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Subject: Calendar FAQ, v. 2.9 (modified 4 April 2008) Part 3/3

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Archive-name: calendars/faq/part3 Posting-Frequency: monthly Last-modified: 2008/04/04 Version: 2.9 URL: http://www.tondering.dk/claus/calendar.html
FREQUENTLY ASKED QUESTIONS ABOUT CALENDARS Part 3 of 3 Version 2.9 - 4 April 2008 Copyright and disclaimer ------------------------ This document is Copyright (C) 2008 by Claus Tondering. E-mail: claus@tondering.dk. (Please include the word "calendar" in the subject line.) The document may be freely distributed, provided this copyright notice is included and no money is charged for the document. This document is provided "as is". No warranties are made as to its correctness. Introduction ------------ This is the calendar FAQ. Its purpose is to give an overview of the Christian, Hebrew, Persian, and Islamic calendars in common use. It will provide a historical background for the Christian calendar, plus an overview of the French Revolutionary calendar, the Maya calendar, and the Chinese calendar. Comments are very welcome. My e-mail address is given above. Contents -------- In part 1 of this document: 1. What Astronomical Events Form the Basis of Calendars? 1.1. What are equinoxes and solstices? 2. The Christian Calendar 2.1. What is the Julian calendar? 2.1.1. What years are leap years? 2.1.2. What consequences did the use of the Julian calendar have? 2.2. What is the Gregorian calendar? 2.2.1. What years are leap years? 2.2.2. Isn't there a 4000-year rule? 2.2.3. Don't the Greeks do it differently? 2.2.4. When did country X change from the Julian to the Gregorian calendar? 2.3. What day is the leap day? 2.4. What is the Solar Cycle? 2.5. What is the Dominical Letter? 2.6. What day of the week was 2 August 1953? 2.7. When can I reuse my 1992 calendar? 2.8. What is the Roman calendar? 2.7.1. How did the Romans number days? 2.9. What is the proleptic calendar? 2.10. Has the year always started on 1 January? 2.11. Then what about leap years? 2.12. What is the origin of the names of the months? In part 2 of this document: 2.13. What is Easter? 2.13.1. When is Easter? (Short answer) 2.13.2. When is Easter? (Long answer) 2.13.3. What is the Golden Number? 2.13.4. How does one calculate Easter then? 2.13.5. What is the Epact? 2.13.6. How does one calculate Gregorian Easter then? 2.13.7. Isn't there a simpler way to calculate Easter? 2.13.8. Isn't there an even simpler way to calculate Easter? 2.13.9. Is there a simple relationship between two consecutive Easters? 2.13.10. How frequently are the dates for Easter repeated? 2.13.11. What about Greek Orthodox Easter? 2.13.12. Did the Easter dates change in 2001? 2.14. How does one count years? 2.14.1. How did Dionysius date Christ's birth? 2.14.2. Was Jesus born in the year 0? 2.14.3. When does the 3rd millennium start? 2.14.4. What do AD, BC, CE, and BCE stand for? 2.15. What is the Indiction? 2.16. What is the Julian period? 2.16.1. Is there a formula for calculating the Julian day number? 2.16.2. What is the modified Julian day number? 2.16.3. What is the Lilian day number? 2.17. What is the correct way to write dates? 3. ISO 8601 3.1. What date format does the Standard mandate? 3.2. What time format does the Standard mandate? 3.3. What if I want to specify both a date and a time? 3.4. What format does the Standard mandate for a time interval? 3.5. Can I write BC dates and dates after the year 9999 using ISO 8601? 3.6. Can I write dates in the Julian calendar using ISO 8601? 3.7. Does the Standard define the Gregorian calendar? 3.8. What does the Standard say about the week? 3.9. Why are ISO 8601 dates not used in this Calendar FAQ? 3.10. Where can I get the Standard? 4. The Hebrew Calendar 4.1. What does a Hebrew year look like? 4.2. What years are leap years? 4.3. What years are deficient, regular, and complete? 4.4. When is New Year's day? 4.5. When does a Hebrew day begin? 4.6. When does a Hebrew year begin? 4.7. When is the new moon? 4.8. How does one count years? 4.9. When was Passover in AD 30? 5. The Islamic Calendar 5.1. What does an Islamic year look like? 5.2. So you can't print an Islamic calendar in advance? 5.3. How does one count years? 5.4. When will the Islamic calendar overtake the Gregorian calendar? 5.5. Doesn't Saudi Arabia have special rules? In part 3 of this document: 6. The Persian Calendar 6.1. What does a Persian year look like? 6.2. When does the Persian year begin? 6.3. How does one count years? 6.4. What years are leap years? 7. The Week 7.1. What is the origin of the 7-day week? 7.2. What do the names of the days of the week mean? 7.3. What is the system behind the planetary day names? 7.4. Has the 7-day week cycle ever been interrupted? 7.5. Which day is the day of rest? 7.6. What is the first day of the week? 7.7. What is the week number? 7.8. How can I calculate the week number? 