day cycle, but the days around the new moon when it was invisible were not included. In the Jewish scheme, the 7-day interval between Sabbaths runs independently of the months and years. There are no epagomenal days. The days are numbered 1 to 7. Only the Sabbath, the seventh day, is named, although day 6 is sometimes called ereb shabbat, "the day preceding the Sabbath."
In the 2nd and 3rd centuries CE, the Jewish calendar was reformed. The primary purpose of this reform was to regularize the intercalation of months and the length of the months. Using the Metonic cycle of 19 solar years, months are intercalated in years 3, 6, 8, 11, 14, 17, and 19 of the cycle, exactly the same spacing as in the Babylonian cycle. In a regular year, the months alternate between 30 and 29 days (Tishri has 30, Marheshvan 29, etc.). The embolismic month has 30 days, and intercalated between Adar and Nissan (never after Elul). It is called Second Adar, or Weadar. Nissan still has 30 days.
Certain customs about the days of the week upon which the High Holy Days may be celebrated require adding a day to certain years and then subtracting a day from the following year. The shorter years are called "defective", and Kislev is decreased to 29 days. The longer years are called "perfect," and increase Marshevan to 30 days. Those interested in the precise formulation of these rules should consult the references.
The epoch that Hebrew calendar currently uses, the Hillel world era, begins October 7, 3761 BCE. This epoch was calculated by Hillel II in the 4th century CE, but did not become universal practice until the end of the Middle Ages. Other epochs used before then were the so-called era of Adam (3760 BCE), and the Selucid (312 BCE).
The Athenian calendar is the best known and most intensively studied, and I shall therefore use it as a model. The Athenian months were named Hekatombion, Metageitnion, Boedromion, Pyanepsion, Maimakterion, Poseidon, Gamelion, Anthesterion, Elaphebolion, Munychion, Thargelion, and Skirophorion. (For a list of the known month names in other Greek areas, see Ginzel, vol. 2, pp. 335-6). The intercalary month usually came after Poseidon, and was called second Poseidon. Hekatombion, and hence the beginning of the year, fell in the summer. Other Greek regions started their year at different times (e.g., Sparta, Macedonia in fall, Delos in winter).
For the historian inclined towards tidy orderliness, the regrettable fact is that the Athenians were simply unwilling to stick to a completely regular calendar, which makes reconstruction difficult. Their irregularity was not from lack of astronomical knowledge. In 432 BCE, the Athenian astronomer Meton instituted his 19-year cycle, fixing regular intercalations (whether Meton got this cycle from Babylonia or discovered it himself is not known). From that point, a small group of Greek astronomers used the Metonic cycle in their calculations, but this should be regarded as an astronomer's ideal calendar. Abundant epigraphical evidence demonstrates that in the civil calendar, while the archons inserted approximately the correct number of intercalary months over the long term, the specific corrections were somewhat arbitrary, as the archons saw fit. This irregularity doesn't really affect the long-term workings of the calendar, but it does make things very confusing when trying to establish a precise date for an event.
The Athenians seem to have taken a rather casual attitude towards their calendar. It appears they used neither a regular formula nor continuous direct observation to determine the length of the months. Most likely, they followed a general rule of alternating months (29 and 30 days long), subject to periodic correction by observation.
In addition to this calendar, which has been called the festival calendar, Athenians maintained a second calendar for the political year. This "conciliar" year divided the year into "prytanies," one for each of the "phylai," the subdivisions of Athenian citizens. The number of phylai, and hence the number of prytanies, varies over time. Until 307 BCE, there were 10 phylai.
After that the number varies between 11 and 13 (usually 12). Even more confusing, while the conciliar and festival years were basically the same length in the 4th century BCE, such was not regularly the case earlier or later. Thus documents dated by prytany are frequently very difficult to assign to a particular equivalent in the Julian calendar, although we are usually secure in assigning an approximate date. Since the prytany will play no role in my argument for establishing a basic chronology, I will not go into the intricacies here. The references cited below, however, go into the problem in mind-numbing detail.
Ordinary records of Greek city-states were dated according to the eponymous year of the person in power, be that the archon, king, priest of Hera, etc. For Athens, our list of archons from the 4th c. BCE to the later 1st c. CE is complete for all but a few years, which is a great help in verifying our chronology. Regional eponymous years, however, are awkward for historians trying to correlate the various areas, a problem no less evident to the ancient Greek historians than it is to us. The solution that seemed obvious to them was to reckon time by the intervals between Olympiads, in addition to giving eponymous years.
