Kasshi lunisolar calendar

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The Kasshi lunisolar calendar is currently used to determine religious holidays. The (calculated) dates of full moon are also used as holidays in the civil calendar. This article describes the modern form of the lunisolar calendar. For earlier forms, see History of the Kasshi calendar

Half-months

Most months are 18 days. The average length of a synodic month is about 18.169 days, just a hair over 181/6 days. Thus, most months are 18 days with the occasional 19-day month. Each month is divided into two half-months, which are the origin of the weeks in the solar calendar. The first half-month is referred to as the Upper half-month while the second half-month is referred to as the Lower half-month. Each day within the half-months are named:

1/10. Dark/Bright
2/11. Fasting
3/12. First Council
4/13. Second Council
5/14. Middle
6/15. Market
7/16. Preparation
8/17. Worship
9/18. Rest

Note that, except for the first day, these are the same names as the days of the week in the solar calendar. The adjectives "solar" and "lunar" can be used to distinguish when needed. 19-day months are formed by duplicating one of the days other than New Moon or Full Moon, using the adjective "second" in front of the name, or "repeated" in the case of First Council and Second Council. Occasionally, a day may also be skipped.

Determining days

In order to determine what a particular day is named, one must determine the segments in which the Sun and Moon are located at the beginning of the day. The solar segment is calculated according to the computed orbit, the same method used to calculate the solar calendar's months. The lunar segment is calculated according to the assumption that the Moon travels a constant speed around Galhaf. The orbital period is calculated as being 16 days, 54 daymins, 50 daysecs, 21 daysecs. It is assumed that Sasalh travels its orbit at a constant rate. Due to the complexities of determining Sasalh's exact orbit, this simplifying assumption is necessary. It thus travels just a little more than 68.1 segments per day. Each day thus sees Sasalh's calculated (i.e., mean) position as 68 or 69 segments further, while the Sun travels between 4-6 segments each day. The day is determined by taking the number of segments by which Sasalh is ahead of the Sun, dividing by 64, and taking the integer and adding 1. Thus, day 1 is 0-63 segments ahead, day 2 is 64-127 segments, etc. The difference can increase by anywhere between 62 and 65 segments. This can result in the occasional doubled day (every year has 2 or 3 months with a double day) and, much more rarely a skipped day. A special rule exists that every month must have one and only one each of New Moon and Full Moon. If the calculations would result in a doubled New Moon or Full Moon, the second version is pushed to Fasting, causing a duplication of Fasting that half-month. Likewise, if New Moon or Full Moon would've been skipped, then what would've been Fasting is shifted to New/Full Moon.

An example showing both a doubled day and a shifted day, Late Winter, 970. Doubling is highlighted with red and the shifted day by blue. To make discussion simpler, each day is marked by a letter

Day Solar Segment Lunar Segment Difference Day (initial) Day (adjusted)
A 299 299 0 1 1
B 304 367 63 1 2
C 308 435 127 2 2
D 313 503 190 3 3
E 318 571 253 4 4
F 322 639 317 5 5
G 327 707 380 6 6
H 332 775 443 7 7
I 336 844 508 8 8
J 341 912 571 9 9
K 345 980 635 10 10
L 350 1,048 698 11 11
M 354 1,116 762 12 12
N 359 32 825[1] 13 13
O 363 100 889 14 14
P 368 168 952 15 15
Q 372 236 1,016 16 16
R 377 305 1,080 17 17
S 381 373 1,144 18 18

Note that day A began with the Sun and Sasalh in the same segment. Sasalh moved ahead 68 segments between day A and day B, while the Sun moved ahead 5, causing the difference to increase by 63, making it still less than 64 segments ahead. Thus, days A and B are initially calculated as being New Moon. To satisfy the One New Moon rule, day B is shifted to Upper Fasting, making day C Second Upper Fasting. Shifts are relatively uncommon.