7.9. Do weeks of different lengths exist? 8. The French Revolutionary Calendar 8.1. What does a Republican year look like? 8.2. How does one count years? 8.3. What years are leap years? 8.4. How does one convert a Republican date to a Gregorian one? 9. The Maya Calendar 9.1. What is the Long Count? 9.1.1. When did the Long Count start? 9.2. What is the Tzolkin? 9.2.1. When did the Tzolkin start? 9.3. What is the Haab? 9.3.1. When did the Haab start? 9.4. Did the Mayas think a year was 365 days? 10. The Chinese Calendar 10.1. What does the Chinese year look like? 10.2. What years are leap years? 10.3. How does one count years? 10.4. What is the current year in the Chinese calendar? 11. Frequently Asked Questions about this FAQ 11.1. Why doesn't the FAQ describe calendar X? 11.2. Why doesn't the FAQ contain information X? 11.3. Why don't you reply to my e-mail? 11.4. How do I know that I can trust your information? 11.5. There is an error in one of your formulas! 11.6. Can you recommend any good books about calendars? 11.7. Do you know a web site where I can find information about X? 12. Date 6. The Persian Calendar ----------------------- The Persian calendar is a solar calendar with a starting point that matches that of the Islamic calendar. Apart from that, the two calendars are not related. The origin of the Persian calendar can be traced back to the 11th century when a group of astronomers (including the well-known poet Omar Khayyam) created what is known as the Jalaali calendar. However, a number of changes have been made to the calendar since then. The current calendar has been used in Iran since 1925 and in Afghanistan since 1957. However, Afghanistan used the Islamic calendar in the years 1999-2002. 6.1. What does a Persian year look like? ---------------------------------------- The names and lengths of the 12 months that comprise the Persian year are: 1. Farvardin (31 days) 7. Mehr (30 days) 2. Ordibehesht (31 days) 8. Aban (30 days) 3. Khordad (31 days) 9. Azar (30 days) 4. Tir (31 days) 10. Day (30 days) 5. Mordad (31 days) 11. Bahman (30 days) 6. Shahrivar (31 days) 12. Esfand (29/30 days) (Due to different transliterations of the Persian alphabet, other spellings of the months are possible.) In Afghanistan the months are named differently. The month of Esfand has 29 days in an ordinary year, 30 days in a leap year. 6.2. When does the Persian year begin? -------------------------------------- The Persian year starts at vernal equinox. If the astronomical vernal equinox falls before noon (Tehran true time) on a particular day, then that day is the first day of the year. If the astronomical vernal equinox falls after noon, the following day is the first day of the year. 6.3. How does one count years? ------------------------------ As in the Islamic calendar (section 5.3), years are counted since Mohammed's emigration to Medina in AD 622. At vernal equinox of that year, AP 1 started (AP = Anno Persico/Anno Persarum = Persian year). Note that contrary to the Islamic calendar, the Persian calendar counts solar years. In the year AD 2008 we have therefore witnessed the start of Persian year 1387, but the start of Islamic year 1429. 6.4. What years are leap years? ------------------------------- Since the Persian year is defined by the astronomical vernal equinox, the answer is simply: Leap years are years in which there are 366 days between two Persian new year's days. However, basing the Persian calendar purely on an astronomical observation of the vernal equinox is rejected by many, and a few mathematical rules for determining the length of the year have been suggested. The most popular (and complex) of these is probably the following: The calendar is divided into periods of 2820 years. These periods are then divided into 88 cycles whose lengths follow this pattern: 29, 33, 33, 33, 29, 33, 33, 33, 29, 33, 33, 33, ... This gives 2816 years. The total of 2820 years is achieved by extending the last cycle by 4 years (for a total of 37 years). If you number the years within each cycle starting with 0, then leap years are the years that are divisible by 4, except that the year 0 is not a leap year. So within, say, a 29 year cycle, this is the leap year pattern: Year Year Year Year 0 Ordinary 8 Leap 16 Leap 24 Leap 1 Ordinary 9 Ordinary 17 Ordinary 25 Ordinary 2 Ordinary 10 Ordinary 18 Ordinary 26 Ordinary 3 Ordinary 11 Ordinary 19 Ordinary 27 Ordinary 4 Leap 12 Leap 20 Leap 28 Leap 5 Ordinary 13 Ordinary 21 Ordinary 6 Ordinary 14 Ordinary 22 Ordinary 7 Ordinary 15 Ordinary 23 Ordinary This gives a total of 683 leap years every 2820 years, which corresponds to an average year length of 365 683/2820 = 365.24220 days. This is a better approximation to the tropical year than the 365.2425 days of the Gregorian calendar. The current 2820 year period started in the year AP 475 (AD 1096). This "mathematical" calendar currently coincides closely with the purely astronomical calendar. In the years between AP 1244 and 1531 (AD 1865 and 2152) a discrepancy of one day is seen twice, namely in AP 1404 and 1437 (starting at vernal equinox of AD 2025 and 2058). However, outside this period, discrepancies are more frequent. 