Sexagenal sliding Calendar[]
The meaning of "sexagenal" is "by sixty". Hours and minutes are sexagenal, which is a legacy of the Mesopotamians. The Sexagenal sliding Calendar makes use of number sixty too.
Its years are the same as the usual years.
Like the usual calendar, months of the Sexagenal sliding Calendar are about 30 days long, which makes around 60 days for a pair of them. As a departure from common calendar systems the month of February always has 29 days while December can have 30 or 31 days according to leap year calculations.
The Sexagenal sliding Calendar has a sixty-two year cycle for leap years. A group of sixty-one cycles, which is around 3800 years, is called a sar. The first sar started in year -3848, around the time the Sumerians started keeping track of years in Mesopotamia. The current sar started in year -0066. It means 2024 is year 2090 of current sar, or the 45th year of the 34th cycle in that sar which began in 1980.
| Sexagenal SC date | (Proleptic) Gregorian date | Notes | |
|---|---|---|---|
| First sar | 1 Jan -3848 | 3 Jan -3848 | |
| Current sar | 1 Jan -0066 | 1 Jan -0066 | |
| Current cycle | 1 Jan 1980 | 1 Jan 1980 | |
| Next cycle | 1 Jan 2042 | 31 Dec 2041 | leap year (catches up on 31 Dec 2042) |
| Start of year | 1 Jan 2024 | 1 Jan 2024 | |
| Today (when added) | 19 May 2024 | 20 May 2024 | leap year (catches up on 31 Dec 2024) |
| End of year | 31 Dec 2024 | 31 Dec 2024 |
Leap year rules[]
Like the Julian calendar, a leap year in the Sexagenal sliding Calendar occurs every four years, but one leap year is moved forward by two years at the end of the 62-year cycle.
This setup smoothes out the distribution of leap years over time as compared to the Gregorian calendar which moves the next leap year forward by a whole four years when there is a gap.
The mean year of the Sexagenal sliding calendar is 365.24194 days, which is remarkably accurate (read: better than the Gregorian calendar).
| Leap years in current cycle (1980-2041) and next cycle (2042-2103) | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1980 | 1984 | 1988 | 1992 | 1996 | 2000 | 2004 | 2008 | 2012 | 2016 | 2020 | 2024 | 2028 | 2032 | 2036 |
| 2042 | 2046 | 2050 | 2054 | 2058 | 2062 | 2066 | 2070 | 2074 | 2078 | 2082 | 2086 | 2090 | 2094 | 2098 |
Leap year slide calculation[]
If one knows the year a cycle started, add sixty to that year to find the next leap year "slide".
Example for the cycle started in year 1980: add sixty to find year 2040 which will not be a leap year as the Julian calendar would dictate, instead the leap year is pushed to 2042 which is the start of a new cycle.
Lunar cycle[]
This calendar follows a lunisolar cycle, as the solar and lunar cycles align after an arran of 372 years or six 62-year cycles.
The lunar cycle is as follows:
- Lunar month length alternates between 30 and 29 days for 17 lunar months
- The above repeats 13 times in full then a fourteenth repetition stops early at the fourteenth lunar month
- The resulting 235 lunar months form a Great-Year of 19 years
- The last lunar month of a Great-Year has either 29 or 30 days to synchronise with the solar year
- At the end of an arran there are three consecutive lunar months of 30 days length then a new arran begins
That scheme synchronises the lunar month with solar years every 6939 or 6940 days within an arran (Great-Year length). The Great-Years of the arran with only 6939 days are 4, 6, 8, 10, 13, 16 and 18 (mnemonic 468-then-368). There is a small correction at the end of 372 years to align with the solar year for an average length of:
The current arran started in 1794. Lunar months in a Great-Year are distributed into years according to the 19-year Metonic cycle.
| Lunar month | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Repet. 1 to 13 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 |
| Repet. 14 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 or 30 | — | ||
| End of arran (Repet. 8) | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 29 | 30 | 30 | 30 |
Glossary[]
amec:
A period of 63 days or nine weeks. It can also be used informally for "two months" (60 to 62 days), for example:
"I will call you back in one amec."
Which means, "I will call you back in two month's time."
arran:
A period of 372 years or six cycles which contains 4601 lunar months.
cycle:
A sixty-two year long leap year cycle.
February:
The second and shortest month of the year with a fixed twenty-nine days length.
Great-Year:
Nineteen years composed of 235 lunar months.
leap day:
The 31st of December, a day added at the end of leap years to adjust for the mean length of the solar year and keep the months in sync with seasons.
sar:
A period of 3782 years or sixty-one cycles. Canonical sars are counted from year -3848, which means we are currently in the second sar which started in year -66.
slide:
Used to describe the gap of two years at the end of a cycle when there is no leap year, breaking the four-year pattern for leap years.