Everything related to the history of the Roman calendar and its transmission until today is very complex, especially for us who are used to a system of nomination of days of the month truly simple, each day is called the number it occupies in the whole month: January 1st, February 2nd or February 15th or March 3rd …
The Romans named the days of the month in a much more complicated way. Not in vain the calendar is a religious tool to determine especially religious holidays. This is the reason why the calendar was determined by the priest in many aspects.
First of all, the month was divided into three periods: Kalends (Kalendae), Nones (Nonae) and Ides (Idus) which correspond respectively with the new moon, half moon and full moon. This means that they did not know the division in "weeks", which actually was not imposed until the Emperor Constantine.
The kalends, (word that some people relate with Kalare = to call) indicated the beginning of the month, when the crescent moon appeared, and therefore correspond to day 1.
The nones indicated the first quarter of the moon and corresponded to the fifth day of the months of January, February, April, June, August, September, November and December; and to the seventh day of the months of March, May, July and October.
The ides indicated the full moon and corresponded to the 13th day in the months when the nones fell on day five and to the day 15th in which the nones fell on seven.
These monthly milestones were referred in adjectival form; i.e., January 1st was called “Kalendae Ianuariae”; January Kalends, or better say considering the termination for the ablative case of circumstance of time "Kalendis Ianuariis"; February 1st was called "Kalendae Februariae”; February Kalends; January 5th was called "Nonae Ianuariae"; March 7th “Nonae Martiae".
March 15th (the day Julius Caesar was assassinated) was call "Idus Martiae". "Beware of the Ides of March" is precisely what Caesar was advised by a fortune teller, who Caesar did not listened, and since then the phrase has become a prototype of warning, a prototype of a precautionary statement before a dangerous situation is announced.
"Ad kalendas graecas" is a Latin sentence that means "for greek kalends", that is "for never", because de greek months do not have "kalends".
This certainly seems complicated, but it is much more complex how were known to the rest of the days of the month. Well, a day was always called by reference at the prior key day (Kalends, Nones, Ides). That is, they counted the days until a key day would take place.
For example, January 2nd was the "sixth day before the nones of January", that is to say “ante diem VI Nonas Ianuarias”; January 16th (given that January has 31 days), will be the day "seventeenth before the Kalends of February", Latin for " ante diem XVII (decimum septimum) kalendas februarias "; the 17th will be the sixteenth day before the Kalends of February (ante diem XVI kalendas februarias) and so on.
Only the day before each milestone (kalendae, nonae, ides) was called "pridie” = the day before) and the next “postridie” = the day after). "Eve", derived from "vesper", Latin for "afternoon", naturally the afternoon before the next day.