7. The Week ----------- The Christian, the Hebrew, the Islamic, and the Persian calendars all have a 7-day week. 7.1. What is the origin of the 7-day week? ------------------------------------------ Digging into the history of the 7-day week is a very complicated matter. Authorities have very different opinions about the history of the week, and they frequently present their speculations as if they were indisputable facts. In short, nothing can be said with certainty about the origin of the 7-day week. The first pages of the Bible explain how God created the world in six days and rested on the seventh. This seventh day became the Jewish day of rest, the Sabbath, Saturday. Extra-biblical locations sometimes mentioned as the birthplace of the 7-day week include: Babylon, Persia, and several others. The week was known in Rome before the advent of Christianity. 7.2. What do the names of the days of the week mean? ---------------------------------------------------- An answer to this question is necessarily closely linked to the language in question. Whereas most languages use the same names for the months (with a few Slavonic languages as notable exceptions), there is great variety in names that various languages use for the days of the week. A few examples will be given here. Except for the Sabbath, Jews simply number their week days. A related method is partially used in Portuguese and Russian: English Portuguese Russian Meaning of Russian name ------- ---------- ------- ----------------------- Monday segunda-feira ponedelnik After "do-nothing" Tuesday terca-feira vtornik Second Wednesday quarta-feira sreda Middle Thursday quinta-feira chetverg Fourth Friday sexta-feira pyatnitsa Fifth Saturday sabado subbota Sabbath Sunday domingo voskresenye Resurrection Most Latin-based languages connect each day of the week with one of the seven "planets" of the ancient times: Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn. French, for example, uses: English French "Planet" ------- ------ -------- Monday lundi Moon Tuesday mardi Mars Wednesday mercredi Mercury Thursday jeudi Jupiter Friday vendredi Venus Saturday samedi Saturn Sunday dimanche (Sun) The link with the sun has been broken in French, but Sunday was called "dies solis" (day of the sun) in Latin. It is interesting to note that also some Asiatic languages (for example, Hindi, Japanese, and Korean) have a similar relationship between the week days and the planets. English has retained the original planets in the names for Saturday, Sunday, and Monday. For the four other days, however, the names of Anglo-Saxon or Nordic gods have replaced the Roman gods that gave name to the planets. Thus, Tuesday is named after Tiw, Wednesday is named after Woden, Thursday is named after Thor, and Friday is named after Frigg. 7.3. What is the system behind the planetary day names? ------------------------------------------------------- As we saw in the previous section, the planets have given the week days their names following this order: Moon, Mars, Mercury, Jupiter, Venus, Saturn, Sun Why this particular order? One theory goes as follows: If you order the "planets" according to either their presumed distance from Earth (assuming the Earth to be the centre of the universe) or their period of revolution around the Earth, you arrive at this order: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn Now, assign (in reverse order) these planets to the hours of the day: 1=Saturn, 2=Jupiter, 3=Mars, 4=Sun, 5=Venus, 6=Mercury, 7=Moon, 8=Saturn, 9=Jupiter, etc., 23=Jupiter, 24=Mars The next day will then continue where the old day left off: 1=Sun, 2=Venus, etc., 23=Venus, 24=Mercury And the next day will go 1=Moon, 2=Saturn, etc. If you look at the planet assigned to the first hour of each day, you will note that the planets come in this order: Saturn, Sun, Moon, Mars, Mercury, Jupiter, Venus This is exactly the order of the associated week days. Coincidence? Maybe. 7.4. Has the 7-day week cycle ever been interrupted? ---------------------------------------------------- There is no record of the 7-day week cycle ever having been broken. Calendar changes and reform have never interrupted the 7-day cycles. It is very likely that the week cycles have run uninterrupted at least since the days of Moses (c. 1400 BC), possibly even longer. Some sources claim that the ancient Jews used a calendar in which an extra Sabbath was occasionally introduced. But this is probably not true. 7.5. Which day is the day of rest? ---------------------------------- For the Jews, the Sabbath (Saturday) is the day of rest and worship. On this day God rested after creating the world. Most Christians have made Sunday their day of rest and worship, because Jesus rose from the dead on a Sunday. Muslims use Friday as their day of rest and worship. The Qur'an calls Friday a holy day, the "king of days". 