That the Olympics were held every four years is well known, but some evidence for that assertion is not out of place. Ancient writers all refer to the Olympics as a 5-year period (in Greek, pentaeterikoi, Latin quinquennales). This might seem strange, but Greeks and Romans most commonly counted inclusively; that is to say:
1 2 3 4 5 Olympiad . . . Olympiad
which we would call a four-year interval. NB: our way of counting implies a zero start, a concept both Greeks and Romans lacked. Since the Greek calendars all differed slightly, you might wonder how everyone managed to get to the games on time. The Pindar scholiast claims that for the early Olympiads, the festival was held alternately after 49 or 50 months, which is essentially equivalent to four years in a lunisolar calendar. This scheme makes perfect sense, because no matter what specific intercalary months the various cities did or did not decide to include, they could all simply count forward to 49 or 50. It also implies, by the way, that a rule of 8 years = 99 months was being used to determine this interval (although not that every Greek city used this formula for their own intercalations).
Since the Olympiad was a summer festival, it was eventually correlated to the Attic (Athenian) calendar, so as to begin on Hekatombion 1, which might imply a certain agreement about when intercalations should be added, or simply indicate Athenian cultural dominance.
Ancient historians date by Olympiad by giving both the number of the Olympiad and the year within the cycle, 1-4 (the Olympiad itself was held on year 1). Additionally, lists of Olympic winners were maintained, and the 3rd c. BCE writer Timaios compiled a synchronic list comparing Olympic winners, Athenian archons, Spartan kings, and the priests of Hera from Argos.
Olympiad 1,1 correlates to 776 BCE. We do not actually need to believe an actual festival was held on this date, but when Greek historians are writing in later times, they date their own events using this as the epoch. We can establish a precise correlation to the common era from a variety of different sources, but the most definitive comes from a passage in Diodorus, where he dates the year of a total solar eclipse to the reign of the Athenian archon Hieromnemon, which he also gives as Ol. 117,3. The only astronomically possible date for this event is August 15, 310 BCE, which fixes our epoch.
One thing to be wary of with reckoning by Olympiad is that writers calculated the start of the year by their local convention (spring, summer, winter, or fall). For example Ol. 1,1 correspond to Fall, 777 - Fall 776 BCE by Macedonian reckoning. Byzantine writers who use Olympiads take the year to begin on September 1.
Most of the other eras used by Greek writers are of little importance. One worth mentioning, however, is the Trojan Era (from the destruction of Troy), which is found in a number of historians' works. This date, of course, is purely conventional, and can be seen as analogous to the various world eras (e.g., Hillel's above). A wide variety of starting points are found, but the one with the widest currency, developed by Eratosthenes, set it 407 years before the first Olympiad (1183 BCE).
There were 12 months in an ordinary year, but many of the months were shorter than they are now (see the Julian reform). Their Latin names will largely look familiar. A regular year thus had 355 days. The lengths of the months indicate that by the time of our earliest records the year was not measured by direct observation, as no month so measured could have 31 days, but by conventional rule.
The number-names of the last six months indicate not, as is sometimes said, that there were originally 10 months (a number that if true would yield a nonsensical year length), but that the year originally began in March. There is a fair amount of confusion in different accounts of the Roman calendar about the beginning of the year. Sometimes it will be said that the year began on March 1 until Julius Caesar reformed the calendar. This theory was disproved by the excavation of an actual republican calendar in the 1920s, which clearly shows the year started in January. It is also sometimes said that the beginning of the year changed in 153 BCE, but in fact what happened this year was that the time when consuls took office was synchronized with the calendar year. January seems to have become the beginning of the year when the republican calendar was introduced, but there is so little information about that reform (taking place, it appears, in the 5th-century BCE) that we can say little more.
To keep the calendar roughly in line with the seasons, a leap month (it had no name other than "the intercalary month") was inserted at the end of February. This position, which falls more or less at the end of the year when the year began in March, implies that the intercalary month predates the change in observation of the new year. The decision to insert the intercalary month was made by the pontifexes. In theory the intercalation was roughly every other year. In practice, pontifexes seem to have been rather lackadaisical in carrying out their offices, and the calendar was sometimes allowed to get drastically out of synchronization with the seasons. Roman intercalation was peculiar. February was reduced to either 23 or 24 (it varied from year to year), and a 28-day month was added afterwards. This peculiar habit was a result of the ways that days of the month were counted in the Roman system.
There were two important festivals, Refugium and Equirria, which fell at the end of February and which could not be separated from the beginning of March. They are transferred to the intercalary month, but notice with the Roman method of counting backwards, they keep their day numbering constant whether it's a regular or intercalary year. Note that our general conversion rule applies for intercalary years as well. If February has 23 days, February 15 = a. d. x Kal. intercal. (xi if Feb. has 24).
The Roman calendar also had a recurring cycle of 8-days, similar to our week, called the nundinae = nine-days (once again, we have that habit of inclusive counting). This "week" was not religious in significance, but originally indicated days upon which a market would be held in Rome. Extant Roman calendars indicate this interval by giving each consecutive day a letter A through H. Note that this was simply a mnemonic marker. They did not call them "day A," etc. The 7-day week and its names were not introduced into Roman civil life until the imperial period.
