Timely Revolutions

In summary:

1. On average, earth’s solar year is about 365 ¼ average days. The average day is divided into 24 hours. On average.
2. The physical reality is that Earth is a rough ovoid ball affected by the gravity of other rough balls all going around the sun in a slightly complex orbit.
   1. The average time of day (clock time) differs from the actual direction to the sun (sundial time) over the course of the year because of its near elliptical orbit.
      https://en.wikipedia.org/wiki/Equation_of_time
      Furthermore, the directions of the Earth axial tilt and elliptical orbit rotate, resulting in changes to the lengths of seasons (equinox to solstice).
   2. The Earth’s rotation is very gradually slowing due to tidal deceleration (https://en.wikipedia.org/wiki/Tidal_acceleration), so the average second was getting longer. (UT1)
      The second has been redefined in terms of ticks of atomic clocks around the world, resulting in occasional removal or insertion of leap seconds. (UTC)
      https://en.wikipedia.org/wiki/Universal_Time
3. To align this average day time seconds with average atomic seconds, a leap second can be added or removed several times a year, by observation.
4. To align this average year with the solar year, a leap day is added every 4 years by calculation.
5. The widely used Gregorian calendar improved the leap year calculation of the Julian Calendar, which improved previous Roman calendars;
   but left the calendar months somewhat irregular, as this is what was politically and religiously possible at the time.
6. The 7 day week is even more widespread; a previous attempts to introduce a perpetual calendar was nearly successful, but skipping days of the week was vetoed on religious grounds.
7. There is still a desire for further calendar reforms, principally to
   1. Move leap days to end of calendar
   2. Regularise the calendar
   3. Support multiple ways to evenly group calendar days (into 12, 6, 4, 2)
   4. Support lunar calendars.

For Solar Calendars, I recommend:

• A further reform of Roman Calendar, to move leap days to end of calendar, to simplify the calendar with 12 symmetrical months of 30 or 31 days. Either:
  • January start:
    Make February 30 days, with a day from July, and end Dec with a leap day.
  • March start:
    Make February 30 or 31 days, with a day from August and a day from January.
    + restores *ember months to correct position.
    + Aligns seasons with quarters.
    – changes year start, and year counts.
• An alternative leap year rule of having 2 leap days every eight years, which would allow a progression of 1 day for 7 years,
  creating a simple predictable cycle for 8 year leap groups.
• Using overlays for
  • 4 quarters of 91 days which align with the 12 months.
    (where leap days and the first day of the first month are outside of quarters)
  • 6 sixths of 61 days
    (the sixth sixth has the leap day and its absence).

For Luni Solar Calendars, I recommend further investigation of 12+12 approach. The features are:

• Fully Solar, each year starts on same offset to Winter Solstice.
• Fully Lunar, has 12 synodic months evenly distributed, but which start on what phase of the moon started the year.
• Thus it is possible to have a predictable calendar. For the year, the day of the moon can be calculated and/or observed for the entire year.