The day of the full moon retained the old name of -idus- (perhaps "dividing-day").
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.

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.
The retention moreover of the reckoning by months or--which is the same thing--by years of ten months implies a tacit, but not to be misunderstood, confession of the irregularity and untrustworthiness of the oldest Roman solar year.

This Roman calendar may be regarded, at least in its essential features, as that generally current among the Latins.

When we consider how generally the beginning of the year and the names of the months are liable to change, minor variations in the numbering and designations are quite compatible with the hypothesis of a common basis; and with such a calendar-system, which practically was irrespective of the lunar course, the Latins might easily come to have their months of arbitrary length, possibly marked off by annual festivals--as in the case of the Alban months, which varied between 16 and 36 days.

It would appear probable therefore that the Greek -- trieteris-- had early been introduced from Lower Italy at least into Latium and perhaps also among the other Italian stocks, and had thereafter been subjected in the calendars of the several cities to further subordinate alterations.
For the measuring of periods of more than one year the regnal years of the kings might have been employed: but it is doubtful whether that method of dating, which was in use in the East, occurred in Greece or Italy during earlier times.