7.6. What is the first day of the week? --------------------------------------- The Bible clearly makes the Sabbath (correspondiong to our Saturday) the last day of the week. Therefore it is common Jewish and Christian practice to regard Sunday as the first day of the week (as is also evident from the Portuguese names for the week days mentioned in section 7.2). However, the fact that, for example, Russian uses the name "second" for Tuesday, indicates that some nations regard Monday as the first day. In international standard ISO 8601 (see chapter 3) the International Organization for Standardization has decreed that Monday shall be the first day of the week. 7.7. What is the week number? ----------------------------- International standard ISO 8601 (see chapter 3) assigns a number to each week of the year. A week that lies partly in one year and partly in another is assigned a number in the year in which most of its days lie. This means that Week 1 of any year is the week that contains 4 January, or equivalently Week 1 of any year is the week that contains the first Thursday in January. Most years have 52 weeks, but years that start on a Thursday and leap years that start on a Wednesday have 53 weeks. Note: This week numbering system is not commonly used in the United States. 7.8. How can I calculate the week number? ----------------------------------------- If you know the date, you can calculate the corresponding week number (as defined in ISO 8601) as descibed below. (The divisions are integer divisions in which the remainder is discarded.) For dates in January and February, calculate: a = year-1 b = a/4 - a/100 + a/400 c = (a-1)/4 - (a-1)/100 + (a-1)/400 s = b-c e = 0 f = day - 1 + 31*(month-1) For dates in March through December, calculate: a = year b = a/4 - a/100 + a/400 c = (a-1)/4 - (a-1)/100 + (a-1)/400 s = b-c e = s+1 f = day + (153*(month-3)+2)/5 + 58 + s Then, for any month continue thus: g = (a + b) mod 7 d = (f + g - e) mod 7 n = f + 3 - d We now have three situations: If n<0, the day lies in week 53-(g-s)/5 of the previous year. If n>364+s, the day lies in week 1 of the coming year. Otherwise, the day lies in week n/7 + 1 of the current year. This algorithm gives you a couple of additional useful values: d indicates the day of the week (0=Monday, 1=Tuesday, etc.) f+1 is the ordinal number of the date within the current year. 7.9. Do weeks of different lengths exist? ----------------------------------------- If you define a "week" as a 7-day period, obviously the answer is no. But if you define a "week" as a named interval that is greater than a day and smaller than a month, the answer is yes. The ancient Egyptians used a 10-day "week", as did the French Revolutionary calendar (see section 8.1). The Maya calendar uses a 13 and a 20-day "week" (see section 9.2). The Soviet Union has used both a 5-day and a 6-day week. In 1929-30 the USSR gradually introduced a 5-day week. Every worker had one day off every week, but there was no fixed day of rest. On 1 September 1931 this was replaced by a 6-day week with a fixed day of rest, falling on the 6th, 12th, 18th, 24th, and 30th day of each month (1 March was used instead of the 30th day of February, and the last day of months with 31 days was considered an extra working day outside the normal 6-day week cycle). A return to the normal 7-day week was decreed on 26 June 1940. 8. The French Revolutionary Calendar ------------------------------------ The French Revolutionary Calendar (or Republican Calendar) was introduced in France on 24 November 1793 and abolished on 1 January 1806. It was used again briefly during the Paris Commune in 1871. 8.1. What does a Republican year look like? ------------------------------------------- A year consists of 365 or 366 days, divided into 12 months of 30 days each, followed by 5 or 6 additional days. The months were: 1. Vendemiaire 7. Germinal 2. Brumaire 8. Floreal 3. Frimaire 9. Prairial 4. Nivose 10. Messidor 5. Pluviose 11. Thermidor 6. Ventose 12. Fructidor (The second e in Vendemiaire and the e in Floreal carry an acute accent. The o's in Nivose, Pluviose, and Ventose carry a circumflex accent.) The year was not divided into weeks, instead each month was divided into three "decades" of 10 days, of which the final day was a day of rest. This was an attempt to de-Christianize the calendar, but it was an unpopular move, because now there were 9 work days between each day of rest, whereas the Gregorian Calendar had only 6 work days between each Sunday. The ten days of each decade were called, respectively, Primidi, Duodi, Tridi, Quartidi, Quintidi, Sextidi, Septidi, Octidi, Nonidi, Decadi. The 5 or 6 additional days followed the last day of Fructidor and were called: 1. Jour de la vertu (Day of virtue) 2. Jour du genie (Day of genius) 3. Jour du travail (Day of labour) 4. Jour de l'opinion (Day of opinion) 5. Jour des recompenses (Day of rewards) 6. Jour de la revolution (Day of the revolution) (the leap day) (Different sources refer to these days as either "jour" ("day") or "fete" ("celebration" or "feast").) Each year was supposed to start on autumnal equinox (around 22 September), but this created problems as will be seen in section 8.3. 