While dating by Olympiad was occasionally used, Roman writers most often reckoned years by the eponymous names of the consuls in office that year. This habit persisted through the imperial period as well, even though (excepting those occasions when the emperor was also consul), consular power was much reduced. An unbroken list of consuls from the founding of the republic (conventionally, 509 BCE) through the late empire survives. Some have questioned whether all the earliest names in this are historical, but the later ones certainly are, and provide many opportunities for correlation to the Common Era.
The so-called Varronic Era, named for the late Republican antiquarian Marcus Terentius Varro, was only rarely used during the Republic, but became more popular under the emperors. In it, years were dated from the founding of Rome, or AUC (ab urbe condita), which was correlated to the Greek reckoning by saying that it fell in Olympiad 6,3 (olympiadis sextae anno tertio), i.e., 753 BCE. Like most eras calculated from a foundational date in the distant past, the Varronic Era should be seen as purely conventional. That is, even if Rome wasn't founded in 753 BCE, dating in this system can still work just fine, as long as it remains consistent.
Here's a general rule to convert to Roman day reckoning: first, find the nearest fixed point (Ides, Nones or Kalends) that comes on or after your day. If it falls on one of these days, you're done. Otherwise, take the day number on which that fixed point falls and add one. Since the Kalends is the first of the next month, treat it as the n+1 day of the month (where n is the total number of days in the month). Example: for March, before Nones use 8; Ides, use 16; Kalends use 33. Then subtract the day in question, and you have your backward count. For example, November 11 = a. d. iii Ides Nov.; May 6 = a.d. pridie Non. Mai.
To convert from Roman reckoning, take the same number from the Ides, Nones of Kalends and subtract the Roman day number. For example, a.d. x Kal. Sext. = 21 Sextilis.
In 709 AUC (45 BCE), the real Julian calendar begins. Not only did Caesar decree the leap year rule, but he lengthened several months by putting 10 more days into the regular year. The new leap day was inserted exactly where the old leap month was, i.e., after the 24th of February. Both the 24th and the leap day were counted as vi Mar., the second was called bis vi or the bisextile.
In adding the new days to the calendar, Caesar tried to disturb the separation between festivals as little as possible (relative to the Kalends system of dating), and the new days were actually added just before the last day of each month that was extended, except for April, where it was inserted between the 6th and 5th Kalends. The month of July (Julius, from earlier Quinctilis) got its name in 44 BCE by decree of the senate. Notice that while our general rule for converting days of the month still applies, the Kalends numbering in the lengthened months is different in the Julian and Republican calendars. E.g., December 25 = vi kal Jan. in the Republican, but viii kal. Jan. in the Julian.
Because the pre-Julian Roman calendar was not regular, the custom of historians is to use the Julian calendar proleptically for earlier dates. That is, dates before 45 BCE, which are naturally recorded in different calendars, are translated into the Julian calendar. This convention explains one seeming paradox: the first year of the Julian calendar should have been a leap year in the new sense, but one was not celebrated that year. Thus the Kalends of January that year actually fell on January 2, 45 BCE.
After Caesar's death, his new rules were faithfully followed. Unfortunately, the new pontifices do not seem to have understood his rules quite as they were intended. Caesar specified a leap year at four-year intervals, and since Romans typically counted inclusively (see the remarks on Olympiads), they took this to mean every three years. So leap years were observed in 42 (712 AUC), 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, and 9 BCE. At this point, someone must have brought the problem to Augustus Caesar's attention, because he decreed that there should be no leap year at all for the next 12 years, and carefully rephrased the rule to say "intercalate at five year intervals," so dense Romans would get their counting right. The first correctly observed leap year was in AD 8. Augustus also took the opportunity to rename the month Sextilis after himself at the same time, which is how we wound up with August, but there is no evidence to support the story that he lengthened that month so that it would not be inferior to Julius's month. In fact, as indicated above, the month lengths were all changed by Julius Caesar.
For those interested, the rough formula is Y = 1/(MCY - 365.2422), where MCY is the mean civil year length in days. To even more precise, we could take into account the gradually decreasing length of the tropical year. That requires we consider the calendar over a specific span of years and replace the approximate value for the tropical year with: 365.24231533 - (y1 + y2) * 3.06713e-8, where y1 is the start year and y2 the stop year in astronomical years (= Common Era, but for BCE dates, use negative number and add one, e.g., 1 BC = 0, 2 BC = -1, etc.). This kind of precision will be irrelevant unless we have precise astronomical observations in the relevant years against which to compare it. Otherwise, rounding the number to the nearest 10th gives a good value for comparison.
A similar value, M, could be generated to show the number of months it takes for a lunar calendar to slip 1 day, assuming the calendar works by rule rather than direct observation.
In the Egyptian calendar, Y = 4.1; clearly, no one who used this calendar was seriously concerned to keep it aligned with the seasonal year. Using the approximate formula, Y for the Julian calendar is 128.2; the precise formula, considered over the span -44 to 1582, gives 129.3.
