NOTES TO BE DELETED, MOVED, OR FLESHED OUT
The following units -- days / months / years -- perhaps belong on the Calendar page.
Relationship between natural time units -- day, 'moonth' (29.5306 days) and year (365.2422 days)
Early calendars (discuss on separate page, for non-Western? prehistoric, Mayan, Chinese, Jewish, Islamic, etc)
Western/preWestern calendars (Babylonian, Roman, Egyptian, Julian, Gregorian)

This page consists of notes copied from lab class presentations; in some cases they have been fleshed out a bit, in others not so much. There are also comments to myself about things that could be added or deleted, and some of the details are almost certainly incorrect, as they were typed on the fly during electronic presentations, and may involve typographical errors or memory glitches. Still, some interesting points are covered that are rarely discussed, so a quick look at the following may be of interest; but if you want to use any of the following for a report, you should also check elsewhere to confirm its accuracy.

Weeks
     Our system of seven-day weeks is sometimes attributed to the biblical story of creation, in which God created the heavens and the Earth and its contents in six days, and rested on the seventh day. This is not, however, the basis of our current week, which is based on the Roman seven-day week, and is thought to correspond either to the seven planetes, or "planets", which were the five naked-eye planets, the Sun and the Moon; or to a quarter of the cycle of lunar phases, which is just over four weeks long. It is uncertain which theory is correct, but the one involving the planets seems more likely, based on the tradition of naming the days after the seven heavenly bodies, and the fact that although the Roman calendar (see below) is loosely based on the phases of the Moon, it pays little heed to the actual quarter-phases.
     There is no reason, other than tradition, to use a seven-day week. Our week is based on one version of the Roman week, but other counts of days were used independently of that; for instance, market-days were held every nine days, regardless of the day of the seven-day week, or the calendar date. Ancient Egyptians used a ten-day "week", with three "weeks" in each 30-day month, and an identical calendar was adopted in France (save for the names of the days), after the French revolution. However, the switch from a seven-day week with six work days between each day of rest, to a ten-day week with nine work days between each day of rest was very unpopular, and the new calendar was abolished by Napoleon, only a dozen years later.

Months
     

Years
     Seasonal (tropical) year (refer to page about length of seasons?)
     Orbital (anomalistic) year / comparison with sidereal year (need to add page about orbital changes)
     Calendar year -- Julian calendar (created by Sosigenes at the request of Julius Caesar) is about 11 minutes shorter than the orbital year, but about 11 minutes longer than the seasonal year. Gregorian calendar is almost exactly the same as the seasonal year.

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Purpose of the Calendar
(agricultural, financial, etc)

Types of Calendars
     Event-Based and Regnal Calendars
     In ancient times, and to a lesser extent in modern times, time-keeping was based on memorable events, or the reign of the various rulers of a country. (Babylonian and other ancient examples) As modern examples, the Japanese regnal calendar is a count of the years since the beginning of the current emperor's reign (Showa xx, Taiho xx, etc); and for many years, "The Night That Stars Fell On Alabama" -- the 1833 Leonid meteor storm -- was referred to as 'The Year That Stars Fell'.
     Lunar Calendars
     Brief discussion of lunar calendars. Example -- the Islamic Calendar. Problems with lunar calendars, leading into...
     Luni-Solar Calendars
     Brief discussion of luni-solar calendars. Examples -- the Babylonian and Hebraic calendars...
     Solar Calendars
     Brief discussion of strictly solar calendars. Examples -- the Egyptian Calendar

The Early History of Our Calendar
     Our calendar is based, a bit loosely, on the calendar of the Roman republic, modified in various ways, over the millenia since the end of the republic.
     (Discussion of the Roman calendar -- or more accurately, calendars -- and comparison to the Japanese calendar; leading into...)
     The Julian Calendar The Roman calendar (or calendars, since many were in use at various times, and even at the same time) was one of the most complicated and abused calendar in the history of calendars (I once read a quote attributed to Voltaire that "Roman generals were always victorious, but they never knew on which date they were victorious"; unfortunately, I don't remember where I read it, and haven't been able to verify whether Voltaire was its author).
     At the end of the Roman civil war (49 - 45 BCE), Julius Caesar decided to replace the numerous Roman calendars with a single, regularized calendar which would serve not only as a count of days for economic and political purposes, but would also restore its astronomical and agricultural purpose, as a measure of the seasons. Caesar had a well-known love of all things Egyptian (particularly Cleopatra, whom he had elevated to Queen of Egypt), and relied on Sosigenes of Alexandria, a mathematician and astronomer, to devise what is now known as the Julian Calendar. This calendar altered the Egyptian calendar of twelve 30-day months and a few feast days, to a more regular count of the days, in which the year started and ended with 31-day months, and working forward from March to August, backward from December to September, and forward from the (new) start of the year in January (remembering that when January and February didn't exist, December was the end of the year, and March the start; and when they did, February 23 was the end of the year) (Note: there are a couple of errors in the following table/discussion; so though the basic ideas are useful, this page should not be viewed as authoritative until this note is removed)
     January 31
     February 30 (had been 23, so adding a day was done after February 23rd)
     March 31
     April 30
     May 31
     June 30
     July 31 (originally Quintilius -- the 5th month)
     August 30 (originally Sextilius -- the 6th month)
     December 31 (Decembris -- the 10th (and last) month)
     November 30 (Novembris -- the 9th month)
     October 31 (Octobris -- the 8th month)
     September 30 (Septembris -- the 7th month)
     Note that this is almost the same as our calendar, save for February and August. Part of the difference is because the strict alternation of months gives a year which is 366 days long, which is nearly a day longer than the seasonal year. Sosigenes therefore recommended making February 30 days only in leap years, in which the Romans had traditionally intercalated an extra month of 23 days, but (by now) usually added only an extra day (bissextile year should be mentioned somewhere around here? or in the 'earlier' discussion of the Roman calendar?). After Augustus became Augustus Caesar, he (aprocryphally?) took another day from February, so that Sextilius -- now renamed Augustus -- could be 31 days, and therefore equal to Julius. (Of course, to help clean up the calendar, in the Year of Confusion, 46 BCE, there was a 23-day leap month after February, plus another month and a half (where?), to make a total correction of (67?) days.

