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Sanmra Calendar
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Notes on the Sanmra calendar.
This public article was written by alynnidalar, and last updated on 12 Jan 2018, 02:27.

?FYI...
The Sanmra year is 365 days long, with a leap year every twelve years, with a varying number of leap days each time. Historically, there was a complex system for determining the number of leap days each leap year, to keep the calendar roughly in sync with seasons, but since 1872, the calendar has been pegged to the Gregorian calendar; the number of leap days in a leap year is equivalent to the number of leap days that have occurred in the Gregorian calendar since the last leap year.

Sanmra years are further grouped into "cycles" of two years each; a year can thus be identified by either its year number (e.g. Year 2406) or cycle number (e.g. Year 1 of Cycle 1203).

April 12, 1872 is the first day that the Sanmra calendar was officially lined up with the Gregorian calendar; in the Sanmra calendar, this was the first day of the year 2262, or the first day of the first year of the cycle 1131. For some more modern dates, the Gregorian year 2017 is the second year of the Sanmra cycle 1203, or the Sanmra year 2407.

For convenience and making certain conversions simpler, chronometrists often also use twelve-year cycles (or kerun) from Sanmra leap year to leap year; a new twelve-year cycle begins the year after a Sanmra leap year, and ends on the next leap year. (e.g. the Sanmra year beginning in the Gregorian year 1872 to the Sanmra year beginning in the Gregorian year 1883)

[top]Conversions

Gregorian Year -> Sanmra Year -> Sanmra Cycle
To convert from a Gregorian year to a Sanmra year, simply add 390 years. (assuming it's after the first day of the Sanmra new year--if not, add 389)

e.g. 1872 (Gregorian year) + 390 = 2262 (Sanmra year)
e.g. 2016 (Gregorian year) + 390 = 2406 (Sanmra year)
e.g. 1903 (Gregorian year) + 390 = 2393 (Sanmra year)
e.g. March 1, 1903 (Gregorian) + 389 = 2392 (Sanmra year)

To convert from a Sanmra year to a Sanmra cycle/year, divide by 2. If the remainder is 0, it's Year 1; if the remainder is 1, it's Year 2. (in other words, year mod 2 + 1)

e.g. 2262 / 2 = Cycle 1131, Year 1
e.g. 2351 / 2 = Cycle 1175, Year 2
e.g. 2407 / 2 = Cycle 1203, Year 2

Cycle/year pairs are written with a space in Sanmra texts (e.g. "1131 1" is "Cycle 1131, Year 1"), but in English texts are usually separated with a period (e.g. "1131.1")

Sanmra Cycle -> Sanmra Year -> Gregorian Year
Converting from a Sanmra cycle to a Sanmra year is simple, just reverse the process. Double the cycle number, and add 1 if it's Year 2.

e.g. Cycle 1131, Year 1 = 1131 * 2 + 0 = year 2262
e.g. Cycle 1203, Year 2 = 1203 * 2 + 1 = year 2407

And to a Gregorian year, subtract 390, unless it's after the beginning of the Gregorian year, in which case subtract 389:

e.g. 2262 - 390 = 1872 (Gregorian year)
e.g. 2407 - 390 = 2017 (Gregorian year)
e.g. 2407 - 389 = sometime in early 2018 (Gregorian year)

[top]Year Length

Most years will have 365 days, but leap years will be either 368 days or 367 days. Ordinarily, three Gregorian leap years are passed for every Sanmra leap year, and thus three leap days are added to the calendar. However, if only two Gregorian leap years occur, then only two leap days are added to the Sanmra calendar. (e.g. there is no leap year in years divisible by 100 but not divisible by 400, like 1900, so the Sanmra leap year beginning in 1907 and ending in 1908 only had two leap days--for the leap years 1904 and 1908)

To determine how many leap days occur in a given leap year, break the year into two groups. If the last two digits are 89, 93, or 97 (Sanmra year; 00, 04, or 08 for a Gregorian year (use the Gregorian year the leap year ends in)) and the first two digits + 1 are not divisible by 2 (Sanmra year; for a Gregorian year, don't add 1 before dividing by 2), the Sanmra leap year has 2 leap days. In all other scenarios, the Sanmra leap year has 3 leap days.
(thanks to @KathTheDragon for the above!)

Examples:
Sanmra year 2297 (which would end in the Gregorian year 1908) = 22 97
Ends in 97.
22 + 1 = 23, which is not evenly divisible by 4
Therefore, Year 2297 has 2 leap days.

Sanmra year 2261 (which would end in the Gregorian year 1872) = 22 61
Does not end in 89, 93, or 97.
Therefore, Year 2261 has 3 leap days.

Sanmra year 2393 (which would end in the Gregorian year 2004) = 23 - 93
Ends in 93.
23 + 1 = 24, which is evenly divisible by 4.
Therefore, Year 2393 has 3 leap days.