These numbers should suggest why the Julian calendar remained unreformed for so long. Within any one person's lifespan, only an astronomer would notice the difference. Even if a culture keeps records over a long period of time, the change is not all that great: less than 8 days in a millennium. While an extremely long period of time (about 27,700 years) might change "the darling buds of May" into the darling buds of December (in the northern hemisphere, of course), it hardly seems like a pressing problem.
The fact is, however, that from the beginning of the 13th century, there was a constant call among leading intellectuals (most notably Roger Bacon in 1267) for a modification to correct this drift. The press of other urgent matters and general inertia delayed matters until the late 16th century, but eventually a change was made. To understand why, we first need to look at the calculation of Easter.
I won't go into the doctrinal disputes to which these ambiguities gave rise. The interested reader should consult the "Easter" entry in a good encyclopedia of theology (e.g., the Dictionnaire de Théologie Catholique). The generally favored solution was that Easter should always be on a Sunday, and that there should be some rule for determining a time fairly close to Passover. Just what this rule should be took a long time to hammer out. Relying upon the Jewish definition of Passover was uncongenial to many Christians, and as the Jewish calendar was not yet fixed by rule there was also the practical problem of waiting for the determination of the Sanhedrin in Jerusalem for a date which then had to be transmitted to widely separated churches throughout the Roman empire. To calculate Easter, then, Christians needed to find a lunar month in spring, which required both a definition exactly when spring began and a method of computing lunar months (i.e., a lunar calendar) that could be converted into the Julian calendar.
The rule eventually agreed upon was that Easter should be celebrated on the Sunday after the 14th day of the "Paschal" month. That Paschal, or Easter, month (essentially a Christian version of Nisan) is the one where the 14th day is on or next after the vernal equinox.
Even after this definition was generally accepted, there were still problems. When, exactly is the vernal equinox, and what sort of lunar calendar does one keep to track the Paschal month?
The Romans took the vernal equinox to be on March 25, a traditional date, to which they clung stubbornly for many years. Many of the eastern churches, however, took March 21 as the equinox. This measurement was fixed by direct observation of astronomers in Alexandria in the early third century. During that time, Alexandria was famous as a center of astronomic knowledge, and it was a natural place to go for expert consultation.
The lunar calendar used to track the new moons was also a subject of debate. The earliest surviving Easter tables show that the approximation 8 years = 99 months was used. This approximation results in an error of 1 day every 5.2 years. Clearly, for any long-term calculation of the moon, this rule will very quickly accumulate significant errors. In the early third century, a Roman named Augustalis introduced a new approximation: 84 years = 1039 months. This equation leads to an error of 1 day every 64.6 years—a significant improvement. Meanwhile the eastern churches, undoubtedly advised by Alexandrian astronomers, had found an even more accurate cycle: the familiar Metonic equation of 19 years = 235 months. This approximation has an error of only 1 day in 316.6 years.
Rome did not actually abandon the 84-year cycle or March 25th equinox (which, of course, led to periodic differences in date between the Alexandrian and Roman churches), but often Rome seems to have accepted Alexandrian calculations. Not always, however. From time to time, the Roman church expressed its unhappiness with dates that it considered unsatisfactory. Ironically, every time the Romans consulted experts, they were essentially told that their way was inaccurate, and that they should adopt the Alexandrian computation.
|B||M iiii||ii||xxvi||vi||xiii||v i
|M v||iii||vii||vii||xv||iiii k
|END||M vi||iiii||xviii||i||xvi||xv k
|ANNI DNI||INDICT||EPACTE||CCVRR||CICLLVN||XIIIIma LVNA||DIES DOM POST||LVNA IPSIUS|
|M vii||v||Nvlla||ii||xvii||Non apr
|B||M viii||vi||xi||iiii||xviii||viii k
|M x||viii||iii||vi||i||iiii non apr
|M xi||viiii||xiiii||vii||ii||xi k
|B||M xii||x||xxv||ii||iii||iiii i
|M xiii||xi||vi||iii||iiii||iii k
|OGD||M xiiii||xii||xvii||iiii||v||xiiii k
So, what does it all mean? Let's start with the column headings, which in this case actually come in the middle of the table. Expanding the abbreviations, the headings mean: anni domini (years of the lord); indictiones (indictions); epactæ (epacts); concurrentes; cicli lunae (lunar cycles), 14ma Luna (the 14th moon); dies dominica post (the Sunday afterwards); luna ipsius (this moon).