A further example showing the rare skipped day, Lunar Mid-Spring, 955:

Day Solar Segment Lunar Segment Difference Day (initial) Day (adjusted)
A 816 820 4 1 1
B 820 888 68 2 2
C 825 956 131 3 3
D 829 1,024 195 4 4
E 834 1,092 258 5 5
F 839 8 321 6 6
G 843 76 385 7 7
H 848 144 448 8 8
I 853 212 511 8 8
J 857 281 576 10 10
K 862 349 639 10 11
L 867 417 702 11 11
M 872 485 765 12 12
N 876 553 829 13 13
O 881 621 892 14 14
P 886 689 955 15 15
Q 891 757 1,018 16 16
R 896 825 1,081 17 17
S 900 894 1,146 18 18

There is no 9th day in this month, instead, it jumps from Second Uppper Worship Day to Full Moon. In turn, Full Moon would've been doubled, except that day K was shifted from being Full Moon to Lower Fasting, and causing L to become Second Lower Fasting. Skipped days are always accompanied by two doubled days very close, not always immediately adjacent as here, but never more than 2 or 3 days away.

Further notes on doubling

Doubled days are most common in the Summer months, due to the fact that those months occur near perihelion, when the sun is moving fastest in the sky, and rares in the Winter months for the converse reason, but any month can contain a double day.

Months

Each month is named according to the solar month (traditionally called solar periods) that its full moon is in. Because a lunar month is 18 or 19 days, and the solar months can be longer than that, there may be 2 full moons in a given solar month, especially in the Winter months, when the solar months are longest. Any solar month of 19 or more days thus has the potential to have two full moons, which means any month except Early Summer or Mid-Summer may be doubled. In this case, the first month is given the simple name (such as Early Fall) while the second month is prefixed with the adjective Second (e.g., Second Early Fall). The Winter months are the most commonly doubled, being the longest. Every year has at least one doubled month, and two in almost half of all years.

Conversely, it is possible in the short summer months for a solar month to have no full moons. This is only possible in months of 17 or 18 days[2]. Only Late Spring to Late Summer can do that. Years with a skipped month will invariably have three doubled months, for a total of 14 months.

Controversies

In some regions, the skipped days and months are abolished. As a skipped day or month is always accompanied by two doubled days, this is handled by simply shifting other days/months. For example, in the example above of Mid-Spring, 955, there are two Upper Worships and (after the shift) two Lower Fastings but no Upper Rest. There are two ways to fix it, which are used by different groups. The "forward-shifters" would shift Second Upper Worship forward to Upper Rest, while the "backwards shifters" would shift Full Moon back to Upper Rest and Lower Fasting to Full Moon making Second Lower Fasting into simply Lower Fasting. Similar processes work to avoid skipped months.

Lengths

There are 4 possible lengths of a year. Each year can have 13 or 14 months, of which 2 or 3 may be long. A year may thus be:

  • 13 months, of which 2 are long: 236 days (13 * 18 + 2)
  • 13 months, of which 3 are long: 237 days (13 * 18 + 3)
  • 14 months, of which 2 are long: 254 days (14 * 18 + 2)
  • 14 months, of which 3 are long: 255 days (14 * 18 + 3)

Example

By way of example, this is the year 965. The first day is equivalent to Late Winter, 964 in the solar calendar

Early Spring Mid-Spring Late Spring
1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
  		1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
  		1
  		2
  		3
  		4
  		5
  		6 7
  		8
  		9
 
6
10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
  		10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
  		10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
 
Early Summer Mid-Summer Late Summer
1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
  		1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
  		1
  		2
  		3
  		4
  		5 6
  		7
  		8
  		9
 
5
10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
  		10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
  		10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
 
Early Fall Mid-Fall Late Fall Second Late Fall
1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
  		1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
  		1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
  		1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
 
10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
  		10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
  		10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
  		10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
 
Early Winter Mid-Winter Late Winter Second Late Winter
1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
  		1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
  		1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
  		1
  		2
  		3
  		4
  		5
  		6
  		7
  		8
  		9
 
10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
  		10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
  		10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
  		10
  		11
  		12
  		13
  		14
  		15
  		16
  		17
  		18
 

Notes

  1. ↑ 1152 + 32 - 359; segment 32 represents the moon having simply passed the starting point again, and thus 1,152 representing a complete cycle must be added to 32 to compute how far ahead it is; same applies to the remaining days of this month
  2. ↑ And only with long lunar months in the case of an 18-day solar month
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