8.2. How does one count years? ------------------------------ Years are counted since the establishment of the first French Republic on 22 September 1792. That day became 1 Vendemiaire of the year 1 of the Republic. (However, the Revolutionary Calendar was not introduced until 24 November 1793.) 8.3. What years are leap years? ------------------------------- Leap years were introduced to keep New Year's Day on autumnal equinox. But this turned out to be difficult to handle, because equinox is not completely simple to predict. In fact, the first decree implementing the calendar (5 Oct 1793) contained two contradictory rules, as it stated that: - the first day of each year would be that of the autumnal equinox - every 4th year would be a leap year In practice, the first calendars were based on the equinoxial condition. To remove the confusion, a rule similar to the one used in the Gregorian Calendar (including a 4000 year rule as described in section 2.2.2) was proposed by the calendar's author, Gilbert Romme, but his proposal ran into political problems. In short, during the time when the French Revolutionary Calendar was in use, the following years were leap years: 3, 7, and 11. 8.4. How does one convert a Republican date to a Gregorian one? --------------------------------------------------------------- The following table lists the Gregorian date on which each year of the Republic started: Year 1: 22 Sep 1792 Year 8: 23 Sep 1799 Year 2: 22 Sep 1793 Year 9: 23 Sep 1800 Year 3: 22 Sep 1794 Year 10: 23 Sep 1801 Year 4: 23 Sep 1795 Year 11: 23 Sep 1802 Year 5: 22 Sep 1796 Year 12: 24 Sep 1803 Year 6: 22 Sep 1797 Year 13: 23 Sep 1804 Year 7: 22 Sep 1798 Year 14: 23 Sep 1805 9. The Maya Calendar -------------------- (I am very grateful to Chris Carrier for providing most of the information about the Maya calendar.) Among their other accomplishments, the ancient Mayas invented a calendar of remarkable accuracy and complexity. The Maya calendar was adopted by the other Mesoamerican nations, such as the Aztecs and the Toltec, which adopted the mechanics of the calendar unaltered but changed the names of the days of the week and the months. The Maya calendar uses three different dating systems in parallel, the "Long Count", the "Tzolkin" (divine calendar), and the "Haab" (civil calendar). Of these, only the Haab has a direct relationship to the length of the year. A typical Mayan date looks like this: 12.18.16.2.6, 3 Cimi 4 Zotz. 12.18.16.2.6 is the Long Count date. 3 Cimi is the Tzolkin date. 4 Zotz is the Haab date. 9.1. What is the Long Count? ---------------------------- The Long Count is really a mixed base-20/base-18 representation of a number, representing the number of days since the start of the Mayan era. It is thus akin to the Julian Day Number (see section 2.16). The basic unit is the "kin" (day), which is the last component of the Long Count. Going from right to left the remaining components are: uinal (1 uinal = 20 kin = 20 days) tun (1 tun = 18 uinal = 360 days = approx. 1 year) katun (1 katun = 20 tun = 7,200 days = approx. 20 years) baktun (1 baktun = 20 katun = 144,000 days = approx. 394 years) The kin, tun, and katun are numbered from 0 to 19. The uinal are numbered from 0 to 17. The baktun are numbered from 1 to 13. Although they are not part of the Long Count, the Mayas had names for larger time spans. The following names are sometimes quoted, although they are not ancient Maya terms: 1 pictun = 20 baktun = 2,880,000 days = approx. 7885 years 1 calabtun = 20 pictun = 57,600,000 days = approx. 158,000 years 1 kinchiltun = 20 calabtun = 1,152,000,000 days = approx. 3 million years 1 alautun = 20 kinchiltun = 23,040,000,000 days = approx. 63 million years 9.1.1. When did the Long Count start? ------------------------------------- Logically, the first date in the Long Count should be 0.0.0.0.0, but as the baktun (the first component) are numbered from 1 to 13 rather than 0 to 12, this first date is actually written 13.0.0.0.0. The authorities disagree on what 13.0.0.0.0 corresponds to in our calendar. I have come across three possible equivalences: 13.0.0.0.0 = 8 Sep 3114 BC (Julian) = 13 Aug 3114 BC (Gregorian) 13.0.0.0.0 = 6 Sep 3114 BC (Julian) = 11 Aug 3114 BC (Gregorian) 13.0.0.0.0 = 11 Nov 3374 BC (Julian) = 15 Oct 3374 BC (Gregorian) Assuming one of the first two equivalences, the Long Count will again reach 13.0.0.0.0 on 21 or 23 December AD 2012 - a not too distant future. The date 13.0.0.0.0 may have been the Mayas' idea of the date of the creation of the world. 