Alternately, for quick reference/programming: take the Gregorian year mod 1200. The year numbers with 2 days are: 89, 197, 293, 497, 593, 689, 893, 989, 1097. 2297 % 1200 = 1097, so 2 leap days. 2261 % 1200 = 1061, so 3 leap days. 2393 % 1200 = 1193, so 3 leap days.

If calculating based on the cycle, things actually get a little easier: if the last two digits of the cycle are 44, 46, or 48, OR 94, 96, or 98 AND the first two digits are even, there's 2 leap days. Otherwise, there's 3 leap days.

Moar Examples:
1148.2 (corresponding to the Sanmra year ending in the Gregorian year 1908) = 11 48
Ends in 48.
Therefore, Year 1148.2 has 2 leap days.

1196.2 (corresponding to the Sanmra year ending in the Gregorian year 2004) = 11 96
Ends in 96.
11 is odd.
Therefore, Year 1196.2 has 3 leap days.

1298.2 (corresponding to the Sanmra year ending in the Gregorian year 2208) = 12 98
Ends in 98.
12 is even.
Therefore, Year 1298.2 has 2 leap days.

1154.2 (corresponding to the Sanmra year ending in the Gregorian year 1918) = 11 54
Does not end in 44, 46, 48, 94, 96, or 98.
Therefore, Year 1154.2 has 3 leap days.

[top]New Year's Day

Because the length of the Sanmra year can differ from the Gregorian year, the first day of the Sanmra calendar will vary in relation to the Gregorian calendar. The first day of each twelve-year cycle is always April 12, and the next three years of a twelve-year cycle will also begin on April 12. The next four years will begin on April 11 if a leap year occurred in the Gregorian calendar, and the final four years will begin on April 10, again if a leap year occurred in the Gregorian calendar.

Some examples:
1131.1: April 12, 1872 to April 11, 1873
1131.2: April 12, 1873 to April 11, 1874
1132.1: April 12,1874 to April 11, 1875
1132.2: April 12, 1875 to April 10, 1876 (Gregorian leap year)
1133.1: April 11, 1876 to April 10, 1877
1133.2: April 11, 1877 to April 10, 1878
1134.1: April 11, 1878 to April 10, 1879
1134.2: April 11, 1879 to April 9, 1880 (Gregorian leap year)
1135.1: April 10, 1880 to April 9, 1881
1135.2: April 10, 1881 to April 9, 1882
1136.1: April 10, 1882 to April 9, 1883
1136.2: April 10, 1883 to April 8, 1884 + 3 leap days (Gregorian and Sanmra leap year--three extra days added to end of Sanmra year to sync it back up)
1137.1: April 12, 1884 (start of next twelve-year cycle)

However, if a Gregorian leap year is skipped, only two days are added to the Sanmra calendar:
1142.1: April 12, 1896 to April 11, 1897
1142.2: April 12, 1897 to April 11, 1898
1143.1: April 12, 1898 to April 11, 1899
1143.2: April 12, 1899 to April 11, 1900 (not a Gregorian leap year!)
1144.1: April 12, 1900 to April 11, 1901
1144.2: April 12, 1901 to April 11, 1902
1145.1: April 12, 1902 to April 11, 1903
1145.2: April 12, 1903 to April 10, 1904 (Gregorian leap year)
1146.1: April 11, 1904 to April 10, 1905
1146.2: April 11, 1905 to April 10, 1906
1147.1: April 11, 1906 to April 10, 1907
1147.2: April 11, 1907 to April 9, 1908 + 2 leap days (Gregorian and Sanmra leap year--only two days added to the end of the year)

Determining when the first day of the year occurs, then, is similar to determining the number of leap years--it depends on how many Gregorian leap days have occurred. However, in a 3-leap-day cycle, it can be calculated by taking the Gregorian year (in which the Sanmran year begins) and dividing by 12. If the remainder is 0, 1, 2, or 3, the year begins on April 12. If the remainder is 4, 5, 6, or 7, the year begins on April 11. If the remainder is 8, 9, 10, or 11, the year begins on April 10.

Furthermore, if the remainder is 11, the year is a leap year.

alternately: Gregorian year mod 12

If you're working off the Sanmra year, first add 2, then mod 12.

[top]Months

The Sanmra year consists of 12 months of either 30 or 31 days apiece. The following table shows the start/end dates and length of each month. The dates given are for the first year of a kerun (twelve-year cycle between Sanmran leap years). For years where the corresponding Gregorian year has a leap day, adjust accordingly.

#Tirina NameGregorian Equivalent# of Days
1PinaApril 12 to May 1130
2May 12 to June 1131
3AtmanJune 12 to July 1130
4YeskeraJuly 12 to August 1131
5PedosaAugust 12 to September 1030
6September 11 to October 1131
7October 12 to November 1030
8MetakanNovember 11 to December 1131
9December 12 to January 1030
10KeironJanuary 11 to February 1031
11February 11 to March 1230
12March 13 to April 1130 