Harmonic Solar Calendar

A solar calendar is a foundational tool for the advanced organization of a society. Its importance is undervalued and its ability to influence nearly all aspects of life is overlooked. It is rarely, if ever, analyzed critically, or considered an aspect of our daily life that can be improved. So, can it be improved?

Analysis

In the most common calendar, the Gregorian calendar, we have the day, the week, the month, and the year. Seven named days in a week, a variable amount of weeks in a month, and twelve months in a year. A month can have anywhere between 28 and 31 days. Every year has 365 days with a semi-regular exception of a 366-day year almost every four years. This is done because the real solar year, the time it takes for the Earth to revolve around the Sun, is nearly 365.25 days long. Fractions of a day don't work for a calendar, so an average approximates with a variable amount of days every couple of years.

Interestingly, the Solar Hijri used in Iran appears to be more practical and accurate, and makes more astronomical sense. The first day of the year is not an arbitrary day; it is the March Equinox. Months are more predictable with half being 30 days and half being 31, except the last month becomes 30 during a leap year and is otherwise 29. The timing of the March Equinox also determines whether the year is long or short.

Unfinished Notes

Six days in a week, two triads of three-day pairs: (Red|Blue) Sunday, Moonday, Earthday

Five weeks in a month, five weeks in the last month in a short year (360 days) or six weeks in a long year (366 days).

The day of the week is always the same in every year: if today is Sunday, the same day will be Sunday in the next year.

One long year puts the calendar 0.75 days ahead of the true orbit, one week ahead after eight years.

Eight years in a Vesper. Each Vesper has one short year and seven long years. (Vesper is another name for Venus, which has an observable cyclical relationship with the Earth that has an eight-year period.

To account for a rounding error, every 1,152nd Vesper will have two short years and six long years. For further precision, every 3,456th Vesper will have three short years and five long years, every 10,368th Vesper will have four short and four long years. These are estimations: more precision is possible and necessary. The calendar will never drift more than nine days from the true orbit, which is less than a 3% error. For reference, a drift of one day in a lunar calendar is more than 3% off-sync.

Due to changes in astronomical orbit, particularly that the length of the day will start slowing down noticeably over tens of thousands of years, short years will become much more frequent. However, when possible, there will never be two short years in a row. Short and long years alternate as a priority.

The first phase of this calendar is characterized by the dominance of long years over short years. Eventually, long years and short years will alternate with each other until they are perfectly equally distributed. The second phase will be when short years dominate long years, until long years cease to exist. The third phase will be when 360 days will be considered the long year, and a shorter year, 354 days, will be introduced (the Earth may be uninhabitable by then due to the incredibly long length of the day millions of years from now).

The main benefit of this calendar is the increased consistency and stability for human use. The predictable six-day week is the most significant change, followed by the eleven 30-day months and the superior leap year logic.

The main drawbacks are the increased drift error, the larger size difference between long and short years, and the introduction of a new unit greater than a year.