An extract on #tnpsg
The Republican calendar only had 355 days, which meant that it would quickly unsynchronize from the solar year, causing, for example, agricultural festivals to occur out of season. The Roman solution to this problem was to periodically lengthen the calendar by adding extra days within February. February was broken into two parts, each with an odd number of days. The first part ended with the Terminalia on the 23rd (a.d. VII Kal. Mart.), which was considered the end of the religious year; the five remaining days beginning with the Regifugium on the 24th (a.d. VI Kal. Mart.) formed the second part; and the intercalary month Mercedonius was inserted between them. In such years, the days between the ides and the Regifugium were counted down to either the Intercalary Kalends or to the Terminalia. The intercalary month counted down to nones and ides on its 5th and 13th day in the manner of the other short months. The remaining days of the month counted down towards the March Kalends, so that the end of Mercedonius and the second part of February were indistinguishable to the Romans, one ending on a.d. VII Kal. Mart. and the other picking up at a.d. VI Kal. Mart. and bearing the normal festivals of such dates.
Apparently because of the confusion of these changes or uncertainty as to whether an intercalary month would be ordered, dates after the February ides are attested as sometimes counting down towards the Quirinalia (Feb. 17), the Feralia (Feb. 21), or Terminalia (Feb. 23) rather than the intercalary or March kalends.
The third-century writer Censorinus says:
When it was thought necessary to add (every two years) an intercalary month of 22 or 23 days, so that the civil year should correspond to the natural (solar) year, this intercalation was in preference made in February, between Terminalia [23rd] and Regifugium [24th].
The fifth-century writer Macrobius says that the Romans intercalated 22 and 23 days in alternate years (Saturnalia, 1.13.12), the intercalation was placed after 23 February and the remaining five days of February followed (Saturnalia, 1.13.15). To avoid the nones falling on a nundine, where necessary an intercalary day was inserted "in the middle of the Terminalia, where they placed the intercalary month".
This is historically correct. In 167 BC Intercalaris began on the day after 23 February and in 170 BC it began on the second day after 23 February. Varro, writing in the first century BC, says "the twelfth month was February, and when intercalations take place the five last days of this month are removed." Since all the days after the Ides of Intercalaris were counted down to the beginning of March Intercalaris had either 27 days (making 377 for the year) or 28 (making 378 for the year).
There is another theory which says that in intercalary years February had 23 or 24 days and Intercalaris had 27. No date is offered for the Regifugium in 378-day years. Macrobius describes a further refinement whereby, in one 8-year period within a 24-year cycle, there were only three intercalary years, each of 377 days. This refinement brings the calendar back in line with the seasons, and averages the length of the year to 365.25 days over 24 years.
The Pontifex Maximus determined when an intercalary month was to be inserted. On average, this happened in alternate years. The system of aligning the year through intercalary months broke down at least twice: the first time was during and after the Second Punic War. It led to the reform of the 191 BC Acilian Law on Intercalation, the details of which are unclear, but it appears to have successfully regulated intercalation for over a century. The second breakdown was in the middle of the first century BC and may have been related to the increasingly chaotic and adversarial nature of Roman politics at the time. The position of Pontifex Maximus was not a full-time job; it was held by a member of the Roman elite, who would almost invariably be involved in the machinations of Roman politics. Because the term of office of elected Roman magistrates was defined in terms of a Roman calendar year, a Pontifex Maximus would have reason to lengthen a year in which he or his allies were in power or shorten a year in which his political opponents held office.
Although there are many stories to interpret the intercalation, a period of 22 or 23 days is always synodic month. Obviously, the month beginning shifts forward (from the new moon, to the third quarter, to the full moon, to the first quarter, back the new moon) after intercalation.