In writing about the musical adventures of the monastic community I pray with I used the term hebdomadarian. I first encountered this word many years ago in Rumer Godden's In This House of Brede - and thank heavens there was a glossary in the back! It's the term for the assigned leader of sung prayer in a monastic community. The assignments were usually rotated weekly, and this is reflected in hebdomadarian's etymology, it derives from the Greek for seven, hepta. I have to say, to this day when I see or hear this word, my first thought is not the Divine Office, but camels (dromedary!).
The Augustinians I pray with use a weekly rota (I used to be Thursdays), with substitutes filling at need, but the title persists.