|Interconverting Tibetan and Western Years|
|by Peter Meyer|
This note was found in January 2000 among the author's papers. It has not been published before. It was written c. 1977 in India and is presumably based upon the author's study of Tibetan calendars published there. It is reproduced here without change.
Since a Tibetan year is uniquely determined by an element name, an animal name and a number, each Tibetan year may be represented as an ordered triple (e,a,k), where e and a are the numerals given below corresponding to the element name and the animal name of the year, and k is the number of the cycle in which the year occurs. For example, the wood-hare year of the present [c. 1977 (- Ed.)] cycle is (4,0,16), and the first year of the Tibetan chronology is represented as (0,0,1).
Given the Tibetan year (e,a,k) the corresponding Western year may be determined as follows. (e,a,k) is the mth year of the cycle, where m = 12e - 5a + j, and
Fire Earth Iron Water Wood 0 1 2 3 4
Hare Dragon Snake Horse Sheep Monkey Bird Dog Pig Mouse Ox Tiger 0 1 2 3 4 5 6 7 8 9 10 11
j = 1 if 2e >= a and a is even 61 if 2e < a and a is even -5 if 2e > a and a is odd 115 if e = 0 and a = 11 55 otherwise
and the corresponding Western year is m + 60k + 966. Thus the Western year n corresponding to the Tibetan year (e,a,k) is given by the formula
n = 12e - 5a + j + 60k + 966
where j is determined as above.
The value of m for any given Tibetan year in the cycle may be obtained directly from the following table:
Fire Earth Iron Water Wood Hare 1 13 25 37 49 Dragon 50 2 14 26 38 Snake 51 3 15 27 39 Horse 40 52 4 16 28 Sheep 41 53 5 17 29 Monkey 30 42 54 6 18 Bird 31 43 55 7 19 Dog 20 32 44 56 8 Pig 21 33 45 57 9 Mouse 10 22 34 46 58 Ox 11 23 35 47 59 Tiger 60 12 24 36 48
Having found the value of m corresponding to a given Tibetan year in the kth cycle, the corresponding European year is m + 60k + 966.
For converting Western years into Tibetan, for any positive integers x and y, let rem(x,y) denote the remainder on dividing x by y. [That is, rem(x,y) = x mod y (- Ed.)] Then given a Western year n, the Tibetan year (e,a,k) may be determined as follows: Let i = rem(n+4,10) if n is even, rem(n+4,10) - 1 otherwise. Then e = ½ i. (Note that rem(n+4,10) is simply the last digit of n+4.) a = rem(n+5,12), and k is the largest integer k' such that 60k' <= n - 967 (provided that n >= 1027). Having determined e and a by these means, the element name and the animal name are obtained from the above correspondence.
Added January 2000:
To illustrate this conversion, consider the Western year 1996. Then i = 2000 mod 10 = 0, so e = 0. Since 60.17 = 1020 < 1029 = 1996 - 967, k = 17. a = 2001 mod 12 = 9. Thus 1996 corresponds to the fire-mouse year in the 17th cycle.
Converting back from (0,9,17), we have e = 0 and a = 9, so j = 55, so m = 10, so the corresponding Western year is 10 + 60.17 + 966 = 1996.
For the Western year 2000 we have i = 4 so e = 2. k is the same and a = 2005 mod 12 = 1, so the corresponding Tibetan year is the iron-dragon year in the 17th cycle.
Finally, for the first year in the Tibetan Calendar (0,0,1) we have m = j = 1 so the corresponding Western year is 1 + 60 + 966 = 1027.
Added April 2003:
The above algorithm for converting Tibetan calendar years into their Western equivalents has been implemented as an online calculator at Tibetan Calendar Converter.
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