9.2. What is the Tzolkin? ------------------------- The Tzolkin date is a combination of two "week" lengths. While our calendar uses a single week of seven days, the Mayan calendar used two different lengths of week: - a numbered week of 13 days, in which the days were numbered from 1 to 13 - a named week of 20 days, in which the names of the days were: 0. Ahau 5. Chicchan 10. Oc 15. Men 1. Imix 6. Cimi 11. Chuen 16. Cib 2. Ik 7. Manik 12. Eb 17. Caban 3. Akbal 8. Lamat 13. Ben 18. Etznab 4. Kan 9. Muluc 14. Ix 19. Caunac As the named week is 20 days and the smallest Long Count digit is 20 days, there is synchrony between the two; if, for example, the last digit of today's Long Count is 0, today must be Ahau; if it is 6, it must be Cimi. Since the numbered and the named week were both "weeks", each of their name/number change daily; therefore, the day after 3 Cimi is not 4 Cimi, but 4 Manik, and the day after that, 5 Lamat. The next time Cimi rolls around, 20 days later, it will be 10 Cimi instead of 3 Cimi. The next 3 Cimi will not occur until 260 (or 13*20) days have passed. This 260-day cycle also had good-luck or bad-luck associations connected with each day, and for this reason, it became known as the "divinatory year." The "years" of the Tzolkin calendar are not counted. 9.2.1. When did the Tzolkin start? ---------------------------------- Long Count 13.0.0.0.0 corresponds to 4 Ahau. The authorities agree on this. 9.3. What is the Haab? ---------------------- The Haab was the civil calendar of the Mayas. It consisted of 18 "months" of 20 days each, followed by 5 extra days, known as "Uayeb". This gives a year length of 365 days. The names of the month were: 1. Pop 7. Yaxkin 13. Mac 2. Uo 8. Mol 14. Kankin 3. Zip 9. Chen 15. Muan 4. Zotz 10. Yax 16. Pax 5. Tzec 11. Zac 17. Kayab 6. Xul 12. Ceh 18. Cumku In contrast to the Tzolkin dates, the Haab month names changed every 20 days instead of daily; so the day after 4 Zotz would be 5 Zotz, followed by 6 Zotz ... up to 19 Zotz, which is followed by 0 Tzec. The days of the month were numbered from 0 to 19. This use of a 0th day of the month in a civil calendar is unique to the Maya system; it is believed that the Mayas discovered the number zero, and the uses to which it could be put, centuries before it was discovered in Europe or Asia. The Uayeb days acquired a very derogatory reputation for bad luck; known as "days without names" or "days without souls," and were observed as days of prayer and mourning. Fires were extinguished and the population refrained from eating hot food. Anyone born on those days was "doomed to a miserable life." The years of the Haab calendar are not counted. The length of the Tzolkin year was 260 days and the length of the Haab year was 365 days. The smallest number that can be divided evenly by 260 and 365 is 18,980, or 365*52; this was known as the Calendar Round. If a day is, for example, "4 Ahau 8 Cumku," the next day falling on "4 Ahau 8 Cumku" would be 18,980 days or about 52 years later. Among the Aztec, the end of a Calendar Round was a time of public panic as it was thought the world might be coming to an end. When the Pleiades crossed the horizon on 4 Ahau 8 Cumku, they knew the world had been granted another 52-year extension. 9.3.1. When did the Haab start? ------------------------------- Long Count 13.0.0.0.0 corresponds to 8 Cumku. The authorities agree on this. 9.4. Did the Mayas think a year was 365 days? --------------------------------------------- Although there were only 365 days in the Haab year, the Mayas were aware that a year is slightly longer than 365 days, and in fact, many of the month-names are associated with the seasons; Yaxkin, for example, means "new or strong sun" and, at the beginning of the Long Count, 1 Yaxkin was the day after the winter solstice, when the sun starts to shine for a longer period of time and higher in the sky. When the Long Count was put into motion, it was started at 7.13.0.0.0, and 0 Yaxkin corresponded with Midwinter Day, as it did at 13.0.0.0.0 back in 3114 B.C. The available evidence indicates that the Mayas estimated that a 365-day year precessed through all the seasons twice in 7.13.0.0.0 or 1,101,600 days. We can therefore derive a value for the Mayan estimate of the year by dividing 1,101,600 by 365, subtracting 2, and taking that number and dividing 1,101,600 by the result, which gives us an answer of 365.242036 days, which is slightly more accurate than the 365.2425 days of the Gregorian calendar. (This apparent accuracy could, however, be a simple coincidence. The Mayas estimated that a 365-day year precessed through all the seasons *twice* in 7.13.0.0.0 days. These numbers are only accurate to 2-3 digits. Suppose the 7.13.0.0.0 days had corresponded to 2.001 cycles rather than 2 cycles of the 365-day year, would the Mayas have noticed?) 