The indiction we have already seen. It plays no direct role in the calculation of Easter, but note that the cycle remains consistent with that given by Dionysius. The epacts indicate the age of the moon (i.e. days into the lunar month) on March 22, the earliest possible date of Easter Sunday. The concurrentes give the day of the week (the so-called ferial numbers) of March 24th. The lunar cycles track the Metonic, 19-year cycle. Later in the Middle Ages, this cycle will be determined by the numerus aureus, the golden number, so called because it is the key to figuring out the date of Easter. Note, however, that this lunar cycle, while it has the same practical effect as the golden number, is not exactly the same. For example, 1010, which has a golden number 4, is listed as the first year of the lunar cycle. The 14th moon is the 14th day of the lunar month, i.e., the full moon. The Sunday afterwards is Easter. The "moon itself" is the age of the moon, i.e., the day of the lunar month, on Easter.
Apart from the numbers and dates, the other abbreviations in the margin are B, for bisextilis, i.e. a leap-year; END for endecadas and OGD for ogdoadas mark the subdivisions of the Metonic cycle. The first is a period of 11 years, the second of 8. They coordinate the insertion of lunar leap.
|Year||Indct||Epct||3/24||Gldn#||Full Moon||Easter||Moon on Easter|
|L||1004||2||26||6||14||April 9||March 17||21|
|1005||3||7||7||15||March 29||April 1||17|
|1006||4||18||1||16||April 17||April 21||18|
|1007||5||0||2||17||April 5||April 6||15|
|L||1008||6||11||4||18||March 25||March 28||17|
|1009||7||22||5||19||April 13||April 17||18|
|1010||8||3||6||1||April 2||April 9||21|
|1011||9||14||7||2||March 22||March 25||17|
|L||1012||10||25||2||3||April 10||April 13||17|
|1013||11||6||3||4||March 29||April 5||20|
|1014||12||17||4||5||April 18||April 25||21|
If you check these years (for example with the ChurchCalendar applet) you will find only one (March 17) is wrong. This one is an obvious scribal blunder. Easter must come after the full moon. The scribe wrote 16 Kalends of April when he should have written 16 Kalends of May, which is April 16, the correct date. Further, if you calculate the week day of the 24th, you will find that all of them match up correctly (1 = Sunday, etc.).
From a seasonal point of view, a the difference between the Gregorian and the Julian calendar wasn't yet really all that pressing a matter, only 10 days in 1582, only 14 days in the twentieth century. The logical question thus becomes, why did it matter? The short answer is religion, which is, in most cultures, very concerned with keeping time. For Christianity, the fundamental chronological problem was the calculation of Easter, and this difficulty drove the reform. Recall that Easter is supposed to be the first full moon after the spring equinox. But as Easter was calculated by rule, not astronomical observation, the slip of the equinox meant that the rule was badly in error. The Gregorian calendar was designed to restore the spring equinox to the March 21 date that had been traditional since the Council of Nicaea (see Alexandrian Easter).
Most countries adopted the Gregorian calendar in a single, one-time correction. Catholic countries quickly adopted the reform when Pope Gregory proclaimed it. Many of the major countries (Italy, Spain, Portugal, Poland), skipped from Thursday, October 4, 1582 to Friday, October 15, 1582, which we now take, for simplicity's sake, to be the canonical point of switch. Notice that the day-of-the-week cycle is not altered in the switch (October 15, 1582 would have been a Monday in the Julian calendar). The reformers wanted to preserve the seven-day cycle unaltered, as they believed it was biblically ordained. The other Catholic countries quickly followed suit. Some, like France, by the end of 1582, others, like the Catholic parts of Switzerland (and, interestingly, the Spanish colonies in America—probably the result of delays in communication—waited until 1584. For some odd reason, the Spanish Netherlands switched over at the very end of 1582 (from December 21 to January 1), which means they skipped Christmas that year. (The October time was originally picked to omit as few feasts as possible from the church calendar, and Christmas seems a doozy of a feast to skip.)
In an age of intense religious passion, the simple fact that the Pope instituted the reform was enough to make Protestant countries reject the change. The greater part of protestant Germany did not switch to the Gregorian calendar until 1700, the Protestant Cantons of Switzerland and Protestant Netherlands until 1701.
The Swedish dithered. In 1700 they began what was intended to be a gradual switch to the Gregorian calendar. They planned to stop observing leap years until their calendar was in line with the Gregorian one. They did omit the leap year in 1700, but observed the leap year in 1704 and 1708 (apparently they forgot the plan). Thus they were 10 days out of step with the Gregorian calendar and 1 day off from the Julian. Then, in 1712, they changed their minds, and went back to the Julian system by adding two leap days to February. Somewhere in Sweden, there are probably some unique baptismal records of people whose birthday was on a date never to be seen again: February 30. Lithuania and Lativia, which were under Polish rule at the time of the reform (and hence changed in 1582), actually reverted to the Julian calendar, so strong were the feelings. They did not change back again until the 20th century.
