The original Roman calendar is believed to have been a lunar calendar, which may have been based on one of the Greek lunar calendars. As the time between new moons averages 29.5 days its months were constructed to be either hollow (29 days) or full (30 days).he calendar year originally began on 1 March, as is shown by the names of the six months following June (Quintilis = fifth month, Sextilis = sixth month, September = seventh month, etc.).