The months are:
Empesos
Secondos
Tertios
Quartos
Quintos
Sextos
Septimos
Octimos
Novimos
Decimos
Ektos
Elos
Domos
A week-number designator is combined with the day of the week to form the day name. In cases where this would sound clunky, an "n" is added between them. Thus, the 28 days common to all months are officially, in order:
Primalunis
Primanaris
Primameric
Primatorres
Primaveris
Primanodis
Primasolis
Secolunis
Seconaris
Secomeric
Secotorres
Secoveris
Seconodis
Secosolis
Trilunis
Triaris
Trimeric
Tritorres
Triveris
Triodis
Trisolis
Quaterlunis
Quaternaris
Quatermeric
Quatertorres
Quaterveris
Quaternodis
Quatersolis
(Unofficially, certain names have been shortened, such as Primaris for Priminaris, Secodis for Seconodis.)
Dates are given as "the [day name] of [month], Year of Annos [year]". So one might speak of an event happening on the Triodis of Tertios, Year of Annos 1375.
The added days are treated as if they were added to Domos, the last month. So the day after the Quatersolis of Domos is officially called the Quinlunis of Domos. However, since there is only one month with a Quinlunis, most people omit the month. If Annos, the Year Star, rises during the Quinlunis, the next day is the start of the year (i.e., the Primalunis of Empesos). If not, the next day is the Quinaris of Domos (again, most people omit the month), and the following day is the start of the year. The Royal Observatory in Spira, the Capital of Cafren, has an enchanted roof that allows starlight and moonlight to be observed even when obscured by clouds and sun, so there is never a doubt as to when Annos rises.
As for modern equivalence, the Primalunis of Empesos is best equated with our March 1.
The Hessian calendar (also called the Xi An calendar) is based on seasons. There are five recognized seasons, each 73 or 74 days long. Leap Years, which follow the Gregorian rules, add a 74th day to the first season (Cherry).
The seasons, and their modern equivalents, are:
Cherry (Jan. 19 - Apr. 1)
Lilac (Apr. 2 - Jun. 13)
Sunflower (Jun. 14 - Aug. 25)
Rice (Aug. 26 - Nov. 6)
Mistletoe (Nov. 7 - Jan. 18)
The days of the week run normally, and are ordered as follows:
Sunis
Monis
Gallis
Atoris
Falsis
Veris
Elmentis
Dates are normally given as "[day of week], [number] Day of [season], Year [year] of His Holiness". So a typical date might be Veris, 35th Day of Rice, Year 135 of His Holiness.