Although Queen Elizabeth I initially expressed some interest in changing the calendar in 1582, the Church of England effectively tabled the idea, which was not taken up again for nearly 170 years. By that time, passions had sufficiently cooled that when the idea was introduced as an act of Parliament in 1752, it passed with hardly a murmur. The English colonies in America changed at the same time. By that time, 11 days now had to be added, which the English did by skipping from September 2 to September 14, 1752.
In some areas of Europe, there were riots when authorities tried to introduce the Gregorian calendar (in the 16th century), but the notion that there was popular discontent in England over the shift seems to rest entirely upon a William Hogarth print, which shows a mass demonstration through a window, with the protesters holding up the famous banner saying "give us back our 11 days." Contemporary newspapers and other records, however, give no such indication, although there are some surviving sermons that indicate the authorities took pains to explain the situation carefully so that there should be no misunderstanding. The entire idea probably rests on Hogarth's rather jaundiced view of lower-class ignorance, rather than historical reality.
In 1753, Sweden finally caved in, following Great Britain's lead.
The last Christian countries to accept the Gregorian calendar were the Orthodox ones. Many (those under Russian domination), did not do so until the Bolsheviks decreed the change in 1918 (the October revolution actually took place in November, according to the Gregorian calendar), although there was a history of failed attempts at reform in the 19th century. The Greeks didn't switch over until 1923.
Many Protestant countries (but not England), eventually reformed their civil calendars, but switched to a different method of calculating Easter. The so-called "improved" calendar used astronomical tables to find the Easter full moon, and, while it generally matched the Gregorian tables, differed in a few years. Most countries had given up the improved calendar for the Gregorian easter by the end of the eighteenth century.
Orthodox churches also refused to accept the Gregorian method for Easter. They, however, continue to calculate Easter in the Julian calendar. Some orthodox churches never adopted the Gregorian calendar at all, and so also use the Julian calendar for fixed holidays like Christmas.
The political map has changed enormously since the 16th century. Areas are listed more or less under their current affiliations, but some regions, e.g. Silesia, have been divided up since the conversion, and in these instances I've been arbitrary (Silesia is listed under Poland). This table lists only dates for those countries already using the Julian calendar before adopting the Gregorian one. Countries like Japan and China are therefore not shown. I have also not given separate entries for all the countries that formed out of the Spanish colonial empire. See under Spain for them.
|Country/Region||Last Julian||First Gregorian|
|Czech Republic (Bohemia, Moravia)||1584.1.6||1584.1.17|
|Finland (see note on Sweden)||1753.2.17||1753.3.1|
|Germany, Catholic Regions|
|Cologne (archdiocese, incl. Aachen)||1583.11.3||1583.11.14|
|Münster (city and archdiocese)||1583.11.16||1583.11.27|
|Strasbourg (diocese only)||1583.11.16||1583.11.27|
|Germany, Protestant Regions|
|Holy Roman Empire, Imperial Court
(see also Germany, Austria, Hungary, Czech Republic)
|Holland, North Brabant||1582.12.21||1583.1.1|
|Sweden (final conversion -- see note)||1753.2.17||1753.3.1|
|Lucern, Uri, Schwyz, Zug, Freiburg, Solothurn||1584.1.11||1584.1.22|
|Zürich, Bern, Basel, Schaffhouse, Geneva, Thurgovia||1700.12.31||1701.1.12|
|Appenzell, Glarus, St. Gallen||1724||1724|
This applet works from a database of about 450 feast days, and will place them on the appropriate day and month depending on the year/region you select. In particular, it contains information about all the Vatican II revisions to the calendar, so for earlier dates, you will see the saints as they were celebrated traditionally. The default settings will automatically exclude saints that weren't celebrated in a particular year (e.g., because they hadn't been born yet).
If you need additional help using the applet, you can read the instructions. Before you send me any comments, you might also want to read the implementation notes.
To navigate in the calendar, you can click on the buttons beneath the grid display, which will scroll one unit at a time. Alternately, you can select the month by pulling down the choice box, or the year by clicking on the year box and editing it to the desired year (you need to hit the "enter" key for the year to change in the calendar grid). The calendar will correctly display BCE dates, but because of the year filtering, no holidays will appear in the list box.
In general, saints who died before there was a formal process of canonization appear on the calendar sometime shortly after their deaths. For the earliest saints these dates are arbitrary and should not be regarded as indicating the historically attested appearance of a cult at this point in time. Later saints are added to the calendar at their date of canonization.
The default locale when the applet starts is "Western." This locale gives the traditional dates for many saints whose celebrations were moved or suppressed by the Roman Catholic church in the revisions of 1969. It is, in other words, a kind of convenient fiction that lets you see the old style of observance in a modern calendar.
Locales are organized in a hierarchy. As of the latest revision, the hierarchy was organized as shown in the list above. The feast filter enforces an inheritance rule: feasts defined in a parent locale are inherited by the child locale unless the child overrides that feast with different behavior. The "English" locale, for example, will show feasts common to the Anglican Rite churches (at the moment, I've only entered data for the Church of England and the Episcopal Church), or if you set the date before 1549, the date of Cranmer's prayer book, the medieval English church.
