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The Olympiad Calendar with Smoothly Spread Month Lengths is a four year calendar of months having 30 or 31 days, the lengths of which are evenly distributed over the four years.  The months form two cycles, one long 9 month cycle of 30-31-30-31-30-31-30-31-30 or 274 days, and one short 7 month cycle of 30-31-30-31-30-31-30 or 213 days, forming a joint cycle of 487 days.  Three such joint cycles have 1,461 days, which is the exact number of days in a typical four year solar Olympiad.  

The actual distribution of the months can vary depending upon the point at which a cycle begins.   For instance, If the cycle starts one month later in the first year, then the 2nd, 6th, and 10th months will have an average of 30.25 days per Olympiad, whereas all the rest will have an average of 30.5 days per Olympiad:

Days per month in the four different years per olympiad
Month Year 1  Year 2  Year 3  Year 4
1                30 30 31 31
2                30 31 30 30
3                31 30 30 31
4                 30 31 31 30
5                  31 30 30 31
6             30 30 31 30
7             31 31 30 30
8               30 30 31 31
9                31 31 30 30
10            30 30 30 31
11        30 31 31 30
12           31 30 30 31
Totals 365 365  365  366

This "one month late" distribution will cause 2 of the 3 months with shorter average lengths to fall on two of the short months of the Gregorian calendar (February and June).  There is no way for all three to fall on a short Gregorian month. 

Organized in this way, the 1st, 2nd and 4th quarters of each year have an average length of 91.25 days, whereas the third quarter has an average length of 91.5 days.  Every four month third has an average length of 121.75 days.   

Notice that, although the fourth year is the leap year with 366 days, there is no leap day as such, because the even distribution of 31 day months over the 4 years provides all of the additional days needed to complete the 1,461 day Olympiad.   

Century year adjustments break the cycle somewhat, and need a special rule.  If a century year is a common year in the Gregorian Calendar, or in the Revised Julian Calendar, then that year is treated as though it were the 2nd year of an Olympiad, rather than the 4th year.  This minimizes the cyclical break somewhat, but does result in one 3 month sequence of 30 day months.   

If a 33 year calendar like the Dee or Dee-Cecil Calendar is used, then the 33rd year is treated as if it were a 1st year, and then the very next year is the 1st year of the next Olympiad, essentially causing the 1st year to be repeated.   

Now, although the Olympiad does not contain a whole number of 7 day weeks, the month length cycles can be extended somewhat to created 5 and 6 year cycles with a whole number of weeks.  For instance, a five year cycle, which can be called a Pentiad, can have the 4th year month sequence added to the beginning of the Olympiad, creating a 5 year sequence of 366-365-365-365-366  or 1,827 days of 261 weeks.  Also, six year cycles, that can be called Hexiads, can be created either by adding years 1 and 2 after an Olympiad, creating a 6 year sequence of 365-365-365-366-365-365 or 2,191 days of 313 weeks.  Or, years 2, 3 and 4 can be followed by years 1, 2 and 3 to create a 6 year sequence of 365-365-366-365-365-365, or 2,191 days, also of 313 weeks.  These Pentiads and Hexiads can be combined a number of ways (such as super cycles of 6-5, or 6-5-6 years) to create accurate, whole week cycles of 62, 231, 293 or 400 years, that can be reconciled with leap week calendars and the ISO week numbering scheme.  The symmetrical cycles of months can be maintained over super cycles of 11 or 17 years, but there are cyclical breaks between super cycles.    

Walter Ziobro has created a set of Italianate sounding names for use with the months of the Olympiad Calendar.  There are two sets, one for the 30 day months, which end in -o, and one for the 31 day months, which end in -a:

30 day months
Undembro - Dodembro - Primembro - Secondembro - Terzembro - Quartembro - Qunintembro - Sestembro - Settembro - Ottobro - Novembro - Dicembro
31 day months
Undembra - Dodembra - Primembra - Secondembra - Terzembra - Quartembra - Qunintembra - Sestembra - Settembra - Ottobra - Novembra - Dicembra

The names of the months switch throughout the year according to the length of that month in a particular year.

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