10. The Chinese Calendar ------------------------ Although the People's Republic of China uses the Gregorian calendar for civil purposes, a special Chinese calendar is used for determining festivals. Various Chinese communities around the world also use this calendar. The beginnings of the Chinese calendar can be traced back to the 14th century BC. Legend has it that the Emperor Huangdi invented the calendar in 2637 BC. The Chinese calendar is based on exact astronomical observations of the longitude of the sun and the phases of the moon. This means that principles of modern science have had an impact on the Chinese calendar. I can recommend visiting Helmer Aslaksen's web site at http://www.chinesecalendar.net for more information about the Chinese calendar. 10.1. What does the Chinese year look like? ------------------------------------------- The Chinese calendar - like the Hebrew - is a combined solar/lunar calendar in that it strives to have its years coincide with the tropical year and its months coincide with the synodic months. It is not surprising that a few similarities exist between the Chinese and the Hebrew calendar: * An ordinary year has 12 months, a leap year has 13 months. * An ordinary year has 353, 354, or 355 days, a leap year has 383, 384, or 385 days. When determining what a Chinese year looks like, one must make a number of astronomical calculations: First, determine the dates for the new moons. Here, a new moon is the completely "black" moon (that is, when the moon is in conjunction with the sun), not the first visible crescent used in the Islamic and Hebrew calendars. The date of a new moon is the first day of a new month. Secondly, determine the dates when the sun's longitude is a multiple of 30 degrees. (The sun's longitude is 0 at Vernal Equinox, 90 at Summer Solstice, 180 at Autumnal Equinox, and 270 at Winter Solstice.) These dates are called the "Principal Terms" and are used to determine the number of each month: Principal Term 1 occurs when the sun's longitude is 330 degrees. Principal Term 2 occurs when the sun's longitude is 0 degrees. Principal Term 3 occurs when the sun's longitude is 30 degrees. etc. Principal Term 11 occurs when the sun's longitude is 270 degrees. Principal Term 12 occurs when the sun's longitude is 300 degrees. Each month carries the number of the Principal Term that occurs in that month. In rare cases, a month may contain two Principal Terms; in this case the months numbers may have to be shifted. Principal Term 11 (Winter Solstice) must always fall in the 11th month. All the astronomical calculations are carried out for the meridian 120 degrees east of Greenwich. This roughly corresponds to the east coast of China. Some variations in these rules are seen in various Chinese communities. 10.2. What years are leap years? -------------------------------- Leap years have 13 months. To determine if a year is a leap year, calculate the number of new moons between the 11th month in one year (i.e., the month containing the Winter Solstice) and the 11th month in the following year. If there are 13 new moons from the start of the 11th month in the first year to the start of the 11th month in the second year, a leap month must be inserted. In leap years, at least one month does not contain a Principal Term. The first such month is the leap month. It carries the same number as the previous month, with the additional note that it is the leap month. 10.3. How does one count years? ------------------------------- Unlike most other calendars, the Chinese calendar does not count years in an infinite sequence. Instead years have names that are repeated every 60 years. (Historically, years used to be counted since the accession of an emperor, but this was abolished after the 1911 revolution.) Within each 60-year cycle, each year is assigned a name consisting of two components: The first component is a "Celestial Stem": 1. jia 6. ji 2. yi 7. geng 3. bing 8. xin 4. ding 9. ren 5. wu 10. gui These words have no English equivalent. The second component is a "Terrestrial Branch": 1. zi (rat) 7. wu (horse) 2. chou (ox) 8. wei (sheep) 3. yin (tiger) 9. shen (monkey) 4. mao (hare, rabbit) 10. you (rooster) 5. chen (dragon) 11. xu (dog) 6. si (snake) 12. hai (pig) The names of the corresponding animals in the zodiac cycle of 12 animals are given in parentheses. Each of the two components is used sequentially. Thus, the 1st year of the 60-year cycle becomes jia-zi, the 2nd year is yi-chou, the 3rd year is bing-yin, etc. When we reach the end of a component, we start from the beginning: The 10th year is gui-you, the 11th year is jia-xu (restarting the Celestial Stem), the 12th year is yi-hai, and the 13th year is bing-zi (restarting the Terrestrial Branch). Finally, the 60th year becomes gui-hai. This way of naming years within a 60-year cycle goes back approximately 2000 years. A similar naming of days and months has fallen into disuse, but the date name is still listed in calendars. It is customary to number the 60-year cycles since 2637 BC, when the calendar was supposedly invented. In that year the first 60-year cycle started. 