The Roman Month its several days divides By reckoning backwards, calends Calends, Nones, and ides Ides.
2011, Robert A. Kaster trans. w:Macrobius Macrobius, Saturnalia, Book I, Chapter xiii, Section 18:
As for the Nones, it was thought that the multitudes should avoid mass meetings then because after the kings were expelled, the Roman people particularly celebrated what they took to be w:Servius Tullius|Servius Tullius's birthday: because crowds notoriously thronged all the Nones—it being well-known that Servius was born on the Nones, though the exact month was uncertain—those in charge of the calendar were afraid that if the whole population gathered on a market day it might start to revolt out of yearning for the king, and so they took the precaution of keeping the Nones and market days distinct.
2011, Robert A. Kaster trans. w:Macrobius Macrobius, Saturnalia, Book I, Chapter xiv, Section 8:
March, May, Quintilis, and October also have their Nones on the seventh, as w:Numa Pompilius|Numa ordained, because w:Julius Caesar|Julius changed nothing about them. As for January, Sextilis, and December, they still have their Nones on the fifth, though they began to have thirty-one days after w:Julius Caesar|Caesar added two days to each, and it is nineteen days from their ides Ides to the following kalends Kalends, because in adding the two days w:Julius Caesar|Caesar did not want to insert them before either the Nones or the ides Ides, lest an unprecedented postponement mar religious observance associated with the Nones or ides Ides themselves, which have a fixed date.
The interesting thing about these ceremonies is that they must have originated in a period when the Romans were using true lunar months based on the observation of the crescent moon. The kalends Kalends then would have been the day after the evening on which the crescent had been first sighted, the Nones would have been the first day when the moon was at the first quarter... In the calendar of the late Republic the lunar months have disappeared and the days have been fixed into a rigid pattern.
The third day before the nones of March is March 5th; the third nones of August is August 3rd; and the third of the nones of November is November 3rd.