(Wikipedia) - The Inter-Hours (Greek: Mesoria) are brief services in the Daily Office of the Eastern Orthodox and Greek Catholic Churches. The Inter-Hours are called for during the Lenten seasons of the Church year. They are styled after the Little Hours—First Hour, Third Hour, Sixth Hour, and Ninth Hour—only briefer.
The Inter-Hours are called for during the Lesser Fasts (Nativity Fast, and the Apostles' Fast. According to Nikolsky Ustav, they are to be read during Great Lent if the Ladder of Divine Ascent is not read during the Little Hours.
Each Inter-Hour follows one of the Little Hours is named for the Hour it follows (i.e., the Inter-Hour of the First Hour, etc.).