10.4. What is the current year in the Chinese calendar? ------------------------------------------------------- The current 60-year cycle started on 2 Feb 1984. That date bears the name bing-yin in the 60-day cycle, and the first month of that first year bears the name gui-chou in the 60-month cycle. This means that the year wu-zi, the 25th year in the 78th cycle, started on 7 Feb 2008. 11. Frequently Asked Questions about this FAQ --------------------------------------------- This chapter does not answer questions about calendars. Instead it answers questions that I am often asked about this document. 11.1. Why doesn't the FAQ describe calendar X? ---------------------------------------------- I am frequently asked to add a chapter describing the Japanese calendar, the Ethiopian calendar, the Hindu calendar, etc. But I have to stop somewhere. I have discovered that the more calendars I include in the FAQ, the more difficult it becomes to ensure that the information given is correct. I want to work on the quality rather than the quantity of information in this document. It is therefore not likely that other calendars will be added in the near future. 11.2. Why doesn't the FAQ contain information X? ------------------------------------------------ Obviously, I cannot include everything. So I have to prioritize. The things that are most likely to be omitted from the FAQ are: - Information that is relevant to a single country only. - Views that are controversial and not supported by recognized authorities. 11.3. Why don't you reply to my e-mail? --------------------------------------- I try to reply to all the e-mail I receive. But occasionally the amount of mail I receive is so large that I have to ignore some letters. If this has caused your letter to be lost, I apologize. But please don't let this stop you from writing to me. I enjoy receiving letters, even if I can't answer them all. 11.4. How do I know that I can trust your information? ------------------------------------------------------ I have tried to be accurate in everything I have described. If you are unsure about something that I write, I suggest that you try to verify the information yourself. If you come across a recognized authority that contradicts something that I've written, please let me know. 11.5. There is an error in one of your formulas! ------------------------------------------------ Is that a question? Anyway, I very much doubt that that the formulas given in this document are wrong. Most of the formulas have been tested for all possible dates between AD 1 and AD 10,000. When people think they have found an error in a formula, the most frequent reason is that they have used ordinary division instead of integer division. 11.6. Can you recommend any good books about calendars? ------------------------------------------------------- This is a big question because there are so many excellent books. At this point I shall only recommend three books: Edward M. Reingold & Nachum Dershowitz: "Calendrical Calculations. The Millennium Edition". Cambridge University Press 2001. ISBN 0-521-77752-6. http://emr.cs.iit.edu/home/reingold/calendar-book/second-edition/index.html This book contains a lot of information about a huge number of calendars. As the title indicates, it has a strong emphasis on algorithms for calendrical calculations, so if you want to use your computer to compute calendars, this is a great book. Bonnie Blackburn & Leofranc Holford-Strevens: "The Oxford Companion to the Year". Oxford University Press 1999. ISBN 0-19-214231-3. A very thorough (900+ pages) book about the history of calendars. The book includes a large collections about customs related to each day of the year. Finally, I have myself written a book: Claus Tondering: "Julius og Gregor". 2007. ISBN 978-87-92032-58-4. Unfortunately, this book is in Danish, but if you can read the Scandinavian languages, this is a useful handbook. One of its main strengths is a huge collection of tables of various calendars. 11.7. Do you know a web site where I can find information about X? ------------------------------------------------------------------ Probably not. Good places to start your calendar search include: http://www.calendarzone.com http://personal.ecu.edu/mccartyr/calendar-reform.html 12. Date -------- This version 2.9 of this document was finished on Friday before the second Sunday after Easter, the 4th day of April anno ab Incarnatione Domini MMVIII, indict. I, epacta XXII, luna XXVII, anno post Margaretam Reginam Daniae natam LXVIII, on the feast of Saint Isidore of Seville. The 28th day of Adar II, Anno Mundi 5768. The 27th day of Rabi' al-awwal, Anno Hegirae 1429. The 16th day of Farvardin, Anno Persico 1387. The 28th day of the 2nd month of the year wu-zi of the 78th cycle. Julian Day 2,454,561. --- End of part 3 ---