Western Semitic Calendars were composed of a year and a day. The year and a day rule had some significance in European common law up through 1996. In the context of a solar year and a day composed of 13 lunar months; The months were composed of 28 days or 4 weeks of 7 days plus one day. Adding a day to the year considered as a year and the month considered separately as a month gives them a close approximation to a solar year and a lunar cycle.
Examples
One example might be the Phaistos Disk, with a month represented on one side and a year on the other. Others such calendars are found in similar disks with holes punched around their perimeter. One vestige of the calendar of 13 months and the concept of a year and a day often found in romantic literature or fairy tales is a deck of cards with 13 cards per suit in four suits for a total of 52 cards each representing a seven day week plus a couple of jokers to represent the extra day for the year and the month.
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