If you are in the "Roman Catholic" locale and set the date before 1970, you will notice that the saints move to their traditional days. The Anglican churches make comparable revisions beginning with the year 1980.
In the "Options" panel you can set how the calendar and feast days are to be displayed. If you want, you can select a different Gregorian conversion date from the standard one (October 15, 1582). I've pre-set a few conversion dates that I consider interesting or important, but you can also pick your own conversion date. If you want to see more detail about the conversion, I've prepared a fairly detailed table.
The "Filters" panel allows you to display only those categories of feasts you want to see. A feast can have multiple categories (e.g., virgin, martyr). Most types should be self-explanatory. The less obvious types are explained in the list below.
If you're seeing only a gray box instead of the applet, it's still loading. The program code is about 62k, and the database is another 20k. Thus depending on the state of the connection between your server and mine, it can take some time to download everything, or the load might be interrupted. If the load seems to be stalled, you might try reloading the page.
The feast-day data is downloaded after the applet starts. This can take some time, so the process runs in a separate thread while the graphics are initialized. If the internet connection is very slow, the applet will give up on trying to read the feast data after a certain amount of time (about a minute) and just run the basic application.
Most moveable feasts are based on Easter. The Easter algorithm I use is an implementation of the formula devised by Zeller, which correctly generates Easter dates both before and after the Gregorian shift. After the Gregorian shift, Easter differs depending upon the locale you select. The "Eastern" locale uses the Orthodox method, which calculates Easter in the Julian calendar (as if the shift had never occurred). All other locales use the Western method, which not only takes the vernal equinox based on the Gregorian calendar, but also makes an adjustment to the lunar calendar used to determine the date of the full moon.
Stay tuned for additional locales that use different rules for Easter. For example, in the years after the original Gregorian shift, several Protestant countries used something known as the "improved" calendar, which sometimes had conflicting dates for Easter, and if I can come up with a formula to generate Victorine Easters (the method used by the Irish that Bede complains about in his History of the Englich Church), that too.
Note that while the calendar will calculate Easter for any date after 33 CE (the conventional date of Christ's death), for the early centuries of the Church, particularly before the Council of Nicaea (325 CE), this date is merely a convenient fiction. Even after Nicaea it took a long time for all churches to conform to the Alexandrian method of Easter calculation.
The database can also specify feasts that fall on a weekday n weeks before or after a fixed date (e.g., Advent = 4th Sunday before December 25), or the nth weekday of a month (e.g., Thanksgiving in the Episcopal calendar). As of
Version 2.0, the program can also find a weekday between two other dates, including two moveable dates, if necessary. Thus I can now support quite complicated rules, but currently I only have one of this type implemented: in the Roman Catholic locale, the rule for the Holy Name of Jesus is "the Sunday between the octave of the nativity (i.e., Jan 1) and Epiphany (Jan. 6), or if that is lacking, the 2nd of January."
I have implemented a moderately lengthy list of feast days (mostly saints' days, but also including other commemorative days like the Invention of the Cross), but it could be much longer still. Fixed feasts appear on the same day and month every year, with one minor exception (see Not a Bug below).
I am, by training, a medievalist, so the feasts I list tend towards those that were celebrated in the Middle Ages. My initial list of feast days was taken from the Golden Legend, cross-referenced with the Oxford Dictionary of the Saints. With only a few exceptions, any saint that appears in both works is included, and I have also included a number of other saints (mostly of later date than the Golden Legend) that I felt were important.
Anyone who has ever tried to trace the veneration of saints in any detail knows that practices change over time and from region to region. The program filters feasts for year and locale, so for example you will not see Thomas Becket before the year his canonization (1173) or (in the Roman Catholic locale) Margaret of Antioch after her cult was suppressed by the Vatican (1969). These date filters also let me implement saints whose feasts change days at various points in time, but my implementation of these changes is not thorough. In general, if the Oxford Dictionary gives a clear date of the switch, I have implemented it, but not all of their entries are equally detailed. When the dictionary merely notes that a saint was formerly observed on another date, I have generally made the assumption that the change was in the 1969 revisions to the calendar. But a glance at the 1962 calendar will show that some of these saints actually moved earlier, as they are already found on their present dates in that calendar. I have yet to make an effort to track down the actual dates of these changes. More precise information would be welcome.
Most of the historical data about the Anglican rite churches I've taken from Hatchett.
The starting date of many of the early saints is somewhat vague, and I have balanced several different criteria. For later saints, I've gone with the date of formal canonization. For earlier saints I've used either the date of their death (or a little later when unknown), or when I had the information available, the first known appearance of their cult.
In version 1.1 I implemented locales, to account for the fact that the same feast is often celebrated on different days in different regions. Locales are hierarchical, and each child locale inherits the feasts of its parents. Switching between Eastern and Western locales will change the method of calculating Easter (after the Gregorian change in 1582—they are the same before that).
