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year *

The passage of the sun through the seasons. There are several years, such as is given in the following table.

365.24218967	tropical	repeats of seasons, eg midwinter
365.24675686	lunisolar	235/19 lunar months of 29.5305888531 days.
365.25636	siderial	repeats of earth - sun - star lines
365.2594	anomistic	repeats of perihelions

The calendars seek to make these equal in days, so that extra days or months are added to keep the sun and moon in line with the day. Here are some calendar-lengths representing assorted years.
      In these, a correction of 1/4 overstates the issue. One then proceeds to drop x leap years in y years, to get x/y.
      In the following, the Gregorian calendar, and the Metonic cycle of 12 7/19 mo. is taken to be the base, for which one has to drop different days from years of the sun and the Metonic cycles.

365.2416666	Twelfty	365 + 1/4 - 1/120
365.2421875	Binary	365 + 1/4 - 1/128
365.24218967	Nature	the tropical year.
365.24222222	Russian	365 + 1/4 - 7/900
365.24242424	c1	365 + 8/33
365.24250000	Gregorian	The calendar since 1752 = 365 + 1/4 - 3/400
365.24609375	Binary	365 + 1/4 - 1/256 = Epact every 256 years.
365.246600877	twelfty G	Twelfty, with 3 Golden Jump in 960 years.
365.24675324	c1e	365 + 8/33 + 1/231 = 1 epact shift every 231 years.
365.24675686	Nature	12 7/19 months of 29.5305888531 days
365.246773959	c1g	365 8/33 + A/363, A=30/19 ; Golden jump every 363 yrs.
365.246800000	Gregorian E	8 Epact shifts in 25 centuries.
365.246875000	Twelfty E	3 epact shifts in 960 years.
365.25000000	Julian	The calendar to 1752 = 365 + 1/4

C1 adds 8 leap years every 33 years.
calendars in e are epact shifts, in g are golden jumps.