(Note: due to hasty cutting and pasting, some of the material below repeats some of the material above; so as stated above, keep in mind that this page is merely an extension of brief lecture notes, and not an authoritative text)
     The orbital period of the Earth (the anomalistic year) is (approximately) 365.258 days; but the seasonal (tropical) year is 365.2422 days, which is about 25 minutes less (actually 24 to 26 minutes less, depending upon the date of perihelion), because of precession. If we want the seasonal year (e.g., the first day of Spring) to stay the same from year to year, we need to have a calendar whose average length is equal to that value. But of course the calendar has to have a whole number of days, and the length of the seasonal year (tropical year) is not a whole number, so we need to intercalate (add occasional extra) days...
     Julius Caesar, in 44 BC, decreed that the year would have 365 days, most years, and a leap day, every fourth year = JULIAN CALENDAR.
     Prior to this, Rome used a luni-solar calendar. That means that they watched the Moon, to determine the months, and tried, on the average, to make the number of months per year work out as one year. But there are 12 1/2 (?) moonths (lunations) in a year, so you have to use 12 lunar months in some years, and 13 in others (leap months).
     Islamic and Hebrew calendars work this way. The Hebrew calendar goes back to the Babylonian imprisonment of Jews about 3000 years ago; the Jewish months have the same names, the same number of days, and intercalate extra months exactly the same as the Babylonian calendar of 600 BC. The Islamic calendar does not intercalate months, being a strictly lunar calendar, and starting a new year every twelve lunations. This is less than a regular solar year, so over a dozen and a half years, the Islamic calendar gains a year relative to the ‘standard’ calendar.
     The Egyptian calendar was much simpler -- a strict solar calendar, with twelve 30-day months, plus a few feast days tossed in at the end, to make up for any error. The average was known to be 365 1/4 days.
     Liking this idea of a much simpler calendar, Julius Caesar ‘fixed’ the Roman calendar by adding about 2 1/2 months to 45 BC (The Year Of Confusion), and then switched to a strict 12-month Julian calendar, averaging 365 1/4 days. This was not an entirely popular move, but he probably would have been assassinated even if he'd left the calendar alone, as people have always been more interested in politics than astronomy.
     Things were 'regularized', to get rid of the 'feast days' at the end of the year, by working forward from the beginning of the year, and backwards from the end of the year, with alternating 31 and 30 day months. This made 366 days, so February was reduced to 29 days, being traditionally the shortest month, anyway (also, considered unlucky, if remember correctly)
     This gives you 365 days. In leap years, every fourth year, you add 1 more day, so that the average is 365 1/4. The leap day, traditionally, was the sixth day before the 1st of March.
     Now, there’s a slight problem here. This year averages 365.25000 days. The REAL, seasonal year (Tropical Year) = 365.2422 days, which is about 10 minutes less. As a result, every 140 years, the Julian Year has 1 day too many. And, over a period of a thousand years, you end up with an error of a week in the time that the seasons start, and the dates on the calendar.
     As early as 150 AD, people were worrying about this; but nothing was done, until 1582, when Pope Gregory held a council, and decided, as a result, to decree a new (Gregorian) calendar, in which leap century years not divisible by 400 are not leap years. 1600, 2000, 2400, 2800 are still leap years. 1700, 1800, 1900, 2100, 2200, 2300, are not leap years.
     He also decreed that Thursday, October 4, 1582 would be followed by Friday, October 15, 1582.
     Because Protestant countries refused to obey the Pope’s edict, the old Julian calendar was in use in many areas until the late 1700’s, whereas in Roman Catholic countries, the new Gregorian calendar was in use from Oct 15, 1582.
     By 1583, Joseph Scaliger realized this was going to be a big problem:
     George Washington was born in the American colonies in February of some year.
     In England, on that day, and therefore in America, it was February 11, 1731 (OS = Old Style)
     In Scotland, it was February 11, 1732
     In France, it was February 22, 1732 (NS = New Style)
     The difference in the year is because poetically, and in many places, historically, the year begins in March (SPRING), but Caesar put the beginning of the year back to January, and many (but not all) places have used that.
     The difference in the date is because in the Gregorian calendar we left out 10 days in October of 1582, and in 1700, there was no leap year.
     Eventually, England the colonies switched over (mid-late-1700’s). At that time, there were bloody riots all over, by people who wanted their 11 days back. (brief discussion of the two centuries or so required to make the switch?)