Corpus Rhythmorum Musicum is the critical edition both printed and digital, with linguistical, metrical, paleographic and musicological analysis, of the Latin poems set to music of the IV-IX centuries composed in rhythmic verse, i.e. in the syllabic-tonic system from which it was born modern western poetry. It presents for the first time the texts together with the music and the complete reproduction of all the handwritten witnesses with relative transcriptions. It includes songs of non-liturgical tradition, computational-astronomical rhythms and rhythmic hymns. The project, conceived and directed by Francesco Stella (Università di Siena) with the collaboration of international specialists, is coordinated by Sam Barrett (University of Cambridge) for the music edition, and carried out thanks to the support of the European Commission (TMR1998-2000 project) and PRIN 2004-2006.