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==Cyclic, or ''Kanshi'' 干支, system==
 
==Cyclic, or ''Kanshi'' 干支, system==
Japan early took over  the [[Sexegenary cycle]] (''kanshi'' 干支) system from China.  Japan and China use completely different ''nengô'', but 1504 was the year of 甲子 throughout east Asia. In this system, two series of characters, the ten stems (''kan'' 干) and the twelve branches (''shi'' 支 ) are used cyclically. They can be combined into a series of sixty elements (see the article on the cycle), which may be used to indicate years.  甲子, the first element of the series, can indicate the years 904, 964, 1024, 1084, 1144, 1204, and all other years separated from these by a multiple of 60. 乙巳, the 42nd element in the series, can be 886, 946, 1006, 1066, 1126, 1186, 1246, etc.  It is also common to indicate a year using only the branch, or ''shi'', part of the cycle.  Thus 巳 occurs every twelve years, as 886, 898, 910, etc. As the branches have gotten animal names attached to them, the years expressed by branches are often translated using animal names. A 巳 year is a "Year of the Snake," for example. Note, however, that since the cyclic terms repeat, one needs some more information than just the cyclic name to completely identify the year.
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Japan early took over  the [[Sexegenary cycle]] (''kanshi'' 干支) system from China.  Japan and China use completely different ''nengô'', but 1504 was the year of 甲子 throughout east Asia.  
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The system appears as a way of indicating days in the earliest Chinese writings, the 13th-century BC Shang-period oracle bones, but around the 2nd century BC it came to be used also for years. Japan adopted this system in the earliest dates we have, a sword dated 辛亥, probably 471 from the reign of [[Emperoro Yuryaku|Emperoro Yûryaku]], and a mirror from Wakayama dated 癸未年, probably 443 or 503. Also, on the 7th-century administrative wooden tablets found in various capitals, the years are indicated using the cycle.
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In this system, two series of characters, the ten stems (''kan'' 干) and the twelve branches (''shi'' 支 ) are used cyclically. They can be combined into a series of sixty elements (see the article on the cycle), which may be used to indicate years.  甲子, the first element of the series, can indicate the years 904, 964, 1024, 1084, 1144, 1204, and all other years separated from these by a multiple of 60. 乙巳, the 42nd element in the series, can be 886, 946, 1006, 1066, 1126, 1186, 1246, etc.  It is also common to indicate a year using only the branch, or ''shi'', part of the cycle.  Thus 巳 occurs every twelve years, as 886, 898, 910, etc. As the branches have gotten animal names attached to them, the years expressed by branches are often translated using animal names. A 巳 year is a "Year of the Snake," for example. Note, however, that since the cyclic terms repeat, one needs some more information than just the cyclic name to completely identify the year.
    
The cycles do have the advantage over the era system of being predictable.  There is an Ôei 25 (1418) contract selling "the ten harvests of the ten years from the ''inu'' year to the following ''hitsuji'' year." While at the time the contract was written there was no way of knowing whether or not there would be a Ôei 34, there was bound to be a ''hitsuji'' year.  
 
The cycles do have the advantage over the era system of being predictable.  There is an Ôei 25 (1418) contract selling "the ten harvests of the ten years from the ''inu'' year to the following ''hitsuji'' year." While at the time the contract was written there was no way of knowing whether or not there would be a Ôei 34, there was bound to be a ''hitsuji'' year.  
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Most modern books will translate a date expressed in the cycles into either nengô years or Western years or both, but here is how to determine a date if necessary.
 
Most modern books will translate a date expressed in the cycles into either nengô years or Western years or both, but here is how to determine a date if necessary.
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First you have to make a guess (G) or estimate as to the year. This is necessary because the cycles repeat every 60 years.  You can look up the kanshi in the table at the end of the article on the  [[Sexegenary cycle]]  and add or subtract multiples of 60 of the "sample year" till you get near your year. Another way is this: Divide your guess (G) by 60 and throw away the remainder to get the quotient (Q). Calculate the position (P) of the ''kan-shi'' pair in the 60 cycle  or get it from the table chart.  The year is P+3+(60*Q). However, you may have to add or subtract 60 years (one cycle).  For example, assume we have a letter dated  甲寅 written by someone who died in 1580.  Let's take the guess G as 1570.  1570/60=26, so Q = 26. 甲寅 is 50th on the chart, so P=50.  So  50+3+(60*26)= 1613, so 1613 was a 甲寅  year.  But as the writer was already dead then, we subtract 60 to get 1653.
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First you have to make a guess (G) or estimate as to the year. This is necessary because the cycles repeat every 60 years.  You can look up the kanshi in the table at the end of the article on the  [[Sexegenary cycle]]  and add or subtract multiples of 60 of the "sample year" till you get near your year. Another way is this: Divide your guess (G) by 60 and throw away the remainder to get the quotient (Q). Calculate the position (P) of the ''kan-shi'' pair in the 60 cycle  or get it from the table chart.  The year is P+3+(60*Q). However, you may have to add or subtract 60 years (one cycle).  For example, assume we have a letter dated  甲寅 written by someone who died in 1580.  Let's take the guess G as 1570.  1570/60=26, so Q = 26. 甲寅 is 51st on the chart, so P=51.  So  51+3+(60*26)= 1614, so 1614 was a 甲寅  year.  But as the writer was already dead then, we subtract 60 to get 1654.
 
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If a letter is dated using just the branch, use 12 instead of 60.  Thus a letter from around 1610, dated 巳ノ三月十七日 , was written in 6+3+(12*134)= 1617, or maybe 1605.  
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If a letter is dated using just the branch, use 12 instead of 60.  Thus a letter from around 1610, dated 巳ノ三月十七日 , was written in 6+3+(12*134)= 1617, or maybe 1605.
    
==Combined and Non-combined Era and Cyclic Years==
 
==Combined and Non-combined Era and Cyclic Years==
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