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The names of the months from Quintilis to December simply denote an ordinal numeric counting, from fifth to 10th. Scholars have speculated endlessly concerning the meaning of the names of the first four months.
The story continues to claim that Numa Pompilius, the second king of Rome added two months, Ianuarius and Februarius, and moved the start of the year forward from Martius to Ianuarius. Both Censorinus and Macrobius state that the six months of 30 days were reduced to 29 days, and both state that this was done to maximize the number of odd numbers, which the Romans traditionally considered to be lucky.
Such a year, supposedly implemented around 700 B.C., would have the following structure:
Name of MonthNumber of Days
Ianuarius mensis
29
Februarius mensis
28
Martius mensis
31
Aprilis mensis
29
Maius mensis
31
Iunius mensis
29
Quintilis mensis
31
Sextilis mensis
29
September mensis
29
October mensis
31
November mensis
29
December mensis
29

9.1.1.3
The Apocryphal Numan Calendar
At this point, I should call a halt. The various authors disagree on various details. Macrobius states that an intercalary month was introduced into this calendar at a later unspecified date. Plutarch claims that the intercalation was introduced but disagrees about the number of days involved.
Looking at all of the evidence, the most likely scenario is that a calendar of Numa Pompilius is apocryphal and never existed at all. The relevant Roman literature is very likely ill-informed rationalization and backward speculation, projected from knowledge of a pre-Julian Republican calendar into an earlier period when Rome used a lunar calendar based on observations of the visible crescent.

 
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