Reference edition:

Anicii Manlii Seuerini Boetii, De institutione arithmetica libri duo, De institutione musica libri quinque, accedunt Geometria quae fertur Boetii, edidit G. Friedlein, Lipsiae 1867, 178-371 (Bibliotheca Scriptorum Graecorum et Romanorum Teubneriana).

Boethius’ De institutione musica (or musicae), consisting of five books (though the last is defective), was considered the most important musical treatise during the Middle Ages.  It is based on Neo-Pythagorean cosmological concepts, and divides music into three types: mundana (music of the universe, i.e. the celestial spheres), humana (harmony of the human microcosm), and instrumentalis (i.e. music proper).

Boethius considers music to be the most important art of the quadrivium because of its psychagogic power to bring man to a higher ethical state.  This is evident from its description of a musicus as someone who uses his knowledge of musical material non servitio operis, sed imperio speculationis (1.34), i.e. for philosophical rather than merely functional ends.

The treatise considers musical material in both symbolic and technical terms, demonstrating a profound musicological and mathematical knowledge that makes reading the text difficult for anyone but experts in musicology. As is often the case in ancient music, the theory of intervals is discussed in detail. [M. Manca; tr. C. L. Caterine].