In the Martyrologium Romanum, each day has a heading with the Roman date, and a table that gives the status of the lunar cycle. These are the first things read each day in the Martyrology.
The Roman Date
Each month contains three reference dates: the Kalends, Nones, and Ides. While the Kalends is always the first day of the month; for eight months, Nones and Ides are on the fifth and thirteenth, but in March, May, July, and October, they fall two days later on the seventh and fifteenth.
For example, on July 4th, the Roman date (as styled since Medieval times) is “Quarto Nonas Iulii,” or “Four days before the Nones of July.” While the Nones of July is the 7th, the Roman custom is to count inclusively, so the 4th is considered four days before the 7th.
The day before each reference date is the pridie, so the 6th of July is called: “Pridie Nonas Iulii.”
The Ecclesiastical Moon
The lunar calendar and the phases of the moon are key components in determining the date of Easter, which is set as the Sunday following the first full moon of Spring. On average, there is a new moon (when the moon goes dark) every 29.53 days. In whole numbers, this is figured as each lunar cycle being either 29 or 30 days, depending on the month of the year.
The current Martyrology letter corresponds to the epact, or the difference (in days) between the lunar and solar years. On the table for each day, the numeral beneath the current Martyrology letter corresponds with the age of the moon in its current cycle, from 1 to 29 or 30, with a full moon at 14 or 15.
So, on July 4th 2018, the current Martyrology letter is n, which corresponds to an age of 21 (out of 30), which is said: “Luna vigesima prima.” Which is a moon waning in its last or third quarter phase (about half bright and half dim).