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Please note that Mommsen uses the AUC chronology (Ab Urbe Condita), i.e. from the founding of the City of Rome. You can use this reference table to have the B.C. dates

THE HISTORY OF OLD ROME

I. The Period Anterior to the Abolition of the Monarchy

From: The History of Rome, by Theodor Mommsen
Translated with the sanction of the author by William Purdie Dickson


The History of Old Rome

CHAPTER XIV - Measuring and Writing

ELPENOR EDITIONS IN PRINT

The Original Greek New Testament

» Contents of this Chapter

Page 14

The motive lying at the bottom of this strange remodelling of the calendar seems chiefly to have been a belief in the salutary virtue of odd numbers;(9) and while in general it is based on the oldest form of the Greek year, its variations from that form distinctly exhibit the influence of the doctrines of Pythagoras, which were then paramount in Lower Italy, and which especially turned upon a mystic view of numbers.

9. From the same cause all the festival-days are odd, as well those recurring every month (-kalendae- on the 1st. -nonae- on the 5th or 7th, -idus- on the 13th or 15th), as also, with but two exceptions, those of the 45 annual festivals mentioned above (xii. Oldest Table Of Roman Festivals). This is carried so far, that in the case of festivals of several days the intervening even days were dropped out, and so, for example, that of Carmentis was celebrated on Jan. 11, 15, that of the Grove-festival (-Lucaria-) on July 19, 21, and that of the Ghosts-festival on May 9, 11, and 13.

But the consequence was that this Roman calendar, clearly as it bears traces of the desire that it should harmonize with the course both of sun and moon, in reality by no means so corresponded with the lunar course as did at least on the whole its Greek model, while, like the oldest Greek cycle, it could only follow the solar seasons by means of frequent arbitrary excisions, and did in all probability follow them but very imperfectly, for it is scarcely likely that the calendar would be handled with greater skill than was manifested in its original arrangement.
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Reference address : https://www.ellopos.net/elpenor/rome/1-14-measuring-writing.asp?pg=14