My first additional locale was the Sarum (Salisbury) calendar, a widespread Use in medieval England. In the latest version I've added all the feasts in the Episcopal (American) Book of Common Prayer (1979 version). Note that the Episcopal church observes days of comemoration for people who are not saints (indeed, they don't have saints in the Roman Catholic sense). Merely because I have set up a locale, you should by no means consider that I have systematically consulted all the relevant calendars. Also, because the earlier versions of this program did not use locales, there are still feasts that show up in all locales that really should be limited to narrower regions. The
Eastern locale is particularly scanty at the moment, but it's next on my list of locales to add. If anyone would care to send me a systematic list of feasts in any particular use I would be extremely grateful.
In many Eastern Orthodox churches, fixed feasts are still celebrated on their dates in the Julian (Old Style) calendar. As of version 1.3, the program can handle both Old Style and New Style dating. If you select the "Orthodox Old-Style" checkbox in the Options panel, feast days will be translated from their Julian dates before being displayed in the Gregorian calendar.
New to version 2.0, I now allow filtering of feasts by what kind of person or thing the day commemorates. For the most part these types are the characteristics of the saints that generally appear on calendars, e.g., "virgin" "martyr" "pope", etc. There are also types for commemoration of objects (e.g., the cross), events, etc. Some types are undifferentiated. "bishop" includes "archbishop", "deacon" includes "archdeacon", and most significantly, "religious" includes all those vowed to religious orders (monks, friars, etc.) as well as hermits.
These feast types are bound to the feast itself, not the locale-dependent rules, so characteristics that are specific to one church or another will be included no matter what locale you have selected. Thus Roman Catholic doctors of the church who are culted more widely will be called "doctor" in other locales as well (and for that matter, before the actual dates that they were declared doctors by Rome).
Feasts vary in importance, but one major limitation of the program is that it does not calculate precedence rules. These rules sometimes require the omission or transference of a feast if it conflicts with a more important one. The rules, and indeed the relative importance of different feasts, vary over locale and time. It is possible I will add this feature in the future, if I can track down sufficient historical data about past rules.
If you are sharp-eyed, you might notice that the feast for Matthias, on February 24 (until 1969 for Roman Catholics), appears on the 25th in leap years. This behavior is not a bug. Traditionally, the leap day is inserted before the 6th kalends of March (in Latin, the leap day was called the bissextus), i.e., February 24, which has the effect of pushing any fixed feasts that happen to be on that day one day later. So, for example, the 1962 Roman Missal says In anno bisextili mensis februarius est dierum 29, et festum Matthiae celebratur die 25 februarii...et bis dicitur Sexto Kalendtas, id est die 24 et die 25. If you have the Roman day count turned on, you will note it displays "vi kal. mar." for both the 24th and the 25th in leap years.
As of version 2.0 of the program, I've revised my rule handling so this behavior can change from locale to locale. The Episcopal church still observes Matthias on the 24th, but they do not change the date in leap years any more. I don't know when the practice actually ceased, but until I can dig up more authoritative information I have assumed that it was in the 1928 revision to the prayer book.
[Update: I was informed (by someone whose name I have misplaced, alas) that the change occurred in the 17th century, but the database hasn't been updated to reflect this.]
I wrote my own Date class for this application. When I originally wrote the program, Java 1.1 was just being introduced, and the (now deprecated) Date class with 1.0 wasn't adequate. Even the Calendar classes with 1.1 didn't have everything that I needed. The class I use generates the correct dates even in odd cases (for example, if the change from the Julian to the Gregorian calendar spans a month or year boundary).
I welcome suggestions for new feasts to add as well as corrections to the current database. I am particularly looking for additional information about changes in feast days and local variations in practice, which will help me implement further locales.
|2.0||Mar. 15, 1998||Filter by feast type; Indictions; Span and in-span rules|
|1.5||Feb. 14||Added Church of England days|
|1.4||Feb. 7||Internal changes to reduce program size and load time.|
|1.3||Feb. 5||Variable Gregorian conversion, Julian feast dates, etc.|
|1.2||Feb. 3||Added Episcopal days of observance|
|1.11||Nov. 3, 1997||Fixed bug in locale lookup routine|
|1.10||Oct. 31||Locale support|
|1.03||Oct. 22||Fixed bug in moveable feast rule-parsing.|
|1.02||Oct. 20||Roman day counting|
|1.01||Oct. 19||Added more saints|
|1.00||Oct. 15||Base version|
I have tried to make this program as accurate as I can, but I make no warranty of any sort about the correctness of the information here. Don't rely on it for anything critical.
The Book of Common Prayer and Administration of the Sacraments and other Rites and Ceremonies of the Church Together with the Psalter or Psalms of David According to the use of The Episcopal Church. (1979).