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This scheme would produce an estimate of the solar year, which is about one day too long. This error could be corrected by omitting an intercalation every 22 or 24 years. |
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I do not suggest that the Romans followed exactly such a plan. It is known that they followed the general scheme of lunar years with alternating intercalations of a 27-day month and a truncated Februarius. And it is known that the calendar contained some error, since the office of the pontifex was deemed necessary. |
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9.1.2.4
The Intercalation Scheme of Macrobius |
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In this context, I will now examine Macrobius's statements regarding intercalation. Macrobius, of course, states that these rules apply to the calendar of Numa. According to Macrobius, intercalation was originally performed by rule, such that 22 or 23 days were intercalated in every second year, 90 days were intercalated at the end of eight years (two quadrennia), but only 66 days intercalated in the next two quadrennia. Macrobius does not state how the days were arranged, but you may surmise from the numbers that the patterns for the two quadrennia were {22, 23, 22, 23} and {22, 22, 22, 0}. This scheme would produce the following arrangement: |
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