A simple, efficient, zero-based numbering calendar system that is accucate to almost a half million years. Containing 13 identical months of 28 days each, this calendar includes an addtional short month at the beginning of each year containing a single day plus a leap year day every four (or so) years. Each year of the 13 moons calendar is synchronized with the winter solstice in the northern hemisphere and the start of year zero of the 13 moons calendar has been synchronized with the end of the 13thb'ak'tun of the Mayan Long Count Calendar which occured on December 21, 2012 in the Gregorian Calendar.
Purpose:
Like any other clock or tool to measure time, this calendar's only true purpose is to measure time efficiently and accurately. It is simple in it's design, easy to calculate, easy to convert, and accurate to a loss of only one day per half a million years (see the Calendar Accuracy Section).
Time Measurement Units:
Zero-based Numbering:
The 13 moons calendar utilizes a zero-based numbering system for all time measuring units (like years, months, days, hours, minutes, seconds) so that each time measuring unit uses 0 as it's initial position. Therefore, the birth of the 13 moons calendar using the 13 moons calendar units would be: year 0, month 0, day 0, hour 0, minute 0, second 0. A 0th year, month, day, & hour can be very useful and friendly for calculation purposes.
Years & Yero Zero:
Years in the 13 moons calendar function essentially as integers (…, -3, -2, -1, 0, 1, 2, 3, …). One might think of Year 0 (Year Zero) as being the 0th year or year zero of the 13 moons calendar. The majority of year zero takes place in 2013 of the gregorian calendar.
Months:
For each year, there are 13 identical months containing 28 days each, in addtion to a short 1 or 2 day Zeroth Month preceding the other 13. So, in effect, there are actually 14 months: a single month with 1 or 2 days and 13 months containing 28 days.
(1 moon cycle ~= 28 days)
(13 moon cycles = 364 days)
Month Zero:
At the beginning of each year, the 1 or 2 extra calendar days necessary to complete a full year are put into Month 0 (Month Zero) which precedes the other 13 normal months in the calendar. This special 0th month has either 1 or 2 days in it. These 1 or 2 days correspond to day zero of the year and a leap year day (which occurs every 4 years with the exception of years that are a multiple of 128). Month 0 only contains 1 or 2 days and therefore is not counted as a full month, though undoubtably, it is still a real month in the 13 moons calendar used to denote specific dates.
Days & Day Zero:
As the 13 moons calendar utilizes zero-based numbering, the zeroth day (day zero) in each month should is denoted by a 0. Therefore each month (with the exception of month zero) will have days 0-27.
The Zeroth Day of the Year:
The zeroth day of the year is also the day zero (and usually the only day) in Month Zero.
(364 days + 1 new years day = 365 days)
Leap Year Days:
Leap year days, if they exist in a given leap year, are day one in the year and also day one in Month Zero. Leap year days will generally recur once every four years during years that are a multiple of 4 with exception to years that are a multiple of 128.
(365 days + 1 leap year day = 366 days)
Omitted Leap Year Days:
Exceptions to the regular 4 year - leap year cycle is that a leap year day will be skipped once every 128 (27) years or 32 (25) leap year cycles. In other words, there will be no leap year day when the remainder of dividing the year by 128 is 0 (when the year is exactly divisible by 128 & the year is a multiple of 128). This inludes the year 0 and any negative multiples of 128, so, for example, there would be no leap years in the years …, -512, -384, -256, -128, 0, 128, 256, …
(1 earth cycle ~= 365.2421897 days & an average year with leap year day every 4 = (365 + 365 + 365 + 366) = 365.25 days & 1 average year - 1 earth cycle ~= 0.0078103 days to make up per year & so if we want to make this up in a single day, we will divide that one day by the 0.0078103 days per year to find that we need to make up that day once every 128.036054953 years (or 1 day / 0.0078103 days/year = 128.036054953 years), which is extremely close to 128 years)
Hours:
Hours in the 13 moons calendar function the same as a 24-hour clock and therefore hours range from 0 to 23 and midnight occurs right between hour 23 and hour 0.
Minutes & Seconds:
Both minutes and seconds have a range from 0 to 59.
Syncronizations:
Birth of the 13 Moons Calendar:
Year Zero of the 13 moons calendar began at the stroke of midnight in each local timezone between the 20th and the 21st of December in 2012 of the Gregorian Calendar. For example, in UNIX time, year zero of the 13 moons calendar began 1356152400 seconds after the unix epoch in Coordinated Universal Time (UTC).
Year zero of the 13 moons calendar begins as soon as the 13thb'ak'tun of the Mayan Long Count Calendar ends. In other words, day zero of the 14thb'ak'tun of the Mayan Long Count Calendar is the day zero of the 13 moons calendar, the day after the last day of the 13thb'ak'tun. Please note that the 13 moons calendar is not an extension of the Mayan Long Count Calendar; it just uses the solstice and the end/start of the 13th/14th b'ak'tun as a reference point.
The 13 moons calendar is synchronized with the solstice and each quarter or season occurs approximately 13 weeks after one another. In the northern hemisphere, the vernal equinox (end of Q1) will occur around 1 week into the 3rd month, the summer solstice (end of Q2) will occur around 2 weeks into the 6th month, the autumnal equinox (end of Q3) will occur around 3 weeks into the 9th month, and the winter solstice (end of Q4) will occur in or around Month Zero. Please note that, in contrast to quarters, different seasons are actually slightly different in their duration. For example, winter is 89 days, spring is nearly 93, summer is 93 and a half, and fall is almost 90 days.
Omitting leap years in this fashion (see the omitted leap year section) creates an extremely efficient time keeping method accurate to almost half a million years (based on the 365.2421897 day mean tropical year). Accuracy is equal to about 16 equinoctial precession cycles.
(In calculations for the Omitted Leap Year Days section, we found that we need to correct for leap years once every 128.036054953 years, but since we require an integer year to do this, we chose to correct the leap years once every 128 years. If we subtract the integer value we used in the calendar for omitting leap year days (128) by the value from our calculations, we get one day every 128 years - one day every 128.036054953 years = (1 day/128 years) - (1 day/128.036054953 years) = 0.0078103 days a year - 0.0078125 days a year = −0.0000022 days a year & to find out the accuracy of this method of time keeping, we will do what we did previously to arrive at 128, so if we want to make this up in a single day, we will divide that one day by the 0.0000022 days per year to find that we need to make up that day once every 454545 years or so (or 1 day / 0.0000022 days/year ~= 454545 years), which in calendar terms is a really really long time.)
